[brahms-md] r63 committed - Adding doc/

[brah...@googlecode.com]

Revision: 63
Author: orsimario
Date: Wed Dec 21 02:20:08 2011
Log: Adding doc/
http://code.google.com/p/brahms-md/source/detail?r=63

Added:
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=======================================
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+\citation{marioTriclos}
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=======================================
--- /dev/null
+++ /trunk/doc/latexSource/acknowledgement.tex Wed Dec 21 02:20:08 2011
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+\chapter*{Preface and acknowledgments}
+
+
+\brahms is a molecular dynamics program specifically designed for the
+simulation of lipid and water systems modeled with the ELBA coarse-grain
+force field.~\cite{orsi11elba}
+\brahms is mainly based at the University of Southampton (Southampton,
UK). Ongoing collaborative work is also taking place
+at the ``Politecnico di Torino'' university (Turin, Italy). Funding for
\brahms has so far been received by:
+\begin{itemize}
+\item UK taxpayers, through government science-funding agencies (BBSRC,
EPSRC);
+\item private companies: Johnson \& Johnson, Unilever.
+\end{itemize}
+The main author of \brahms is Mario Orsi ({\tt
www.personal.soton.ac.uk/orsi}). The \brahms project has been constantly
+supported by Prof. Jonathan W. Essex.
+Many crucial components of {\sc brahms}, such as the main data structures,
the cell-subdivision/neighbor-list algorithm,
+and several useful macro definitions, have been developed following the
excellent book ``The Art of Molecular Dynamics Simulation''
+by D.C. Rapaport.~\cite{rapa}
+The efficiency of {\sc brahms} has been optimized thanks to the advanced
molecular dynamics integration scheme invented by Dullweber et
al.~\cite{dullw97a}
+The ``official'' \brahms website is {\tt
www.personal.soton.ac.uk/orsi/brahms}.\medskip
+\\\brahms has been used to carry out research described in a number of
publications;~\cite{orsi11elba,mario08,marioSmall,marioDmpcDopc,marioDH,marioTriclos}
please cite these papers if you use or reference {\sc brahms}.
+\medskip
+\\\brahms is free software - ``free'' as in ``freedom'' (although \brahms
is also offered at no charge). More information on the free software
movement can be found at {\tt http://www.fsf.org} and {\tt
http://www.fsfe.org}. In general, free software is used extensively in
this project. The {\sc brahms} code is developed on computers running the
GNU/Linux operating system and can be compiled with the GNU C compiler.
Analysis code has been written in {\it Python}. The \brahms project employs
the {\em Subversion} revision-control system. %will be hosted soon on the
Savannah software forge ({\tt https://savannah.nongnu.org/projects/brahms}).
+This manual is edited with {\it Emacs} and formatted using~\LaTeX.
Diagrams are prepared with {\em Grace}. Images are edited with the {\em
Gimp}.
+\medskip
+\\Your feedback on this manual is greatly valued. If you find
mistakes/typos, have suggestions on how to improve/clarify any topic, or
have any constructive criticism, please email Mario Orsi ({\tt
or...@soton.ac.uk}).
+
+
=======================================
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+\chapter{Analysis}
+
+\section{``On-the-fly'' analysis in Brahms}
+
+Most properties of interest can be calculated and averaged by \brahms
while the simulation is running (``on-the-fly'' analysis). \brahms analysis
options can be controlled via the input file {\tt brahms.an}, described in
detail in \textsection\ref{sec:brahms.an}.
+Examples of \brahms analysis results can be seen in Figures~2-5 of Orsi et
al;~\cite{marioDmpcDopc} in particular, these curves were obtained from the
averages taken over all profiles periodically outputted by Brahms. To carry
out such analysis it is possible to use the script {\tt
getAverageProfile.py} located in the {\tt analysisScripts/general/}
directory (read first comment lines for usage instructions).
+
+
+\section{Post-processing analysis}
+
+Not all the possible analysis of simulation data is carried out
``on-the-fly''. In some cases it is better to output data files for
post-processing. Such post-processing can be done through simple Python
scripts or command line instructions; such tools are collected in the
directory {\tt analysisScripts}.
+For example, compressibility moduli are most conveniently obtained via
post-processing (see \textsection\ref{sec:regDims}); nice images produced
with simple post-processing can be seen in Figure~6 of Orsi et
al.~\cite{marioDmpcDopc} (see \textsection\ref{sec:lld} for suggestions on
how to reproduce such plots).
=======================================
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+\chapter{Benchmarks}
+
+In this chapter, \brahms performances are tested, for various systems,
using different processors/compilers. The integration timestep is 15\,fs.
+
+\section{Single processor}
+
+\subsection{Water systems}
+
+\begin{table}[h]
+\begin{center}
+%\vspace{14pt}
+\begin{tabular}{r|c|c} % put @{} if you want to eliminate horizontal space
between columns
+Processor & Compiler (flags) & Sampling speed \\
+\hline
+%(My new desktop)
+Intel Xeon X5680 @3.33\,GHz & Intel (-fast) & 8.7\,ns/day\\
+& Gcc (-O3) & 7.1\,ns/day\\
+(Half load 12/24 50\,\% CPU) & Intel (-fast) & 8.7\,ns/day\\ %2m28s
+(Full load 24/24 100\,\% CPU) & Intel (-fast) & 5.9\,ns/day\\ %3m41s
+\hline
+%(My old desktop)
+Intel Q9550 @2.83\,GHz (Full load 4/4 100\,\% CPU) & Intel (-fast)&
7.3\,ns/day\\ % 2m58s
+%& Gcc (-O3) & \,ns/day\\
+\hline
+%(My old desktop)
+%Intel Core2 @2.83\,GHz&Gcc (-O3)& 3.9\,ns/day\\
+%\hline
+%(Iridis head-node)
+Intel Xeon E5530 @2.40\,GHz & Intel (-fast) & 6.9\,ns/day\\ %3m09s
+& Gcc (-O3) & 5.6\,ns/day\\
+\hline
+%(polito cluster dmalice)
+Intel Xeon X7350 @2.93\,GHz& Intel (-fast)& 6.3\,ns/day\\ % 3m26s
+& Gcc (-O3) & 4.6\,ns/day\\ %4m39s
+%\hline
+%(1 Iridis compute-node, 6 concurrent jobs)
+%Intel Nehalem @2.27\,Ghz & Intel (-fast)& 4.3\,ns/day\\
+%& Gcc (-O3) &3.2\,ns/day
+\end{tabular}
+\caption[Brahms performances, 23328 water molecules]{Brahms performances.
23328 water molecules, 0.9\,nm cutoff.}
+\label{tab:bench23328wats}
+\end{center}
+\end{table}
+
+\subsection{Hydrated lipid bilayers}
+
+\begin{table}[h]
+\begin{center}
+%\vspace{14pt}
+\begin{tabular}{r|c|l} % put @{} if you want to eliminate horizontal space
between columns
+Processor & Compiler (flags) & Sampling speed \\
+\hline
+%(My new desktop)
+Intel Xeon X5680 @3.33\,GHz & Intel (-fast) & 8.4\,ns/day (6.5\,steps/s)\\
+& Gcc (-O3) & 6.6\,ns/day (5.1\,steps/s)\\
+(Half load 12/24 50\,\% CPU) & Intel (-fast) & 8.3\,ns/day\\ %2m35s
+(Full load 24/24 100\,\% CPU) & Intel (-fast) & 5.8\,ns/day\\ %3m44s
+\hline
+%(My old desktop)
+Intel Q9550 @2.83\,GHz (Full load 4/4 100\,\% CPU) & Intel (-fast)&
7.0\,ns/day\\ % 3m5s
+%& Gcc (-O3) & \,ns/day\\
+\hline
+%(Iridis head-node)
+Intel Xeon E5530 @2.40\,GHz & Intel (-fast) & 6.5\,ns/day\\ %3m18s
+& Gcc (-O3) & 4.8\,ns/day\\
+\hline
+%(polito cluster dmalice)
+Intel Xeon X7350 @2.93\,GHz& Intel (-fast)& 5.9\,ns/day\\ % 3m41s
+& Gcc (-O3) & 4.4\,ns/day\\ %4m53s
+%\hline
+%(1 Iridis compute-node, 2 concurrent jobs)
+%Intel Nehalem @2.27\,Ghz & Intel (-fast)& 3.9\,ns/day\\
+%& Gcc (-O3) & 2.9\,ns/day\\
+\end{tabular}
+\caption[Brahms performances, 512 lipids, 16810 waters]{Brahms
performances. 512 lipids, 16810 waters (24490 sites total). Lipid-lipid \&
lipid-water cutoff: 1.2\,nm. Water-water cutoff: 0.9\,nm.}
+\label{tab:bench512lips}
+\end{center}
+\end{table}
+
+\begin{table}[h]
+\begin{center}
+%\vspace{14pt}
+\begin{tabular}{r|c|c} % put @{} if you want to eliminate horizontal space
between columns
+Processor & Compiler (flags) & Sampling speed \\
+\hline
+Intel Xeon X5680 @3.33\,GHz & Intel (-fast) & 5.5\,ns/day\\
+\end{tabular}
+\caption[Brahms performances, 1058 lipids, 16000]{Brahms performances.
1058 lipids, 16000 waters (31870 sites total). Lipid-lipid \& lipid-water
cutoff: 1.2\,nm. Water-water cutoff: 0.9\,nm.}
+\label{tab:bench1058lips}
+\end{center}
+\end{table}
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--- /dev/null
+++ /trunk/doc/latexSource/biophys/biophys.tex Wed Dec 21 02:20:08 2011
@@ -0,0 +1,249 @@
+\chapter{Lipids and membranes}
+%\chapter{Lipids, membranes, and cellular transport}
+\label{ch:biophys}
+%\begin{flushright}\emph{}\\- \end{flushright}
+
+
+Lipids\footnote{From the Greek {\it lipos}, meaning ``fat''.} are the
fundamental building blocks of any biological
membrane~(Figure~\ref{fig:memECM}); they are generally defined as
substances that are soluble in organic solvent but only sparingly soluble
in water.~\cite{voet} % 383
+\begin{figure}%[ht]
+\centering
+\includegraphics[scale=.5]{biophys/memECM.eps}
+\caption[The plasma membrane]{The plasma membrane. Schematic
representation of a plasma membrane patch at molecular resolution;
characteristic elements are highlighted.~\cite{simmons}}
+\label{fig:memECM}
+\end{figure}
+As a class of molecules, lipids display a wide diversity in both structure
and biological function, and they self-organise into many intriguing
structures, with extraordinary material properties that have been optimised
by evolutionary principles over billions of years.~\cite{dowhan,mouritsen}
+Lipid membranes play crucial roles in compartmentalisation, they represent
a solvent for other species (such as proteins) to function, and they
contribute to the structural scaffolding of cells. Along with these rather
passive functions, it has recently become evident that lipids can actively
contribute to fission and fusion events, and in general to the regulation
of membrane proteins. It is now accepted that lipids are as important for
life as proteins, sugars, and genes.~\cite{mouritsen}
+In this chapter, the fundamental properties and phenomena regarding lipids
and lipid bilayers are summarised, along with some of the most popular
experimental techniques employed to study membrane systems. %Particular
emphasis is placed on the phospholipid bilayer and transport therein. %,
which are we propose the model described in the subsequent chapters of this
thesis.
+
+\section[Types of membrane lipids]{Types of membrane lipids}
+
+ There are three common classes of membrane lipids: phospholipids,
glycolipids and cholesterol. Phospholipids are the major class of membrane
lipids,~\cite{berg} %p322
+and are the main object of the modelling work presented in this thesis.
Hence, in the following sections, we will focus on this particular lipid
species.
+However, we give here a brief account on the two other common lipid types.
+
+{\em Glycolipids}, as their name implies, are sugar-containing lipids.
They are formed by association of a carbohydrate chain with lipids on the
external surface of the cell membrane. Glycolipids thus extend from the
plasma membrane into the aqueous environment outside the cell, acting as a
recognition site for specific chemicals as well as helping to maintain the
stability of the membrane and attaching cells to one another to form
tissues. They also serve a role as energy stores.
+
+{\em Cholesterol} is a lipid with a unique structure compared with the
other lipids; it is a steroid, built from four linked hydrocarbon rings,
terminated at one end by a hydrocarbon tail and on the other by a hydroxyl
group. Cholesterol is universally present in the plasma membranes of all
animals, in ratios of 25-50$\%$ of the total lipid content; however, it is
essentially absent from some intracellular membranes, such as mitochondrial
and Golgi.~\cite{mouritsen} %p325
+Cholesterol is important in stabilising membranes, as its presence makes
them thicker and less leaky; it is also an essential component of lipid
``rafts'', membrane microdomains believed to favour specific
protein-protein interactions resulting in the activation of signalling
cascades.~\cite{simons00}
+
+
+
+\section[Phospholipid structure and self-assembly]{Phospholipids:
structure and self-assembly}
+ The most important class of lipids in natural membranes is represented by
the {\em phospholipids}.~\cite{berg} Phospholipids are
amphiphilic %\footnote{From the Greek {\it amphi}, that means ``on both
ends'', and {\it philos}, that means ``loving''.}
+molecules constructed from four components: fatty acids, a ``backbone'' to
which the fatty acids are attached, a phosphate, and an alcohol attached to
the phosphate. The fatty acid components constitute a hydrophobic barrier,
whereas the rest of the molecule has hydrophilic properties to enable
interaction with the environment. The backbone component may be {\em
glycerol}, a 3-carbon alcohol, in which case the phospholipid is called
{\em phosphoglyceride}, or it may be {\em sphingosine}, a (more complex)
amino alcohol, which constitutes {\em sphingolipids}. Sphingolipids
comprise important lipid species such as {\em ceramide}, a fundamental
constituent of the skin and an important molecule involved in programmed
cell death.~\cite{mouritsen}
+ However, the main lipid components of biological membranes are {\em
phosphoglycerides} (or {\em glycerophospholipids}).~\cite{voet} %p.385
+Figure~\ref{fig:pl}
+\begin{figure}%[ht]
+\centering
+\includegraphics[scale=.5]{biophys/phospholipid.eps}
+\caption[Phospholipid molecule]{Phospholipid molecule. It is possible to
identify the polar head group, the glycerol moiety, the ester groups and
the hydrocarbon chains.\cite{ualr}}%/~botany.}
+\label{fig:pl}
+\end{figure}
+shows a typical phosphoglyceride, in particular a {\em
phosphatidylcholine} lipid: the polar head comprises a positive group
(choline (CH$_3$)$_3$N-CH$_2$-CH$_2$) and a negative group (phosphate
O-PO$_2$-O), whereas the hydrophobic part is made of the glycerol backbone
(CH$_2$-CH-CH$_2$), two ester groups (O-CO-CH$_2$) and two hydrocarbon
``chains'' (also called ``tails'') of fatty acids. Hydrocarbon chains are
formed by consecutive methylene (CH$_2$) segments terminating with a methyl
(CH$_3$) segment. Hydrocarbon tails often comprise one or more double bonds
between C atoms along the tail.
+In general, when dispersed in water, lipids are driven together by the
{\em hydrophobic effect}, and self-organise in various aggregates depending
on the specific lipid structure, temperature and level of hydration
(Figure~\ref{fig:lipStructs}~a).
+\begin{figure}
+\centering
+\mbox{\subfigure[]{\includegraphics[width=70mm]{biophys/lipidStructures.eps}}\quad
+ \subfigure[]{
+ \includegraphics[width=40mm]{biophys/vesicle.eps}
+}}
+\caption[Lipid aggregates]{The most common aggregates formed by lipid
molecules. (a) Non-bilayer phases.~\cite{scq} (b) Lipid bilayer vesicle.
Water molecules, hydrating the interior and exterior of the vesicle, are
also schematically represented.~\cite{steve}}
+\label{fig:lipStructs}
+\end{figure}
+ The hydrophobic effect, that is, the tendency for oil and water to
separate, is a complex phenomenon that manifests different characteristics
depending on the system's temperature and pressure, the shape of the
oil-like components and the size of the aggregates
involved.~\cite{southall02,chandler05} In the particular case of
lipid/water mixtures at biological temperature and pressure, the
hydrophobic effect is believed to be mainly of entropic
origin.~\cite{mouritsen} Pure water systems are characterised by a
tetrahedral arrangement of hydrogen-bonded molecules which maximises the
system's entropy. When insoluble species (such as hydrocarbon molecules)
are introduced in water, a loss in entropy is produced due to the induced
local ordering of water around every insoluble molecule. To reduce such
ordering, and hence to minimise entropy loss, the insoluble molecules are
driven together so that the total surface area exposed to water,
corresponding to the total area involved in local ordering phenomena, is
decreased. This gain in entropy of the water upon assembly formation
outweighs the enthalpy penalty (caused by the demixing of water and the
insoluble species) and the loss of configurational entropy of the insoluble
molecules due to the constraints typically imposed by the aggregate
structure.\cite{hamley}
+Owing to the fact that lipids form assemblies by self-aggregation
processes that do not involve strong chemical forces, such assemblies can
be categorised as {\em soft matter} materials. Soft matter comprises a
large and ubiquitous class of systems including for example polymers,
emulsions, colloids, liquid crystals and many biological materials. All
these systems exist in a condensed phase which cannot be described
unambiguously as either liquid or solid, as it typically possesses mixed
properties. For instance, soft matter may display long-range ordering
properties typical of solid matter. However, unlike conventional solid
materials, soft materials have physical properties which are largely
dominated by entropy. Soft matter is highly deformable, and typically
constructed in a hierarchical manner with substructures subtly interacting
on several length and time scales.~\cite{mouritsen} All aggregates formed
by lipids represent specific examples of soft matter structures.
+From a biological perspective, {\em bilayer} structures
(Figure~\ref{fig:lipStructs}~b) are considered the most important category
of lipid assemblies, as they form the fundamental backbone of the
majority of biological membranes.
+%Many cellular properties are consequences of the pfundamental physical
principles of self-organisation that rule when many molecules act in
concert. A key player in this concert is water, which functions as the
unique biological solvent: the peculiar properties of water force lipid
molecules to self-assemble and organise into subtle structures, as for
instance bilayer membranes.
+%: softness is a feature that lipid membranes share with other forms of
condensed matter, like polymers and liquid crystals.~\cite{mouritsen}
+%The hydrophobic effect arises from the disruption of the water hydrogen
bonding network caused by the presence of hydrophobic molecules: these
destibilise the hydrogen bonding network thus lowering the entropy of the
system. The hydrophobic effect acts to drive the hydrohpbic molecules
together to minimise the contact with water and hence to restore as much as
possible the hydrogen bonding network.~\cite{mouritsen}
+%From a vesicle, one can imagine to isolate a small bilayer patch
+ %The molecules that play the dominant roles in membrane formation all
have higly polar head groups and, in most cases, {\em two} hydrocarbon
tails\footnote{There is a molecular sense to this. If a large headgroup is
attached to a single hydrocarbon chain, the molecule is wedge-shaped and
will tend to form spherical micelles. A double tail yields a roughly
cylindrical molecule, which can easily pack in parallel to form extended
sheets of bilayer membranes~\cite{mathews}.}.
+%Indeed geometric factors dictate that for most two-chain phospholipids,
bilayers are the favoured structure, rather than micelles or inverted
hexagonal phases~\cite{cevc}. % p.2
+%The occurrence of phospholipids as an essential membrane component is
attributable to their ability to form bilayer vescicles spontaneously when
dispersed in water~\cite{cevc}.
+%In the remainder of this chapter, we will focus on the lipid bilayer,
which forms
+\section{Phospholipid bilayers}
+
+Phospholipid bilayers constitute the basic material employed to
encapsulate the cell and its sub-compartments.
+In the following sections, the main features of lipid bilayers are
summarised.
+
+\subsection{Structure}
+
+%The phospholipid bilayer is the structural foundation of biomembranes and
+Structural data on lipid bilayers are widely used as basic information to
help understand and model biomembrane structure and the functions that take
place therein.~\cite{nagle00a} % Reliable experimental data, though
incomplete, also provide a guide to modelling and a necessary check on the
reliability of simulations.~\cite{nagle00a}
+%Measurements of the volume per lipid can be performed using different
techniques. The simplest method employs neutral flotation: the density of
the aqueous solvent is varied by mixing D$_2$O with H$_2$O, with the
density of the lipid being given by the density of the aqueous mixture in
which the bilayers neither sink nor float.~\cite{nagle00a} % p.163
+%The internal structure of bilayers is studied by neutron or X-ray
diffraction methods.
+Most %diffraction
+experimental studies are performed on stacks of hydrated bilayers,
especially on multi-lamellar vesicles (Figure~\ref{fig:mlvs}).
+\begin{figure}%[ht]
+\centering
+\includegraphics[scale=.7]{biophys/mlvs.eps}
+\caption[Multi-lamellar vesicles]{Schematic representation of
multi-lamellar vesicles. The black areas represent regions of excess water.
From Koenig et al.~\cite{koeni97a}}
+\label{fig:mlvs}
+\end{figure}
+The internal structure is investigated by X-ray, neutron scattering,
molecular-probe, and magnetic resonance techniques.
+The measurements obtained provide information about the membrane
thickness, and, most importantly, can resolve the depth-dependent
distribution of specific lipid segments across the bilayer
(Figure~\ref{fig:bilayerEdp}).
+\begin{figure}
+\centering
+\includegraphics[scale=1.1]{biophys/bilTransStruct.eps}
+\caption[Transbilayer structure]{Transbilayer structure. The top panel
shows a phospholipid bilayer model; hydrogens are coloured in white,
oxygens in red, carbons in turquoise, nitrogens in blue and phosphoruses in
dark yellow (adapted from Feller~\cite{feller-dppc}). The bottom panel
shows corresponding density profiles obtained from neutron-scattering and
X-ray techniques; the curves give the relative probabilities of finding the
different molecular segments of the phospholipid molecules (adapted from
Nagle and Tristram-Nagle~\cite{nagle00a}).}
+\label{fig:bilayerEdp}
+\end{figure}
+
+\subsubsection{Structure of the hydrocarbon region: intramolecular order
parameters}
+The hydrocarbon tail region of a bilayer can be investigated by deuterium
magnetic resonance; this technique allows tail ordering to be quantified in
terms of order parameters. Order parameters generally describe the tail
orientation as a function of depth. %;~\cite{jseelig74} they also provide a
basis for understanding the concept of membrane fluidity.~\cite{douliez95}
+%The middle panel of~Figure~\ref{fig:stevBeadSpring} offers a schematic
descritpion: the molecular axis $Z_D$ is normal to the plane defined by the
CH bonds.
+%Experiments are carried out after deuteration, so the actual bond vectors
can also be called CD.
+For each methylene group $k$ along a lipid tail, the intramolecular order
parameter $S^k_\textrm{CD}$ can be defined as:~\cite{akuts91a}
+\begin{equation}
+S^k_\textrm{CD} = \langle 3\cos^2\theta-1 \rangle / 2
+\end{equation}
+with $\theta$ the instantaneous angle between the $k$-th C$-^2$H bond
vector and the overall molecular axis. The overall molecular axis is the
main axis of a lipid molecule, which, on average in the
biologically-relevant fluid phase, is parallel to the ``bilayer normal'',
that is, the direction perpendicular to the bilayer plane.~\cite{akuts91a}
+ It is also possible to define the molecular axis of a chain segment
$k$ %(either a CH$_2$ or a CH$_3$ group)
+as the normal direction to the plane spanned by the two CH bonds of the
$k$-th methylene group.~\cite{jseelig74} For each methyl segment $k$, the
intramolecular {\em segmental} order parameter $S^k_\textrm{mol}$ is then:
+\begin{equation}
+S^k_\textrm{mol} = \langle 3\cos^2\eta -1\rangle / 2
+\end{equation}
+with $\eta$ the instantaneous angle between the
+ molecular axis of the $k$-th segment and the bilayer normal.
$S^k_\textrm{mol}$ are thus the order parameters of the segments' molecular
axes with respect to the %director; they represent the fluctuation of the
molecular axis around the
+bilayer normal. %~\cite{akuts91a}
+ Experiments can accurately determined $S^k_\textrm{CD}$, which can then
be related to the segmental order parameters $S^k_\textrm{mol}$ using the
formulae:~\cite{jseelig74}
+\begin{displaymath}
+ S^k_\textrm{mol} =
+\left\{ \begin{array}{cl} -2\,S^k_\textrm{CD} & \textrm{for the {\em
k}-th CH$_2$ segment}\\
+-3\,S^k_\textrm{CD} & \textrm{for the terminal CH$_3$ segment %(where for
example $k=14$ for DMPC)
+}
+\end{array} \right.
+\end{displaymath}
+In general, $S^k_\textrm{mol} = 0$ indicates a completely random mean
orientation, $S^k_\textrm{mol} = 1$ indicates alignment of the segment
molecular axis along the bilayer normal, whereas $S^k_\textrm{mol} = -0.5$
indicates that the segment molecular axis lies in the bilayer plain (thus
being perpendicular to the normal direction).
+
+\subsection{Phase behaviour of lipid bilayers}
+Lipids are able to adopt a range of phases depending on temperature and
level of hydration, as already mentioned. In particular, fully hydrated
bilayers composed of a single phospholipid species undergo a well-defined
thermotropic phase transition in which the lipid chains change from an
ordered, or gel, state to a fluid, or liquid-crystalline,
state.~\cite{cevc} % p.12
+As an example, the phase diagram for the dimyristoylphosphatidylcholine
(DMPC) bilayer is reported in Figure~\ref{fig:dmpcPhaseDiag}.
+\begin{figure}
+\begin{center}
+\includegraphics[scale=.2]{biophys/dmpcPhaseDiagram_Janiak79}\caption[DMPC
phase diagram]{Phase diagram of hydrated DMPC bilayers, together with
representations of the L$_\alpha$, P$_{\beta'}$ and L$_{\beta'}$ phases.
The hydrocarbon chain packing is a hexagonal array for the P$_{\beta'}$
phase and a ``distorted'' hexagonal lattice for the L$_{\beta'}$ phase.
From Janiak et al.~\cite{janiak79}}
+\label{fig:dmpcPhaseDiag}
+\end{center}
+\end{figure}
+Biologically, the most important phase is the liquid $L_\alpha$ phase,
characterised by a high degree of disorder in the alkyl chains of the
hydrophobic core.
+
+
+%\subsection{Mechanical properties}
+\subsection{The lateral pressure profile}
+%Lipid bilayers are generally tensionless: the repulsive (inter-tail and
inter-headgroup) interactions exactly balance the attractive
(``hydrophobic'') forces.~\cite{harries97}
+The transbilayer lateral pressure profile $\pi(z)$, where $z$ is a spatial
coordinate along the bilayer normal, is defined as the difference between
the lateral and the normal pressures acting inside the bilayer: $\pi(z) =
p_L(z) - p_N(z)$. The lateral pressure profile thus characterises the
transmembrane distribution of forces; Figure~\ref{fig:lppTempler} is an
example of the proposed shape of such a distribution.
+\begin{figure}
+\begin{center}
+\includegraphics[scale=.9]{biophys/lppTempler}
+\caption[Lateral pressure profile]{Lateral pressure profile. Proposed
distribution of lateral pressure $\pi$ within a flat monolayer as a
function of the position along the interfacial normal $z$. From Templer et
al.~\cite{templer98}}
+\label{fig:lppTempler}
+\end{center}
+\end{figure}
+In terms of magnitude, peak pressures of the order of several hundreds of
atmospheres are predicted; the pressure profile results from an interplay
of enormous opposing forces, that ultimately compensate each other.
+The lateral pressure profile changes in relation to the lipid composition
(or the state of the lipid headgroups, e.g., by proton or ion binding), and
as a result of the presence of cholesterol or solutes (such as drugs); the
consequent depth-dependent changes in the stress distribution are predicted
to affect lipid phase behaviour and the conformation of inclusions such as
proteins.~\cite{sedd95} %[Sec.~6.4].
+In fact, the lateral pressure profile controls a very large number of
membrane features and phenomena: it determines the interfacial area, it is
at the basis of phase transitions and
fusion,~\cite{sedd95,yang03,kozlovsky04,siegel04,shearman06} %seddon
@p.144 %
+it affects permeability,~\cite{kamo06} drug transport,~\cite{curnow04}
and anaesthesia,~\cite{mohr05}
+it modulates the insertion and folding of membrane
proteins,~\cite{curran99,meijberg02,brink04,hong04,bowie05}
+ and it is believed to directly control the functioning of several
membrane proteins, such as the lipid synthesis regulatory enzyme
CCT,~\cite{attard00,davies01} diacylglycerol kinase,~\cite{fanani04}
phospholipase A2~\cite{sen91} and C,~\cite{ruiz98}
rhodopsin,~\cite{botelho02,wang02,botelho06} and several transbilayer
channels.~\cite{keller93,perozo02,jensen04,brink04,rosto06}
+%~\cite{mouritsen}, channel conductance~\cite{keller93}, mechanosensitive
channels~\cite{perozo02} and the potassium channel KcsA~\cite{brink04}.
+%Despite so many effotrs, there are many apparently simple questions about
lipids that still need to be answered~\cite{bagatolli06}: for instance, why
do cell membranes contain thousands of different molecular lipid species?
+The lateral pressure profile is also directly related to the elastic
curvature constants that characterise the Helfrich expression for the
bending free energy.~\cite{helfrich73,sedd95,marsh06} %~\cite{helfrich73}.
+According to Helfrich's theory, the surface curvature elastic energy per
unit area $g$ is concisely expressed as: \begin{equation}\label{eq:helfrich}
+g = \kappa\left(c_1 + c_2 -c_0\right)^2/2 + \kappa_\textrm{G}\, c_1\,c_2
+\end{equation}
+with $\kappa$ the bending rigidity, $c_1$ and $c_2$ the (local) principal
curvatures, $c_0$ the spontaneous (or intrinsic) curvature and
$\kappa_\textrm{G}$ the Gaussian curvature modulus. Equivalently, the
Helfrich equation can also be written:
+\begin{equation}\label{eq:helfrichBis}
+g = 2\kappa\left(H-H_0\right)^2+ \kappa_\textrm{G}K
+\end{equation}
+with $H=(c_1+c_2)/2$ the mean curvature, $H_0 = c_0/2$ the equilibrium
mean curvature and $K=c_1c_2$ the Gaussian curvature. The constants
appearing in Helfrich's expressions in turn control membrane
shape, %~\cite{zim-koz06},
+ and play specific roles in the mechanisms modulated by the lateral
pressure profile (mathematical relations between the Helfrich constants and
the pressure distribution $\pi(z)$ can be found
elsewhere.~\cite{mario08,marioDmpcDopc}
+
+Experimentally, it has been so far impossible to quantitatively measure
the pressure profile. The only experiments performed to date have yielded
qualitative and partial pictures for the hydrocarbon region only. In these
experiments,~\cite{templer98, kamo06} changes in the lateral pressure along
the bilayer normal were ``sensed'' using a series of di-pyrenyl
phosphatidylcholine (dipyPC) fluorescence probes. DipyPCs are PC lipids
carrying pyrene moieties attached to their tail ends. Ultraviolet
stimulation produces both monomer and excimer fluorescence from pyrene. The
excimer signal, which is entirely intramolecular at low dilutions of
dipyPC, results from (excited) dimerization of adjacent pyrene groups, and
depends on the frequency with which the two pyrene moieties collide to form
excimers; this frequency, in turn, is proportional to the lateral
pressure. % are brought into close proximity (aggregation frequency).
+The relative intensity of the excimer to monomer signal is thus a measure
of the pressure; by using dipyPCs of different acyl chain lengths it is
possible to qualitatively estimate the pressure variations across different
depths in the bilayer.~\cite{templer98}
+
+\subsection{The dipole potential}
+In typical physiological conditions, the presence of ions in the water
phases at the interface with both sides of a membrane, along with the
orientational ordering of interfacial water dipoles and the intramembrane
distribution of charged groups along the lipids
(Figure~\ref{fig:chgsDipoles}), create a characteristic electrical
potential distribution along the direction normal to the membrane plane
(Figure~\ref{fig:proposed-epp}).
+\begin{figure}
+\begin{center}
+\includegraphics[scale=.15]{biophys/lipWatElectrostatics}\caption[Charges
and dipoles of lipids and water]{Electrostatics at the lipid/water
interface. The signs and arrows represent the main charges and dipoles
possessed by lipid segments and water molecules. Adapted from Shinoda et
al.~\cite{shinoda98}}
+\label{fig:chgsDipoles}
+\end{center}
+\end{figure}
+%\begin{figure} \begin{center}
\includegraphics[scale=.3]{biophys/electricalPotential_Clarke.eps}\caption[Trans-bilayer
electrical potential]{The electrical potential across a phospholipid
membrane. The trans-membrane potential $\Delta\Psi$ is due to the
difference in anion and cation concentrations between the two aqueous bulk
phases. The surface potential $\Psi_s$ arises from charged residues
(charged headgroups) at the membrane-solution interface. The dipole
potential $\Psi_d$ results from the alignment of dipolar residues of the
lipids and associated water molecules within the membrane. From
Clarke.~\cite{clarke01}} \label{fig:proposed-epp} \end{center} \end{figure}
+\begin{figure} \begin{center}
\includegraphics[scale=1.2]{biophys/elPot.eps}\caption[Trans-bilayer
electrical potential]{The electrical potential profile $\Psi$ across a
phospholipid membrane. The trans-membrane potential $\Delta\Psi$ is due to
the difference in anion and cation concentrations between the two aqueous
bulk phases. The surface potential $\Psi_s$ arises from charged residues
(charged headgroups) at the membrane-solution interface. The dipole
potential $\Psi_d$ results from the alignment of dipolar residues of the
lipids and associated water molecules within the membrane. From
Clarke.~\cite{clarke97}} \label{fig:proposed-epp} \end{center} \end{figure}
+In particular, the membrane {\em dipole potential} $\Psi_d$ %is an
electrical potential which
+originates from the alignment of dipolar residues of the lipids and water
dipoles in the bilayer-water interfacial region.
+ $\Psi_d$ is positive inside the membrane with respect to the outer water
phase; its exact value is unknown, but it is believed to be of the order of
$0.2-0.5$\,V. Since this potential drops across a very small distance
within the headgroup region of the membrane,~\cite{clarke01} the
corresponding electric field strength is enormous, with peak values in the
range $10^8-10^9$ V/m. %the much higher field strength associated with the
dipole potential would certainly be capable of affecting the orientation of
dipolar or charged protein segments which are located in the interfacial
region of the membrane; the only factor that could lessen this effect would
be an electrical shielding from the protein by other charged
residues.~\cite{clarke01}
+The membrane dipole potential, and associated electric field, are involved
in a great number of biological processes, such as membrane
fusion,~\cite{cladera99,cladera01} permeation,~\cite{franklin93} the
regulation of membrane proteins (Na$^+$,K$^+$-ATPase,~\cite{starke05}
gramicidin channel,~\cite{rokitskaya02} phospholipase
A$_2$~\cite{maggio99}) insertion and folding of amphiphilic
peptides,~\cite{cladera98} the kinetics of DNA-lipid
complexes,~\cite{gelbart00} % from Saiz and Klein, jcp, 2002
+the kinetics of redox reactions at membrane surfaces,~\cite{alakoskela01}
human skin permeability,~\cite{cladera03} general
anaesthesia,~\cite{qin95,cafiso98} membrane partitioning of
pregnanolone,~\cite{alakoskela04} the binding capacity of
saquinavir,~\cite{asawakarn01} and the modulation of molecule-membrane
interactions in lipid rafts with possible effects on cells
signalling.~\cite{luker01,oshea03}
+%anesthesia and %~\cite{cafiso98} and %the modulation of molecule-membrane
interactions in lipid rafts with effects on and
signalling.~\cite{starke06} % luker01
+Despite the growing evidence for its importance, the dipole potential
$\Psi_d$ has received so far relatively little attention;~\cite{clarke01}
for instance, the overall transmembrane potential~$\Delta\Psi$, which
regulates numerous ion channels, is much more popular. The reason is that,
while $\Delta\Psi$ can be easily measured and controlled by placing
electrodes in the solution phases on each side of the membrane, the dipole
potential $\Psi_d$ cannot be directly measured, as it is impossible to
insert electrodes at different depths within the membrane.~\cite{clarke01}
Therefore, the dipole potential can only be estimated by indirect
measurements. One method involves studying the membrane conductivity
associated with the translocation of different hydrophobic ions; due to the
presence of the dipole potential, hydrophobic anions permeate much faster
than hydrophobic cations, and the magnitude of this effect can be used to
quantify~$\Psi_d$.~\cite{gawrisch92,schamberger02} It is also possible to
consider the bilayer dipole potential to be equivalent to the potential
across a monolayer, which can be directly obtained using electrodes after
spreading a monolayer of lipids onto the surface of a Langmuir
trough.~\cite{lairion04} However, this measurement relies on the
questionable assumption that such isolated monolayers are equal to each of
the monolayers paired into a bilayer assembly. Recently, the dipole
potential has been estimated using cryo-EM, by recording the interactions
of electrons with regions of different electrostatic potentials across
rapidly frozen bilayers.~\cite{wang06} Unfortunately, this technique also
relies on a number of approximations that might affect its reliability. For
instance, it is expected that the bilayer structure remains intact during
the freezing, which occurs at a rate of~$10^6\,$K/s $=1\,$K/$\mu$s; in
fact, this cooling rate might be slow enough to allow artificial
rearrangements of water and lipid molecules. The available experimental
estimates for the dipole potential of ester-PC lipids are collected in
Table~\ref{tab:dipPotExp}.
+\begin{table}
+\caption[Dipole potential: experimental measurements]{Measurements of the
dipole potential $\Psi_d$ in phosphocholine bilayers.}
+\begin{center}
+%\vspace{8pt}
+\begin{tabular}{|l|c|c|} % put @{} if you want to eliminate horizontal
space between columns
+\hline
+{\em Method} & {\em Lipid} & $\Psi_d$ / V \\\hline
+Ion translocation~\cite{gawrisch92} & DPPC & 0.227\\
+Ion translocation~\cite{schamberger02} & DPPC & 0.346\\
+Monolayer~\cite{lairion04} & DMPC & 0.449 \\
+Cryo-EM~\cite{wang06} & DPhPC & 0.510 \\\hline
+%Atomic-level MD~\cite{feller96a} & DPPC & 0.800-2.300\\
+%Atomic-level MD~\cite{berge97a} & DPPC & 0.150-0.750\\
+%Atomic-level MD~\cite{smond99a} & DPPC & 0.600\\
+%Atomic-level MD~\cite{mashl01} & DOPC & 0.500\\Atomic-level
MD~\cite{saizl02b} & DMPC & 0.500\\
+%Atomic-level MD~\cite{anezo03a} & DPPC & 0.620-0.830\\
+%Atomic-level MD~\cite{patra03a} & DPPC & 0.570 \\
+%Atomic-level MD~\cite{sachs04} & DMPC & 0.950\\
+%Atomic-level MD~\cite{shinoda04} & DPhPC & 1.002\\
+%Atomic-level MD~\cite{wohle04a} & DPPC & 0.500-0.850\\
+%Atomic-level MD~\cite{villarreal04} & DPPC & 0.557\\
+%Atomic-level MD~\cite{song05} & DPPC & 0.8\\
+%Coarse-grain MD~[{\em this work}] & DMPC & 1.2\\
+\end{tabular}
+\label{tab:dipPotExp}
+\end{center}
+DPPC = dipalmitoylphosphatidylcholine, DMPC =
dimyristoylphosphatidylcholine, DPhPC = diphytanoylphosphatidylcholine.
+\end{table}
+
+\subsection{Dynamics}
+Despite displaying structural integrity typical of solid materials, the
biologically relevant state of lipid bilayers is that of a liquid crystal
characterised by substantial fluidity and disorder.
+In their biological state, lipids typically display various dynamic
features: they change conformation, diffuse laterally in the membrane
plane, rotate around their main molecular axis, protrude into the water
phase and flip through the monolayers. These characteristic motions are
represented in Figure~\ref{fig:lipDyn}.
+\begin{figure}%[ht]
+\centering
+\includegraphics[scale=1]{biophys/lipMotion.eps}
+\caption[Lipid characteristic motions]{Lipid dynamics. Characteristic
motions of lipid molecules inside a bilayer: a)~tail conformational change,
b)~rotation around molecular axis, c)~diffusion (swap), d)~protrusion,
e)~flip-flop. From Mouritsen.~\cite{mouritsen}}
+\label{fig:lipDyn}
+\end{figure}
+The lateral mobility of lipids in the plane of the membrane (diffusion) is
particularly important, as it defines the liquid-like nature of membranes.
+The diffusion of lipids can be measured by a number of different
experimental methods. The motion of a single lipid can be detected by
single-particle tracking.~\cite{sonnleitner99} A colloidal particle of a
typical diameter of 40\,nm is attached to the lipid molecule and the
particle's motion is followed by microscopy; the spatial resolution of this
kind of experiment is~$\approx50$\,nm, and the time resolution
is~$\approx5$\,ms.
+Diffusion coefficients have been obtained by quasi-elastic neutron
scattering, which measures short-range diffusion taking place over
sub-nanosecond timescales.~\cite{tabony91} Alternatively, long-range
methods such as NMR spectroscopy~\cite{filip03b} and fluorescence recovery
after photobleaching~\cite{almeida92} can be used; these methods probe
millisecond time-scales. Interestingly, the lateral diffusion coefficients
measured with short-range methods turn out to be~$\approx2$ orders of
magnitude higher than those obtained by long-range
observations.~\cite{vaz91}
+To understand the reason of this discrepancy, it is useful to take into
account the {\em free-volume} diffusion theory, which was proposed more
than 50\,years ago to describe transport in soft condensed
matter.~\cite{cohen59, turnbull61, turnbull70} The foundation of the theory
is that diffusion is related to the average free volume per particle;
molecular diffusion proceeds by jumps occurring when a large enough free
volume is created (by free volume redistribution) next to the diffusing
molecule.
+Lipid diffusion is then assumed to proceed by ``hopping'' of molecules
into vacancies formed by lateral density fluctuations in the
membrane.~\cite{oleary87}
+ %,almeida92}
+%According to the free-volume model, lateral diffusion occurs by discrete
jumps of lipid molecules %, of length roughly equal to the diameter of a
lipid molecule, into nearby vacancies formed by lateral density
fluctuations;
+In between jumps, a lipid molecule spends a relatively long time
``rattling in a cage'' formed by its neighbours. Over short ($<1$\,ns)
time-scales, the diffusion coefficient is high because it is determined by
the rapid short-range lipid motion mainly due to such ``rattling-about''
behaviour. % it is also partly due to lipid jumps, although over such short
time-scale the motion of rattling vs jumping lipids cannot be discriminated.
+Over longer times, this rattling motion averages out, yielding no net
displacement. The true, long-range diffusion coefficient is thus determined
by the lipid jumps, that give rise to effective displacement over extended
($>10$\,ns) time-scales.
+
+\section{Summary}
+
+
+Membrane lipids are driven together by water, through the hydrophobic
effect, into various self-assembling structures. The most abundant lipid
aggregate is the bilayer, which constitutes the backbone of the plasma
membrane encapsulating cells. Owing to many peculiar molecular
characteristics of lipids (such as shape and charge anisotropy) and to the
fact that they interact through ``weak'', non-covalent forces, the
resulting bilayers are multifaceted materials:
+\begin{itemize}
+\item the internal structure is highly stratified and characteristically
(dis)ordered;
+\item there is a steeply varying depth-dependent distribution of pressures;
+\item the charges present give rise to a large potential difference
between the hydrocarbon core and the outer water phase;
+\item there are various dynamic phenomena, such as lipid diffusion in the
bilayer plane.
+\end{itemize}
+All these different bilayer characteristics, often involved in a complex
interplay with proteins, are integral to many biological phenomena, such as
transport, growth and signalling.
+
+
+%Fluidity is a central physical feature of membranes.
+
+%The fact that the lipid bilayers of almost all biological membranes are
fluid under physiological conditions is almost certainly dictated by the
requirement that most of the integral membrane proteins spanning the
bilayer must undergo conformational transitions in order to function:
membrane fluidity, in turn, implies {\it zero} shear restoring
force.~\cite{lipow95a} <-- ... WHAT ABOUT THE LATERAL PRESSURE? SURELY IT
DETERMINES DIFFERENT NON-ZERO RESTORING FORCES!!!
+
+
+%\section[Transport Across Membranes]{Transport Across Membranes} There
are three categories of membrane transport phenomena: passive, facilitated,
and active. Here we will focus on the passive mechanism only, as this is
the phenomenon that we have modeled as reported in
Chpaters~\ref{ch:permSmall} and ~\ref{perm:Drugs}. The fundamental
principle of passive permeation is described by Fick's first law of
diffusion: a substance diffuses in the direction that eliminates its
concentration gradient, at a rate proportional to the magnitude of this
gradient. % \cite[p.727]{voet}
+
+
=======================================
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***The diff for this file has been truncated for email.***
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/biophysj.bst Wed Dec 21 02:20:08 2011
@@ -0,0 +1,1652 @@
+%%
+%% This file is biophysj-natbib.bst
+%% The original biophysj.bst was generated with 'latex makebst'
+%% and then adapted for natbib by patching with natbib.diff and resolving
+%% failed patches manually.
+%% (c) 2005 Oliver Beckstein
+%%
+%%
+%% This is file `biophysj.bst',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% merlin.mbs (with options:
`head,exlang,annote,seq-no,nm-rev1,jnrlst,dt-beg,xmth,yrpp-xsp,vnum-x,num-xser,jnm-x,btit-rm,bt-rm,pre-pub,in-it,english,ppx,xedn,and-com,and-com-ed,url,url-nt,nfss,,{}')
+%% english.mbs (with options:
`exlang,annote,seq-no,nm-rev1,jnrlst,dt-beg,xmth,yrpp-xsp,vnum-x,num-xser,jnm-x,btit-rm,bt-rm,pre-pub,in-it,english,ppx,xedn,and-com,and-com-ed,url,url-nt,nfss,,{}')
+%% merlin.mbs (with options:
`tail,exlang,annote,seq-no,nm-rev1,jnrlst,dt-beg,xmth,yrpp-xsp,vnum-x,num-xser,jnm-x,btit-rm,bt-rm,pre-pub,in-it,english,ppx,xedn,and-com,and-com-ed,url,url-nt,nfss,,{}')
+%% ----------------------------------------
+%% *** Biophysical Journal (> Spring 2005) ***
+%%
+%% Copyright 1994-2004 Patrick W Daly
+ % ===============================================================
+ % IMPORTANT NOTICE:
+ % This bibliographic style (bst) file has been generated from one or
+ % more master bibliographic style (mbs) files, listed above.
+ %
+ % This generated file can be redistributed and/or modified under the terms
+ % of the LaTeX Project Public License Distributed from CTAN
+ % archives in directory macros/latex/base/lppl.txt; either
+ % version 1 of the License, or any later version.
+ % ===============================================================
+ % Name and version information of the main mbs file:
+ % \ProvidesFile{merlin.mbs}[2004/02/09 4.13 (PWD, AO, DPC)]
+ % For use with BibTeX version 0.99a or later
+ %-------------------------------------------------------------------
+ % This bibliography style file is intended for texts in
+ % ENGLISH
+ % This is a numerical citation style, and as such is standard LaTeX.
+ % It requires no extra package to interface to the main text.
+ %
+ % It can be used with the natbib package (using citep, citet, etc)
+ %
+ % The form of the \bibitem entries is
+ % \bibitem{key}...
+ % Usage of \cite is as follows:
+ % \cite{key} ==>> [#]
+ % \cite[chap. 2]{key} ==>> [#, chap. 2]
+ % where # is a number determined by the ordering in the reference list.
+ % The order in the reference list is that by which the works were
originally
+ % cited in the text, or that in the database.
+ %---------------------------------------------------------------------
+
+ENTRY
+ { address
+ author
+ booktitle
+ chapter
+ edition
+ editor
+ eid
+ howpublished
+ institution
+ journal
+ key
+ month
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ url
+ volume
+ year
+ }
+ {}
+ { label extra.label sort.label short.list }
+INTEGERS { output.state before.all mid.sentence after.sentence after.block
}
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+ #2 'after.sentence :=
+ #3 'after.block :=
+}
+STRINGS { s t}
+FUNCTION {output.nonnull}
+{ 's :=
+ output.state mid.sentence =
+ { ", " * write$ }
+ { output.state after.block =
+ { add.period$ write$
+ newline$
+ "\newblock " write$
+ }
+ { output.state before.all =
+ 'write$
+ { add.period$ " " * write$ }
+ if$
+ }
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+ s
+}
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ "empty " t * " in " * cite$ * warning$ }
+ 'output.nonnull
+ if$
+}
+FUNCTION {fin.entry}
+{ add.period$
+ write$
+ newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+ 'skip$
+ { after.block 'output.state := }
+ if$
+}
+FUNCTION {new.sentence}
+{ output.state after.block =
+ 'skip$
+ { output.state before.all =
+ 'skip$
+ { after.sentence 'output.state := }
+ if$
+ }
+ if$
+}
+FUNCTION {add.blank}
+{ " " * before.all 'output.state :=
+}
+
+FUNCTION {no.blank.or.punct}
+{ "\hspace{0pt}" * before.all 'output.state :=
+
+}
+
+FUNCTION {date.block}
+{
+ new.block
+}
+
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+FUNCTION {new.block.checka}
+{ empty$
+ 'skip$
+ 'new.block
+ if$
+}
+FUNCTION {new.block.checkb}
+{ empty$
+ swap$ empty$
+ and
+ 'skip$
+ 'new.block
+ if$
+}
+FUNCTION {new.sentence.checka}
+{ empty$
+ 'skip$
+ 'new.sentence
+ if$
+}
+FUNCTION {new.sentence.checkb}
+{ empty$
+ swap$ empty$
+ and
+ 'skip$
+ 'new.sentence
+ if$
+}
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "\emph{" swap$ * "}" * }
+ if$
+}
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$
+}
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ %-------------------------------------------------------------------
+ % Begin module:
+ % \ProvidesFile{english.mbs}[2003/11/06 4.2 (PWD)]
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "and"}
+
+FUNCTION {bbl.etal}
+{ "et~al." }
+
+FUNCTION {bbl.editors}
+{ "editors" }
+
+FUNCTION {bbl.editor}
+{ "editor" }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "edition" }
+
+FUNCTION {bbl.volume}
+{ "volume" }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "number" }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "" }
+
+FUNCTION {bbl.page}
+{ "" }
+
+FUNCTION {bbl.chapter}
+{ "chapter" }
+
+FUNCTION {bbl.techrep}
+{ "Technical Report" }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+ % End module: english.mbs
+%% Copyright 1994-2004 Patrick W Daly
+MACRO {acmcs} {"ACM Computing Surveys"}
+
+MACRO {acta} {"Acta Informatica"}
+
+MACRO {cacm} {"Communications of the ACM"}
+
+MACRO {ibmjrd} {"IBM Journal of Research and Development"}
+
+MACRO {ibmsj} {"IBM Systems Journal"}
+
+MACRO {ieeese} {"IEEE Transactions on Software Engineering"}
+
+MACRO {ieeetc} {"IEEE Transactions on Computers"}
+
+MACRO {ieeetcad}
+ {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}
+
+MACRO {ipl} {"Information Processing Letters"}
+
+MACRO {jacm} {"Journal of the ACM"}
+
+MACRO {jcss} {"Journal of Computer and System Sciences"}
+
+MACRO {scp} {"Science of Computer Programming"}
+
+MACRO {sicomp} {"SIAM Journal on Computing"}
+
+MACRO {tocs} {"ACM Transactions on Computer Systems"}
+
+MACRO {tods} {"ACM Transactions on Database Systems"}
+
+MACRO {tog} {"ACM Transactions on Graphics"}
+
+MACRO {toms} {"ACM Transactions on Mathematical Software"}
+
+MACRO {toois} {"ACM Transactions on Office Information Systems"}
+
+MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}
+
+MACRO {tcs} {"Theoretical Computer Science"}
+FUNCTION {bibinfo.check}
+{ swap$
+ duplicate$ missing$
+ {
+ pop$ pop$
+ ""
+ }
+ { duplicate$ empty$
+ {
+ swap$ pop$
+ }
+ { swap$
+ pop$
+ }
+ if$
+ }
+ if$
+}
+FUNCTION {bibinfo.warn}
+{ swap$
+ duplicate$ missing$
+ {
+ swap$ "missing " swap$ * " in " * cite$ * warning$ pop$
+ ""
+ }
+ { duplicate$ empty$
+ {
+ swap$ "empty " swap$ * " in " * cite$ * warning$
+ }
+ { swap$
+ pop$
+ }
+ if$
+ }
+ if$
+}
+STRINGS { bibinfo}
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+ duplicate$ empty$ 'skip$ {
+ 's :=
+ "" 't :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ duplicate$ #1 >
+ { "{f.~}{vv~}{ll}{, jj}" }
+ { "{vv~}{ll}{, f.}{, jj}" }
+ if$
+ format.name$
+ bibinfo bibinfo.check
+ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ "," *
+ s nameptr "{ll}" format.name$ duplicate$ "others" =
+ { 't := }
+ { pop$ }
+ if$
+ t "others" =
+ {
+ " " * bbl.etal *
+ }
+ {
+ bbl.and
+ space.word * t *
+ }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+ } if$
+}
+
+FUNCTION {format.key}
+{ empty$
+ { key field.or.null }
+ { "" }
+ if$
+}
+
+FUNCTION {format.names.ed}
+{
+ 'bibinfo :=
+ duplicate$ empty$ 'skip$ {
+ 's :=
+ "" 't :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{f.~}{vv~}{ll}{, jj}"
+ format.name$
+ bibinfo bibinfo.check
+ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ "," *
+ s nameptr "{ll}" format.name$ duplicate$ "others" =
+ { 't := }
+ { pop$ }
+ if$
+ t "others" =
+ {
+
+ " " * bbl.etal *
+ }
+ {
+ bbl.and
+ space.word * t *
+ }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+ } if$
+}
+FUNCTION {format.authors}
+{ author "author" format.names
+}
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+ {
+ "," *
+ " " *
+ get.bbl.editor
+ *
+ }
+ if$
+}
+FUNCTION {format.note}
+{
+ url empty$
+ 'skip$
+ { "\urlprefix\url{" url * "}" * output }
+ if$
+ note empty$
+ { "" }
+ { note #1 #1 substring$
+ duplicate$ "{" =
+ 'skip$
+ { output.state mid.sentence =
+ { "l" }
+ { "u" }
+ if$
+ change.case$
+ }
+ if$
+ note #2 global.max$ substring$ * "note" bibinfo.check
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title
+ duplicate$ empty$ 'skip$
+ { }
+ if$
+ "title" bibinfo.check
+}
+FUNCTION {format.full.names}
+{'s :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{vv~}{ll}" format.name$ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ numnames #2 >
+ { "," * }
+ 'skip$
+ if$
+ t "others" =
+ { " et~al." * }
+ { " and " * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {author.editor.full}
+{ author empty$
+ { editor empty$
+ { "" }
+ { editor format.full.names }
+ if$
+ }
+ { author format.full.names }
+ if$
+}
+
+FUNCTION {author.full}
+{ author empty$
+ { "" }
+ { author format.full.names }
+ if$
+}
+
+FUNCTION {editor.full}
+{ editor empty$
+ { "" }
+ { editor format.full.names }
+ if$
+}
+
+
+
+FUNCTION {make.full.names}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.full
+ { type$ "proceedings" =
+ 'editor.full
+ 'author.full
+ if$
+ }
+ if$
+}
+
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem[" write$
+ label write$
+ ")" make.full.names duplicate$ short.list =
+ { pop$ }
+ { * }
+ if$
+ "]{" * write$
+ cite$ write$
+ "}" write$
+ newline$
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+ 't :=
+ ""
+ { t empty$ not }
+ { t #1 #1 substring$ "-" =
+ { t #1 #2 substring$ "--" = not
+ { "--" *
+ t #2 global.max$ substring$ 't :=
+ }
+ { { t #1 #1 substring$ "-" = }
+ { "-" *
+ t #2 global.max$ substring$ 't :=
+ }
+ while$
+ }
+ if$
+ }
+ { t #1 #1 substring$ *
+ t #2 global.max$ substring$ 't :=
+ }
+ if$
+ }
+ while$
+}
+
+FUNCTION {word.in}
+{ bbl.in capitalize
+ emphasize
+ " " * }
+
+FUNCTION {format.date}
+{
+ ""
+ duplicate$ empty$
+ year "year" bibinfo.check duplicate$ empty$
+ { swap$ 'skip$
+
+ { "there's a month but no year in " cite$ * warning$ }
+ if$
+ *
+ }
+ { swap$ 'skip$
+ {
+ swap$
+ " " * swap$
+ }
+ if$
+ *
+ }
+ if$
+}
+FUNCTION {format.btitle}
+{ title "title" bibinfo.check
+ duplicate$ empty$ 'skip$
+ {
+ }
+ if$
+}
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+FUNCTION {format.bvolume}
+{ volume empty$
+ { "" }
+ { bbl.volume volume tie.or.space.prefix
+ "volume" bibinfo.check * *
+ series "series" bibinfo.check
+ duplicate$ empty$ 'pop$
+ { swap$ bbl.of space.word * swap$
+ emphasize * }
+ if$
+ "volume and number" number either.or.check
+ }
+ if$
+}
+FUNCTION {format.number.series}
+{ volume empty$
+ { number empty$
+ { series field.or.null }
+ { series empty$
+ { number "number" bibinfo.check }
+ { output.state mid.sentence =
+ { bbl.number }
+ { bbl.number capitalize }
+ if$
+ number tie.or.space.prefix "number" bibinfo.check * *
+ bbl.in space.word *
+ series "series" bibinfo.check *
+ }
+ if$
+ }
+ if$
+ }
+ { "" }
+ if$
+}
+
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+ {
+ output.state mid.sentence =
+ { "l" }
+ { "t" }
+ if$ change.case$
+ "edition" bibinfo.check
+ " " * bbl.edition *
+ }
+ if$
+}
+INTEGERS { multiresult }
+FUNCTION {multi.page.check}
+{ 't :=
+ #0 'multiresult :=
+ { multiresult not
+ t empty$ not
+ and
+ }
+ { t #1 #1 substring$
+ duplicate$ "-" =
+ swap$ duplicate$ "," =
+ swap$ "+" =
+ or or
+ { #1 'multiresult := }
+ { t #2 global.max$ substring$ 't := }
+ if$
+ }
+ while$
+ multiresult
+}
+FUNCTION {format.pages}
+{ pages duplicate$ empty$ 'skip$
+ { duplicate$ multi.page.check
+ {
+ n.dashify
+ }
+ {
+ }
+ if$
+ "pages" bibinfo.check
+ }
+ if$
+}
+FUNCTION {format.journal.pages}
+{ pages duplicate$ empty$ 'pop$
+ { swap$ duplicate$ empty$
+ { pop$ pop$ format.pages }
+ {
+ ":" *
+ swap$
+ n.dashify
+ "pages" bibinfo.check
+ *
+ }
+ if$
+ }
+ if$
+}
+FUNCTION {format.journal.eid}
+{ eid "eid" bibinfo.check
+ duplicate$ empty$ 'pop$
+ { swap$ duplicate$ empty$ 'skip$
+ {
+ ":" *
+ }
+ if$
+ swap$ *
+ }
+ if$
+}
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+ duplicate$ empty$ 'skip$
+ {
+ "volume" bibinfo.check
+ }
+ if$
+ eid empty$
+ { format.journal.pages }
+ { format.journal.eid }
+ if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ 'format.pages
+ { type empty$
+ { bbl.chapter }
+ { type "l" change.case$
+ "type" bibinfo.check
+ }
+ if$
+ chapter tie.or.space.prefix
+ "chapter" bibinfo.check
+ * *
+ pages empty$
+ 'skip$
+ { ", " * format.pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.booktitle}
+{
+ booktitle "booktitle" bibinfo.check
+}
+FUNCTION {format.in.ed.booktitle}
+{ format.booktitle duplicate$ empty$ 'skip$
+ {
+ editor "editor" format.names.ed duplicate$ empty$ 'pop$
+ {
+ "," *
+ " " *
+ get.bbl.editor
+ ", " *
+ * swap$
+ * }
+ if$
+ word.in swap$ *
+ }
+ if$
+}
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+ month empty$ year empty$ note empty$
+ and and and and and
+ { "all relevant fields are empty in " cite$ * warning$ }
+ 'skip$
+ if$
+}
+FUNCTION {format.thesis.type}
+{ type duplicate$ empty$
+ 'pop$
+ { swap$ pop$
+ "t" change.case$ "type" bibinfo.check
+ }
+ if$
+}
+FUNCTION {format.tr.number}
+{ number "number" bibinfo.check
+ type duplicate$ empty$
+ { pop$ bbl.techrep }
+ 'skip$
+ if$
+ "type" bibinfo.check
+ swap$ duplicate$ empty$
+ { pop$ "t" change.case$ }
+ { tie.or.space.prefix * * }
+ if$
+}
+FUNCTION {format.article.crossref}
+{
+ key duplicate$ empty$
+ { pop$
+ journal duplicate$ empty$
+ { "need key or journal for " cite$ * " to crossref " * crossref *
warning$ }
+ { "journal" bibinfo.check emphasize word.in swap$ * }
+ if$
+ }
+ { word.in swap$ * " " *}
+ if$
+ " \cite{" * crossref * "}" *
+}
+FUNCTION {format.crossref.editor}
+{ editor #1 "{vv~}{ll}" format.name$
+ "editor" bibinfo.check
+ editor num.names$ duplicate$
+ #2 >
+ { pop$
+ "editor" bibinfo.check
+ " " * bbl.etal
+ *
+ }
+ { #2 <
+ 'skip$
+ { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+ {
+ "editor" bibinfo.check
+ " " * bbl.etal
+ *
+ }
+ {
+ bbl.and space.word
+ * editor #2 "{vv~}{ll}" format.name$
+ "editor" bibinfo.check
+ *
+ }
+ if$
+ }
+ if$
+ }
+ if$
+}
+FUNCTION {format.book.crossref}
+{ volume duplicate$ empty$
+ { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+ pop$ word.in
+ }
+ { bbl.volume
+ capitalize
+ swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of
space.word *
+ }
+ if$
+ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { series empty$
+ { "need editor, key, or series for " cite$ * " to crossref " *
+ crossref * warning$
+ "" *
+ }
+ { series emphasize * }
+ if$
+ }
+ { key * }
+ if$
+ }
+ { format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+FUNCTION {format.incoll.inproc.crossref}
+{
+ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { format.booktitle duplicate$ empty$
+ { "need editor, key, or booktitle for " cite$ * " to
crossref " *
+ crossref * warning$
+ }
+ { word.in swap$ * }
+ if$
+ }
+ { word.in key * " " *}
+ if$
+ }
+ { word.in format.crossref.editor * " " *}
+ if$
+ " \cite{" * crossref * "}" *
+}
+FUNCTION {format.org.or.pub}
+{ 't :=
+ ""
+ address empty$ t empty$ and
+ 'skip$
+ {
+ t empty$
+ { address "address" bibinfo.check *
+ }
+ { t *
+ address empty$
+ 'skip$
+ { ", " * address "address" bibinfo.check * }
+ if$
+ }
+ if$
+ }
+ if$
+}
+FUNCTION {format.publisher.address}
+{ publisher "publisher" bibinfo.warn format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization "organization" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {article}
***The diff for this file has been truncated for email.***
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/depot/biophysRubbish.tex Wed Dec 21 02:20:08 2011
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+
+\paragraph{Precise structural quantities: $V_L$ and $D$}
+Measurements of total lipid volume $V_L$ have been performed using a
variety of techniques. Agreement between the different methods is about 3
parts in 1000 and the errors in each method alone is of order 2 parts in
1000~\cite{nagle00a}. The lipid volume of DMPC was first measured
by~\cite{nagle78}, and remarkably that value is still valid.
+An important experimental result is that the total lipid volume does not
change measurably with hydration~\cite{nagle00a}.
+\paragraph{Area per lipid $A_L$}
+Knowledge of surface \index{area per lipid} can be correlated with many of
the membrane structural and physical properties (e.g., order parameters,
bilayer thickness, conformation of acyl chains, etc.) and hence this is
considered to be the most central structural quantity~\cite{sanka04}.
+\cite{kucer05a} obtained a result for the area of DMPC about 1\,\AA$^2$
larger than the earlier value (59.6\,A$^2$) reported by~\cite{nagle00a}
(that was obtained by x-ray method~\cite{petra98a}, and by
NMR~\cite{koeni97a, petra00a}). Although agreement is satisfactory within
estimated uncertainties of 0.5\,\AA$^2$, the refined structure used
by~\cite{kucer05a} was obtained with much better x-ray data, so the new
value of $A_L=60.6\,$\AA$^2$ should be more accurate.
+
+\paragraph{Bilayer thickness}
+The bilayer thickness \index{thickness} is defined as the head-head
separation $D_{HH}$~\cite{nagle00a}.
+
+\subsection{Electron density profile}\index{electron density profile - EDP}
+
+The electron density profile (EDP)
+We can now compare the average from quartets of segmental order parameters
$S^k_\textrm{mol}$ to the corresponding order parameters of our
coarse-grain units.
+
+The second order Legendre polynomial $P_2$ is widely used:
+\[P_2=\frac{1}{2}(3\cos^2\theta-1)\,,\]
+where $\theta$ is the angle between the direction of the bond and the
bilayer normal.
+\begin{equation}
+S_{CD}^{(i)}=
+\left<
+\frac{1}{2}
+\left(
+3{cos^{2}}\beta_{i}-1
+\right)
+\right>
+=
+\left<
+P_{2}(cos{\beta_{i}})
+\right>.
+\label{scd}
+\end{equation}
+Full alignment to the bilayer normal (i.e. $\theta=0$) is indicated by
$P_2=1$, full order perpendicular to the bilayer normal with $P_2=-0.5$ and
a random orientation with $P_2=0$.
+For a perfectly ordered system, $\theta=0$ and the order parameter takes
its maximum value, i.e. $P_2=1$; for a system perfectly ordered
perpendicularly to the director.
+For a uniform distribution, $P_2=0$. Experimentally, $P_2\approx0.2$ for
the top and middle parts of the chains of DPPC, consistent with the partial
order~\cite{pas02}.
+\begin{figure}%[ht]
+\centering
+\includegraphics[scale=1]{biophys/douliezAxesSystemsEdited}
+\caption[Phospholipid intermolecular and intramolecular motions]{Schematic
representation of a phospholipid molecule with the axes systems needed for
the description of the intermolacular and intramolecular motions. $Z_N$ and
$Z_D$ represent the bilayer normal and the diffusion axis of the molecule,
$S_k^{CD}$ and $S_k^{CC}$ the $C_k-D$ and the $C_k-C_{k-1}$ bond order
parameters, $l_k$ and $L_k$ the average segment length projected onto the
diffusion axis and onto the bilayer normal, respectively. $\theta_{inter}$
accounts for intermolecular averages, and $\psi_{isom}$ and $\theta_{isom}$
account for the intramolecular motions. Adapted from Douliez et
al.~\cite{douliez95}}
+\label{fig:stevBeadSpring}
+\end{figure}
+
+\subsubsection{Compressibility moduli}
+The response of the bilayer surface area $A$ to an isotropic tension
$\overline{T}$ is specified by the isothermal modulus of the surface
compressibility:
+\begin{equation}
+K_A= A \left(\frac{\partial \overline{T}}{\partial A}\right)_T
+\end{equation}
+The area compressibility modulus~$K_A$ is alternatively defined as the
energy~$E_{K_A}$ per unit area to spend in order to stretch an interface
$A_0$ to produce an area change $\Delta A$ according to Hooke's law:
+\begin{equation}
+E_{K_A}=\frac{1}{2}K_A\left(\frac{\Delta A}{A_0}\right)^2
+\end{equation}
+$K_A$ describes an elastic property of the membrane and can be related to
the variance of the lipid area $\sigma^2_{A}$:
+\begin{equation}
+K_A=\frac{k_BTA}{N_l\sigma^2_{A}}
+\end{equation}
+with $A$ the average area per lipid, $N_l$ the number of lipid molecules
per layer, $T$ the temperature and $k_B$ the Boltzmann
constant. %~\cite{anezo03a}.
+
+\begin{equation}
+K_A=A\,\frac{\partial\gamma}{\partial A}
+\end{equation}
+
+%The experimentalists~\cite{petra98a} have estimated the area
compressibility of fully-hydrated DMPC at 30\textcelsius:
K$_A=108\pm35$\,dyn/cm.
+
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{lcccc} % put @{} if you want to eliminate horizontal space
between columns
+%Stretch modulus
+&\cite{evans90}& \cite{koeni97a} & \cite{petra98a}&\cite{rawicz00} \\
+K$_A$\,[dyn/cm] &$145\pm10$ &$137\pm15$ & $108\pm35$ &$234\pm23$
+\end{tabular}
+\caption[Area compressibility modulus]{Fluid-phase DMPC area
compressibility modulus. Experimental measurements of~$K_A$ reported in the
literature.}
+\label{tab:structData}
+\end{center}
+\end{table}
+
+\cite{ipsen90}
+
+
+\subsection{Volume compressibility modulus}\index{elasticity!volume
compressibility modulus $K_V$}
+The volume (or bulk) compressibility modulus~$K_V$ is defined
as~\cite[Chapter~12]{cevc}: %p.348
+\begin{equation}
+K_V=-V\left(\frac{\partial P}{\partial V}\right)_T
+\end{equation}
+$K_V$ describes the response of the bilayer volume $V$ to uniform
hydrostatic pressure $P$.
+Typical values of the bulk modulus are $K_V\sim10-30$\,kbar for fluid
lipid bilayers~\cite[Chapter~12]{cevc}. These are in the range found for
normal incompressible fluids, in contrast to the considerable greater
surface compressibility of the bilayer.
+
+
+Experimental measurements of the bending modulus for fluid-phase DMPC
bilayers are reported in Table~\ref{tab:bendMod}.
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{cccc} % put @{} if you want to eliminate horizontal space
between columns
+ $\kappa$ / $10^{-19}$J & $\kappa$ / $k_BT$ & T / $^{\circ}{\rm C}$ &
{\em experiment}\\
+ 1.30 & & 30& shape fluctuation~\cite{meleard97}\\
+ 0.56 & 14 & 29 & pipette aspiration~\cite{rawicz00}\\
+ 1.33 & 33 & 30 & all-optical~\cite{lee01} \\
+ 0.69 & 17 & 30 & x-ray scattering~\cite{chu05}
+\end{tabular}
+\caption[Bending modulus of fluid-phase DMPC bilayers]{Bending modulus
$\kappa$ of fluid-phase DMPC bilayers.}
+\label{tab:bendMod}
+\end{center}
+\end{table}
+There are clear discrepancies in the data obtained by different groups
using different techniques.
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{lll} % put @{} if you want to eliminate horizontal space
between columns
+ & $k$ / $k_BT$ & $c_0$ / nm$^{-1}$\\
+DMPC$_{\,29^{\circ}{\rm C}}$ & 7~\cite{rawicz00} & \\
+DMPC$_{\,30^{\circ}{\rm C}}$ & 16~\cite{lee01} & \\
+DOPC$_{\,18^{\circ}{\rm C}}$ & 10~\cite{rawicz00} & \\
+DOPC$_{\,32^{\circ}{\rm C}}$ & & $-0.114$~\cite{chen97} \\
+DOPC$_{\,30^{\circ}{\rm C}}$ & & $-0.112$~\cite{keller93} \\
+DOPE$_{\,30^{\circ}{\rm C}}$ & & $-0.526$~\cite{keller93}
+%DOPE/tetradecane$_{\,22^{\circ}{\rm C}}$ & & $-0.340$~\cite{chen97} \\
+\end{tabular}
+\caption[Curvature elastic and geometric data]{Curvature elastic and
geometric data of fluid-phase monolayers.}
+\label{tab:curvData}
+\end{center}
+\end{table}
+
+\subsection{Lipid diffusion}\index{diffusion!lipid!experimental data}
+
+The average distance $s$ traversed in time $t$ depends on $D$ according to
the
expression: %http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=stryer.section.1687
+
+\begin{equation}\label{eq:diffDist}
+s = \sqrt{4Dt}
+\end{equation}
+
+The diffusion coefficient of lipids in a variety of membranes is about
1\,$\mu$m$^2$/s. Thus, a phospholipid molecule diffuses an average distance
of 2\,$\mu$m in 1\,s. This rate means that a lipid molecule can travel from
one end of a bacterium to the other in a second. The magnitude of the
observed diffusion coefficient indicates that the viscosity of the membrane
is about 100 times that of water, rather like that of olive oil~\cite{berg}.
+
+Lipid lateral diffusion can be measured using the pulsed field gradient
NMR method~\cite{oradd02, filippov03}: this method is non-perturbing and in
most cases does not need any labeling.
+
+Experimental data for DMPC at $30^{\circ}{\rm C}$ are collected in
Table~\ref{tab:diffData}.
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{lccc} % put @{} if you want to eliminate horizontal space
between columns
+Experiment & NMR~\cite{filippov03} & NMR~\cite{oradd02}& Fluorescence
recovery~\cite{almeida92}%
&FRAP~\cite{blume93}&Excimer~\cite{blume93} %values from Hogberg JCPB 110
+\\Diffusion [nm$^2$/$\mu$s] & 9 & 9 &
6 %&$2-8\times10^{-8}$&2-30$\times10^{-8}$
+\end{tabular}
+\caption[DMPC experimental diffusion data]{DMPC experimental diffusion
data, full hydration, $30^{\circ}{\rm C}$.}
+\label{tab:diffData}
+\end{center}
+\end{table}
+Considering the diffusion for fluid DMPC, we compute an average travelling
distance of $6$\,nm per $\mu$s.
+
+\cite{haibel98} estimated the translational diffusion from the
orientational relaxation of the lipid headgroup in alternating electric
fields; the diffusion coefficients are about one order of magnitudes larger
than FRAP and NMR measurements.
+
+Free-volume diffusion theory~\cite{cohen59, turnbull61, turnbull70}.
+
+Lipid diffusion is assumed to proceed by ``hopping'' of molecules into
vacancies formed by lateral-density fluctuations~\cite{oleary87}.
+
+For diffusion coefficients of the order of $D\sim1\,$nm$^2/\mu$s,
\cite{vaz91} predicted that each lipid performs a ``jump'' every 160\,ns,
on average.
+
+
+\subsubsection{Curvature elasticity theory}
+
+According to the general theory developed by
Helfrich,~\cite{helfrich73,sedd95,marsh06} the surface curvature elastic
energy per unit area $g$ is expressed as:
+\begin{equation}\label{eq:helfrich}
+g = \kappa\left(c_1 + c_2 -c_0\right)^2/2 + \kappa_\textrm{G}\, c_1\,c_2
+\end{equation}
+with $\kappa$ the bending rigidity, $c_1$ and $c_2$ the (local) principal
curvatures, $c_0$ the spontaneous (or intrinsic) curvature, and
$\kappa_\textrm{G}$ the Gaussian curvature modulus.
+%Helfrich's formula contains the physical principles underlying shape
creation, that must be universal for all cells.~\cite{zim-koz06}
+Equation~\ref{eq:helfrich} can be used to calculate the elastic energy of
a whole lipid bilayer: in this case the total and Gaussian curvatures
describe the bilayer midsurface, and the elastic constant characterising
the bilayer can be denoted by $\kappa^b$, $\kappa_G^b$ and $c_0^b$.
+Helfrich's model can also describe the curvature energy of each of the two
monolayers: in this case it is convenient to define the so-called neutral
surface (identical to the pivotal surface where the interfacial curvature
is not great~\cite{templer98}) of the monolayer, which is shifted by
distance $\xi$ from the bilayer midplane toward the lipid-water interface.
The monolayer elastic characteristics are denoted $\kappa^m$, $\kappa_G^m$
and $c_0^m$. For the case where the monolayer is held flat, the stored
curvature elastic energy is simply $2\kappa^m (c_0^m)^2$. % templer 98
+Lipid monolayers typically display a so-called {\em spontaneous
curvature}. When a bilayer is made of monolayers with nonzero spontaneous
curvature, it is affected by a built-in frustration defined as
\index{curvature!stress field} {\em curvature stress field}. % mouritsen,
p.49
+If the bilayer cannot sustain the curvature stress, non-lammellar
structures will form.
+
+
+\subsubsection{Bending modulus}\index{bending modulus}
+CHECK~\cite[2.6.1]{seifert95}, where a summary of exp techniques is
given!!!!!
+The bending modulus $\kappa$ for a flat surface is defined via the energy
per unit area $E_\kappa$ that is required to produce a mean curvature $H$
of the surface:
+\begin{equation}
+E_\kappa = 2\kappa H^2
+\end{equation}
+where the mean curvature is given by the two principal curvature radii
$R_1$ and $R_2$ as $H=(1/R_1+1/R_2)/2$.
+
+\subsubsection{Gaussian curvature modulus}\index{gaussian curvature
modulus}
+The Gaussian curvature modulus $\kappa_G$ controls the topological
complexity of the interface; $\kappa_G$ is difficult to determine
experimentally, but it is believed to be of the same order of magnitude of
the mean curvature modulus $\kappa$~\cite{mouritsen}. \cite{templer98b}
proposed the relation $-1<\kappa_G/\kappa<0$.
+For fluid phase DMPC, the Gaussian curvature is therefore bound to lie
within the range $-7\,k_BT<\kappa_G<0$.
+
+\subsubsection{Torque tension}\index{lateral pressure profile!torque
tension}
+At mechanical equilibrium, the summed lateral pressure ditribution must be
zero, but the first moment, the torque tension $\tau$, is in general
nonzero. The torque tension can be espressed as:
+\begin{equation}
+\tau = \int_{0}^{h}z\,\pi(z)\:\de z
+\end{equation}
+where $z=0$ at the centre of the bilayer and $z=\pm h$ at the aqueous
interfaces. The first moment of the lateral pressure $\tau$ is also called
the {\em torque tension}, because it is the torque stored in a monolayer
which is forced to remain flat~\cite{attard00}. The first moment is in
essence a measure of a shift in the centre of the lateral pressure
distribution in each monolayer away from ($\tau>0$) or toward ($\tau<0$)
the bilayer centre~\cite{cantor01}.
+The first moment of the pressure profile gives the product of the splay
curvature elastic modulus $k$ and the spontaneous curvature $c_o$ of the
monolayer:
+\begin{equation}
+\tau = k c_0
+\end{equation}
+the value of $c_0$ being important in determining the ``non-lamellar''
tendency, i.e. the tendency of the lipid to form cylindircal aggregates
such as inverted hexagonal phases.
+The torque tension of a monolayer is related to the curvature elastic
parameters via
+\begin{equation}
+\tau = 2\kappa c_0
+\end{equation}
+being $\kappa$ the bending rigidity and $c_0$ the monolayer spontaneous
curvature. Since $c_0$ is positive for type-I micelle-forming lipids, and
negative for type-II lipids (that wish to bend towards the water), the
torque tension is positive for type-I lipids and negative for type-II
lipids.
+
+The elastic stress \index{elastic stress} changes the membrane's physical
properties and manifests itself in at least two biologically relevant
functional aspects~\cite{bezrukov00}:
+\begin{itemize}
+\item by modifying the energetics of hydrophobic inclusions, it influences
protein-lipid interactions;
+\item by changing the energetics of spontaneous formation of non-lamellar
local structures, it influences membrane stability and fusion.
+\end{itemize}
+
+\subsubsection{Gaussian curvature modulus}\index{lateral pressure
profile!Gaussian curvature modulus}
+The Gaussian curvature modulus is given by the second moment of the
lateral pressure profile~\cite{kozlov89, shearman06}:
+\begin{equation}
+\kappa_G = \int_{0}^{h}z^2\,\pi(z)\:\de z
+\end{equation}
+The Gaussian modulus $\kappa_G$ describes the energy required to change
the Gaussian curvature\footnote{The Gaussian curvature $K$ is defined as
$K=c_1c_2$, being $c_1$ and $c_2$ the principal curvatures in a point on a
monolayer~\cite{shearman06}.} of a (monolayer) surface~\cite{shearman06}.
+\cite{attard00}
+mechanosensitive channels~\cite{perozo02}
+
+
+\subsubsection{Integral moments of the pressure profile}
+At mechanical equilibrium, the summed lateral pressure ditribution must be
zero. However, the {\em integral moments} of the lateral pressure
distribution are in general nonzero, and they are directly related to
fundamental curvature geometric and elastic parameters. We will compute the
first and second integral moments of $\pi(z)$, which yield the {\em torque
tension} and the {\em gaussian curvature modulus}.
+
+\paragraph{Torque tension and spontaneous curvature}
+The torque tension $\tau$ of a monolayer (i.e. half the bilayer) is the
first moment of the lateral pressure profile $P_1$:
+\begin{equation}
+\tau =P_1= \int_{0}^{h}z\,\pi(z)\:\de z
+\end{equation}
+\begin{equation}
+\kappa c_0 = \int_{0}^{h}z\,\pi(z)\:\de z
+\end{equation}
+where $z=0$ at the centre of the bilayer and $z= h$ at the aqueous
interface.
+ The first moment of the lateral pressure is called the {\em torque
tension} because it is the torque stored in a monolayer which is forced to
remain flat~\cite{attard00}.
+The torque tension $\tau$ of a monolayer is related to the curvature
elastic parameters via:
+\begin{equation}\label{eq:taukc0}
+\tau = \kappa c_0
+\end{equation}
+being $\kappa$ the bilayer bending rigidity (also called {\em splay
curvature elastic modulus}) and $c_0$ the monolayer spontaneous curvature.
Table~\ref{tab:spontCurvData} reports experimental estimates for a
selection of lipid species, along with our value for DMPC computed from
Equation~\ref{eq:taukc0} considering the experimental value for
$\kappa_{DMPC}$.
+\begin{table}
+\begin{center}
+%\vspace{8pt}
+\begin{tabular}{lcl} % put @{} if you want to eliminate horizontal space
between columns
+%\hline
+{\em Method~[reference]} & {\em Lipid} & $c_0$ / nm$^{-1}$ \\
+Exp.~\cite{leikin96} & DOPE & $-0.333$\\
+Exp.~\cite{chen97,szule02} & DOPC & $-0.050\div-0.115$\\
+Exp.~\cite{fuller03} & DOPS & $+0.069$ \\
+Coarse-grain MD~[{\em this work}] & DMPC &
+\end{tabular}
+\caption[Monolayer spontaneous curvatures]{Monolayer spontaneous
curvatures. Collection of experimental data for a number of abundant lipid
species. The last line reports our estimate from Molecular Dynamics
calculation.}
+\label{tab:spontCurvData}
+\end{center}
+\end{table}
+
+\paragraph{Gaussian curvature modulus}
+The Gaussian curvature modulus $\kappa_G$ of a monolayer derives from the
first and second integral moments $P_1$ and $P_2$ of the lateral pressure
profile via:
+\begin{eqnarray}
+P_2 =& \int_{0}^{h}z^2\,\pi(z)\:\de z& \\
+\kappa_G =& - \int_{0}^{h}(z-\xi)^2\,\pi(z)\:\de z =& 2\xi P_1 - P_2
+\end{eqnarray}
+being $\xi$ the distance to the {\em pivotal surface}, defined as the
surface at which there is no change in the molecular cross-sectional area
upon bending~\cite{shearman06}. The pivotal surface \index{pivotal surface}
has been experimentally identified close to the polar/apolar
interface~\cite{rand90,chung94,templer95,chen97}: we therefore set
$\xi=D_C$, considering the experimental hydrophobic thickness
$2D_C=2.54$\,nm of fluid-phase DMPC bilayers~\cite{kucer05a}.
+As for the first integral moment, $z=0$ at the centre of the bilayer and
$z= h$ at the aqueous interfaces.
+The gaussian curvature modulus describes the energy required to change the
gaussian curvature of a (monolayer) surface~\cite{kozlov89, shearman06}.
The Gaussian curvature $K$ is defined as $K=c_1c_2$, being $c_1$ and $c_2$
the principal curvatures in a point on a monolayer. The Gaussian curvature
modulus $\kappa_G$ is then related to the general expression for the
bending energy through equation~\ref{eq:helf}.
+The value of the monolayer Gaussian curvature modulus, which is difficult
to determine experimentally, is predicted to be negative from theoretical
arguments. In fact, \cite{templer98b} have shown that the monolayer
Gaussian curvature modulus is bound to the bending rigidity according
to %\footnote{Note that our convention for the sign of the lateral pressure
profile is opposite to that of~\cite{templer98}, hence the gaussian
curvature modulus signs are also opposite.}
+$-1 \le\kappa_G^m/\kappa^m\le 0$: this prediction has been confirmed by
the (few) available experimental data~\cite[Table~3]{shearman06}.
+\cite{marsh06} has observed that experimental data suggest the relation
$\kappa_G\approx-0.8\kappa$ for lipid monolayers in general.
+
+\cite{cantor99b} predicted the first and second moments of the pressure
profile for the hydrocarbon region of 14:0 lipid bilayers to be
$P_1=-1.74\,k_BT/$\AA, and $P_2=-29.4\,k_BT$. These results cannot be
representative of a complete DMPC bilayer as they do not take into account
headgroups and hydrating water.
+
+\subsubsection{Biophysical importance of the lateral pressure profile}
+ The intrinsic curvature $c_0$ minimizes the bending energy of a lipid
monolayer, and quantitatively gives the tendency to curl~\cite{gruner85}.
The value of $c_0$ also relates to the tendency of the lipid to aggregate
into non-lamellar structures.
+\cite{attard00} showed how both the sign and the magnitude of the torque
tension play a key role in controlling membrane lipid synthesis. It seems
reasonable to argue that the stored curvature elastic energy, via the
integral moments of the lateral pressure distribution, generally regulates
the activity of membrane proteins. This purely physical mechanism is simple
and robust, and it ensures membrane's integrity. There is in fact growing
evidence about the plausibility of this
theory~\cite{gruner85,gruner94,curnow04,lundbaek04,booth05}.
+
+\subsection{Water permeation}
+
+Experimental data for the permeability coefficient of water through
phospholipid bilayers are collected in Tab.~\ref{tab:watPermData}.
+
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{lcc} % put @{} if you want to eliminate horizontal space
between columns
+{\em Lipid} & $P_\textrm{W}$ [$\mu$m/s] & {\em Reference } \\
+diC(14:0)PtdCho (DMPC) & 70 & \cite[fig.~17b]{bloom91}\\
+diC(16:0)PtdCho (DPPC) & 24 & \cite[p.~96]{cevc}\\
+diC(14:1)PtdCho & 240 & \cite{paula96}\\
+diC(18:1c$\Delta^9$)PtdCho (DOPC) & 42 & \cite{olbrich00}\\
+diC(18:1c$\Delta^9$)PtdCho (DOPC) & 97 & \cite{huster97}\\
+Egg lecithin & 2 & \cite{carruthers83}\\
+\end{tabular}
+\caption[Experimental water permeability]{Experimental water permeability
coefficient. Measurements taken at full hydration in the L$_\alpha$ phase.}
+\label{tab:watPermData}
+\end{center}
+\end{table}
+
+%Also, \cite{olbrich00} measured the water permeability of polyunsaturated
lipid bilayers: the apparent coefficient for water permeability, at
21\textcelsius, varied modestly in a range from approximately 30 to
40\,$\mu$m/s for mono- and dimono-unsaturated PCs.
+
+
+\section[The matrix of life]{The matrix of life: weak interactions in an
aqueous environment}
+
+Table~\ref{tab:elInt}.
+
+\begin{table}\centering
+\begin{tabular}{lc}
+Type & Dependence of energy on distance\smallskip\\
+Charge-charge & $1/r$\\
+Charge-dipole & $1/r^2$\\
+Dipole-dipole & $1/r^3$
+\end{tabular}
+\caption[Electrostatic interactions]{Electrostatic
interactions.}\label{tab:elInt}
+\end{table}
+
+
+\subsection{Charge-charge interactions}
+
+Many of the molecules present in cells, including macromolecules like DNA
or proteins, carry a net electrical charge. At the same time, the cell
contains an abundance of small ions, like Na$^+$ and Cl$^-$.
+The force between a pair of charges $Q_i$ and $Q_j$, separated in a vacuum
by a distance $r$, is given by Coulomb's law:
+\begin{equation}\label{eq:coulForce}
+F(r)=k\frac{Q_iQ_j}{r^2}
+\end{equation}
+where $k$ is a constant whose value depends on the units used.
+A fundamental problem with equation~(\ref{eq:coulForce}) as it stands is
that the biological environment is never a vacuum.
+The charges are always separated by water or other molecules or parts of
molecules. The existence of such a {\em dielectric medium} between charges
has the effetc of screening them from one another, so that the actual force
is always less than that given by equation~(\ref{eq:coulForce}).
+This screening effect is expressed by inserting a dimensionless number,
the {\em dielectric constant} $\epsilon$, in equation~(\ref{eq:coulForce}):
+\begin{equation}\label{eq:coulForceScreened}
+F(r)=k\frac{Q_iQ_j}{\epsilon \,r^2}
+\end{equation}
+The dielectric constant of water is very high, approximately 80, whereas
organic substances usually have much lower values, in the range 1-10. The
major consequence of this large value in water is obvious: charged
particles like ions interact rather weakly in an aqueous environment unless
they are very close to one another~\cite{mathews}.
+
+\subsection{Interactions involving permanent dipoles}
+
+Some molecules carry no net charge but have an asymmetric internal
distribution of charge.
+For instance, in the water molecule the electron distribution is such that
the end towards the oxygen is slightly negative and the end toward the two
hydrogen atoms is slightly positive. Such a molecule is a {\em dipole},
with permanent dipole moment $\mu$. In particular, if a molecule has
fractional charges $+q$ and $-q$, separated by a distance $x$, the dipole
moment is a vector whose magnitude is:
+\begin{equation}\label{eq:dipMag}
+\mu=qx
+\end{equation}
+The common units of dipole moment are {\em debyes}~(D), being 1\,D equal
to $3.34\times10^{-30}$\:C\,m.
+The water dipole moment in the liquid phase has an average value of about
3\,D, as reported by~\cite{silve99a, gubsk02a}.
+
+Perhaps the most interesting property of phospholipids is their large
dipole moment. The tendency to orient their dipoles parallel to the
surface, which is favourable in terms of the free energy of electrostatic
interactions, and the larger degree of motional freedom in the water phase
and steric orientation, are expected to result in a wide distribution of
headgroup tilt angles~\cite{tiele97a}.
+Indeed, the conformation of the polar head group of lipids in the
liquid-crystalline state (L$_\alpha$) has been experimentally deduced: the
P-N vector makes an angle between 60 and $90^{\circ}$ with the membrane
normal, i.e. it lies approximately parallel, within $30^{\circ}$, to the
membrane plane, slightly pointing towards the water phase\footnote{Similar
results have been obtained for all major classes of phospholipids (PGs,
PCs, PEs), for temperatures well into the (fluid lamellar) $L_\alpha$
phase; hence, this behaviour has been considered a common feature of lipid
headgroup dipoles in the $L_\alpha$
phase~\cite{saizl02abis}.}~\cite{akuts91a, sch89}.
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/depot/brahmsRubbish.tex Wed Dec 21 02:20:08 2011
@@ -0,0 +1,571 @@
+A global flow scheme for MD in \brahms is given in
Figure~\ref{fig:mdGlobal}.
+\begin{figure}
+\begin{center}
+\addtolength{\fboxsep}{0.5cm}
+\begin{shadowenv}[12cm]
+{\large \bf THE BRAHMS MD ALGORITHM}
+\rule{\textwidth}{2pt} \\
+{\bf 1. Input initial conditions}\\[2ex]
+Force-field and simulation parameters\\
+Positions and velocities of all sites in the system \\
+$\Downarrow$\\
+\rule{\textwidth}{1pt}\\
+{\bf repeat 2,3,4} for the required number of steps:\\
+\rule{\textwidth}{1pt}\\
+{\bf 2. Compute forces and torques} \\[1ex]
+Energies and pressure are also computed and averaged at a certain
frequency. \\
+$\Downarrow$\\
+{\bf 3. Update configuration - Integration} \\[1ex]
+The movement of the particles is simulated by numerically solving Newton's
and Euler's equations of motion \\[1ex]
+{\bf 4.} {\bf Output step} \\
+write positions, velocities, energies, temperature, pressure, etc. \\
+\end{shadowenv}
+\caption[The molecular dynamics algorithm]{The global molecular dynamics
algorithm as implemented in \brahms.}
+\label{fig:mdGlobal}
+\end{center}
+\end{figure}
+
+ The integration of the equations of motion can be done by using the
simplest (possibly) of numerical techniques: the Verlet
scheme~\cite{verlet67}. In general, Verlet-like integrators are
time-reversible and symplectic\footnote{Symplecticity implies that volume
in phase space is conserved~\cite{allen04}.}: time reversibility and
symplecticity have been shown to produce a favourable propagation of
errors, hence better numerical methods, especially when interested in
long-term behaviour~\cite{mclac05a}.
+All the algorithms presented in the following sections are explicit, i.e.
not requiring any iteration.
+It should be pointed out that the speed of the integrator itself is not
very relevant, because the fraction of computing time spent on integrating
the equations of motion is very small compared to the interaction
computation usually involve extremely expensive double loops over all the
particles in the system). Accuracy for large time steps is far more
important, because the longer the time step that we can use, the fewer
evaluations of the forces are needed per unit of simulation time.
+\subsection{Centre of mass motion}
+Centre of mass velocities are integrated through the following formula:
\begin{equation} \mathbf{v}(t+\delta t/2)=\mathbf{v}(t-\delta
t/2)+\frac{\delta t}{m} \mathbf{f}(t) \end{equation}
+ Coordinates are advanced through: \begin{equation} \mathbf{r}(t+\delta
t)=\mathbf{r}(t)+\delta t\mathbf{v}(t+\delta t/2) \end{equation}
+The above equations are applied to each molecule~\cite[p~78-82]{allen}.
+
+\paragraph{COM translation removal}
+Being no external force acting on the system, the COM velocity should
remain constant, say, zero. However, the integrator invariably develops a
very slow change in the COM velocity. If such behaviour is not quenched, an
appreciable COM motion develops eventually in long runs, and the
temperature will be significantly misinterpreted\footnote{The same may
happen due to overall rotational motion, but only when an isolated cluster
is simulated. In periodic systems with filled boxes the overall rotation is
coupled to other degrees of freedom and does not give any
problems~\cite{gmx31}}. Hence in \brahms the COM net velocity is removed
periodically.
+
+
+The most popular integrator for solving Equation~\ref{eq:newton} is the
venerable algorithm invented by Verlet:~\cite{verlet67} equivalent
formulations are available, yielding identical trajectories but computing
velocities with slightly improved accuracy. The algorithm employed in this
work is the so-called {\em velocity Verlet} scheme:\cite{swope82a}
+\begin{eqnarray}
+\mathbf{v}(t+\Delta t/2)&=&\mathbf{v}(t)+\Delta t\, \mathbf{f}(t)/2m \\
+\mathbf{r}(t+\Delta t)&=&\mathbf{r}(t)+\Delta t\,\mathbf{v}(t+\Delta t/2)\\
+\mathbf{v}(t+\Delta t)&=&\mathbf{v}(t+\Delta t/2)+\Delta t\,
\mathbf{f}(t+\Delta t)/2m
+\end{eqnarray}
+The above equations are applied to the mass centre of each site.
Verlet-like schemes are employed in the great majority of MD programs due
to their simplicity and exceptional stability; these algorithms are both
symplectic and time-reversible%\footnote{It is impressive that an almost
40 years-old numerical scheme is still state-of-the-art. It was gradually
realized during the 19th century that the laws of motion embody extra,
hidden, properties called {\em symplectic conservation}, in addition to
more well-known conservation laws like conservation of energy and angular
momentum. By the late 1960s the study of this structure gave rise to a new
branch of geometry, symplectic geometry, which eventually, by the late
1980s, began to influence numerical analysts who developed special methods
that obey the law of symplectic conservation. The Verlet method is the
simplest method of this class, and still one of the best. At last, after
being in popular use for several decades, the surprisingly good performance
of the leapfrog method was explained. It's been possible to show that,
although you can't stop the quantitative errors building up during the
simulation, by obeying the law of symplectic conservation, you won't commit
any qualitative errors and so the overall results will be far more
reliable.}
+.
+
+
+Equation~\ref{eq:euler} is more problematic than Newton's, since the
treatment of rotational degrees of freedom is much less straightforward
than that of linear motion; indeed, good integrators for Euler's equation
are a relatively recent invention.
+One of the unique features of \brahms is the ability to handle efficiently
rigid-body dynamics. Rigid bodies are not included in most simulation
softwares because of the algorithmic complexity involved in propagating
orientational degrees of freedom, as opposed to the relatively trivial
problem of integrating the motion of point masses. Integrators that
propagate rigid body orientational motion with an acceptable level of
energy conservation for molecular dynamics are relatively new
inventions.~\cite{meine05a}
+Rigid body models possess symplectic structure and time-reversal
symmetry: standard numerical integration methods for rotational motion
destroy both properties, introducing nonphysical dynamical behaviour and
drift in the energy during long term simulations. For instance, the
traditional and simple scheme by~\cite{finch81} (also reported
in~\cite[p.~89]{allen}), based on a representation of rotations through
quaternions\footnote{For a definition of quaternion and some notions on
quaternion algebra, see Appendix~\ref{app:nlrb}.}, is neither symplectic
nor reversible, and has indeed proved to yield a rather poor performance in
terms of energy conservation, thus severely limiting the integration step
size.
+
+In the last ten years, the mathematical community has developed more
sophisticated but far superior rotational algorithms, that allow to
enlarge markedly the time-step, the key property being
symplecticity\footnote{The development of symplectic rigid-body integrators
is a significant methodology advance that generally regards non-symmetric
rigid particles. The particular case of symmetric bodies can be readily
treated with minor modifications, therefore it would be possible to
greatly enlarge the timestep in the simulation of Gay-Berne systems.
However, symplectic integration appears to have gone unappreciated by the
Gay-Berne community at large.}.
+In particular, \cite*{dullw97a} have proposed an integrator, that we
shall call DLM, based on the propagation of the full rotation matrix
associated with each rigid body: in every time step, the orientational
dynamics is integrated by a sequence of five planar rotations. The use of
rotation matrices offers improved numerical stability, and since the method
belongs to the leapfrog family of integrators, it means that simple
leapfrog integration techniques can be used for the entire set of dynamical
equations appearing in the problem.
+
+
+The DLM integrator is symplectic and time-reversible, and conserves both
the total linear and angular momentum. %Furthermore, if the rigid-body is
linear (e.g. a Gay-Berne site) then the five rotations reduce to one, thus
lowering the computing time.
+ The detailed algorithm is reported in Appendix~\ref{app:brahms}; it is
interesting to note that the structure of the DLM scheme resembles the
velocity Verlet algorithm, and indeed the two are identical in the way they
treat linear motion. Simulations on a system of 1000 rigid water molecules
have shown that the step size allowed by the DLM scheme is about ten times
larger than that possible with Fincham's scheme~\cite{fenne04a}.
\cite{dullw97a} have also reported that the gap between their method and
non-symplectic schemes increases with system size. The scheme has also been
employed to simulate polymer helix formation using rigid-link
methods~\cite{rapa02}.
+
+%Other recent studies on rigid-body integration are the ones
by~\cite{matub99a} (development of a reversible, though non-symplectic,
integrator), \cite{mille02a} (reversible and symplectic scheme),
and~\cite{kambe05a} (reversible and symplectic, but tested on linear
molecules only). %It is interesting to note that all these algorithms rely
on a quaternion representation, just as old~\cite{finch81}.
+
+\paragraph{Gaussian themrostat Algorithm (velocity-Verlet form)}
+At first, the momenta of all molecules are advanced from $t$ to $t+\Delta
t$:
+\begin{equation}
+\label{eq:splitFirstStep1}
+\mathbf{v}(t+\Delta t/2)=\mathbf{v}(t)+\Delta t\mathbf{f}(t)/2m
\end{equation}
+\begin{equation}
+\label{eq:splitFirstStep2}
+\mathbf{h}^b(t+\Delta t/2)=\mathbf{h}^b(t)+\Delta t \mathbf{T}^b(t)/2
\end{equation}
+where $\mathbf{h}^b$ and $\mathbf{T}^b=\mathbf{Q}(t)\mathbf{T}^S(t)$ are
the body-frame angular momentum and torque, respectively.\\
+Then mass centre positions and orientation matrices are moved a full time
step according to the DLM scheme; subsequently, forces and torques at
$t+\Delta t$ are computed.
+Now the momenta at $t+\Delta t$ are estimated:
+\begin{equation}
+\label{eq:splitFirstStep1}
+\mathbf{v}(t+\Delta t)=\mathbf{v}(t+\Delta t/2)+\frac{\Delta t}{2}
\mathbf{f}(t + \Delta t)/m \end{equation}
+\begin{equation}
+\label{eq:splitFirstStep2}
+\mathbf{h}^b(t+\Delta t)=\mathbf{h}^b(t+\Delta t/2)+\frac{\Delta t}{2}
\mathbf{T}^b(t+\Delta t) \end{equation}
+Then the Lagrange multiplier $\alpha$ is computed according
to~\ref{eq:alpha}.
+
+
+Jensen~\cite{jensen04} demonstrated that the CHARMM27 parameter set does
not reproduce the experimental value for the area per lipid or the
experimental order parameter profile when the bilayer is allowed to adjust
its area freely, as in the N-P-T ensemble. In the N-P-T ensemble the area
per lipid is severely underestimated and is steadily decreasing in time.
Therefore, many membrane simulations using the CHARMM27 parameters are
carried out in the N-P-A-T (A is the area of the bilayer in the xy plane)
or N-Pz-$\gamma$-T ensembles~\cite{feller99}.
+However, \cite{sonne05} have chosen to conduct all simulations in the
N-P-T ensemble, using a new parameter set specifically developed.
+\cite{benz05} simulated DOPC in the NPT ensemble, in a
flexible-orthorombic cell, both with CHARMM27 and GROMACS. The CHARMM27
simulation resulted in an average d-spacing that was too high and an
area/lipid that was (again) too low, suggestive of a bilayer that is less
fluid than observed experimentally. The GROMACS simulation, on the other
hand, yielded values that agreed reasonably well with experiment within
experimental uncertainties.
+
+\cite{ander80a} was the first to modify Newtonian equations of motion to
sample ensembles other than the microcanonical: the volume is a dynamical
variable while the generalised force acting on this variable is
proportional to the difference between the internal and an externally fixed
pressure.
+
+
+\subsection{Nose'-Hoover}
+\cite{melchionna93} have extended the NPT scheme proposed
by~\cite{hoove85a} to take into account a (size- and) shape-varying box.
+\subsubsection{Equations of motion}
+Setting the external parameters $T_\mathrm{ext}$ and $P_\mathrm{ext}$ to
the desired values of temperature and pressure, the isothermal-isobaric
equations of motion can be written:
+\begin{eqnarray}
+\dot{\mathbf{r}}_i&=&\mathbf{v}_i+\boldeta\,(\mathbf{r}_i-\mathbf{r}_\mathrm{COM})\\
+\dot{\mathbf{v}}_i&=&\mathbf{f}_i/m_i-(\boldeta+\zeta\mathbf{1})\mathbf{v}_i\\
+\dot{\mathbf{h}}^b_i&=&\mathbf{T}^b_i/I_i-\zeta\mathbf{h}^b_i\\% not sure
+\dot{\zeta}&=&\left[T(t)/T_\mathrm{ext}-1\right]/\tau_T^2\\
+\dot{\boldeta}&=&V\left[\mathbf{P}(t)-P_\mathrm{ext}\mathbf{1}\right]/(\mathrm{DOFs}\,k_B\,T_\mathrm{ext}\,\tau_P^2)\\
+\dot{\mathbf{H}}&=&\boldeta\mathbf{H}
+\end{eqnarray}
+being:
+\begin{itemize}
+%\item $\eta$ tHe piston variable tHat acts as a strain-rate factor in
order to balance the deviations of the instantaneous pressure from the
preset value $P_\mathrm{ext}$.
+\item $\boldeta$ the barostat, or rather a ``piston'' tensor variable that
acts as a strain-rate factor in order to balance the deviations of the
instantaneous pressure from the preset value~$P_\mathrm{ext}$ - the
diagonal elements of~$\boldeta$ tend to adjust the internal pressure to the
preset hydrostatic value~$P_\mathrm{ext}$, while the off-diagonal elements
tend to eliminate nonzero fluctuations of the off-diagonal elements of the
stress tensor~$\mathbf{P}$;
+\item $\mathbf{r}_\mathrm{COM}=\sum_im_i\mathbf{r}_i/\sum_im_i$ the system
centre of mass;
+\item $\zeta$ the thermostat, or rather a ``frictional'' coefficient which
evolves in time following the deviation of instantaneous temperature from
the corresponding external parameter;
+\item $\mathbf{1}$ is the identiy matrix\footnote{Explicitily,
\begin{displaymath}
+\mathbf{1}=\left(
+\begin{array}{ccc}
+ 1 & 0 &0 \\
+ 0 & 1 & 0 \\
+ 0 & 0& 1
+\end{array}
+\right)
+\end{displaymath} };
+\item DOFs the total number of degrees of freedom of the system;
+\item $T(t)$ the instantaneous temperature;
+\item $\tau_T$ the time constant for relaxation of the temperature to the
desired value - typically $\tau_T=1\div10\,$ps;
+\item $\tau_P$ the time constant for relaxation of the pressure to the
desired value - typically $\tau_P=10\div100\,$ps;
+%\item $P(t)$ the sum of the kinetic and virial pressure terms;
+\item $\mathbf{P}(t)$ the stress tensor;
+\item $f$ the number of degrees of freedom in the system;
+\item $\mathbf{H}=(\mathbf{a}, \mathbf{b}, \mathbf{c})$ the box matrix,
where $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are the basis vectors of the box.
+\item $V$ the volume, given by\footnote{In general, the determinant of a
$3\times3$ matrix is: $\det{[a_x b_x c_x; a_y b_y c_y; a_z b_z c_z]}=
a_xb_yc_z-a_xc_yb_z-b_xa_yc_z+b_xc_ya_z+c_xa_yb_z-c_xb_ya_z$.}
$V=\mathbf{c}\times\mathbf{b}\cdot\mathbf{a}=\det{\mathbf{H}}$
+\end{itemize}
+The values of $\tau_T$ and $\tau_P$ must be determined empirically: they
have no particular physical meaning and are simply part of the
computational technique. In principle, their values do not affect the final
equilibrium results, but they do influence their accuracy and reliability,
because if the fluctuations of kinetic energy and pressure are allowed to
become too large it is difficult to think of the system existing in
equilibrium at a particular temperature and stress~\cite{rapa}.
+The trace\footnote{The trace of a matrix is just the sum of the diagonal
elements - more rigorously, the trace of an $n\times n$ matrix $A$ is
defined as: $\mathrm{tr}(A)=\sum_{i=1}^na_{ii}$.} of
$\boldeta=\mathbf{H}\mathbf{H}^{-1}$ has the property:
+\begin{equation}
+\mathrm{tr}(\boldeta)=\dot{V}/V
+\end{equation}
+The pressure tensor is computed as:
+\begin{eqnarray}
+\mathbf{P}(t)&=&\left[\sum_im_i\mathbf{v}_i(t)\otimes\mathbf{v}_i(t)\right]/V(t)
+
\mathbf{W}(t) \\
+\mathbf{W}(t)&=&\left[\sum_i\sum_{j>i}\mathbf{r}_{ij}(t)\otimes\mathbf{f}_{ij}(t)\right]/V(t)
+\end{eqnarray}
+with $\mathbf{W}(t)$ the stress tensor\footnote{Explicitely:
+\begin{displaymath}
+\mathbf{W}=\frac{1}{V}\sum_i\sum_{j>i}\left(
+\begin{array}{ccc}
+ r_{ij}^xf_{ij}^x & r_{ij}^xf_{ij}^y &r_{ij}^xf_{ij}^z \\
+ r_{ij}^yf_{ij}^x&r_{ij}^yf_{ij}^y &r_{ij}^yf_{ij}^z \\
+ r_{ij}^zf_{ij}^x& r_{ij}^zf_{ij}^y&r_{ij}^zf_{ij}^z
+\end{array}
+\right)
+\end{displaymath}}.
+The instantaneous pressure is $P(t)=\mathrm{Tr}[\,\mathbf{P}(t)\,]\,/\,3$.
+
+\subsubsection{Integration scheme}
+The DLM scheme is extended as follows.
+\paragraph{Part A}
+\begin{eqnarray}
+T(t)&:=&2\mathcal{K}[\mathbf{v}_i(t),
\mathbf{h}_i^b(t)]\,/\,(k_B\,\mathrm{DOFs})\\
+\mathbf{P}(t) &:=& \left[\sum_im_i\mathbf{v}_i(t)\otimes\mathbf{v}_i(t) +
\sum_i\sum_{j>i}\mathbf{r}_{ij}(t)\otimes\mathbf{f}_{ij}(t)\right]\,/\,V(t)
\\
+\mathbf{v}_i(t+\Delta t/2)&:=&\mathbf{v}_i(t)+\Delta
t\,\left\{\,\mathbf{f}_i(t)/m\,-\,\left[\,\boldeta(t)+\zeta(t)\mathbf{1}\,\right]\cdot\mathbf{v}_i(t)\,\right\}\,/\,2\\
+\mathbf{h}_i^b(t+\Delta t/2)&:=&\mathbf{h}_i^b(t)+\Delta
t\,\left\{\,\mathbf{T}_i^b(t)\,-\,\left[\,\zeta(t)\mathbf{h}_i^b(t)\,\right]\right\}\,/\,2\\
+\mathbf{Q}_i(t+\Delta
t)&:=&\mathbf{Q}_i(t)\mathbf{R}_i^T[\mathbf{h}_i^b(t+\Delta t/2)]\\
+\boldeta(t+\Delta t/2)&:=&\boldeta(t)+\Delta
t\,V(t)\,\left[\,\mathbf{P}(t)-P_\mathrm{ext}\mathbf{1}\,\right]\,/\,\left[\,2Nk_BT(t)\tau_\mathrm{P}^2\,\right]\\
+\mathbf{r}_i(t+\Delta t)&:=&\mathbf{r}_i(t)+\Delta
t\,\left\{\,\mathbf{v}_i(t+\Delta t/2)\,+\,\boldeta\,(\,t+\Delta
t/2)\,\cdot\,[\mathbf{r}_i(t+\Delta t)-\mathbf{r}_\mathrm{COM}]\right\}\\
+\zeta(t+\Delta t/2)&:=&\zeta(t)+\,\Delta
t\,[\,T(t)\,/\,T_\mathrm{ext}\,-\,1\,]\,/\,(2\tau_T^2)\\
+\mathbf{H}(t+\Delta t)&:=&\mathbf{H}(t)\,\cdot\,\exp{[\Delta t\,
\boldeta\,(t+\Delta t/2)]} \end{eqnarray}
+Now forces and torques are computed at $t+\Delta t$; note that the volume
is updated as $V(t+\Delta t)=\det{\mathbf{H}(t+\Delta t)}$.
+\paragraph{Part B}
+\begin{eqnarray}
+T(t+\Delta t)&:=&2\mathcal{K}[\mathbf{v}_i(t+\Delta t),
\mathbf{h}_i^b(t+\Delta t)]\,/\,(k_B\,\mathrm{DOFs})\\
+\mathbf{P}(t+\Delta t) &:=& \left[\sum_im_i\mathbf{v}_i(t+\Delta
t)\otimes\mathbf{v}_i(t+\Delta t) +
\sum_i\sum_{j>i}\mathbf{r}_{ij}(t+\Delta t)\otimes\mathbf{f}_{ij}(t+\Delta
t)\right]\,/\,V(t+\Delta t) \\
+\zeta(t+\Delta t)&:=&\zeta(t+\Delta t/2)+\,\Delta t\,[\,T(t+\Delta
t)\,/\,T_\mathrm{ext}\,-\,1\,]\,/\,(2\tau_T^2)\\
+\boldeta(t+\Delta t)&:=&\boldeta(t+\Delta t/2)+\Delta t\,V(t+\Delta
t)\,\left[\,\mathbf{P}(t+\Delta
t)-P_\mathrm{ext}\mathbf{1}\,\right]\,/\,\left[\,2Nk_B\,T(t+\Delta
t)\,\tau_\mathrm{P}^2\,\right]\\
+\mathbf{v}_i(t+\Delta t)&:=&\mathbf{v}_i(t+\Delta t/2)+\Delta
t\,\left\{\,\mathbf{f}_i(t+\Delta t)/m\,-\,\left[\,\boldeta(t+\Delta
t)+\zeta(t+\Delta t)\mathbf{1}\,\right]\cdot\mathbf{v}_i(t+\Delta
t)\,\right\}\,/\,2\\
+\mathbf{h}_i^b(t+\Delta t)&:=&\mathbf{h}_i^b(t+\Delta t/2)+\Delta
t\,\left\{\,\mathbf{T}_i^b(t+\Delta t)\,-\,\left[\,\zeta(t+\Delta
t)\,\mathbf{h}_i^b(t+\Delta t)\,\right]\right\}\,/\,2
+\end{eqnarray}
+
+\section{Radial Distribution Function}%A/T, p.54 - rapa p. 90
+The fluid state is characterised by the absence of any permanent
structure. There are, nevertheless, well-defined structural correlations
that can be measured experimentally to provide important details about the
average molecular organisation. The radial (or pair) distribution function
$g(r)$ - RDF for short - gives the probability of finding a pair of atoms a
distance $r$ apart, relative to the probability expected for a completely
random distribution at the same density. %; it is most simply thought of as
the number of atoms a distance $r$ from a given atom compared with the
number at the same distance in an ideal gas at the same
density\footnote{Alternatively: the RDF is the ratio between the average
number density at a distance $r$ from any given atom and the density at the
same distance in an ideal gas at the same overall density.}.
+ The RDF can be evaluated through: \begin{equation}
g(r)=\frac{V}{N^2}\left\langle\sum_i\sum_{j\ne
i}\delta(r-r_{ij})\right\rangle=\frac{2V}{N^2}\left\langle\sum_{i}\sum_{j>i}\delta(r-r_{ij})\right\rangle
\end{equation}
+where $V$ is the volume of the simulation region and $\delta$ is the Dirac
function.
+%The radial distribution function $g(r)$ describes the spherically
averaged local organisation around any given atom.
+
+\section{Diffusion}%p122 rapa - p60 A/T
+Transport coefficients describe the material properties of a fluid within
the framework of continuum fluid dynamics. Diffusion is the process whereby
an initially nonuniform concentration profile (e.g. an ink drop in water)
is smoothed in the absence of flow (no stirring). Diffusion is caused by
the molecular motion of the particles in the fluid. The diffusion
coefficient $D$, one of the most familiar transport coefficients, can be
calculated from the Einstein expression (valid at long times):
\begin{equation} 2tD = \frac{1}{3}\left\langle|
\mathbf{r}_j(t)-\mathbf{r}_j(0)|^2\right\rangle \end{equation} where
$\mathbf{r}_j(t)$ is the particle position. In practice, the average is
computed for each of the $N$ particles in the simulation, the results added
together and divided by $N$, to improve statistical accuracy.
+%: \begin{equation} D = \lim_{t \rightarrow \infty }
\frac{1}{6Nt}\left\langle\sum_{j=1}^{N}\left[\mathbf{r}_j(t)-\mathbf{r}_j(0)\right]^2\right\rangle
\end{equation}
+\subsection{Lipid lateral diffusion}
+In the literature, different units are
+used. We use nm$^2$/$\mu$s as it makes for concise writing (no need
+for exponentials) and intuitive meaning (nm and $\mu$s are about the
+scales we investigate in the simulation). Conversions: $1\,\mathrm
+{nm}^2/\mu \mathrm{s} = 1\,\mathrm{\mu m}^2/ \mathrm{s} =
10^{-8}\,\mathrm{cm}^2/\mathrm{s} = 10^{-12}\, \mathrm{m}^2/\mathrm{s} $.
+
+\section{Dipole moment of a pair of equal and opposite point charges}
+Given two equal yet opposite charges $q$, at a distance $l$ apart, the
dipole moment is computed as:$$
+\mu=ql
+$$
+The lipid headgroup dipole can be simply computed in this way; the
average is obtained by adding up and dividing the values of all lipids.
+
+\subsection{Head-group tilt angle}
+Considering $\mathbf{d}$ the headgroup PN vector, the angle \dots
+
+\subsection{Order parameters}
+To describe the ordering of the hydrophobic lipid tails, the second order
Legendre polynomial $P_2$ can be used:
+\[P_2=\frac{1}{2}(3\cos^2\!\theta-1)\,,\]
+where $\theta$ is the angle between the direction of the Gay-Berne tail
site main axes $\mathbf{e}$ and the bilayer normal $\mathbf{n}$.
+Since both $\mathbf{e}$ and $\mathbf{n}$ are unit vecotrs, we obtain
$\cos^2\!\theta=(\mathbf{e}\cdot\mathbf{n})^2$.
+Second-rank Gay-Berne order parameters $\overline{P}_{2}^{\,GB}$ have been
calculated for the GB particles in the hydrocarbon chains.
+ and compared to the experimental S$_{mol}$
+segmental order parameter, which corresponds to the C-C bond order
+parameter: $S_{CC}$. The Gay-Berne order parameter can be
+defined as
+$\overline{P}_{2}^{\,GB}=\left<P_{2}(\text{cos}\beta)\right>$, where
+$\beta$ is the angle between the molecular axis and the director
+\textbf{n} and $\left<\right>$ denotes a time average.
+Whithead et al. evaluated layer order parameter and analysed them versus
temperature; it was clearly shown a phase transition from the solid
(reminiscent of $L_{\beta'}$) to liquid-crystalline (reminiscent of
$L_{\alpha}$) phase between $T^*=0.35$ and $T*=0.4$ (i.e.
$290\,K<T<340\,K$), consistent with that identified previously from the
diffusion coefficient data~\cite{white01a}.
+
+\subsection{Elastic properties}
+
+\subsubsection{Area compressibility modulus}
+In the NPT ensemble (constant pressure and temperature), it is possible to
estimate the area compressibility modulus~$K_A$ from the fluctuations in
the lipid area.
+Having computed the mean area per lipid $\langle A\rangle$ and the mean
squared fluctuation $\langle (A-\langle A\rangle)^2\rangle$ the
compressibility modulus $K_A$ can be calculated as~\cite{feller99}
+\begin{equation}
+K_A=\frac{k_BT\langle A\rangle}{N_{leaflet}\langle (A-\langle
A\rangle)^2\rangle}=\frac{k_BT\langle A\rangle}{N_{leaflet}\sigma^2(A)}
+\end{equation}
+with $N_{leaflet}$ the number of lipids per monolayer.
+This formula is widely used also when the pressure is controlled using the
weak-coupling method~\cite{ber84}, which does not produce a perfect NPT
ensemble. The effect of sampling from this spurious ensemble is negligible
in this case, as:
+\begin{itemize}
+\item the limitations set by small size and time scales are likely to be
much more severe than this ensemble inaccuracy;
+\item test simulations by~\cite{mar01} involving lipid bilayers using
Parrinello-Rahman and Nose'-Hoover coupling schemes have not resulted in
any noticeable effect on the observed fluctuations for correlation times
larger than the coupling time, which is typically set to~$\sim0.5\,$ps.
+\end{itemize}
+Considering area fluctuations, that occur on multi-nanosecond time scales,
it is reasonable to assume that the weak-coupling method produces an
isobaric ensemble.
+\begin{table}[]
+\begin{center}
+\vspace{8pt}
+\begin{tabular}{lccc} % put @{} if you want to eliminate horizontal space
between columns
+&$\kappa$\,[bar$^{-1}$]&$\tau_P$\,[ps]& effective coupling
strength\,[bar$^{-1}$ps$^{-1}$]\\
+Bond et al. [2006] & $1\cdot10^{-5}$&40&$2.5\cdot10^{-7}$\\
+\cite{bond06} & $1\cdot10^{-5}$&40&$2.5\cdot10^{-7}$\\
+\cite{dicke05a} & $5\cdot10^{-6}$&1&$5\cdot10^{-6}$\\
+\cite{falle04a} & $5\cdot10^{-6}$&1&$5\cdot10^{-6}$\\
+\cite{shiqv05a} & $5\cdot10^{-6}$&1&$5\cdot10^{-6}$\\\hline
+\end{tabular}
+%\caption[Electron density comparison]{Total electron density profile:
quantitative comparison. The head-head thickness $D_{HH}$ and selected
electron densities from our simulations and experiments are compared.}
+\label{tab:edp}
+\end{center}
+\end{table}
+
+%\section{Monte-Carlo method} Along with MD, another important simulation
tool is the {\em Monte-Carlo} (MC) method: here random steps are taken in
order to achieve a rapid sampling of the most likely states of the system
studied. It should be stressed that only MD and not MC methods allow the
theoretical possibility of obtaining time-dependent quantities from
simulation, while both schemes can in principle be used for the same
statistical-mechanical calculations.
+
+\subsubsection{Volume compressibility modulus}
+$K_V$ and can be related to the variance of the lipid volume
$\sigma^2_{V}$:
+\begin{equation}
+K_V=\frac{k_BTV}{N_l\sigma^2_{V}}
+\end{equation}
+with $V$ the average volume per lipid, $N_l$ the number of lipid molecules
per layer, $T$ the temperature and $k_B$ the Boltzmann
constant~\cite{venable06}.
+
+\subsection{Lateral pressure distribution} Computer simulations of lipid
bilayers indicate that bilayers have regions with negative lateral pressure
trying to minimize the interfacial area, and regions with positive lateral
pressure trying to expand the bilayer~\cite{goetz98a, lindahl00b, gulli04}.
The mentioned MD bilayer studies, as well as less detailed models, predict
lateral pressure variations in these regions of several hundred
bars~\cite{sonne05}.
+
+For inhomogeneous systems comprising an interface, hydrodynamics
equilibrium requires that the component of the pressure tensor normal to
the interface is constant throughout the system. The components tangential
to the interface can vary in the interfacial region, but must be equal to
the normal component in the bulk liquids~\cite[Sec.~17.1.2]{frenkel}.
+
+For an inhomogeneous fluid there is no unambigous method to compute the
pressure tensor components as a function of the interface normal. The
popular Kirkwood-Buff convention involves dividing the system in $N$ equal
slabs parallel to the interface, and weighing the virial over the slabs
intersected by the line that connects every interacting pair of sites.
+
+
+
+\section{Coda}
+GBMOLDD~\cite{ilnyt01a}, DLPOLY~\cite{smith05c, todor04a, smith02b},
\cite{wilso97b, demig96a, wilson97} use non-symplectic
integrators~\cite{fincham84, fincham93}.
+
+
+
+
+\section{Controlling temperature and pressure}
+Conventional MD simulations are carried out in the constant energy
ensemble; on the other hand, it would be desirable to perform simulations
in conditions closer to the real world, i.e. constant-Temperature and
constant-Pressure.
+
+The control can be achieved following two approaches:
+
+\begin{itemize}
+\item Constraint dynamics: T and P are kept rigorously fixed by
constraints applied each step~\cite{evansHoover83}.
+\item Extended systems: additional degrees of freedom are introduced that
couple dynamically to the rest of the system, thereby keeping T and/or P,
{\em on average}, to the desired value~\cite{ander80a}.
+\end{itemize}
+
+ Pressure and temperature studies of biomembranes make possible the
observation of new pressure-induced phases and changes in the dynamics of
the lipid of which the membranes are composed~\cite{paci96}.
+\subsubsection{Isotropic method}
+In the isotropic control of pressure, the simulation volume retains its
rectangular shape, so that changes consist of uniform contractions and
expansions. % rapa, p 164
+\subsubsection{Shape-changing method}
+\cite{parrinello80} extended the case to a general simulation region in
which the lengths and directions of the edges are allowed to vary
independently, subject to uniform external pressure (an even more general
case where the applied stress components are specified separately has also
been developed~\cite{parrinello81}).
+The more flexible approach allows for the size and shape changes needed to
accomodate lattice formation on freezing and for the study of structural
phase transitions between different crystalline
states~\cite[Section~6.2]{rapa}.
+
+Conditions of constant pressure or stress allow the simulation of a
solid-state phase transition with a change of cell size and shape. In a
constant-stress simulation, the MD cell changes in size and shape in
response to the imbalance between the internal and externally applied
pressure~\cite{refson}.
+Constraint methods~\cite{hoover82, evans83a}.
+
+\cite{parrinello81, parrinello82} have developed MD methodology to apply
to the system the most general condition of stress.
+
+
+A metrix tensor $\mathbf{G}$ can be introduced:
+\[\mathbf{G}=\mathbf{H}^T\mathbf{H}\]
+Intersite distance can be computed:
+\[\mathbf{r}_{ij}^2=\mathbf{s}^T_{ij}\mathbf{G}\mathbf{s}_{ij}\Rightarrow\mathbf{r}_{ij}=\sqrt{\mathbf{s}^T_{ij}\mathbf{G}\mathbf{s}_{ij}}\]
+where $\mathbf{s}_{ij}=\mathbf{s}_i-\mathbf{s}_j$ is the scaled vector
specifying intersite distance in terms of lattice
coordinates~\cite{hernandez01}.
+The scaled coordinates span the unit cube and periodic images have
coordinates $\mathbf{H}(\mathbf{s}+(n_x, n_y, n_z))$~\cite[Sec.~6.2]{rapa}.
+
+To avoid overall cell rotation, the three sub-diagonal elements of
$\mathbf{H}$ can be constrained to zero, that is, the $\mathbf{a}$ cell
vector is constrained to lie along the $x$-axis and $\mathbf{b}$ is
constrained to lie in the $xy-$plane~\cite{procacci97, refson}:
+\begin{displaymath}
+\mathbf{H}=\frac{1}{2}\left(
+\begin{array}{ccc}
+ a & b\,\cos\gamma & c\,\cos\beta \\
+ 0 & b\,\sin\gamma & c\,(\cos\alpha-\cos\beta\cos\gamma)/\sin\gamma \\
+ 0 & 0& (c/\sin\gamma)\sqrt{\sin^2\!\beta\,\sin^2\!\gamma-(\cos\alpha -
\cos\beta\cos\gamma)^2}
+\end{array}
+\right)
+\end{displaymath}
+ Practically, at each time step the acceleration of those components,
$\ddot{\mathbf{H}}_{ij}$, is set to zero (which is equivalent to adding a
fictituous opposing force). This technique may also be used to allow
uniaxial expansion only.
+
+
+\subsection{Isotropic pressure tensor}
+Controlling the pressure tensor so that $P_{xx}=P_{yy}=P_{zz}$, the area
and volume can adjust and/or fluctuate separetely. This constraint,
however, is equivalent to setting $\gamma=0$~\cite{feller95}.
+
+
+\subsection{Changing box-shape}
+
+Periodic boundaries and minimum image convention are most readily handled
when the problem is expressed in terms of scaled coordinates, because the
simulation region is then a {\em fixed unit cube}; use of physical
variables introduces unnecessary complications when handling boundary
crossings, because velocities and accelerations must be adjusted as well as
coordinates.~\cite{rapa} %[Sec.~6.2, p.~158]
+ It is then most convenient to introduce {\em scaled} (or {\em lattice})
coordinates $\mathbf{s}$ %, which give the position of atoms relative to
the simulation cell
+through the linear transformation:
+\begin{equation}
+\mathbf{r}=\mathbf{H}\mathbf{s}
+\end{equation}
+where $\mathbf{H}=(\mathbf{a}, \mathbf{b}, \mathbf{c})$ is a
transformation matrix whose columns are the three vectors ($\mathbf{a},
\mathbf{b}, \mathbf{c}$) representing the edges of the simulation box.
+Conversly, a real-space vector $\mathbf{r}$ can be transformed into a
box-space vector $\mathbf{s}$ via:
+\begin{equation}
+\mathbf{s}=\mathbf{H}^{-1}\mathbf{r}
+\end{equation}
+Since the cell vectors are linearly independent, matrix $\mathbf{H}$ can
be inverted.
+
+
+\subsection{Isotropic box}
+The isotropic pressure $P_{iso}=\mathrm{Tr}[\,\mathbf{P}(t)\,]\,/\,3$ can
be controlled by allowing {\em uniform} expansions and contractions of the
system volume~\cite{ander80a}.
+Obviously, in this case the ratio of surface area to system volume is
implicitely fixed.
+
+\section{Physical constants}
+
+The physical constants employed by \brahms are reported in
Table~\ref{tab:constants}. Some relations between units are collected in
Table~\ref{tab:relations}. % For the charge unit, note that
$e=4.803\times10^{-10}$\,esu, and $e^2 = 331.8$\,(kcal/mol)\AA.
+
+\begin{table}
+\begin{center}
+%\vspace{14pt}
+\begin{tabular}{cll} % put @{} if you want to eliminate horizontal space
between columns
+Symbol & Name & Value \\
+$N_{AV}$ & Avogadro's number & $6.0221367\times10^{23}$\\
+$k_{B}$ & Boltzmann's constant & $1.3806505\times 10^{-23}$\,J/K\\
+$\varepsilon_0$ & Electric constant & $8.854 187 817\times 10^{-12}$\,F/m\\
+$u$& Unified Atomic Mass Unit & $1.660 538 86\times10^{-27}$\,kg\\
+$e$&elementary charge%\footnote{The elementary charge (symbol $e$ or
sometimes $q$) is the electric charge carried by a single proton, or
equivalently, the negative of the electric charge carried by a single
electron. This is a fundamental physical constant and the unit of electric
charge in the system of atomic units.}
+&$1.602 176 53(14)\times10^{-19}$\,C
+\end{tabular}
+\caption[Physical constants]{Physical constants. Note: F/m =
C$^2$N$^{-1}$m$^{-2}$, $e=4.803\times10^{-10}\,$esu,
$e^2=331.8\,$kcal\,\AA/mole. % rapa, p 217
+From~{\tt http://physics.nist.gov/cuu/Units/}.}
+\label{tab:constants}
+\end{center}
+\end{table}
+
+\begin{table}
+\begin{center}
+%\vspace{14pt}
+\begin{tabular}{cll} % put @{} if you want to eliminate horizontal space
between columns
+Symbol & Name & Relation to other units
+\\$V$ & Volt & $V = J / C$
+\end{tabular}
+\caption[Relations between units]{Relations between units.}
+\label{tab:relations}
+\end{center}
+\end{table}
+
+
+\section{Configuration definition of the SSD water model} The atom
coordinates of an SSD molecule located at $x=y=z=0$ and at orientation
$\alpha=\beta=\gamma=0$ are reported in Table~\ref{tab:SSD coords}.
+\begin{table} \begin{center} \vspace{14pt} \begin{tabular}{lccc} % put @{}
if you want to eliminate horizontal space between columns
+Atom & $x_1/$\AA &$x_2/$\AA&$x_3/$\AA\\
+H$_1$& 0 & 0.75 & 0.53 \\
+H$_2$& 0 & -0.75& 0.53\\
+O & 0 & 0& -0.0654
+\end{tabular}
+\caption[SSD coordinates]{SSD coordinates in the principal (body-attached)
frame of reference. Values from~\cite{bratk85a}.}
+\label{tab:SSD coords}
+\end{center}
+\end{table}
+The geometry of the SSD water is indeed equal to that of the TIP3P
model~\cite{jorge81a}. Table~\ref{tab:PMI} reports the SSD principal
moments of inertia corresponding to this geometry.
+\begin{table} \begin{center} \vspace{14pt}
+\begin{tabular}{lcc} % put @{} if you want to eliminate horizontal space
between columns
+Moment of Inertia & Value in physical units & Reduced Value in \brahms
+\\ $I_y=m_Oz_0^2 + 2m_Hz_H^2$& 0.630\,amu\,\AA$^2$&0.003826\\
+$I_z = 2m_Hy_H^2$&1.125\,amu\,\AA$^2$&0.006835\\
+$I_x=m_Oz_0^2 + 2m_H(y_H^2+z_H^2)$&1.755\,amu\,\AA$^2$& 0.010661
+\end{tabular}
+\caption[SSD Principal Moments of Inertia in \brahms reduced units]{SSD
Principal Moments of Inertia, expressed in reduced units. Of course,
$I_x=I_y+I_z$.}
+\label{tab:PMI}
+\end{center}
+\end{table}
+For example, by setting $\sigma=3.4$\,\AA, $\epsilon/k_B=120$\,K and
$m=39.95\times1.6747\times10^{-24}$\,g, then the MD time unit corresponds
to $2.161\times10^{-12}$\,s. \section{Dipolar potential} \begin{equation}
\mathcal{V}_{ij}^{\mathrm{dp}}({\bf{r}}_{ij},{\Omega}_{i},{\Omega}_{j})=
\frac{1}{4\pi\varepsilon\varepsilon_0}\left[ {\bmu_{i} \cdot
\bmu_{j}}{r_{ij}^{3}} - \frac{3(\bmu_{i} \cdot {\bf{r}}_{ij})(\bmu_{j}
\cdot
{\bf{r}}_{ij})}{r_{ij}^{5}}\right]\;[=]\;\frac{Nm^2}{C^2}\frac{D^2}{m^3}\;[=]\;\frac{N}{C^2}\frac{C^2m^2}{m}\;\;[=]\;
Nm \;[=]\; J \end{equation}
+
+
+
+
+\subsection{RDF\index{RDF calculation}} The RDF computation has much in
common with the interaction computation. The minimum image separations
$r_{ij}$ of all the pairs of atoms are calculated and sorted into a
histogram where each bin has a width $\Delta r$ and extends from
$(n-1)\Delta r$ to $n\Delta r$, being $n$ the identifier of a given bin. If
$h_n$ is the number of atom pairs ($i$, $j$) for which $$(n-1)\Delta r \le
r_{ij} < n\Delta r$$ then, assuming that $\Delta r$ is sufficiently small,
we have the result: \begin{equation} g(r_n)=\frac{Vh_n}{2\pi N^2r_n^2\Delta
r} \end{equation} where $r_n=(n-\frac{1}{2})\Delta r$. If the RDF
measurements extend out to a maximum range $r_e$ the required number of
histogram bins is $r_e/\Delta r$. The normalisation factors ensure that
$g(r\rightarrow\infty)=1$. RDF functions are computed every $stepRdf$
steps; when $limitRdf$ computations have been performed and accumulated,
results are averaged and outputted, and the calculation is re-initialised.
+
+\subsection{\index{Diffusion calculation}}
+It is worth noting that in evaluating the diffusion coefficient it is
important not to switch attention from one periodic image to another, which
is why it is sometimes useful to have available a set of particle
coordinates which have not been subjected to periodic boundary corrections
during the simulation. For instance it is possible to keep track of the
``true'' atomic displacement $r_{j_x}'(t)$:
\begin{equation}r_{j_x}'(t)=r_{j_x}(t)+nint((r_{j_x}'(t-\Delta
t)-r_{j_x}(t))/L_x)\cdot L_x\end{equation}
+
+The lateral diffusion coefficient can be computed
+
+\subsection{Quaternion-based integrators for rigid body dynamics}
+An earlier implementation of \brahms employed quaternions to integrate
rotations: this method showed poor stability, as it has been observed by
other researchers~\cite{fenne04a, meine05a}.
+In the following subsection the quaternion-based schemes are reported only
for reference: they are no longer used in real simulations.
+\subsubsection{Symmetric rigid bodies}
+The leapfrog integration for the rotational motion of rigid linear sites
needs at first the defining of a new entity, the ``gorque'' $\mathbf{g}$,
as the equivalent force vector whose cross product with the orientation
vector gives the torque\footnote{The torque $\mathbf{T}$ is therefore:
$\mathbf{T}=\mathbf{e}\times\mathbf{g}$.}. Then we set $\mathbf{g}^\perp$
as:
+\begin{equation}
\mathbf{g}^\perp=\mathbf{g}-(\mathbf{g}\cdot\mathbf{e})\mathbf{e}
\end{equation}
+the orientational velocity can be evaluated:
+\begin{equation} \mathbf{u}(t+\delta t/2)=\mathbf{u}(t-\delta
t/2)+\frac{\delta t}{I} \mathbf{g}^\perp(t) - 2[\mathbf{u}(t-\delta
t/2)\cdot\mathbf{e}(t)]\mathbf{e}(t) \end{equation}
+Orientations update:
+\begin{equation}
+\mathbf{e}(t+\delta t)=\mathbf{e}(t)+\delta t\mathbf{u}(t+\delta t/2)
+\end{equation}
+The above equations are applied to each molecule~\cite[p.~90-91]{allen}.
+
+
+\paragraph{NVT scheme} Constant translational-temperature dynamics is
generated by the equations of motion: \begin{equation}
\dot{\mathbf{r}}_i=\mathbf{p}_i/m_i\end{equation}\begin{equation}
\dot{\mathbf{p}}_i=\mathbf{f}_i+\alpha\mathbf{p}_i \end{equation}
\begin{equation}
\label{lincem}\ddot{\mathbf{r}}_i=\frac{\mathbf{f}_i}{m_i}+\alpha\dot{\mathbf{r}}_i
\end{equation} Imposing $\dot{K}=0$, or equivalently \begin{equation}
\sum_im_i\dot{\mathbf{r}}_i\cdot\ddot{\mathbf{r}}_i=0\end{equation}
results in the following value for the Lagrange multiplier $\alpha$:
\begin{equation}
\alpha=-\frac{\sum_i\dot{\mathbf{r}}_i\cdot\mathbf{f}_i}{\sum_im_i|
\dot{\mathbf{r}}_i|^2} \end{equation}\begin{equation}
\alpha=-\frac{\sum_i\mathbf{p}_i\cdot\mathbf{f}_i}{\sum_i|\mathbf{p}_i|^2}
\end{equation} The algorithm implemented consists at first in the
computation of a projected (unconstrained) velocity $\mathbf{v}'_i$ through
the Verlet scheme: \begin{equation}
\label{com-firstStep}\mathbf{v}'_i(t)=\mathbf{v}_i(t-\delta
t/2)+\frac{\delta t}{2m_i}\mathbf{f}_i(t)\end{equation} then the scaling
factor $\beta\;(=[1+\alpha\,\delta t/2m]^{-1})$ is computed as follows:
\begin{equation} \label{com-secondStep}\beta =
\sqrt{\frac{3(N-1)k_BT_{trans}}{\sum_{i=1}^Nm_i|\mathbf{v}'_i(t)|
^2}}\end{equation} where $N$ is the {\emph total} number of sites.
Eventually, the integration step is: \begin{equation}
\label{com-thirdStep}\mathbf{v}_i(t+\delta t/2)=(2\beta -
1)\cdot\mathbf{v}_i(t-\delta t/2)+\beta\frac{\delta
t}{m_i}\mathbf{f}_i(t)\end{equation} \paragraph{Rotational motion - Linear
rigid sites} Hoover's method can be extended further in order to take into
account linear molecules, so to constraint the rotational kinetic energy as
well. The constrained rotational equation of motion is: \begin{equation}
\label{rotcem}
\dot{\mathbf{\omega}}_i=\frac{\mathbf{\tau}_i}{I_i}+\alpha{\mathbf{\omega}}_i
\end{equation} Combining Eq.~\ref{rotcem} with Eq.~\ref{lincem} and
imposing $\dot{K}=0$, or equivalently \begin{equation} \sum_i (
m_i\dot{\mathbf{r}}_i\cdot\ddot{\mathbf{r}}_i +
I_i{\mathbf{\omega}}_i\cdot\dot{\mathbf{\omega}}_i)=0\end{equation}
results in the following value for the Lagrange multiplier $\alpha$:
\begin{equation} \alpha=-\frac{\sum_i(\dot{\mathbf{r}}_i\cdot\mathbf{f}_i
+{\mathbf{\omega}}_i\cdot\mathbf{\tau}_i)}{\sum_i( m_i|\dot{\mathbf{r}}_i|
^2 + I_i|\mathbf{\omega}_i|^2)} \end{equation} The constrained equation for
integrating the rotational motion is:
\begin{equation}\dot{\mathbf{u}}_i=\mathbf{g}^\perp_i/I_i-\lambda
\mathbf{e}_i+\alpha{\mathbf{u}}_i \end{equation} where $\mathbf{g}^\perp$
is the component of the equivalent force perpendicular to the orientation
vector:
\begin{equation}\mathbf{g}_i^\perp=\mathbf{g}_i-(\mathbf{g}_i\cdot\mathbf{e}_i)\mathbf{e}_i\end{equation}
So in this case there are two constrains, $\alpha$ and
$\lambda=\mathbf{u}^2$. algorithm implemented consists at first in the
computation of a projected (unconstrained) velocity $\mathbf{u}'_i$
through: \begin{equation}
\label{rot-firstStep}\mathbf{u}'_i(t)=\mathbf{u}_i(t-\delta
t/2)-[\mathbf{u}(t-\delta t/2)\cdot\mathbf{e}(t)]\mathbf{e}(t)+\frac{\delta
t}{2I_i}\mathbf{g}^\perp_i(t)\end{equation} e scaling factor
$\beta\;(=[1+\alpha\,\delta t/2]^{-1})$ is computed as follows:
\begin{equation} \label{rot-secondStep}\beta =
\sqrt{\frac{2NT_{rot}}{\sum_{i=1}^NI_i|\mathbf{u}'_i(t)|^2}}\end{equation}
where $N$ is the {\emph total} number of sites. Eventually, the integration
step is: \begin{equation} \label{rot-thirdStep}\mathbf{u}_i(t+\delta
t/2)=(2\beta - 1)\cdot\mathbf{u}_i(t-\delta t/2)+\beta\frac{\delta
t}{I_i}\mathbf{g}^\perp_i(t)-2\beta[\mathbf{u}(t-\delta
t/2)\cdot\mathbf{e}(t)]\mathbf{e}(t)\end{equation}
+
+\paragraph{NPT scheme} The NPH constant-pressure method by~\cite{ander80a}
can be combined with the NVT scheme previously considered: the resulting
NPT algorithm has been implemented in the code\footnote{The main reference
employed is the paper by~\cite{brown94a}, where the equations of motion are
presented in a readily implementable form.}.
+
+\subparagraph{Volume V}
+\begin{equation}
+V(t+\delta t) = 2V(t) - V(t-\delta t) + \frac{\delta
t^2}{Q}\left[P(t)-P_E\right]
+\end{equation}
+\begin{equation}
+\dot{V}(t) = \frac{V(t+\delta t)-V( t-\delta t)}{2\delta t}
+\end{equation}
+\begin{equation}
+\ddot{V}(t) = \frac{P-P_E}{Q}
+\end{equation}
+$P_E$ is the external pressure, $V$ is the volume of the system and $Q$ is
a constant\footnote{The ``piston mass'' $Q$ is an adjustable parameter in
Andersen's method; a low ``mass'' will result in rapid box size
oscillations, which are not damped very efficiently by the random motions
of the molecules. A large ``mass'' will give rise to slow exploration of
volume-space, and an infinite mass restores normal
MD~\cite[p.~234]{allen}.}.
+$Q$ largely influences the rate of relaxation of the pressure and also the
magnitude of the fluctuations of the pressure. As~$Q\rightarrow\infty$, the
NPH ensemble tends towards the NVE ensemble. Static properties are
relatively insensitive to the value of $Q$ within fairly broad limits;
small values of $Q$ promotes faster equilibration to $P_E$, but can lead to
nonphysically rapid fluctuations in the volume or to (explosion)
catastrophic irreversible expansion of the system\footnote{In their
simulation runs on a LJ system, \cite{brown94a} set
$Q^{*}(=Q\sigma^4/m)=0.0027$.}.
+\subparagraph{Translational (centre of mass) motion}
+Computation of a projected (unconstrained) velocity $\mathbf{v}'_i$
through the Verlet scheme:
+\begin{equation}
\label{npt-firstStep}\mathbf{v}'_i\left(t\right)=\mathbf{v}_i\left(t-\delta
t/2\right)+\frac{\delta
t}{2}\left[\frac{\mathbf{f}_i\left(t\right)}{m_i}+\frac{\mathbf{r}_i\left(t\right)}{3V\left(t\right)}\left(\ddot{V}\left(t\right)-\frac{2\dot{V}^2(t)}{3V(t)}\right)\right]\end{equation}
+then the scaling factor $\beta$ is computed as follows:
+\begin{equation} \label{npt-secondStep}\beta =
\sqrt{\frac{3\left(N-1\right)k_BT_{trans}}{\sum_{i=1}^Nm_i|
\mathbf{v}'_i\left(t\right)|^2}}\end{equation}
+where $N$ is the {\emph total} number of sites. The leapfrog step for
updating the velocities becomes:
+\begin{equation} \label{npt-thirdStep}\mathbf{v}_i\left(t+\frac{\delta
t}{2}\right)=\left(2\beta - 1\right)\mathbf{v}_i\left(t-\frac{\delta
t}{2}\right)+\left(1-\beta\right)\mathbf{r}_i\left(t\right)\frac{2\dot{V}\left(t\right)}{3V\left(t\right)}+\beta\delta
t\left[\frac{\mathbf{f}_i\left(t\right)}{m_i}+\frac{\mathbf{r}_i\left(t\right)}{3V\left(t\right)}\left(\ddot{V}\left(t\right)-\frac{2\dot{V}^2(t)}{3V(t)}\right)\right]\end{equation}
+
+
+
+\subsubsection{General (non-symmetric) rigid bodies}
+As it has long been common practise in MD, the orientations of rigid
non-linear molecules can be represented by {\em quaternions} $\mathbf{q}$,
ordered number quartets:~\cite{finch81} developed an algorithm that
propagates the rotational dynamics via the update of the quaternion
associated with each site.
+The first step is to bring all the angular momenta $\mathbf{h}$ up to date:
+\begin{equation}
+\mathbf{h}^S(t)=\mathbf{h}^S(t-\delta t/2)+\frac{\delta
t}{2}\mathbf{T}^S(t)
+\end{equation}
+Then a guess at $\mathbf{q}(t+\delta t/2)$ is made:
+\begin{equation}
+\mathbf{q}(t+\delta t/2)=\mathbf{q}(t)+\frac{\delta
t}{2}\dot{\mathbf{q}}(t)
+\end{equation}
+The main algorithm equations are~\cite[p.~89]{allen}:
+\begin{equation}
+\mathbf{h}^S(t+\delta t)=\mathbf{h}^S(t-\delta t/2)+\delta t\mathbf{T}^S(t)
+\end{equation}
+and:
+\begin{equation}
+\mathbf{q}(t+\delta t)=\mathbf{q}(t)+\delta t\dot{\mathbf{q}}(t+\delta t/2)
+\end{equation}
+At every step, all quaternions have to be adjusted in order to preserve
the constraint $q_1^2+q_2^2+q_3^2+q_4^2=1$: this operation breaks
time-symmetry, hence the algorithm is not reversible. Note that Fincham's
algorithm is not even symplectic: indeed it has shown poor performances in
terms of long-time energy conservation.
+
+\paragraph{Twin-range method}
+When simulating species with a significant electrostatic contribution, it
may be desirable to use a twin-range method, in which two cutoffs are
specified: all interactions below the lower cutoff are calculated as normal
at each step, whereas the interactions due to atoms between the lower and
upper cutoffs are evaluated only when the neighbour list is updated and are
kept constant between these updates~\cite[Sec.~6.7.1]{leach}.
+\paragraph{Group-based cutoff}
+Using simple atom-based cutoffs the interaction energy may fluctuate
violently near the cutoff distance. This problem can be avoided by
calculating the interactions on a group-group basis, being the ``group'' a
collection atoms of zero total charge (e.g. all three atoms in a water
molecule)~\cite[Sec.~6.7.2]{leach}.
+
+\paragraph{Long-range effects}
+In all-atom simulations, the majority of the MD community is currently
oriented towards including long-range electrostatics via Ewald methods.
Nonetheless, some researchers are openly {\it against} the use of Ewald
methods~\cite{scott02a, beckd05a}.
+For example, considering atomic-level membrane studies, some authors have
tested both cutoff and Ewald sums and concluded that cutoff simulations do
not suffer to any great extent from the omission of long-range
electrostatics~\cite{marri01c,rog03,wohle04a}.
+On the other hand, \cite{patra03a, patra04a} have shown that long-range
truncation leads to artifacts such as enhanced order of acyl chains
together with decreased diffusion and areas per lipid (with respect to
experimental data). \cite{polya05a} also found that Ewald performs better
than cutoff, but interestingly, their results in some cases showed opposite
trends compared to Patra and coworkers.
+
+As far as we are concerned, the decision has been made to avoid the
expensive computation of long-range forces in favour of a faster cutoff
scheme, this choice being also consistent with the overall coarse-grained
spirit of the project.
+
+
+
+
+\section{Methodological issues in lipid bilayer simulation}
+
+In this section we consider specific methodology aspects important to
simulate bilayer systems.
+
+\subsection{Equilibration}\index{Equilibration of membrane - MD}
+
+Recent MD studies of hydrated biomembranes have shown that some important
bilayer properties (e.g. the lipid area) fluctuate on the time scale of
several nanoseconds~\cite{lindahl00, mar01, anezo03a, hogberg06}.
+Therefore, to obtain reliable equilibrium properties, membrane systems
must be simulated for realtively long times, at least a few tens of
nanoseconds\footnote{In a time where 1-ns (and less) NPT trajectories were
published without too much worries, \cite{feller99} profhetically warmed
that ``the inherently slow process of area fluctuation requires simulations
close to 10\,ns, rather than~1\,ns, before convergence and/or the
generation of sufficient equilibrium sampling is obtained''.}.
+
+\paragraph{\index{Surface tension}}
+The surface tension $\gamma$ along a bilayer is usually calculated from
the difference between the normal ($P_N=P_{zz}$) and lateral
($P_L=(P_{xx}+P_{yy})/2$) components of the pressure tensor:
+\begin{equation}
+\gamma=\int[P_N(z)-P_L(z)]\,\de z
+\end{equation}
+If sufficient water is placed outside the bilayer, the integrand vanishes
at the endpoints, since bulk water is tension-free: we can therefore
integrate over the entire simulation volume without making any arbitrary
definition of the interface. %~\cite{gulli04}.
+The surface tension per leaflet of a bilayer
+is related to the pressure tensor by~\cite{feller95}:
+\begin{equation}\label{eq:surfTens}
+\boxed{\gamma= \langle L_z\times(P_{zz}-P_{xx}/2-P_{yy}/2)\rangle\,/\,2}
+\end{equation}
+where $L_z$ and $P_{zz}$ denote the length of the unit cell and component
of the pressure tensor normal to the surface, respectively, and $P_{xx}$
and $P_{yy}$ are tangential components of the pressure tensor. Positive
values of the surface tension result from tangential pressures that are
less than the pressure along the normal~\cite{feller99}. Note that
eq.~\ref{eq:surfTens} gives the surface tension {\em per leaflet}; typical
units are dyn/cm/leaflet~\cite{pastor05}.
+
+
+\subsection{Ideal conditions for membrane simulation}
+Simulations have also been performed in the NP$_n$AT ensemble (constant
mole number, pressure normal to the bilayer plane, area/lipid, temperature)
in which the area/lipid is restrained about the experimentally determined
value~\cite{bempo04a, bempo04b}. However, to perform such simulations, one
must have prior experimental knowledge of the area/lipid of the system
being studied. Complicating matters, this parameter has been shown to vary
greatly with lipid type and hydration level~\cite{nagle00a}, so each system
simulated at NP$_n$AT requires an area/lipid value specific for that
system, which may not be available. Consequently, NP$_n$AT simulations will
be of marginal value if simulations are to be used eventually in place of
experimental analyses of new, unstudied bilayer systems, such as those
containing mixtures of lipids and/or membrane proteins. Simulations
performed in the NPT (constant mole number, pressure, and temperature)
ensemble have the potential for accomplishing this objective, because, in
principle, they do not require prior experimental information: this makes
it possible to verify the area per lipid as a result of simulations of
other lipids or lipid-protein systems~\cite{tiele97a}. Historically, a
pressure of 1 \,bar (both lateral and perpendicular components) has been
used: this is actually the same as zero bar within the numerical accuracy
of pressure calculation. Given perfect force fields and constant pressure
and temperature algorithms, an NPT simulation should be adequate for
reproducing accurate experimental results~\cite{benz05}, so that the size
and the shape of the simulation box are free to adjust, allowing the
membrane area and thickness to fluctuate. This offers the possibility to
compare and validate simulations by examining their ability to reproduce
important structural quantities such as the projected area per lipid.
+
+Some workers control the pressure by separate coupling to 1\,atm in the
three space coordinates (normal and lateral directions), corresponding to a
stress-free bilayer; the simulation region is constrained to orthorombic
symmetry~\cite{marri01c, anezo03a, wohle04a, benz05}.
+
+In some MD simulations, DPPC bilayers of 36-40 lipids/leaflet near the
experimental surface area per lipid have shown surface tensions near
20\,dyn/cm. This result is controversial because the experimental surface
tension of macroscopic lipid bilayers is close to or equal to
zero~\cite{jahnig96}.
+\cite{feller96} propose that $\gamma\ne0$ for simulation-sized bilayers
because long-wavelength undulations are not present. Hence a nonzero
surface tension must be applied in NP$\gamma$T simulations in what may be
regarded as a small system correction.
+Others have argued that the nonzero surface tension observed in
simulations is an artifact for the force field, and hence the appropriate
boundary condition for lipid bilayer simulations is constant isotropic
pressure~\cite{jahnig96, tieleman96, berge97a, lindahl00b, marrink01,
benz05, sonne05}; from this point of view, an ideal force field would yield
$\gamma=0$\, dyn/cm for a non-stressed lipid bilayer at the correct surface
area.
+
+\cite{feller95}
+
+In the simulations by~\cite{anezo03a}, the pressure was controlled either
anisotropically or semi-isotropically. In the former case, the three
unit-cell dimensions fluctuate independently from each other, and the total
pressure P remains constant. This corresponds to an NP$_x$P$_y$P$_z$T
ensemble, which is not rigorously defined and stable only when at least two
of the pressure components are equal. The semi-isotropic case corresponds
to NP$_n$P$_l$T. In both cases, the pressure components are kept at 1\,bar
on average. The only difference in the simulations is that in the
anisotropic case the simulation box fluctuates independently in x and y
whereas in the semi-isotropic case the interface maintains a square. When
the lateral pressure and normal pressure are equal, the average surface
tension is zero; at constant box length, specifying zero surface tension
and a normal pressure of 1 bar is equivalent to specifying a lateral and
normal pressure of 1 bar. \cite{anezo03a} ignore the effect of the
fluctuating box length and assume that specifying a lateral and normal
pressure of 1 bar is the same as specifying zero surface tension and a
normal pressure of 1 bar.
+
+A comparison between the original and shifted-force form of the Coulomb
potential is presented in Fig.~\ref{fig:sf}.
+\begin{figure}
+\centering
+\mbox{\subfigure[]{\includegraphics[width=75mm]{methodology/shiftPot.eps}}\quad
+
\subfigure[]{\includegraphics[width=75mm]{methodology/shiftForceInset.eps}}}
+\caption[Coulomb interaction: normal and shifted-force]{Coulomb
interaction. Comparison between the natural and the shifted-force forms.
(a) Potential. (b) Force.
+}
+\label{fig:sf}
+\end{figure}
+
+%If appropriately constructed shift functions are used for the
electrostatic forces, no charge groups are needed, but in principle, the
cutoff scheme should be combined with a lattice sum for long-range
electrostatics~\cite{gmx31}. \cite{brooks85} found that the shifted force
scheme (Equation~\ref{eq:sf}) resulted in a faithful representation of
short-ranged structures.
+
+\subsubsection{Surface tension}\index{lateral pressure profile!surface
tension}
+The surface tension per leaflet of a bilayer
+is simply related to the pressure tensor by:~\cite{feller95}
+\begin{equation}\label{eq:surfTens}
+\gamma= \langle L_z\times(P_{N}-P_{L})\rangle\,/\,2
+\end{equation}
+where $L_z$ and $P_{N}$ denote the length of the unit cell and component
of the pressure tensor normal to the surface, respectively, and $P_{L}$ is
the lateral components of the pressure tensor.
+The surface tension per monolayer $\gamma$ can be also computed from the
lateral pressure profile as:
+\begin{equation}
+\gamma=\frac{1}{2}\int_0^{L_z}[P_{N}(z)-P_{L}(z)]\:\de
z=-\frac{1}{2}\int_0^{L_z}\pi(z)\:\de z
+\end{equation}
+The surface tension measures the intrinsic tendency of the bilayer lateral
dimensions to change relative to the longitudinal one, while the total
pressure measures the tendency of the three dimensions to change
simultaneously. A positive surface tension indicates that the system tends
to a lateral shrinkage and a longitudinal expansion. A zero surface tension
indicates that the system is at equilibrium with respect to its surface
area and stacking distance for a particular pressure.~\cite{devri05a}
+
+
+
+\subsection{Constraint method - Gaussian thermostat}
+\label{ss:hoov}
+The Gaussian thermostat method~\cite{hoover82,evans83} enforces constant
temperature by introducing %nonholonomic
+constraints into the equations of motion to fix the kinetic energy; in
effect this serves as a mathematical thermostat.~\cite{rapa} The
equilibrium properties of this isothermal system can be shown to be those
of the canonical ensemble. %The constraint-temperature method has been
implemented in the code; the main references employed are the papers
by~\cite{brown94a} (for the centre of mass motion) and by~\cite{finch86a}
(extension to take into account linear molecules and hence rotational
motion).
+The total kinetic energy $\mathcal{K}$ is: \begin{equation}
\mathcal{K}=\frac{1}{2}\sum_im_i|\mathbf{v}_i|
^2+\frac{1}{2}\sum_i\sum_xI_{ix}(\omega^b_{ix})^2\end{equation}
+ being, for each particle $i$, $m_i$ the mass, $\mathbf{v}_i$ the linear
velocity, $I_{ix}$ the $x-$component of the principal moments of inertia,
$\omega^b_x$ the $x-$component of the body-frame angular velocity; $\sum_i$
denotes a sum over the system's particles and $\sum_x$ denotes a sum over
the vector components.
+
+by setting $\dot{\mathcal{K}}=0$ we obtain the Lagrange multiplier
$\alpha$:
+\begin{equation}\label{eq:alpha}
+\alpha = -
\frac{\sum_i\mathbf{v}_i\cdot\mathbf{f}_i+\sum_i\bomega^b_i\cdot\mathbf{T}^b_i}{\sum_im_i\mathbf{v}^2_i+\sum_i\sum_xI_{ix}(\omega^b_{ix})^2}
+\end{equation}
+being $\bomega^b$ and $\mathbf{T}^b$ the body-frame angular velocity and
torque; $\alpha$ has the dimension 1/time.
+Forces and torques are modified according to:
+\begin{equation*}
+\mathbf{f}_i := \mathbf{f}_i +\alpha\, m_i\mathbf{v}_i
+\end{equation*}
+\begin{equation*}
+\mathbf{T}_i := \mathbf{T}_i +\alpha\,\mathbf{h}_i
+\end{equation*}
+The constraint method thus reduces to simple scaling of the forces as well
as the velocities. %; for other integrators this may not be the case.
+It must be noticed that the constraint method is only designed to conserve
$\mathcal{T}$, not to fix this quantity at the desired value $T$ (which do
not in fact appear in the algorithm). This means that $\mathcal{T}$ will
tend to drift and it could be necessary to make small corrections every $n$
time-steps. %AllentTildesley 239: addirittura *every* time step!
+This is done through simple velocity scaling.
+
+
+%\subsection{Nose'-Hoover thermostat} The popular Nose'-Hoover algorithm
is described in the next section, where it will be considered coupled to a
barostat for pressure control. Temperature and pressure are not kept fixed
by this scheme; instead, using a negative feedback, the fluctuations are
limited and the mean values are equal to the desired values\footnote{This
actually makes more physical sense, as in reality we do expect some
fluctuations.}.
+
+
+\paragraph{Symmetric rigid-bodies} The DLM method can be modified to
specifically treat the symmetric rigid body, with (say) $I_1=I_2$ in
principal coordinates. \begin{eqnarray*}
\mathbf{R}_1:=\mathbf{R}_z\left(\;\Delta
t\,\left(\frac{1}{I_3}-\frac{1}{I_2}\right)\;\right)&\;\;\rightarrow\;\;
\mathbf{h}^b=&\mathbf{R}_1\mathbf{h}^b\\
\mathbf{R}_2:=\mathbf{R}_{\mathbf{h}^b}\left(\;\Delta t\,\frac{|
\mathbf{h}^b|}{I_2}\;\right)&\;\;\rightarrow\;\;
\mathbf{Q}^T=&\mathbf{Q}^T\mathbf{R}_2^T; \end{eqnarray*}
+These formulae allow the treatment of, for instance, point-dipoles and
Gay-Berne solid ellipsoids.
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/depot/chargeDipoleSwitched.tex Wed Dec 21
02:20:08 2011
@@ -0,0 +1,27 @@
+\subsection{Charge-dipole interaction: linear-switch form}
+The switched potential energy is:
+\begin{equation}
+u^{\mathrm{S}}(r)=u(r)\cdot s(r)
+\end{equation}
+The modulating linear function $s$ is:
+\begin{displaymath}
+s(r)=
+\left\{
+\begin{array}{lll}
+1 &\mathrm{ if } \qquad r < r_{s}\\
+(r_{c}-r)/(r_{c}-r_{s}) &\mathrm{ if } \qquad r_{s} \leqslant r \leqslant
r_{c}\label{eq:ssdmodu} \\
+0 &\mathrm{ if } \qquad r > r_{c}\\
+\end{array}
+ \right.
+\end{displaymath}
+The switched force (for $ r_{s} \leqslant r \leqslant r_{c}$) is:
+\begin{equation}
+%\mathbf{f}=\frac{C(2r_c-r)}{r^3(r_c-r_s)}\hat{\mathbf{e}}=
\frac{C}{r^3}\left[\left(\frac{3r_\mathrm{c}-2r}{r_\mathrm{c}-r_\mathrm{s}}\right)\frac{\mathbf{r}}{r}\cos\theta-\left(\frac{r_\mathrm{c}-r}{r_\mathrm{c}-r_\mathrm{s}}\right)\hat{\mathbf{e}}\right]
+%\boxed{\mathbf{f}=
\frac{C}{r^3}\left[\left(\frac{3r_\mathrm{c}-2r}{r_\mathrm{c}-r_\mathrm{s}}\right)\frac{\mathbf{r}}{r}\cos\theta-\left(\frac{r_\mathrm{c}-r}{r_\mathrm{c}-r_\mathrm{s}}\right)\hat{\mathbf{e}}\right]}
+\mathbf{f}=
\frac{C}{r^3(r_\mathrm{c}-r_\mathrm{s})}\left[\left(\frac{3r_\mathrm{c}}{r}
- 2\right)\cos\theta\,\mathbf{r}+(r-r_\mathrm{c})\,\hat{\mathbf{e}}\right]
+\end{equation}
+The switched torque (for $ r_{s} \leqslant r \leqslant r_{c}$) is:
+\begin{equation}
+\mathbf{T}=\frac{C(r_c-r)}{r^3(r_c-r_s)}\mathbf{r}\times\hat{\mathbf{e}}
+\end{equation}
+
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/depot/force/force.tex Wed Dec 21 02:20:08 2011
@@ -0,0 +1,157 @@
+\chapter{Electrostatic potentials, forces and torques}
+\label{app:force}
+In the following, the derivation of forces and torques from the
electrostatic potentials employed in our model is presented. %Obviously,
the calculation of these quantities is necessary to perform MD simulation.
+General treatments on the derivation of forces and torques from
anisotropic potentials can be found
elsewhere.~\cite{price84a}%~\cite{cheun76a,price84a,popel94a}
+
+\section{Electrostatic interactions}
+
+\subsection{Charge-charge (Coulombic) interactions}
+
+\subsubsection{Charge-charge potential}
+The interaction potential energy $u^{QQ}$ between two point charges $Q_i$
and $Q_j$ located with a distance $r$ between them is defined by Coulomb's
law:
+\begin{equation}~\label{eq:qq}
+u^{QQ}(r)=\frac{Q_iQ_j}{4\pi\epsilon_0r}
+\end{equation}
+with $\epsilon_0$ the dielectric constant in free space (vacuum).
+\subsubsection{Charge-charge forces}
+The electrostatic force corresponding to the potential of
Equation~\ref{eq:qq} is:
+\begin{equation}
+\mathbf{f}_{ij}(r)=\frac{Q_iQ_j}{4\pi\epsilon_0r^3}\mathbf{r}
+\end{equation}
+with $\mathbf{r}=\mathbf{r}_i-\mathbf{r}_j$.
+
+%\subsubsection{Cutoff treatment} To speed up the computation, non-bonded
interactions are typically skipped outside a cutoff radius~$r_\mathrm{c}$.
In \brahms we have implemented the shifted-force cutoff scheme.
+\paragraph{Shifted-force cutoff scheme} The discontinuity at the cutoff
distance $r_\mathrm{c}$ affects both the apparent energy conservation and
the actual atomic motion. This discontinuity can be smeared out by changing
the form of the potential function slightly, adding a small linear term so
that its derivative is zero at the cutoff
distance:~\cite{allen,rapa}%\cite[Section~3.3.2]
+\begin{equation}\label{eq:sf}
u^{\mathrm{SF}}(r)=u(r)-u_\mathrm{c}-(r-r_\mathrm{c})\frac{\de u(r)}{\de
r}\rvert_{r=r_\mathrm{c}} \end{equation} %The force goes smoothly to zero
at the cutoff $r_\mathrm{c}$, removing problems in energy conservation and
any numerical instability in the equations of
motion.~\cite{allen} %\cite[Section~5.2.4]
+For the Coulomb potential, defining a multiplicative shifting function:
+\begin{equation}
+S^M(r)=\left(1-\frac{r}{r_c}\right)^2\end{equation}
+the Coulomb energy is modified as:
+\begin{equation}
+u(r)=\frac{q_iq_j}{r}S^M(r)\end{equation}
+%There is a consensus that this shifting scheme works well~\cite{levit95a}.
+and the force becomes:
+\begin{equation}
+\mathbf{f}=\frac{q_iq_j}{r^2}\left(1-\frac{r}{r_c}\right)\left(\frac{1}{r}+\frac{1}{r_c}\right)\mathbf{r}=\frac{q_iq_j}{r^3}\left(1-\frac{r}{r_c}\right)\left(1+\frac{r}{r_c}\right)\mathbf{r}=\frac{q_iq_j}{r}\left(\frac{1}{r^2}-\frac{1}{r_c^2}\right)\mathbf{r}
+\end{equation}
+
+
+
+\subsection{Charge-dipole interaction}
+
+Interaction between a dipole $\mu$ with associated orientation vector
$\mathbf{e}_\mu$ and a charge $Q$. In the following we will assume site $j$
to be a point-dipole and site $i$ a point-charge. The angle $\theta$
between the dipole orientation vector $\mathbf{e}_\mu$ and the
interparticle distance vector $\mathbf{r}$ can be obtained from the
relation $\cos\theta = \mathbf{e}_\mu\cdot\mathbf{r} / r$. Also, we define
$C = Q\mu / 4\pi\epsilon_0$.
+
+\subsubsection{Charge-dipole potential}
+Considering site $j$ a dipole $\mu$, with corresponding orientation vector
$\mathbf{e}_\mu$, and site $i$ a charge $Q$, the electrostatic interaction
energy is:
+\begin{equation}
+u^{Q\mu}=\frac{C}{r^3}\,(\mathbf{e}_\mu\cdot\mathbf{r})=\frac{C}{r^2}\,\cos\theta
+\end{equation}
+with $\mathbf{r}=\mathbf{r}_i-\mathbf{r}_j=\mathbf{r}_Q-\mathbf{r}_\mu$.
+
+\subsubsection{Charge-dipole force}
+
+Pair force:
+\begin{equation}
+\label{eq:dipChargeForce}
+\mathbf{f}_{ij}=-\mathbf{f}_{ji}=
\frac{C}{r^3}\left(\frac{3\cos\theta}{r}\mathbf{r}-\hat{\mathbf{e}}\right)
=
\frac{C}{r^5}\left[3(\hat{\mathbf{e}}_\mu\mathbf{r})\mathbf{r}-r^2\hat{\mathbf{e}}_\mu\right]
+\end{equation}
+with $\mathbf{r}=\mathbf{r}_i-\mathbf{r}_j=\mathbf{r}_Q-\mathbf{r}_\mu$.
+
+
+\subsubsection{Charge-dipole torque}
+
+Pair torque on site $j$:
+\begin{equation}
+\mathbf{T}_{ji}=\frac{C}{r^3}\left(\mathbf{r}\times\mathbf{e}_{j}\right)=\mathbf{T}_{\mu
Q}=\frac{C}{r^3}(\mathbf{r}\times\mathbf{e}_{\mu})
+\end{equation}
+with $\mathbf{r}=\mathbf{r}_i-\mathbf{r}_j=\mathbf{r}_Q-\mathbf{r}_\mu$.
+
+\subsection{Charge-dipole interaction: shifted-force form}
+Considering a charge $Q$ and a dipole $\mu$, being
$r=\mathbf{r}_Q-\mathbf{r}_\mu$, the interaction energy is:
+\begin{equation}
+u^{\mathrm{SF}}(r)=\frac{C}{r^2}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2+2\,\frac{r-r_\mathrm{c}}{r_\mathrm{c}}\left(\frac{r}{r_\mathrm{c}}\right)^2\right]\cos\theta=
+\frac{C}{r^3}\left[1-3\,\left(\frac{r}{r_\mathrm{c}}\right)^2+2\,\left(\frac{r}{r_\mathrm{c}}\right)^3\right]\mathbf{e}\cdot\mathbf{r}
+\end{equation}
+where $\cos\theta=\mathbf{e}\cdot\mathbf{r}$.\\
+Using the chain rule:
+\begin{equation}
+\mathbf{f}=-\frac{\partial u}{\partial
r}\,\nabla_{\mathbf{r}}r-\frac{\partial u}{\partial
\cos\theta}\,\nabla_{\mathbf{r}}\cos\theta
+\end{equation}
+\begin{equation}
+\frac{\partial u}{\partial r}=
-\frac{2C\cos\theta}{r^3}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^3\right]
+\end{equation}
+Finally we obtain:
+\begin{equation}
+\mathbf{f}_{\mu
Q}=\frac{C}{r^3}\left\{3\,\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2\right]\frac{\mathbf{r}}{r}\cos\theta-\left[1-3\,\left(\frac{r}{r_\mathrm{c}}\right)^2+2\,\left(\frac{r}{r_\mathrm{c}}\right)^3\right]\mathbf{e}\right\} %=
\frac{2C}{r^3}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^3\right]\mathbf{e}
+\end{equation}
+\begin{equation}
+\mathbf{T}_{\mu
Q}=\frac{C}{r^3}\left[1-3\,\left(\frac{r}{r_\mathrm{c}}\right)^2+2\,\left(\frac{r}{r_\mathrm{c}}\right)^3\right](\mathbf{r}\times\mathbf{e})
+\end{equation}
+Consistency check: for $r_\mathrm{c}\rightarrow\infty$ we recover the
unshifted case.
+
+\subsection{Charge-dipole interaction: linear-switch form}
+The switched potential energy is:
+\begin{equation}
+u^{\mathrm{S}}(r)=u(r)\cdot s(r)
+\end{equation}
+The modulating linear function $s$ is:
+\begin{displaymath}
+s(r)=
+\left\{
+\begin{array}{lll}
+1 &\mathrm{ if } \qquad r < r_{s}\\
+(r_{c}-r)/(r_{c}-r_{s}) &\mathrm{ if } \qquad r_{s} \leqslant r \leqslant
r_{c}\label{eq:ssdmodu} \\
+0 &\mathrm{ if } \qquad r > r_{c}\\
+\end{array}
+ \right.
+\end{displaymath}
+The switched force (for $ r_{s} \leqslant r \leqslant r_{c}$) is:
+\begin{equation}
+%\mathbf{f}=\frac{C(2r_c-r)}{r^3(r_c-r_s)}\mathbf{e}=
\frac{C}{r^3}\left[\left(\frac{3r_\mathrm{c}-2r}{r_\mathrm{c}-r_\mathrm{s}}\right)\frac{\mathbf{r}}{r}\cos\theta-\left(\frac{r_\mathrm{c}-r}{r_\mathrm{c}-r_\mathrm{s}}\right)\mathbf{e}\right]
+%\boxed{\mathbf{f}=
\frac{C}{r^3}\left[\left(\frac{3r_\mathrm{c}-2r}{r_\mathrm{c}-r_\mathrm{s}}\right)\frac{\mathbf{r}}{r}\cos\theta-\left(\frac{r_\mathrm{c}-r}{r_\mathrm{c}-r_\mathrm{s}}\right)\mathbf{e}\right]}
+\mathbf{f}=
\frac{C}{r^3(r_\mathrm{c}-r_\mathrm{s})}\left[\left(\frac{3r_\mathrm{c}}{r}
- 2\right)\cos\theta\,\mathbf{r}+(r-r_\mathrm{c})\,\mathbf{e}\right]
+\end{equation}
+The switched torque (for $ r_{s} \leqslant r \leqslant r_{c}$) is:
+\begin{equation}
+\mathbf{T}=\frac{C(r_c-r)}{r^3(r_c-r_s)}\mathbf{r}\times\mathbf{e}
+\end{equation}
+
+\subsection{Dipole-dipole interactions}
+
+Here we consider a pair of (symmetric molecules and, in particular)
dipoles $i$ and $j$. The orientations are defined by the unit vectors
$\mathbf{e}_i$ and $\mathbf{e}_j$; the angles between these orientation
vectors and the interparticle separation vector $\mathbf{r}_{ij}$ are
defined respectively as $\theta_i$ and $\theta_j$. Also, we define
$\gamma_{ij}$ as the angle between %the plane containing
+$\mathbf{e}_i$ and
+%$\mathbf{r}_{ij}$ and the plane containing
+$\mathbf{e}_j$, %and $\mathbf{r}_{ij}$,
+so that $\cos{\gamma}_{ij}=\mathbf{e}_i\cdot\mathbf{e}_j$.
+%as in Figure~\ref{fig:orient}.
+%\begin{figure} \centering \includegraphics[scale=1]{appendices/orient}
\caption[Relative orientation of two dipoles]{The relative orientation of
two vectors associated with dipolar sites. From Allen and
Tildesley.~\cite{allen}} \label{fig:orient} \end{figure}
+
+\subsubsection{Dipolar potential}
+The electrostatic interaction potential energy is:
+\begin{equation}
+u_{ij}^{\mu\mu}=\frac{\mu^2}{r^3}(\cos\gamma_{ij}-3\cos\theta_i\cos\theta_j)
+\end{equation}
+where $r = |\mathbf{r}_{ij}|$. Cosines are computed through:
+\begin{equation}
+\cos\theta_i = \frac{\mathbf{e}_{i}\cdot\mathbf{r}_{ij}}{r|\mathbf{e}_{i}|
}\;\; \;\;\;\cos\theta_j = \frac{\mathbf{e}_{j}\cdot\mathbf{r}_{ij}}{r|
\mathbf{e}_{j}|}
+\end{equation}
+
+
+\subsubsection{Dipolar forces}
+
+Pair force:
+\begin{equation}
+\mathbf{f}_{ij}=-\mathbf{f}_{ji}=\frac{3\mu^2}{r^4}\left[(\cos\gamma_{ij}-5\cos\theta_i\cos\theta_j)(\mathbf{r}_{ij}/r+\cos\theta_j\mathbf{e}_i+\cos\theta_i\mathbf{e}_j)\right]
+\end{equation}
+
+\subsubsection{Dipolar torques}
+
+Pair torques:
+\begin{equation}
+\mathbf{T}_{ij}=-\frac{\mu^2}{r^3}\left[\mathbf{e}_i\times\mathbf{e}_j-3\cos\theta_j(\mathbf{e}_i\times\mathbf{r}_{ij})/r\right]
+\end{equation}
+\begin{equation}
+\mathbf{T}_{ji}=-\frac{\mu^2}{r^3}\left[\mathbf{e}_j\times\mathbf{e}_i-3\cos\theta_i(\mathbf{e}_j\times\mathbf{r}_{ij})/r\right]
+\end{equation}
+\\\\A complete treatment of the dipolar potential, along with the explicit
derivation to obtain forces and torques, can be found
elsewhere.~\cite{allen} %[p~332-334]
+
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/input/inputParameters.aux Wed Dec 21 02:20:08
2011
@@ -0,0 +1,168 @@
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lipid.ff}}{7}}
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=======================================
--- /dev/null
+++ /trunk/doc/latexSource/input/inputParameters.tex Wed Dec 21 02:20:08
2011
@@ -0,0 +1,192 @@
+\chapter{Input parameters}\label{ch:inputParameters}
+\index{file!input data}
+
+This chapter describes the main input files for Brahms: {\tt brahms.md},
{\tt lipid.ff}, {\tt water.ff} and {\tt brahms.an}. Where applicable, units
are reported between square brackets.
+Some parameters are marked as {\em logical}, meaning that they can be
either TRUE (when set to 1 or any other positive integer) or FALSE (for any
other values, including when left blank). They typically control the
activation of various functionalities. The description given below refers
to their behavior when set TRUE; when set FALSE, the corresponding
functionality is simply switched off.
+There are currently no default values assigned by Brahms; if a parameter
is not set, it is normally set to 0 by the compiler.
+Important things to note:
+\begin{itemize}
+\item the input files should contain no blank lines;
+\item the last line of the input files should terminate with a ``newline''
character.
+\end{itemize}
+The examples provided in the \brahms package should clarify these rules.
In general, it is obviously crucial that the input parameters are correctly
loaded in the program. At the start of a simulation, \brahms loads all
input parameters and subsequently writes them out to the file {\tt
inputParameters.log}; in case the simulation behaves unexpectedly, {\tt
inputParameters.log} should be checked against the input files to make sure
the parameters have been properly loaded (see also
section~\ref{sec:outFiles}).
+
+Many of \brahms input parameters have been implemented following
Rapaport;~\cite{rapa} therefore, to understand how they work, it is useful
to look them up also in the original reference~\citep{rapa}[e.g.,
pp.~509-515]. For a really full (yet possibly onerous) understanding,
parameters can be traced in the source code.\footnote{For example, try {\tt
grep anyParameterName *.c *.h} on the command line from the \brahms source
code ({\tt src/}) directory.}
+
+\section{{\tt brahms.md}}\label{sec:brahmsmd}
+The input file {\tt brahms.md} contains general \underline{m}olecular
\underline{d}ynamics parameters, together with parameters used to generate
a system from scratch. See following paragraphs for individual descriptions.
+
+\paragraph{{\tt deltaT}} [fs] Integration timestep. The standard value to
use with \brahms is 15\,fs. Smaller time steps will yield better energy
conservation but a lower sampling speed, possibly resulting in a waste of
computer time. However, short time steps (even 0.1\,fs or shorter) can
sometimes be required to equilibrate a (newly generated) system. Also, time
steps of 1-10\,fs are sometimes necessary to run under ``extreme''
conditions (such as very high temperature). Timesteps larger than 15\,fs
will improve sampling speed but might compromise stability and proper
energy conservation.~\citep{winger09}
+
+\paragraph{{\tt stepAvg}} [number of steps] Output frequency of text
summary printed on screen. For development or checking purposes, any output
frequency from 1 to 1000 steps is typically used. For long ``production''
jobs, 100000 steps or more are normally a better choice.
+
+%\paragraph{{\tt stepEquil}} [number of steps] Duration of initial
equilibration phase, characterized by temperature control and fixed volume.
This is really only useful in simple example runs of pure water systems.
Membrane simulation are typically equilibrated through standard runs in the
NPT ensemble.
+
+\paragraph{{\tt stepLimit}} [number of steps] Total simulation length. See
section~\ref{sec:restarting} about possible ambiguities when restarting a
simulation.
+
+\paragraph{{\tt resetTime}} ({\em logical}) When restarting a simulation,
resets the simulation time to 0.
+
+\paragraph{{\tt doCheckpoint}} ({\em logical}) Activates checkpointing
(Rapaport~\citep{rapa} pp.~500-504). This involves two features: i) if
checkpoint files are available, \brahms will restart the corresponding
simulation; ii) new checkpoint files will be generated and updated every
{\tt stepCheckpoint} steps (see below).
+
+\paragraph{{\tt stepCheckpoint}} [number of steps] Frequency at which
checkpoint files are written (Rapaport~\citep{rapa} pp.~500-504).
+
+\paragraph{{\tt stepPdb}} [number of steps] Frequency at which the system
coordinates, in {\tt pdb} format, are written to the {\tt trajectory.pdb}
output file. This file can be used to visualize the system (for instance
using VMD~\citep{HUMP96}) or to carry out analysis. Warning: a low value of
{\tt stepPdb} can lead to the generation of huge trajectory files. For
example, for membrane simulations, since most of the analysis is carried
out automatically by \brahms while the program is running, a frequency of
100000 can be enough.
+
+\paragraph{{\tt runId}} Simulation identifier (Rapaport~\citep{rapa}
p.~501).
+
+\paragraph{{\tt applyThermostat}} ({\em logical}) Activates
thermostatting; the temperature will be maintained at {\tt extTemperature}
(see below). The temperature-control algorithm used in \brahms is
Berendsen's weak-coupling scheme.~\citep{ber84} The statistical mechanical
ensemble for the weak-coupling thermostat is intermediate between the
canonical and the microcanonical ensembles.~\citep{morishita00}
+
+\paragraph{{\tt extTemperature}} [\textcelsius] ``External'' temperature
of the thermostat. When the thermostat is on ({\tt applyThermostat} set to
1) the system temperature is maintained at this desired value.
+
+\paragraph{{\tt tauT}} [fs] Temperature coupling constant of Berendsen's
weak-coupling scheme.~\citep{ber84} Typically set in relation to {\tt
deltaT}, that is, {\tt tauT} should normally be 10-30 times larger than
{\tt deltaT}. For example, if {\tt deltaT} is set to 15\,fs, {\tt tauT}
should be set to~$\approx200-500$\,fs.
+
+\paragraph{{\tt applyBarostat}} ({\em logical}) Activates barostatting;
the pressure will be maintained at {\tt extPressure} (see below). The
pressure-control algorithm used in \brahms is Berendsen's weak-coupling
scheme.~\citep{ber84}
+
+\paragraph{{\tt extPressure}} [atm] ``External'' pressure of the barostat.
When the barostat is on ({\tt applyBarostat} set to 1) the system pressure
is maintained (on average) at this desired value. Note that it is normal
for the {\em instantaneous} pressure to oscillate significantly, especially
for small systems. The important thing is that the {\em average} value
(over a sufficiently large number of time steps) is kept constant.
+
+\paragraph{{\tt tauP}} [fs] Pressure coupling constant of Berendsen's
weak-coupling scheme.~\citep{ber84} Typically set in relation to {\tt
deltaT}, that is, {\tt tauP} should normally be 20-60 times larger than
{\tt deltaT}.
+
+\paragraph{{\tt flexBox}} ({\em logical}) Allows box flexibility in
response to pressure changes. This should normally be activated for bilayer
simulations. Self-assembly runs might be more stable if {\tt flexBox} is
set to 0.
+
+\paragraph{{\tt keepTetragonal}} ({\em logical}) Keeps the box
``tetragonal'' - the box edges are constrained to remain perpendicular to
each other. {\em This should always be activated when using the barostat},
because currently \brahms cannot deal with non-tetragonal boxes. This
limitation is not a problem for most simulations of systems in the liquid
phase, including fluid-phase bilayers.\footnote{However, non-tetragonal
boxes can be more realistic when simulating solids.}
+
+\paragraph{{\tt keepSquare}} ({\em logical}) Constrains the relative size
of the x and y edges of the simulation box. Typically, this constrains the
membrane interfacial plane (conventionally the xy plane) to remain a
square. {\em This should normally be activated for pre-assembled membrane
simulations}; it does not make them any less realistic (because of
bilayers' ``natural'' homogeneity and symmetry in the xy plane), yet it
prevents potential instabilities (caused by possible box ``thinning''
leading to violations of the minimum image convention).
+
+\paragraph{{\tt rCutLipLip}} [nm] Cutoff radius for nonbonded interactions
within lipid sites and between lipid and water sites. The recommended value
for simulations of lipids modeled with the ELBA force field is 1.2.
+
+
+\paragraph{{\tt rCutWatWat}} [nm] Cutoff radius for nonbonded interactions
between water sites. The recommended value is 0.9.
+
+\paragraph{{\tt rCutSolute}} [nm] Cutoff radius for nonbonded interactions
between solute sites (not currently used).
+
+\paragraph{{\tt rCutSoluteElse}} [nm] Cutoff radius for nonbonded
interactions between solute sites and any other site (not currently used).
+
+\paragraph{{\tt rNebrShell}} [nm] Thickness of the ``shell'' outside the
cutoff sphere used to build the neighbor list (Rapaport~\citep{rapa}
pp.~54-58). ``Typical'' values are 0.1-0.2; optimal values can be found for
each application through trial-and-error refinement tests. This parameter
can affect the accuracy and efficiency of the dynamics integration; see
discussion below for the related parameter {\tt stepNebr}.
+
+\paragraph{{\tt stepNebr}} [number of steps] Neighbor list update
frequency. In other words, the neighbor list will be rebuilt every {\tt
stepNebr} timesteps. Typical values (for a 15-fs timestep) are 5-20. In
general, small values are more likely to guarantee that all interactions
within cutoff range are properly considered, but the frequent
reconstructions of the list will slow down the simulation. On the other
hand, large values of {\tt stepNebr} will increase the simulation speed but
might compromise stability and energy conservation. It is worth testing
empirically which combination of {\tt rNebrShell} and {\tt stepNebr} yields
the best compromise between accuracy (typically in terms of energy
conservation) and efficiency.
+
+\paragraph{{\tt nebrTabFac}} Determines how much storage should be
provided for the neighbor list, per site (Rapaport~\citep{rapa} pp.~54-58).
Typically 100-300. This parameter should not affect simulation speed or
indeed any result.
+
+\paragraph{{\tt removeSystemTranslation}} ({\em logical}) Removes any net
translation of the whole system at every step. This should be normally
activated, to prevent potentially serious artefacts.~\citep{harve98a}
However, this should be off when checking energy conservation in the NVE
ensemble.
+
+\paragraph{{\tt removeMonolayersTranslation}} ({\em logical}) In a
simulation of a lipid bilayer, removes any net translation of each of the
two monolayer (at every step). There is debate whether this operation is
needed/justified.~\citep{patra04a,klauda06b,roark09} This removal should
probably be activated for small systems ($<128$ lipids) and for gel-phase
bilayers, while it should make no difference for large ($>288$ lipids)
membranes in the fluid phase. For sure this should be off when checking
energy conservation. Warning: this operation relies on the assumption that
the bilayer plane is parallel to the xy plane defined by the coordinates'
system; while this is normally the case for preassembled bilayer
simulations in Brahms, self-assembled systems might not be oriented along
the xy plane, in which case {\tt removeMonolayersTranslation} should
definitely be off.
+
+\paragraph{{\tt nSites}} To be set corresponding to the total number of
sites in the simulated system.
+
+\paragraph{{\tt nWaters}} To be set corresponding to the total number of
water sites in the simulated system.
+
+\paragraph{{\tt nDOPCsDSPCs}} To be set corresponding to the total number
of DOPC or DSPC lipids in the simulated system.
+
+\paragraph{{\tt nDOPEs}} To be set corresponding to the total number of
DOPE lipids in the simulated system.
+
+\paragraph{{\tt nLipids}} To be set corresponding to the total number of
lipids in the simulated system.
+
+\paragraph{{\tt nSolutes}} To be set corresponding to the total number of
solutes in the simulated system.
+
+\paragraph{{\tt nTypes}} To be set corresponding to the total number of
site types in the simulated system. Currently there are 7 types in the ELBA
force field.
+
+\paragraph{{\tt region}} [nm nm nm] Used for the generation of a system
from scratch - see section~\ref{sec:initLip}.
+
+\paragraph{{\tt adjustRegion}} ({\em logical}) Changes the box edges to
{\tt regionAdjusted} (see below). Not normally used.
+
+\paragraph{{\tt regionAdjusted}} [nm nm nm] Used to modify the simulation
box edges when restarting a simulation. Not normally used.
+
+\paragraph{{\tt randSeed}} Random number seed (Rapaport~\citep{rapa}
pp.~491-492).
+
+\paragraph{{\tt initHalfCellWat}} Used for the generation of a membrane
system from scratch - see section~\ref{sec:initLip}.
+
+\paragraph{{\tt initUcell}} Used for the generation of a water system from
scratch - see section~\ref{sec:initWat}.
+
+\paragraph{{\tt loadStructure}} Not currently used.
+
+\paragraph{{\tt loadVelocities}} Not currently used.
+
+\paragraph{{\tt centerInputStruct}} Not currently used.
+
+\paragraph{{\tt reCenterBilayer}} ({\em logical}) ``Pulls'' gradually the
bilayer to the origin of the z axis; this can be used after self-assembly
simulations, which typically yield a bilayer which is not in the center of
the simulation box.
+
+\paragraph{{\tt zConstraint}} Not currently used.
+
+\paragraph{{\tt insertSolute}} Not currently used.
+
+\section{{\tt lipid.ff}}
+The input file {\tt lipid.ff} contains the
\underline{f}orce\underline{f}ield parameters of the ELBA model for
coarse-grain lipids.~\cite{orsi11elba} This file is supplied with the
\brahms package and should not be changed, unless the user really wants to
change the force field.
+
+\section{{\tt water.ff}}
+The input file {\tt water.ff} contains the
\underline{f}orce\underline{f}ield parameters of the ELBA model for
coarse-grain water.~\cite{orsi11elba} This file is supplied with the
\brahms package and should not be changed, unless the user really wants to
change the force field.
+
+\section{{\tt brahms.an}}\label{sec:brahms.an}
+The optional input file {\tt brahms.an} controls various
\underline{an}alysis operations that \brahms can carry out ``on the fly'',
that is, while the simulation is running. All parameters of {\tt brahms.an}
are described in the following; subsections collect related sets of
parameters.
+
+\subsection{Region dimensions}\label{sec:regDims}
+
+\paragraph{{\tt writeAreaVol}} ({\em logical}) Write area and volume of
the simulation region at every step on file ({\tt area$\_$volume.dat}). At
the end of the run, these data can be used to calculate the area and volume
compressibility moduli.~\cite{marioDmpcDopc} A script to carry out this
calculation is distributed with the \brahms package, in the directory {\tt
analysisScripts/general}. Open the scripts with any text editor and follow
the usage instructions at the top of the file.
+
+\subsection{Lipid lateral diffusion} \label{sec:lld}
+These parameters are related to the ``lateral'' lipid diffusion process,
that is, the motion of the center of mass of each individual lipid molecule
in the membrane plane (conventionally, the xy plane). To measure diffusion,
\brahms implements the tools described by
Rapaport~\cite{rapa}~(pp.~120-128); please check this reference for more
details.
+Note that the algorithms underlying the diffusion measurements in \brahms
work only for uninterrupted simulations; restarted runs do not retain any
memory from previous (interrupted) diffusion measurements.
+
+\paragraph{{\tt latDiff}} ({\em logical}) Activates lipid lateral
diffusion measurements.
+\paragraph{{\tt nBuffLatDiff}} Number of sets of data being collected at
any time.
+\paragraph{{\tt nValLatDiff}} Number of measurements contributing to the
set used to produce a single unaveraged estimate of the diffusion
coefficient.
+\paragraph{{\tt stepLatDiff}} [number of steps] Measurement frequency.
+\paragraph{{\tt limitLatDiffAv}} Total number of individual estimates used
to produce an average value of the diffusion coefficient; such an average
is written on file.
+\paragraph{{\tt writeLipLatMotion}} ({\em logical}) Writes on file the
mass center coordinates of each lipid in the ``upper'' monolayer every {\tt
stepLatDiff} steps. The file produced can be used to plot and analyze
single lipid lateral traces projected onto the {\em xy} plane. For an
example, see Fig.~6 in Orsi et al.~\cite{marioDmpcDopc} Scripts to produce
such diagrams with the Xmgrace plotting program are distributed with the
Brahms package - see {\tt
analysisScripts/general/lipidDiffusionTraces.txt}. Note that it would not
be possible to obtain the same results from the trajectory file, because
this file contains coordinates that are ``wrapped'' around the periodic
boundaries. Instead, {\tt writeLipLatMotion} generates and updates
auxiliary structures which maintain ``unwrapped'' coordinates throughout
the simulation.
+
+\subsection{Transmembrane profiles}
+
+This section describes the {\tt brahms.an} parameters controlling
measurements of properties as a function of ``depth'' inside the membrane.
The general procedure involves considering ``slices'' of the system along
planes %parallel to the $xy-$plane, i. e.
+perpendicular to the $z$ axis (the interface normal by convention).
+Several bilayer properties are homogeneous inside a particular slice, due
to the intrinsic axial symmetry of the system. %. Hence these properties
depend only on the position along the normal,
+Therefore single curves, {\em profiles} evaluated as a function of $z$,
provide full characterization. Typical membrane profiles are: electron
density, lateral pressure, electric field, water polarization, and
electrostatic potential.
+
+The measurement process for all profiles involve similar parameters, here
generically called {\tt sizeHistProfile}, {\tt stepProfile}, {\tt
limitProfile}. Each profile is constructed as a histogram, with each
histogram ``bin'' corresponding to a particular slice of the system. The
parameter {\tt sizeHistProfile} sets the bin number (which corresponds to
the number of ``slices''). More (fewer) bins yield an increased (decreased)
measurement resolution. The relation between resolution, number of bins and
system size is: $sizeHistProfile\times resolution = zEdge $, with $zEdge$
the length of the simulation box edge perpendicular to the membrane plane
(by convention this is the z-dimension\footnote{For example, a desired
resolution of 0.1\,nm for a box which measures 6.4\,nm in the $z$ dimension
can be obtained by setting {\tt sizeHistProfile} to $zEdge / resolution =
6.4 / 0.1 = 64 $.}).
+The parameter {\tt stepProfile} sets the desired number of steps between
single measurements.\footnote{For example, profiles can be evaluated at
every step by setting {\tt stepProfile} to 1; usually however this is not
necessary, and in fact such a high frequency will slow down the
calculations. More appropriate values of {\tt stepProfile} for ``long''
runs are 100-1000. The ``optimum'' value is to be found empirically through
test runs.} The parameter {\tt limitProfile} sets the number of single
measurements used by \brahms to calculate an average which is then written
on file.\footnote{For example, take a 100\,ns production run, corresponding
to 10\,000\,000 steps with a 10\,fs timestep. Setting {\tt stepProfile} to
10 and {\tt limitProfile} to 10\,000 will produce 100 output files, each
representing an average over a 1-ns ``block'' (corresponding to
$10\times10\,000=100\,000$\,steps). For the same run, setting {\tt
stepProfile} to 100 and {\tt limitProfile} to 10\,000 will produce 10
output files, each representing an average over a 10-ns ``block''
(corresponding to $100\times10\,000=1\,000\,000$\,steps). Note that you
would typically want the total average over the entire simulation; for a
specific value of {\tt stepProfile}, such an average would not depend on
{\tt limitProfile}.}
+
+\subsubsection{Electron density profiles}
+These parameters control the calculation of electron density profiles for
the whole system and for individual site types; see Fig.~2 in Orsi et
al.~\cite{marioDmpcDopc} and Fig.~6 in Orsi et al.~\cite{mario08}
+
+\paragraph{{\tt edp}} ({\em logical}) Activates profile calculation.
+\paragraph{{\tt sizeHistEdp}} Resolution of the electron density profile
histograms.
+\paragraph{{\tt stepEdp}} [number of steps] Interval between individual
profile evaluations (measurement frequency).
+\paragraph{{\tt limitEdp}} Number of individual evaluations used to
produce a single average curve which is then written on file.
+
+\subsubsection{Electrostatic potential profiles}
+These parameters control the calculation of electrostatic potential
profiles for the whole system and for individual site types; see Fig.~4 in
Orsi et al.~\cite{marioDmpcDopc} and Fig.~10 in Orsi et al.~\cite{mario08}
+
+\paragraph{{\tt epp}} ({\em logical}) Activates profile calculation.
+\paragraph{{\tt sizeHistEpp}} Resolution of the electron electrostatic
potential histograms.
+\paragraph{{\tt stepEpp}} [number of steps] Interval between individual
profile evaluations (measurement frequency).
+\paragraph{{\tt limitEpp}} Number of individual evaluations used to
produce a single average curve which is then written on file.
+
+\subsubsection{Lateral pressure profile}
+These parameters control the calculation of the lateral pressure profile;
see Fig.~3 in Orsi et al.~\cite{marioDmpcDopc} and Fig.~7 in Orsi et
al.~\cite{mario08}
+\paragraph{{\tt lpp}} ({\em logical}) Activates profile calculation.
+\paragraph{{\tt sizeHistLpp}} Resolution of the lateral pressure profile
histograms.
+\paragraph{{\tt stepLpp}} [number of steps] Interval between individual
profile evaluations (measurement frequency).
+\paragraph{{\tt limitLpp}} Number of individual evaluations used to
produce a single average curve which is then written on file.
+
+\subsubsection{Water polarization profile}
+These parameters control the calculation of the water polarization
profile; see Fig.~9 in Orsi et al.~\cite{mario08}
+\paragraph{{\tt wpp}} ({\em logical}) Activates profile calculation.
+\paragraph{{\tt sizeHistWpp}} Resolution of the water polarization profile
histograms.
+\paragraph{{\tt stepWpp}} [number of steps] Interval between individual
profile evaluations (measurement frequency).
+\paragraph{{\tt limitWpp}} Number of individual evaluations used to
produce a single average curve which is then written on file.
+
+\subsection{Radial distribution function in pure water systems}
+
+\brahms implements the RDF measurement method from
Rapaport~\cite{rapa}~(pp.~222-225).
+
+\paragraph{{\tt rdfWat}} ({\em logical}) Activates RDF calculation.
+\paragraph{{\tt rangeWatRdf}} [nm] Upper limit of RDF measurement.
+\paragraph{{\tt sizeHistWatRdf}} Resolution of the RDF histograms.
+\paragraph{{\tt stepWatRdf}} [number of steps] Interval between individual
RDF evaluations.
+\paragraph{{\tt limitWatRdf}} Number of individual evaluations used to
produce a single average which is then written on file.
+
+\subsection{Translational self-diffusion and rotational diffusion in pure
water systems}
+\brahms implements the diffusion measurement methods from
Rapaport~\cite{rapa}~(pp.~124-128, 226).
+\paragraph{{\tt diffusion}} ({\em logical}) Activates diffusion
calculation.
+\paragraph{{\tt nBuffDiffuse}} number of sets of data being collected at
any time.
+\paragraph{{\tt nValDiffuse}} Number of measurements contributing to the
set used to produce a single unaveraged estimate of the diffusion
coefficient.
+\paragraph{{\tt stepDiffuse}} [number of steps] Interval between
individual diffusion evaluations.
+\paragraph{{\tt limitDiffuseAv}} Number of individual evaluations used to
produce a single average which is then written on file.
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/introduction.aux Wed Dec 21 02:20:08 2011
@@ -0,0 +1,41 @@
+\relax
+\citation{rapa}
+\citation{gmx31}
+\citation{mouritsen}
+\citation{orsi11elba}
+\citation{dullw97a}
+\FN@pp@footnotehinttrue
+\@writefile{toc}{\contentsline {paragraph}{The Art of Molecular Dynamics
Simulation}{2}}
+\@writefile{toc}{\contentsline {paragraph}{Gromacs manual}{2}}
+\@writefile{toc}{\contentsline {paragraph}{Life - as a matter of
fat\nobreakspace {}\cite {mouritsen}}{2}}
+\@writefile{toc}{\contentsline {paragraph}{Membrane force field}{2}}
+\@writefile{toc}{\contentsline {paragraph}{Rigid-body integration}{2}}
+\FN@pp@footnotehinttrue
+\@setckpt{introduction}{
+\setcounter{page}{3}
+\setcounter{equation}{0}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{0}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{chapter}{0}
+\setcounter{section}{0}
+\setcounter{subsection}{0}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{0}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{r@tfl@t}{0}
+\setcounter{subfigure}{0}
+\setcounter{lofdepth}{1}
+\setcounter{subtable}{0}
+\setcounter{lotdepth}{1}
+\setcounter{pp@next@reset}{1}
+\setcounter{@fnserial}{0}
+\setcounter{NAT@ctr}{0}
+}
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/introduction.tex Wed Dec 21 02:20:08 2011
@@ -0,0 +1,23 @@
+\chapter*{Introduction}
+
+%Many fundamental features of \brahms have been developed by following
accepted standards and sometimes by merging together existing pieces of
work.\footnote{This should hardly be surprising, given that molecular
dynamics is a very simple technique (requiring little more than basic
Newtonian physics and a computer) which has been around for several decades
now. There are in fact many codes around, together with several textbooks
and countless articles. Clearly, it is much better to ``stand on the
shoulders of giants'' than ``reinventing the wheel''.}
+
+The \brahms manual is organized in two parts. Part I is the ``proper''
manual; it describes how to run \brahms and what to do with the data
generated. Part II provides background material on several topics related
to the \brahms project.
+
+\noindent \\The following paragraphs point to references which can be very
useful to fully understand various aspects of the \brahms project.
+
+\paragraph{The Art of Molecular Dynamics Simulation} This excellent book
+by D.C. Rapaport~\cite{rapa} constitutes the basis of many crucial
components of \brahms. There is no better introduction to \brahms than this
textbook and associated
+software. \brahms users are invited to study chapters 1-6, 8 and 9, and
run the examples. \brahms developers should also consider chapters 17 and
18.
+
+\paragraph{Gromacs manual} The manual of the popular Gromacs
code~\cite{gmx31} contains some material which is relevant to Brahms. In
particular, \brahms adopts the same
+convention regarding units. This reference is also recommended as a good
general introduction to practical aspects of molecular dynamics simulations.
+
+\paragraph{Life - as a matter of fat~\cite{mouritsen}} Good book on lipid
membranes, covering both modeling and experimental aspects; this is a very
useful and relevant reference that touches on many aspects of the \brahms
project.
+
+\paragraph{Membrane force field} \brahms implements the coarse-grain ELBA
force field, which is described in the literature.~\cite{orsi11elba}
+
+\paragraph{Rigid-body integration} The efficiency of {\sc brahms} has been
optimized through the implementation of the advanced molecular dynamics
integration
+scheme invented by Dullweber et al;~\cite{dullw97a} this reference also
covers some general background on rigid-body dynamics, which is a
non-standard feature of
+molecular dynamics (most available codes, including for example Gromacs,
Namd and Charmm, cannot simulate rigid body dynamics). See also
section~\ref{sec:rigidBodies}.
+
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/ltx.sh Wed Dec 21 02:20:08 2011
@@ -0,0 +1,8 @@
+#!/bin/bash
+latex main
+bibtex main
+makeindex main
+latex main
+latex main
+dvipdf main.dvi
+mv main.pdf ../manual.pdf
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.aux Wed Dec 21 02:20:08 2011
@@ -0,0 +1,155 @@
+\relax
+\bibstyle{biophysj}
+\providecommand {\FN@pp@footnotehinttrue }{}
+\providecommand {\FN@pp@footnote@aux }[2]{}
+\@input{acknowledgement.aux}
+\FN@pp@footnotehinttrue
+\FN@pp@footnotehinttrue
+\FN@pp@footnotehinttrue
+\FN@pp@footnotehinttrue
+\FN@pp@footnotehinttrue
+\@input{introduction.aux}
+\FN@pp@footnotehinttrue
+\@writefile{toc}{\contentsline {part}{I\hspace {1em}Running Brahms}{3}}
+\@input{input/inputParameters.aux}
+\FN@pp@footnotehinttrue
+\@input{runningSimulations/run.aux}
+\FN@pp@footnotehinttrue
+\@input{output/out.aux}
+\FN@pp@footnotehinttrue
+\@input{visualization/vis.aux}
+\FN@pp@footnotehinttrue
+\@input{analysis/an.aux}
+\FN@pp@footnotehinttrue
+\@input{bench/benchmarks.aux}
+\FN@pp@footnotehinttrue
+\FN@pp@footnotehinttrue
+\@writefile{toc}{\contentsline {part}{II\hspace {1em}Background}{21}}
+\@input{md/md.aux}
+\FN@pp@footnotehinttrue
+\@input{biophys/biophys.aux}
+\FN@pp@footnotehinttrue
+\bibdata{/home/orsi/biblio.bib}
+\bibcite{orsi11elba}{{1}{2011}{{Orsi and Essex}}{{}}}
+\bibcite{rapa}{{2}{2004}{{Rapaport}}{{}}}
+\bibcite{dullw97a}{{3}{1997}{{Dullweber et~al.}}{{Dullweber, Leimkuhler,
and McLachlan}}}
+\bibcite{mario08}{{4}{2008}{{Orsi et~al.}}{{Orsi, Haubertin, Sanderson,
and Essex}}}
+\bibcite{marioSmall}{{5}{2009}{{Orsi et~al.}}{{Orsi, Sanderson, and
Essex}}}
+\bibcite{marioDmpcDopc}{{6}{2010}{{Orsi et~al.}}{{Orsi, Michel, and
Essex}}}
+\bibcite{marioDH}{{7}{2010}{{Orsi and Essex}}{{}}}
+\bibcite{marioTriclos}{{8}{2011}{{Orsi et~al.}}{{Orsi, Noro, and Essex}}}
+\bibcite{gmx31}{{9}{2001}{{van~der Spoel et~al.}}{{van~der Spoel, van
Buuren, Apol, Meulen\discretionary {-}{}{}hoff, Tieleman, Sij\discretionary
{-}{}{}bers, Hess, Feenstra, Lindahl, van Drunen, and Berendsen}}}
+\bibcite{mouritsen}{{10}{2005}{{Mouritsen}}{{}}}
+\bibcite{winger09}{{11}{2009}{{Winger et~al.}}{{Winger, Trzesniak, Baron,
and van Gunsteren}}}
+\bibcite{HUMP96}{{12}{1996}{{Humphrey et~al.}}{{Humphrey, Dalke, and
Schulten}}}
+\bibcite{ber84}{{13}{1984}{{Berendsen et~al.}}{{Berendsen, Postma, van
Gunsteren, Di~Nola, and Haak}}}
+\bibcite{morishita00}{{14}{2000}{{Morishita}}{{}}}
+\bibcite{harve98a}{{15}{1998}{{Harvey et~al.}}{{Harvey, Tan, and
Cheatham~III}}}
+\bibcite{patra04a}{{16}{2004}{{Patra et~al.}}{{Patra, Karttunen, Hyvonen,
Falck, and Vattulainen}}}
+\bibcite{klauda06b}{{17}{2006}{{Klauda et~al.}}{{Klauda, Brooks, and
Pastor}}}
+\bibcite{roark09}{{18}{2009}{{Roark and Feller}}{{}}}
+\bibcite{allen}{{19}{1987}{{Allen and Tildesley}}{{}}}
+\bibcite{leach}{{20}{2001}{{Leach}}{{}}}
+\bibcite{frenkel}{{21}{2002}{{Frenkel and Smit}}{{}}}
+\bibcite{schlick}{{22}{2002}{{Schlick}}{{}}}
+\bibcite{luck90}{{23}{1990}{{Luckhurst et~al.}}{{Luckhurst, Stephens, and
Phippen}}}
+\bibcite{leimkuhler}{{24}{2004}{{Leimkuhler and Reich}}{{}}}
+\bibcite{tuckerman00}{{25}{2000}{{Tuckerman and Martyna}}{{}}}
+\bibcite{mclac93a}{{26}{1993}{{McLachlan}}{{}}}
+\bibcite{grays94a}{{27}{1994}{{Gray et~al.}}{{Gray, Noid, and Sumpter}}}
+\bibcite{mille02a}{{28}{2002}{{Miller~III et~al.}}{{Miller~III,
Eleftheriou, Pattnaik, Ndirango, Newns, and Martyna}}}
+\bibcite{omely02b}{{29}{2002}{{Omelyan et~al.}}{{Omelyan, Mryglod, and
Folk}}}
+\bibcite{prapr05a}{{30}{2005}{{Praprotnik and Janezic}}{{}}}
+\bibcite{allen04}{{31}{2004}{{Allen}}{{}}}
+\FN@pp@footnotehinttrue
+\bibcite{knuth68}{{32}{1968}{{Knuth}}{{}}}
+\bibcite{verlet67}{{33}{1967}{{Verlet}}{{}}}
+\bibcite{thompson09}{{34}{2009}{{Thompson et~al.}}{{Thompson, Plimpton,
and Mattson}}}
+\bibcite{alejandre95}{{35}{1995}{{Alejandre et~al.}}{{Alejandre,
Tildesley, and Chapela}}}
+\bibcite{cheng96}{{36}{1996}{{Cheng and Merz}}{{}}}
+\bibcite{brown95}{{37}{1995}{{Brown and Neyertz}}{{}}}
+\bibcite{carpenter02}{{38}{2002}{{Carpenter}}{{}}}
+\bibcite{gulli04}{{39}{2004}{{Gullingsrud and Schulten}}{{}}}
+\bibcite{veld03}{{40}{2003}{{in~`t Veld and Rutledge}}{{}}}
+\bibcite{procacci97}{{41}{1997}{{Procacci et~al.}}{{Procacci, Darden,
Paci, and Marchi}}}
+\bibcite{refson}{{42}{2001}{{Refson}}{{}}}
+\bibcite{bussi09}{{43}{2009}{{Bussi et~al.}}{{Bussi, Zykova-Timan, and
Parrinello}}}
+\bibcite{voet}{{44}{2004}{{Voet and Voet}}{{}}}
+\bibcite{simmons}{{45}{}{{sim}}{{}}}
+\bibcite{dowhan}{{46}{2004}{{Dowhan and Bogdanov}}{{}}}
+\bibcite{berg}{{47}{2002}{{Berg et~al.}}{{Berg, Tymoczko, and Stryer}}}
+\bibcite{simons00}{{48}{2000}{{Simons and Toomre}}{{}}}
+\bibcite{ualr}{{49}{}{{ual}}{{}}}
+\bibcite{scq}{{50}{}{{scq}}{{}}}
+\bibcite{steve}{{51}{}{{ste}}{{}}}
+\bibcite{southall02}{{52}{2002}{{Southall et~al.}}{{Southall, Dill, and
Haymet}}}
+\bibcite{chandler05}{{53}{2005}{{Chandler}}{{}}}
+\bibcite{hamley}{{54}{2007}{{Hamley}}{{}}}
+\bibcite{nagle00a}{{55}{2000}{{Nagle and Tristram-{N}agle}}{{}}}
+\bibcite{koeni97a}{{56}{1997}{{Koenig et~al.}}{{Koenig, Strey, and
Gawrisch}}}
+\bibcite{feller-dppc}{{57}{}{{fel}}{{}}}
+\bibcite{akuts91a}{{58}{1991}{{Akutsu and Nagamori}}{{}}}
+\bibcite{jseelig74}{{59}{1974}{{Seelig and Niederberger}}{{}}}
+\bibcite{cevc}{{60}{1987}{{Cevc and Marsh}}{{}}}
+\bibcite{janiak79}{{61}{1979}{{Janiak et~al.}}{{Janiak, Small, and
Shipley}}}
+\bibcite{templer98}{{62}{1998}{{Templer et~al.}}{{Templer, Castle, Curran,
Rumbles, and Klug}}}
+\bibcite{sedd95}{{63}{1995}{{Seddon and Templer}}{{}}}
+\bibcite{yang03}{{64}{2003}{{Yang et~al.}}{{Yang, Ding, and Huang}}}
+\bibcite{kozlovsky04}{{65}{2004}{{Kozlovsky et~al.}}{{Kozlovsky, Efrat,
Siegel, and Kozlov}}}
+\bibcite{siegel04}{{66}{2004}{{Siegel and Kozlov}}{{}}}
+\bibcite{shearman06}{{67}{2006}{{Shearman et~al.}}{{Shearman, Ces,
Templer, and Seddon}}}
+\bibcite{kamo06}{{68}{2006}{{Kamo et~al.}}{{Kamo, Nakano, Kuroda, and
Handa}}}
+\bibcite{curnow04}{{69}{2004}{{Curnow et~al.}}{{Curnow, Lorch,
Charalambous, and Booth}}}
+\bibcite{mohr05}{{70}{2005}{{Mohr et~al.}}{{Mohr, Gribble, Lin, Eckenhoff,
and Cantor}}}
+\bibcite{curran99}{{71}{1999}{{Curran et~al.}}{{Curran, Templer, and
Booth}}}
+\bibcite{meijberg02}{{72}{2002}{{Meijberg and Booth}}{{}}}
+\bibcite{brink04}{{73}{2004}{{van den Brink-van~der Laan et~al.}}{{van den
Brink-van~der Laan, Killian, and de~Kruijff}}}
+\bibcite{hong04}{{74}{2004}{{Hong and Tamm}}{{}}}
+\bibcite{bowie05}{{75}{2005}{{Bowie}}{{}}}
+\bibcite{attard00}{{76}{2000}{{Attard et~al.}}{{Attard, Templer, Smith,
Hunt, and Jackowski}}}
+\bibcite{davies01}{{77}{2001}{{Davies et~al.}}{{Davies, Epand, Kraayenhof,
and Cornell}}}
+\bibcite{fanani04}{{78}{2004}{{Fanani et~al.}}{{Fanani, Topham, Walsh, and
Epand}}}
+\bibcite{sen91}{{79}{1991}{{Sen et~al.}}{{Sen, Isac, and Hui}}}
+\bibcite{ruiz98}{{80}{1998}{{Ruiz-{A}rguello et~al.}}{{Ruiz-{A}rguello,
Goni, and Alonso}}}
+\bibcite{botelho02}{{81}{2002}{{Botelho et~al.}}{{Botelho, Gibson,
Thurmond, Wang, and Brown}}}
+\bibcite{wang02}{{82}{2002}{{Wang et~al.}}{{Wang, Botelho, Martinez, and
Brown}}}
+\bibcite{botelho06}{{83}{2006}{{Botelho et~al.}}{{Botelho, Huber, Sakmar,
and Brown}}}
+\bibcite{keller93}{{84}{1993}{{Keller et~al.}}{{Keller, Bezrukov, Gruner,
Tate, Vodyanoy, and Parsegian}}}
+\bibcite{perozo02}{{85}{2002}{{Perozo et~al.}}{{Perozo, Kloda, Cortes, and
Martinac}}}
+\bibcite{jensen04}{{86}{2004}{{Jensen et~al.}}{{Jensen, Mouritsen, and
Peters}}}
+\bibcite{rosto06}{{87}{2006}{{Rostovtseva et~al.}}{{Rostovtseva, Kazemi,
Weinrich, and Bezrukov}}}
+\bibcite{helfrich73}{{88}{1973}{{Helfrich}}{{}}}
+\bibcite{marsh06}{{89}{2006}{{Marsh}}{{}}}
+\bibcite{shinoda98}{{90}{1998}{{Shinoda et~al.}}{{Shinoda, Shimizu, and
Okazaki}}}
+\bibcite{clarke97}{{91}{1997}{{Clarke}}{{}}}
+\bibcite{clarke01}{{92}{2001}{{Clarke}}{{}}}
+\bibcite{cladera01}{{93}{2001}{{Cladera et~al.}}{{Cladera, Martin, and
O'{S}hea}}}
+\bibcite{cladera99}{{94}{1999}{{Cladera et~al.}}{{Cladera, Martin,
Ruysschaert, and O'{S}hea}}}
+\bibcite{franklin93}{{95}{1993}{{Franklin and Cafiso}}{{}}}
+\bibcite{starke05}{{96}{2005}{{Starke-{P}eterkovic
et~al.}}{{Starke-{P}eterkovic, Turner, Else, and Clarke}}}
+\bibcite{rokitskaya02}{{97}{2002}{{Rokitskaya et~al.}}{{Rokitskaya,
Kotova, and Antonenko}}}
+\bibcite{maggio99}{{98}{1999}{{Maggio}}{{}}}
+\bibcite{cladera98}{{99}{1998}{{Cladera and O'{S}hea}}{{}}}
+\bibcite{gelbart00}{{100}{2000}{{{Gelbart} et~al.}}{{{Gelbart},
{Bruinsma}, {Pincus}, and {Parsegian}}}}
+\bibcite{alakoskela01}{{101}{2001}{{Alakoskela and Kinnunen}}{{}}}
+\bibcite{cladera03}{{102}{2003}{{Cladera et~al.}}{{Cladera, O'{S}hea,
Hadgraft, and Valenta}}}
+\bibcite{cafiso98}{{103}{1998}{{Cafiso}}{{}}}
+\bibcite{qin95}{{104}{1995}{{Qin et~al.}}{{Qin, Szabo, and Cafiso}}}
+\bibcite{alakoskela04}{{105}{2004}{{Alakoskela et~al.}}{{Alakoskela,
Soderlund, Holopainen, and Kinnunen}}}
+\bibcite{asawakarn01}{{106}{2001}{{Asawakarn et~al.}}{{Asawakarn, Cladera,
and O'{S}hea}}}
+\bibcite{oshea03}{{107}{2003}{{O'{S}hea}}{{}}}
+\bibcite{luker01}{{108}{2001}{{Luker et~al.}}{{Luker, Flagg, Sha, Luker,
Pica, Nichols, and Piwnica-{W}orms}}}
+\bibcite{gawrisch92}{{109}{1992}{{Gawrisch et~al.}}{{Gawrisch, Ruston,
Zimmerberg, Parsegian, Rand, and Fuller}}}
+\bibcite{schamberger02}{{110}{2002}{{Schamberger and Clarke}}{{}}}
+\bibcite{lairion04}{{111}{2004}{{Lairion and Disalvo}}{{}}}
+\bibcite{wang06}{{112}{2006}{{Wang et~al.}}{{Wang, Bose, and Sigworth}}}
+\bibcite{sonnleitner99}{{113}{1999}{{Sonnleitner et~al.}}{{Sonnleitner,
Schutz, and Schmidt}}}
+\bibcite{tabony91}{{114}{1991}{{Tabony and Perly}}{{}}}
+\bibcite{filip03b}{{115}{2003}{{Filippov et~al.}}{{Filippov, Or{\"a}dd,
and Lindblom}}}
+\bibcite{almeida92}{{116}{1992}{{Almeida et~al.}}{{Almeida, Vaz, and
Thompson}}}
+\bibcite{vaz91}{{117}{1991}{{Vaz and Almeida}}{{}}}
+\bibcite{cohen59}{{118}{1959}{{Cohen and Turnbull}}{{}}}
+\bibcite{turnbull61}{{119}{1961}{{Turnbull and Cohen}}{{}}}
+\bibcite{turnbull70}{{120}{1970}{{Turnbull and Cohen}}{{}}}
+\bibcite{oleary87}{{121}{1987}{{O'{L}eary}}{{}}}
+\FN@pp@footnotehinttrue
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.bbl Wed Dec 21 02:20:08 2011
@@ -0,0 +1,713 @@
+\begin{thebibliography}{121}
+\providecommand{\url}[1]{\texttt{#1}}
+\providecommand{\urlprefix}{ }
+
+\bibitem[Orsi and Essex(2011)]{orsi11elba}
+Orsi, M., and J.~W. Essex, 2011.
+\newblock The ELBA Force Field for Coarse-Grain Modeling of Lipid
Membranes.
+\newblock \emph{PLoS ONE} 6:e28637.
+
+\bibitem[Rapaport(2004)]{rapa}
+Rapaport, D.~C., 2004.
+\newblock The art of molecular dynamics simulation.
+\newblock Cambridge University Press, Cambridge, 2nd edition.
+
+\bibitem[Dullweber et~al.(1997)Dullweber, Leimkuhler, and
McLachlan]{dullw97a}
+Dullweber, A., B.~Leimkuhler, and R.~McLachlan, 1997.
+\newblock Symplectic splitting methods for rigid body molecular dynamics.
+\newblock \emph{J. Chem. Phys.} 107:5840--5851.
+
+\bibitem[Orsi et~al.(2008)Orsi, Haubertin, Sanderson, and Essex]{mario08}
+Orsi, M., D.~Y. Haubertin, W.~E. Sanderson, and J.~W. Essex, 2008.
+\newblock A quantitative coarse-grain model for lipid bilayers.
+\newblock \emph{J. Phys. Chem. B} 112:802--815.
+
+\bibitem[Orsi et~al.(2009)Orsi, Sanderson, and Essex]{marioSmall}
+Orsi, M., W.~E. Sanderson, and J.~W. Essex, 2009.
+\newblock Permeability of small molecules through a lipid bilayer: a
multiscale
+ simulation study.
+\newblock \emph{J. Phys. Chem. B} 113:12019--12029.
+
+\bibitem[Orsi et~al.(2010)Orsi, Michel, and Essex]{marioDmpcDopc}
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+ Bezrukov]{rosto06}
+Rostovtseva, T.~K., N.~Kazemi, M.~Weinrich, and S.~M. Bezrukov, 2006.
+\newblock Voltage gating of VDAC is regulated by nonlamellar lipids of
+ mitochondrial membranes.
+\newblock \emph{J. Biol. Chem.} 281:37496--37506.
+
+\bibitem[Helfrich(1973)]{helfrich73}
+Helfrich, W., 1973.
+\newblock Elastic properties of lipid bilayers - theory and possible
+ experiments.
+\newblock \emph{Z Naturforsch} 28c:693--703.
+
+\bibitem[Marsh(2006)]{marsh06}
+Marsh, D., 2006.
+\newblock Elastic curvature constants of lipid monolayers and bilayers.
+\newblock \emph{Chem. Phys. Lipids} 144:146--159.
+
+\bibitem[Shinoda et~al.(1998)Shinoda, Shimizu, and Okazaki]{shinoda98}
+Shinoda, W., M.~Shimizu, and S.~Okazaki, 1998.
+\newblock Molecular dynamics study on electrostatic properties of a lipid
+ bilayer: Polarization, electrostatic potential, and the effects on
structure
+ and dynamics of water near the interface.
+\newblock \emph{J. Phys. Chem. B} 102:6647--6654.
+
+\bibitem[Clarke(1997)]{clarke97}
+Clarke, R.~J., 1997.
+\newblock Effect of lipid structure on the dipole potential of
+ phosphatidylcholine bilayers.
+\newblock \emph{Biochim. Biophys. Acta} 1327:269--278.
+
+\bibitem[Clarke(2001)]{clarke01}
+Clarke, R.~J., 2001.
+\newblock The dipole potential of phospholipid membranes and methods for
its
+ detection.
+\newblock \emph{Adv. Colloid Interface Sci.} 89:263--281.
+
+\bibitem[Cladera et~al.(2001)Cladera, Martin, and O'{S}hea]{cladera01}
+Cladera, J., I.~Martin, and P.~O'{S}hea, 2001.
+\newblock The fusion domain of {HIV} gp41 interacts specifically with
heparan
+ sulfate on the T-lymphocyte cell surface.
+\newblock \emph{Embo J.} 20:19--26.
+
+\bibitem[Cladera et~al.(1999)Cladera, Martin, Ruysschaert, and
+ O'{S}hea]{cladera99}
+Cladera, J., I.~Martin, J.~M. Ruysschaert, and P.~O'{S}hea, 1999.
+\newblock Characterization of the sequence of interactions of the fusion
domain
+ of the simian immunodeficiency virus with membranes - Role of the
membrane
+ dipole potential.
+\newblock \emph{J. Biol. Chem.} 274:29951--29959.
+
+\bibitem[Franklin and Cafiso(1993)]{franklin93}
+Franklin, J.~C., and D.~S. Cafiso, 1993.
+\newblock Internal electrostatic potentials in bilayers: measuring and
+ controlling dipole potentials in lipid vesicles.
+\newblock \emph{Biophys. J.} 65:289--299.
+
+\bibitem[Starke-{P}eterkovic et~al.(2005)Starke-{P}eterkovic, Turner,
Else, and
+ Clarke]{starke05}
+Starke-{P}eterkovic, T., N.~Turner, P.~L. Else, and R.~J. Clarke, 2005.
+\newblock Electric field strength of membrane lipids from vertebrate
species:
+ membrane lipid composition and {N}a$^+$-{K}$^+$-{ATP}ase molecular
activity.
+\newblock \emph{Am. J. Physiol. Regul. Integr. Comp. Physiol.}
288:R663--R670.
+
+\bibitem[Rokitskaya et~al.(2002)Rokitskaya, Kotova, and
+ Antonenko]{rokitskaya02}
+Rokitskaya, T.~I., E.~A. Kotova, and Y.~N. Antonenko, 2002.
+\newblock Membrane dipole potential modulates proton conductance through
+ gramicidin channel: movement of negative ionic defects inside the
channel.
+\newblock \emph{Biophys. J.} 82:865--873.
+
+\bibitem[Maggio(1999)]{maggio99}
+Maggio, B., 1999.
+\newblock Modulation of phospholipase {A}$_2$ by electrostatic fields and
+ dipole potential of glycosphingolipids in monolayers.
+\newblock \emph{J. Lipid Res.} 40:930--939.
+
+\bibitem[Cladera and O'{S}hea(1998)]{cladera98}
+Cladera, J., and P.~O'{S}hea, 1998.
+\newblock Intramembrane molecular dipoles affect the membrane insertion and
+ folding of a model amphiphilic peptide.
+\newblock \emph{Biophys. J.} 74:2434--2442.
+
+\bibitem[{Gelbart} et~al.(2000){Gelbart}, {Bruinsma}, {Pincus}, and
+ {Parsegian}]{gelbart00}
+{Gelbart}, W.~M., R.~F. {Bruinsma}, P.~A. {Pincus}, and V.~A. {Parsegian},
+ 2000.
+\newblock {DNA-inspired electrostatics}.
+\newblock \emph{Physics Today} 53:38--44.
+
+\bibitem[Alakoskela and Kinnunen(2001)]{alakoskela01}
+Alakoskela, J.-M.~I., and P.~K.~J. Kinnunen, 2001.
+\newblock Control of a redox reaction on lipid bilayer surfaces by membrane
+ dipole potential.
+\newblock \emph{Biophys. J.} 80:294--304.
+
+\bibitem[Cladera et~al.(2003)Cladera, O'{S}hea, Hadgraft, and
+ Valenta]{cladera03}
+Cladera, J., P.~O'{S}hea, J.~Hadgraft, and C.~Valenta, 2003.
+\newblock Influence of molecular dipoles on human skin permeability: use of
+ 6-ketocholestanol to enhance the transdermal delivery of bacitracin.
+\newblock \emph{J. Pharm. Sci.} 92:1018--1027.
+
+\bibitem[Cafiso(1998)]{cafiso98}
+Cafiso, D.~S., 1998.
+\newblock Dipole potentials and spontaneous curvature: membrane properties
that
+ could mediate anesthesia.
+\newblock \emph{Toxicol. Lett.} 101:431--439.
+
+\bibitem[Qin et~al.(1995)Qin, Szabo, and Cafiso]{qin95}
+Qin, Z.~H., G.~Szabo, and D.~S. Cafiso, 1995.
+\newblock Anesthetics reduce the magnitude of the membrane dipole
potential -
+ measurements in lipid vesicles using voltage-sensitive spin probes.
+\newblock \emph{Biochemistry} 34:5536--5543.
+
+\bibitem[Alakoskela et~al.(2004)Alakoskela, Soderlund, Holopainen, and
+ Kinnunen]{alakoskela04}
+Alakoskela, J.-M.~I., T.~Soderlund, J.~M. Holopainen, and P.~K.~J.
Kinnunen,
+ 2004.
+\newblock Dipole potential and head-group spacing are determinants for the
+ membrane partitioning of pregnanolone.
+\newblock \emph{Mol. Pharmacol.} 66:161--168.
+
+\bibitem[Asawakarn et~al.(2001)Asawakarn, Cladera, and
O'{S}hea]{asawakarn01}
+Asawakarn, T., J.~Cladera, and P.~O'{S}hea, 2001.
+\newblock Effects of the membrane dipole potential on the interaction of
+ saquinavir with phospholipid membranes and plasma membrane receptors of
+ caco-2 cells.
+\newblock \emph{J. Biol. Chem.} 276:38457--38463.
+
+\bibitem[O'{S}hea(2003)]{oshea03}
+O'{S}hea, P., 2003.
+\newblock Intermolecular interactions with/within cell membranes and the
+ trinity of membrane potentials: kinetics and imaging.
+\newblock \emph{Biochem. Soc. Trans.} 31:990--996.
+
+\bibitem[Luker et~al.(2001)Luker, Flagg, Sha, Luker, Pica, Nichols, and
+ Piwnica-{W}orms]{luker01}
+Luker, G.~D., T.~P. Flagg, Q.~Sha, K.~E. Luker, C.~M. Pica, C.~G. Nichols,
and
+ D.~Piwnica-{W}orms, 2001.
+\newblock MDR1 P-glycoprotein reduces influx of substrates without
affecting
+ membrane potential.
+\newblock \emph{J. Biol. Chem.} 276:49053--49060.
+
+\bibitem[Gawrisch et~al.(1992)Gawrisch, Ruston, Zimmerberg, Parsegian,
Rand,
+ and Fuller]{gawrisch92}
+Gawrisch, K., D.~Ruston, J.~Zimmerberg, V.~A. Parsegian, R.~P. Rand, and
+ N.~Fuller, 1992.
+\newblock Membrane dipole potentials, hydration forces, and the ordering of
+ water at membrane surfaces.
+\newblock \emph{Biophys. J.} 61:1213--1223.
+
+\bibitem[Schamberger and Clarke(2002)]{schamberger02}
+Schamberger, J., and R.~J. Clarke, 2002.
+\newblock Hydrophobic ion hydration and the magnitude of the dipole
potential.
+\newblock \emph{Biophys. J.} 82:3081--3088.
+
+\bibitem[Lairion and Disalvo(2004)]{lairion04}
+Lairion, F., and E.~A. Disalvo, 2004.
+\newblock Effect of phloretin on the dipole potential of
phosphatidylcholine,
+ phosphatidylethanolamine, and phosphatidylglycerol monolayers.
+\newblock \emph{Langmuir} 20:9151--9155.
+
+\bibitem[Wang et~al.(2006)Wang, Bose, and Sigworth]{wang06}
+Wang, L., P.~S. Bose, and F.~J. Sigworth, 2006.
+\newblock Using cryo-{EM} to measure the dipole potential of a lipid
membrane.
+\newblock \emph{Proc. Natl. Acad. Sci. U.S.A.} 103:18528--18533.
+
+\bibitem[Sonnleitner et~al.(1999)Sonnleitner, Schutz, and
+ Schmidt]{sonnleitner99}
+Sonnleitner, A., G.~J. Schutz, and T.~Schmidt, 1999.
+\newblock Free Brownian motion of individual lipid molecules in
biomembranes.
+\newblock \emph{Biophys. J.} 77:2638--2642.
+
+\bibitem[Tabony and Perly(1991)]{tabony91}
+Tabony, J., and B.~Perly, 1991.
+\newblock Quasielastic neutron scattering measurements of fast local
+ translational diffusion of lipid molecules in phospholipid bilayers.
+\newblock \emph{Biochim. Biophys. Acta} 1063:67--72.
+
+\bibitem[Filippov et~al.(2003)Filippov, Or{\"a}dd, and Lindblom]{filip03b}
+Filippov, A., G.~Or{\"a}dd, and G.~Lindblom, 2003.
+\newblock Influence of cholesterol and water content on phospholipid
lateral
+ diffusion in bilayers.
+\newblock \emph{Langmuir} 19:6397--6400.
+
+\bibitem[Almeida et~al.(1992)Almeida, Vaz, and Thompson]{almeida92}
+Almeida, P. F.~F., W.~L.~C. Vaz, and T.~E. Thompson, 1992.
+\newblock Lateral diffusion in the liquid phases of
+ dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume
+ analysis.
+\newblock \emph{Biochemistry} 31:6739--6747.
+
+\bibitem[Vaz and Almeida(1991)]{vaz91}
+Vaz, W. L.~C., and P.~F. Almeida, 1991.
+\newblock Microscopic versus macroscopic diffusion in one-component fluid
phase
+ lipid bilayer membranes.
+\newblock \emph{Biophys. J.} 60:1553--1554.
+
+\bibitem[Cohen and Turnbull(1959)]{cohen59}
+Cohen, M.~H., and D.~Turnbull, 1959.
+\newblock Molecular transport in liquids and glasses.
+\newblock \emph{J. Chem. Phys.} 31:1164.
+
+\bibitem[Turnbull and Cohen(1961)]{turnbull61}
+Turnbull, D., and M.~H. Cohen, 1961.
+\newblock Free-volume model of the amorphous phase: glass transition.
+\newblock \emph{J. Chem. Phys.} 34:120.
+
+\bibitem[Turnbull and Cohen(1970)]{turnbull70}
+Turnbull, D., and M.~H. Cohen, 1970.
+\newblock On free-volume model of liquid-glass transition.
+\newblock \emph{J. Chem. Phys.} 52:3038.
+
+\bibitem[O'{L}eary(1987)]{oleary87}
+O'{L}eary, T.~J., 1987.
+\newblock Lateral diffusion of lipids in complex biological membranes.
+\newblock \emph{Proc. Natl. Acad. Sci. U.S.A.} 84:429--433.
+
+\end{thebibliography}
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.blg Wed Dec 21 02:20:08 2011
@@ -0,0 +1,561 @@
+This is BibTeX, Version 0.99c (Web2C 7.5.4)
+The top-level auxiliary file: main.aux
+The style file: biophysj.bst
+A level-1 auxiliary file: acknowledgement.aux
+A level-1 auxiliary file: introduction.aux
+A level-1 auxiliary file: input/inputParameters.aux
+A level-1 auxiliary file: runningSimulations/run.aux
+A level-1 auxiliary file: output/out.aux
+A level-1 auxiliary file: visualization/vis.aux
+A level-1 auxiliary file: analysis/an.aux
+A level-1 auxiliary file: bench/benchmarks.aux
+A level-1 auxiliary file: md/md.aux
+A level-1 auxiliary file: biophys/biophys.aux
+Database file #1: /home/orsi/biblio.bib.bib
+You're missing a field name---line 73 of file /home/orsi/biblio.bib.bib
+ :
+ : % title = {{\em Iridis is a {B}eowulf cluster based on {AMD}
{O}pteron processors, running {R}ed{H}at {E}nterprise {L}inux.} {\tt
http://www.southampton.ac.uk/isolutions/computing/hpc/iridis/}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 90 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize "Taking the headgroup conformation suggested by
Seelig et al. [BBA, 1977], the distance between the zwitterionic charges
was estimated to be 3.9 A, giving a dipole moment of 18.7\,D.}"
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 99 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Surface areas and fluctuations evaluated from
50\,ns molecular dynamics simulations of DPPC bilayers in a 1:2
trehalose:lipid ratio carried out at selected surface tensions are compared
with those of pure bilayers under the same conditions. Trehalose increases
the surface area, as consistent with the surface tension lowering observed
in simulations at constant area. The system bulk elastic modulus
\index{elastic moduli!bulk modulus!simulation study by~\cite{venable06}}
$K_b = 1.5 +/- 0.3 x 10(10) dyn/cm(2)$. is independent of bilayer surface
area and trehalose content within statistical error. In contrast, the area
elastic modulus $K_A$ shows a strong area dependence: trehalose lowers
$K_A$, i.e. it increases fluidity of the bilayer.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 109 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Coarse-Grained representation, the Gay-Berne
potential is used to capture the underlying shape of lipid tails.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 118 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Analysis focused on reorientational dynamics of
the chains and lateral diffusion of lipids.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 420 of file /home/orsi/biblio.bib.bib
+ :
+ : %note ={PMID: 17683018},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 441 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The conformation of the polar head group of
phosphatidylcholine in a bilayer in the liquid-crystalline state was
deduced: the polar head group is oriented roughly parallel to the membrane
surface.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 652 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Crytical analysis of the most popular methods
employed in the simulation of bilayers; in particular, different algorithms
to treat electrostatics are compared.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 700 of file /home/orsi/biblio.bib.bib
+ : doi="10.1073/pnas.160260697"
+ : ;
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1008 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1025 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Weak-coupling methods.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1040 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The Bible (or rather, the Old Testament) of
molecular simulation.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1077 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize When two monolayers of a non-lamellar lipid are
brought together to form a planar bilayer membrane, the resulting structure
is under elastic stress. This lipid packing stress changes the energetics
of hydrophobic inclusions (thus influencing protein-lipid interactions) and
the energetics of spontaneous formation of non-lamellar local structures
(thus affecting membrane stability and fusion).}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1114 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize $P_{water}^{dmpc}=0.75\times10^{-2}$\,cm/s.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1224 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize }",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1259 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Model similar to ~\cite{goetz98a} but implicit
solvent here. Lateral pressure profile computed.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1284 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Soft spherocylinders.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1501 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize A mechanism of general anesthesia based on the
trans-bilayer lateral pressure profile is suggested and investigated using
lattice statistical thermodynamics.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1510 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The function of many intrinsic membrane proteins
requires a conformational transition that is often strongly influenced by
the molecular composition of the bilayer in which the protein is embedded.
Recently, a mechanism for this shift in conformational equilibrium was
suggested, in which it is argued that a shift in distribution of lateral
pressures of the bilayer resulting from a change in lipid composition
alters the amount of mechanical work of the protein conformational
transition, if the change in the cross-sectional area profile of the
protein varies with depth within the bilayer. As there is little
information on the change in shape of the transmembrane region of any
protein, various simple geometric models are considered. For both a generic
model, and more specific models that approximate likely cooperative
rearrangements of $\alpha$-helices in bundles, it is found that the
conformational equilibrium depends on the first and second integral moments
of the lateral pressure distribution. In addition to revealing the possible
physical underpinnings of the well-known correlation between protein
activity and the 'nonlamellar' tendency of bilayer lipids, this dependence
on moments of the pressure profile allows for prediction of the relative
effects of different lipid compositional changes even in the absence of
information on specific protein shape changes. Effects of variation in acyl
chain length, degree and position of cis-unsaturation, and addition of
cholesterol and small interfacially-active solutes ($n$-alkanols) are
compared.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1519 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1528 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The lateral pressure profile is predicted with
analytical theory. The mechanisms by which variations in the lipid
composition of cell membranes influence the function of membrane proteins
are not yet well understood. In recent work, a nonlocal thermodynamic
mechanism was suggested in which changes in lipid composition cause a
redistribution of lateral pressures that in turn modulates protein
conformational (or aggregation) equilibria. In the present study, results
of statistical thermodynamic calculations of the equilibrium pressure
profile and bilayer thickness are reported for a range of lipids and lipid
mixtures. Large redistributions of lateral pressure are predicted to
accompany variation in chain length, degree and position of chain
unsaturation, head group repulsion, and incorporation of cholesterol and
interfacially active solutes. Combinations of compositional changes are
found that compensate with respect to bilayer thickness, thus eliminating
effects of hydrophobic mismatch, while still effecting significant shifts
of the pressure profile. It is also predicted that the effect on the
pressure profile of addition of short alkanols can be reproduced with
certain unnatural lipids. These results suggest possible roles of
cholesterol, highly unsaturated fatty acids and small solutes in modulating
membrane protein function and suggest unambiguous experimental tests of the
pressure profile hypothesis. As a test of the methodology, calculated
molecular areas and area elastic moduli are compared with experimental and
simulation results.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1537 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The Meyer-Overton \index{Meyer-Overton rule}
hypothesis (which has dominated the design theory of anesthetics) predicts
that anesthetic potency is related to a molecule's solubility in a nonpolar
solvent (e. g. olive oil) that is thought to mimic the interior of a
bilayer. Exceptions to the Meyer-Overton rule are commonly cited as
evidence against indirect, membrane-mediated mechanisms of general
anesthesia. However, another interpretation is possible within the context
of an indirect mechanism in which solubilization of an anesthetic in the
membrane causes a redistribution of lateral pressures in the membrane,
which in turn shifts the conformational equilibrium of membrane proteins
such as ligand-gated ion channels. It is suggested that compounds of
different stiffness and interfacial activity have different intrinsic
potencies, i.e., they cause widely different redistributions of the
pressure profile (and thus different effects on protein conformational
equilibria) per unit concentration of the compound in the membrane.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1546 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Some membrane peptides, such as Alamethicin,
form barrel-stave aggregates with a broad probability distribution of size
(number of peptides in the aggregate). This distribution has been shown to
depend on the characteristics of the lipid bilayer. A mechanism for this
influence is suggested, in analogy to earlier work on the effects of
changes in bilayer composition on conformational equilibria in membrane
proteins, that is based on coupling of shifts in the distribution of
lateral pressures in the bilayer to depth-dependent changes in the lateral
excluded area that accompanies the formation of an aggregate. Thermodynamic
analysis is coupled with a simple geometric model of aggregates of kinked
cylindrical peptides and with results of previously calculated lateral
pressure distributions to predict the effects of changes in bilayer
characteristics on aggregate size distributions, in qualitative agreement
with experimental results.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1618 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Partition coefficients of short n-alkanols
between bilayers of different lipid composition (equivalently, the
variation in bilayer/water partition coefficients) are calculated as a
function of lipid acyl chain length and unsaturation, the strength of lipid
headgroup repulsions, and the addition of cholesterol. Predictions are
obtained from a statistical thermodynamic approach using a mean field
lattice model identical to that used recently to calculate the lateral
pressure profile in fluid bilayers. Increasing length, and particularly
increasing cis-unsaturation of the acyl chains, are predicted to increase
the bilayer/water partition coefficients of short-chain alkanols, whereas
addition of cholesterol is predicted to have the opposite effect. The
magnitude of the shifts are predicted to be significantly larger for lipids
with headgroups with little or no repulsions, such as
phosphatidylethanolamine, than for more strongly repulsive headgroups such
as phosphatidylcholine.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1693 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Lateral pressure profile measurements from AL
simulations of hydrated lipid bilayers containing highly polyunsaturated
fatty acids.} ",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1702 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Physical principles.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1797 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The partial charges on the lipids were
determined by ab initio self-consistent field calculations and required no
adjustment to produce a fluid phase.} ",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1815 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Explicit formula of forces and torques. NVE
simulations using Ewald for electrostatics.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 1925 of file
/home/orsi/biblio.bib.bib
+ :
+ : abtract = "The effects of alcohols (methanol, ethanol, and n-butanol)
on the hydrogen bonding of dipalmitoylphosphatidylcholine (DPPC) were
studied by Fourier-transform infrared spectroscopy (FTIR) in water-in-oil
(carbon tetrachloride) reversed micelles. Alcohols interact with the
phosphate moiety and replace the bound water. These results indicate that
short-chain alcohols interact with lipid membranes at the phosphate moiety
at the hydrophilic head, weaken the membrane-water interaction, and
destabilize membranes."
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 1942 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Determination of the bending rigidity by the
analysis of diffuse X-ray scattering.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting an "="---line 2023 of file /home/orsi/biblio.bib.bib
+ : Web
+ : of Science-Category = {{Biophysics}},
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2107 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The relationship between the dipole potential
and the interaction of the mitochondrial amphipathic signal sequence known
as p25 with model membranes has been studied using
1-(3-sulfonatopropyl)-4-[beta[2-(di-n-octyl-amino)-6-naphthyl]vinyl]
pyridinium betaine (di-8-ANEPPS) as a fluorescent probe. The dipole
potential of phosphatidylcholine membranes was modified by incorporating
into the bilayer the sterols phloretin and 6-ketocholestanol (KC), which
decrease and increase the dipole potential, respectively. The results
derived from the application of a dual-wavelength ratiometric fluorescence
method for following the variation of the membrane dipole potential have
shown that when p25 inserts into the lipidic bilayer, a decrease in the
dipole potential takes place. The magnitude of this decrease depends on the
initial value of the dipole potential, i.e., before interaction with the
peptide. Thus, when KC was incorporated into the bilayer, the decrease
caused by the membrane insertion of p25 was larger than that caused in PC
membranes. Alternatively, in the presence of phloretin, the decrease in the
potential caused by the peptide insertion was smaller. Complementary
studies involving attenuated total reflectance-fourier transform infrared
spectroscopy of the peptide membrane interactions have shown that
modification of the dipole potential affects the conformation of the
peptide during the course of its interaction with the membrane. The
presence of KC induces a higher amount of helicoidal structure. The
presence of phloretin, however, does not appear to affect the secondary
structure of the peptide. The differences observed in the dipole potential
decreases caused by the presence of the peptide with the PC membranes and
phloretin-PC membranes, therefore, must involve differences in the tertiary
and, perhaps, quaternary conformations of p25.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2116 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The simian immunodeficiency virus fusion peptide
constitutes a 12-residue N-terminal segment of the gp32 protein that is
involved in the fusion between the viral and cellular membranes,
facilitating the penetration of the virus in the host cell. Simian
immunodeficiency virus fusion peptide is a hydrophobic peptide that in
Me2SO forms aggregates that contain beta-sheet pleated structures. When
added to aqueous media the peptide forms large colloidal aggregates. In the
presence of lipidic membranes, however, the peptide interacts with the
membranes and causes small changes of the membrane electrostatic potential
as shown by fluorescein phosphatidylethanolamine fluorescence. Thioflavin T
fluorescence and Fourier transformed infrared spectroscopy measurements
reveal that the interaction of the peptide with the membrane bilayer
results in complete disassembly of the aggregates originating from an Me2SO
stock solution. Above a lipid/peptide ratio of about 5, the membrane
disaggregation and water precipitation processes become dependent on the
absolute peptide concentration rather than on the lipid/peptide ratio. A
schematic mechanism is proposed, which sheds light on how peptide-peptide
interactions can be favored with respect to peptide-lipid interactions at
various lipid/peptide ratios. These studies are augmented by the use of the
fluorescent dye
1-(3-sulfonatopropyl)-4-[beta[2-(di-n-octylamino)-6-naphthyl]vinyl]
pyridinium betaine that shows the interaction of the peptide with the
membranes has a clear effect on the magnitude of the so-called dipole
potential that arises :From dipolar groups located on the lipid molecules
and oriented water molecules at the membrane-water interface. It is shown
that the variation of the membrane dipole potential affects the extent of
the membrane fusion caused by the peptide and implicates the dipolar
properties of membranes in their fusion.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2154 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize "The dipole potential is an electrical potential
within phospholipid membranes, which arises because of the alignment of
dipolar residues of the lipids and/or water dipoles in the region between
the aqueous phases and the hydrocarbon-like interior of the membrane. For a
fully saturated phosphatidylcholine membrane, its value is believed to be
in the range 220-280 mV, positive in the membrane interior. This results in
an enormous electric field strength within the membrane of 10$^8$-10$^9$
Vm$^{-1}$. The dipole potential is thus likely to have great significance
in controlling the conformation of ion-translocating membrane proteins and
so in regulating enzyme function. Because of its location within the
membrane, quantification of the dipole potential is extremely difficult and
presents a great challenge to the experimentalist and theoretician alike.
Both electrical and spectroscopic methods developed for the determination
of the dipole potential on lipid bilayers and monolayers are presented and
possible causes for differences in the values derived are discussed".}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2213 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Three different lipid systems have been
developed to investigate the effect of physicochemical forces within the
lipid bilayer on the folding of the integral membrane protein
bacteriorhodopsin. Each system consists of lipid vesicles containing two
lipid species, one with phosphatidylcholine and the other with
phosphatidylethanolamine headgroups, but the same hydrocarbon chains.
Increasing the mole fraction of the phosphatidylethanolamine lipid
increases the desire of each monolayer leaflet in the bilayer to curve
toward water. This increases the torque tension of such monolayers, when
they are constrained to remain flat in the vesicle bilayer. Consequently,
the lateral pressure in the hydrocarbon chain region increases, and we have
used excimer fluorescence from pyrene-labeled phosphatidylcholine lipids to
probe these pressure changes. We show that bacteriorhodopsin regenerates to
about 95\% yield in vesicles of 100\% phosphatidylcholine. The regeneration
yield decreases as the mole fraction of the corresponding
phosphatidylethanolamine component is increased. The decrease in yield
correlates with the increase in lateral pressure which the lipid chains
exert on the refolding protein. We suggest that the increase in lipid chain
pressure either hinders insertion of the denatured state of bacterioopsin
into the bilayer or slows a folding step within the bilayer, to the extent
that an intermediate involved in bacteriorhodopsin regeneration is
effectively trapped.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2354 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize This article investigates the convergence of
structural and dynamical properties with system size and with time in
molecular dynamics simulations of solvated phospholipid bilayers performed
at constant volume under periodic boundary conditions using lattice-sum
electrostatics. A system size of 72\,lipids has been shown to result in
equivalent electron densities and other structural properties for systems
larger than 72\,lipids. Simulated properties converge significantly faster
under constant volume conditions as compared to constant pressure
conditions.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 2390 of file
/home/orsi/biblio.bib.bib
+ :
+ : address = "University of California"
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2417 of file /home/orsi/biblio.bib.bib
+ : pages="124903",
+ : %-1
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 2466 of file
/home/orsi/biblio.bib.bib
+ :
+ : OPTmonth = {},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2519 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize S$^{CD}$ order parameters for DMPC.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2560 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize DLM integrator. The orientational dynamics is
integrated by a sequence of planar rotations, in a matrix representation.
Excellent long-term stability and fidelity to the properties of solutions
of the continuous model. The DLM scheme has been described in Section~8.5
of~\cite{leimkuhler}, and used by~\cite{rapa02, fenne04a}.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2617 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Hydrated DMPC bilayer. During equilibration, the
atomic mass of water hydrogen is increased to 16\,amu, thus eliminating the
librational motion of the water molecules thereby allowing the use of a
larger timestep.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2685 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize \index{permeability!water!experiment
by \cite{olbrich00}} Micropipette aspiration was used to test mechanical
strength and water permeability of giant-fluid bilayer vesicles composed of
polyunsaturated PC lipids. Eight synthetic-diacyl PCs were chosen with 18
carbon chains and degrees of unsaturation that ranged from one double bond
(C18:0/1, C18:1/0) to six double bonds per PC molecule (diC18:3). Produced
by increasing pipette pressurization, membrane tensions for lysis of single
vesicles at 21\textcelsius ranged from approximately 9 to 10 mN/m for mono-
and dimono-unsaturated PCs (18:0/1, 18:1/0, and diC18:1) but dropped
abruptly to approximately 5 mN/m when one or both PC chains contained two
cis-double bonds (C18:0/2 and diC18:2) and even lower approximately 3 mN/m
for diC18:3. Driven by osmotic filtration following transfer of individual
vesicles to a hypertonic environment, the apparent coefficient for water
permeability, at 21\textcelsius, varied modestly in a range from
approximately 30 to 40\,$\mu$m/s for mono- and dimono-unsaturated PCs.
However, with two or more cis-double bonds in a chain, the apparent
permeability rose to approximately 50 microm/s for C18:0/2, then strikingly
to approximately 90 microm/s for diC18:2 and approximately 150 microm/s for
diC18:3. The measurements of water permeability were found to scale
exponentially with the reduced temperatures reported for these lipids in
the literature. The correlation supports the concept that increase in free
volume acquired in thermal expansion above the main gel-liquid crystal
transition of a bilayer is a major factor in water transport. Taken
together, the prominent changes in lysis tension and water permeability
indicate that major changes occur in chain packing and cohesive
interactions when two or more cis-double bonds alternate with saturated
bonds along a chain.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2711 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize \index{elastic moduli!experiment
by~\cite{rawicz00}} Micropipette pressurization of giant bilayer vesicles
was used to measure both elastic bending $k_c$ and area stretch $K_A$
moduli of fluid-phase phosphatidylcholine (PC) membranes. The direct
stretch moduli varied little with either chain unsaturation or length about
a mean of 243\,mN/m. On the other hand, the bending moduli of
saturated/monounsaturated chain PCs increased progressively with chain
length. For DMPC: $k_A=234\,dyn/cm$, $k_c=0.56\cdot10^{-19}$\,J.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2720 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize \index{elastic moduli!experiment
by~\cite{rawicz00}} Micropipette pressurization of giant bilayer vesicles
was used to measure both elastic bending $k_c$ and area stretch $K_A$
moduli of fluid-phase phosphatidylcholine (PC) membranes. The direct
stretch moduli varied little with either chain unsaturation or length about
a mean of 243\,mN/m. On the other hand, the bending moduli of
saturated/monounsaturated chain PCs increased progressively with chain
length. For DMPC: $k_A=234\,dyn/cm$, $k_c=0.56\cdot10^{-19}$\,J.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2769 of file /home/orsi/biblio.bib.bib
+ :
+ : % OPTnote="{\scriptsize Marrink's model is used; a liquid-gel
phase separation is observed.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2825 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Eight molecular dynamics simulations of a
hydrated lipid bilayer have been carried out differing only in the applied
surface tension, $\gamma$, defining the boundary conditions of the periodic
cell. The calculated surface area per molecule and deuterium order
parameter profile are found to depend strongly on gamma. Several methods to
calculate the area compressibility modulus, K$_A$, from the simulations.
Equivalence between the constant area and constant surface tension
ensembles is investigated by comparing the present simulations with earlier
work: simulation results depend much more strongly on the specified surface
area or surface tension than on the ensemble employed (in contrast to what
reported by~\cite{tieleman96}).}",}
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2874 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize SSD reparameterisation for simulation without
long-range electrostatics. MD integration performed using the DLM method.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 2926 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Physical principles.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 3084 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Explanation of the physics behind the "recipes"
of molecular simulation.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 3196 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Hydration forces, electrical dipole potentials,
and structural parameters of dispersions of DPPC and DHPC have been
compared to evaluate the influence of fatty acid carbonyl groups on
phospholipid bilayers. NMR and x-ray investigations performed over a wide
range of water concentrations in the samples show that in the liquid
crystalline lamellar phase the presence of carbonyl groups is not essential
for lipid structure and hydration. Within experimental error, the two
lipids have identical repulsive hydration forces between their bilayers.
The higher transport rate of the negatively charged tetraphenylboron over
the positively charged tetraphenylarsonium indicates that the dipole
potential is positive inside the membranes of both lipids. The DPPC
internal potential magnitude is 227\,mV; the lack of fatty acid carbonyl
groups in the ether lipid DHPC decreased the potential by (118 +/- 15) mV.
By considering the sign of the potential and the orientation of carbonyl
groups and headgroups, the authors conclude that the first layer of water
molecules at the lipid water interface makes a major contribution to the
dipole potential.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 3222 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize CG model of lipids composed simply of
hydrophobic and hydrophilic beads interacting through van der Waals-type
potentials can self-assemble and exhibit a nonuniform pressure profile
distribution.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 3427 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The function of membrane proteins often depends
on the proteins' interaction with their lipid environment, spectacularly so
in the case of mechanosensitive channels, which are gated through tension
mediated by the surrounding lipids. Lipid bilayer tension is distributed
quite inhomogeneously, but neither the scale at which relevant variation
takes place nor the effect of varying lipid composition or tension has yet
been investigated in atomic detail. Calculation of lateral pressure profile
distributions in lipid bilayers of various composition from all-atom
molecular dynamics.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 3594 of file
/home/orsi/biblio.bib.bib
+ :
+ : @article{harries97,
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 3823 of file /home/orsi/biblio.bib.bib
+ :
+ : %no doi
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4090 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Simpler but equivalent version of the NVT
algorithm by~\cite{nose84}. With fluctuating kinetic energy (hence
different from ~\cite{hoover82}, where the temperature is fixed). Also, the
isothermal-isobaric extension is presented. The methodology developed has
been extended by~\cite{melchionna93}.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+I was expecting a `,' or a `}'---line 4524 of file
/home/orsi/biblio.bib.bib
+ : abstract="Conventional molecular dynamics (MD) simulations are
seriously limited by the slow rate of diffusive mixing in their ability to
predict lateral distributions of different lipid types within mixed-lipid
bilayers using atomistic models. A method to overcome this limitation,
using configuration-bias Monte Carlo (MC) "
+ :
mutation"
moves to transform lipids from one type to another in dynamic
equilibrium, is demonstrated in binary fluid-phase mixtures of lipids whose
tails differ in length by four carbons. The hybrid MC-MD method operates
within a semigrand canonical ensemble, so that an equilibrium composition
of the mixture is determined by a constant difference in chemical potential
(Delta mu) chosen for the components. Within several nanoseconds, bilayer
structures initiated as pure dipalmitoyl phosphatidylcholine (DPPC) or pure
dilauroyl phosphatidylcholine (DLPC) converge to a common composition and
structure in independent simulations conducted at the same Delta mu. Trends
in bilayer thickness, area per lipid, density distributions across the
bilayer, and order parameters have been investigated at three mixture
compositions and compared with results from the pure bilayers at 323 K. The
mixtures showed a moderate increase in DPPC acyl tail sites crossing the
bilayer midplane relative to pure DPPC. Correlations between lateral
positions of the two lipid types within or across the bilayer were found to
be weak or absent. While the lateral distribution is consistent with nearly
ideal mixing, the dependence of composition on Delta mu indicates a
positive excess free energy of mixing.",
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4572 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote = "{\scriptsize Yet, cells exquisitely control membrane
composition. Many phospholipids found in plasma membrane bilayers favor
packing into inverted hexagonal bulk phases. It was suggested that the
strain of forcing such lipids into a bilayer may affect membrane protein
function, such as the operation of transmembrane channels. To investigate
this, we have inserted the peptide alamethicin into bilayer membranes
composed of lipids of empirically determined inverted hexagonal
phase ''spontaneous radii'' Ro, which will have expectably different
degrees of strain when forced into bilayer form. We observe a correlation
between measured Ro and the relative probabilities of different conductance
states. States of higher conductance are more probable in
dioleoylphosphatidylethanolamine, the lipid of highest curvature, 1/Ro,
than in dioleoylphosphatidylcholine, the lipid of lowest curvature.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4671 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4709 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Hydration: 26.6\,water molecules per lipid. DMPC
area per lipid $A_L= 60.6 \pm 0.5\,$\AA$^2$. "The new results for the area
of DMPC are 1\,\AA$^2$ larger than the earlier value (59.6\,A$^2$) that was
obtained by our previous x-ray method~\citep{petra98a}, and by
NMR~\citep{koeni97a, petra00a}. Although agreement is satisfactory within
estimated uncertainties of 0.5\,\AA$^2$, the refined structure in this
article was obtained with much better x-ray data, so the new value of $A_L$
should be more accurate. Also, new value for the bilayer thickness:
$D_{HH}=35.3$\,\AA (old value from~\cite{nagle00a} was $D_{HH}=36$\,\AA
)."}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4780 of file /home/orsi/biblio.bib.bib
+ :
+ : % OPTnote="{\scriptsize Presents the TIP3P water model.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 4981 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize }",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5083 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize In Section 8.5 the dynamics of freely moving
rigid-bodies is solved with the DLM method~\citep{dullw97a}.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5253 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize }",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5389 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The single-site SSD model is a LJ sphere with en
embedded point-dipole plus a tetrahedral sticky potential. An ion-water
potential consisting of a monopole-dipole plus a monopole-quadrupole term
is used to describe the interaction between an ion and a SSD water
molecule.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5463 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize }",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5472 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Knowledge of the mechanism of action of
antimicrobial agents is crucial for the development of new compounds to
combat microbial pathogens. To this end, computational studies on the
interaction of known membrane-active antimicrobial polymers with
phospholipid bilayers reveal spontaneous membrane insertion and cooperative
action at low and high concentrations, respectively. In late-stage attack,
antimicrobials cross the membrane core and occasionally align to provide a
stepping-stone pathway for water permeation; this suggests a possible new
mode of action that does not depend on pore formation for transport to and
across the inner leaflet. The computations rationalize the observed
activity of a new class of antimicrobial compounds.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5738 of file /home/orsi/biblio.bib.bib
+ :
+ : % no doi
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5762 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Review.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5911 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize To understand the effect of the finite size of
simulation cells on the equilibrium properties of bilayers, an extensive
series of glycerolmonoolein (GMO) bilayer molecular dynamics simulations in
which the surface area and system size were systematically changed have
been conducted. Systems ranging from 200 to 1800 lipids were simulated,
covering length scales up to 20\,nm. The dependence of the surface tension
on the area per lipid is shown, although long simulation times were needed
(up to 40 ns) to obtain reliable estimates. As the size of simulated
patches increases, long wavelength undulatory modes appear with a
concomitant increase in the area compressibility due to coupling of
undulation modes to area fluctuations. The effect of system size on surface
tension appears to depend on the stress conditions. Undulations can
decrease the the compressibility modulus by a factor of 2-3. Standard weak
coupling schemes are used. Although pressure coupling using the Berendsen
algorithm does not strictly produce a well-defined ensemble, test
simulations involving lipid bilayers using Parrinello-Rahman and
Nose'-Hoover coupling schemes have not resulted in any noticeable effect on
the observed fluctuations for correlation times larger than the coupling
time (0.5 ps). On the basis of the reported data plus that available from
the literature (neglecting short simulations), the authors conclude that
the application of an external surface tension to compensate for suppressed
fluctuations is unnecessary, unless one wishes to reproduce experimental
data that apply to bilayers actually under some sort of thermodynamic
stress.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5945 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5971 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 5980 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Fully flexible (triclinic) box shape. For
correct computation of the lateral diffusion coefficient of the lipids, the
mass-centre motion per monolayer was removed at each step during the
simulations.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6043 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Following the approach by~\cite{hoove85a,
hoover86} and~\cite{parrinello81, parrinello82}, an exact
isothermal-isobaric scheme is presented, and it is extended to multiple
thermostating rates, to a shape-varying cell and to molecular systems.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6349 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+Repeated entry---line 6378 of file /home/orsi/biblio.bib.bib
+ : @article{jensen04
+ : ,
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6394 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote={{\scriptsize Recently, it has become obvious that the
conventional picture of the fluid lipid-bilayer component of biological
membranes being a fairly structureless 'fluid mosaic' solvent is far from
correct. The lipid bilayer displays distinct static and dynamic structural
organization on a small scale, for example in terms of differentiated lipid
domains, and evidence is accumulating that these structures are of
importance for the functioning of biological membranes, including the
activity of membrane-bound enzymes and receptors and morphological changes
at the cell surface. Insight into the relationship between this small-scale
structure and biological functioning holds promise for a more rational
approach to modulate function via manipulation of the lipid
microenvironment and the lipid/protein interface in particular. Computer
simulation has proved to be a useful tool in investigating membrane
structure on a small scale - specifically the nanometer scale (1-100 nm),
which is in between the molecular scale accessible by various spectroscopic
techniques and molecular dynamics calculations, and the micrometer scale
accessible by scattering and microscopy techniques.}}
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6487 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Review - Experimental fully-hydrated structural
data for DPPC, DMPC, DOPC, EPC, DLPE (collected in~Table~6). }",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6623 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6632 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6674 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Original NVT scheme, later rewritten in an
equivalent but simplified form by~\cite{hoove85a}.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 6950 of file /home/orsi/biblio.bib.bib
+ :
+ : % no doi
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 7198 of file /home/orsi/biblio.bib.bib
+ :
+ : %ISSN = {{0005-2736}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+"}" immediately follows an entry type---line 7205 of file
/home/orsi/biblio.bib.bib
+ : Author-Email = {{sco...@iit.edu
+ : }},
+I'm skipping whatever remains of this entry
+You're missing a field name---line 7338 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote= {{\scriptsize Brownian and molecular dynamics simulations of
a lipid bilayer are described, and the calculated frequency-dependent
$^{13}$C NMR T$_1$ relaxation times are compared with experiment. A
consistent model emerges. Through fast internal motions, individual lipids
average themselves into relatively cylindrical shapes on the 100\,ps time
scale and "wobble" in a cone-like potential on the nanosecond time scale.
These motions take place in a highly fluid environment, much like a liquid
alkane. Lateral diffusion of the lipids is on a significantly longer time
scale because of restrictions at the bilayer/water interface, not because
the interior of the bilayer is highly viscous. }},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 7443 of file /home/orsi/biblio.bib.bib
+ :
+ : %AB: In our earlier studies using quantum chemical methods we had
proposed that propranolol has an extended structure. These results were
confirmed using proton NMR. We have now carried out extensive magnetic
resonance and model building studies to examine the interaction of this
drug with model membranes. The effect of propranolol on organization of
lipid bilayers has been studied using ESR spin labeling technique. Spin
label Tempo and spin labeled stearic acid (5 SASL) have been used to
monitor changes in the fluidity of model membranes. Presence of the drug is
found to fluidize the lipids. In case of 0.2M dipalmitoyl phosphatidyl
choline (DPPC), presence of drug (0.1M) is found to decrease the gel-liquid
crystalline phase transition temperature by about 10°C. The order parameter
measured from the spectrum of 5 SASL shows a 4% decrease on incorporation
of the drug in membranes. 13C spin lattice relaxation time (T1)
measurements have been carried out for different nuclear sites of the drug.
The aromatic moiety shows a high degree of molecular rigidity when the drug
is bound to the lipid bilayers. The oxypropanolamine group is however
relatively flexible. It appears from these studies that the aromatic group
binds strongly to the hydrophobic regions of the lipid bilayer, while the
oxypropanolamine moiety remains relatively free and lies in the hydrophilic
region. The 13C chemical shifts indicate the involvement of the
beta-hydroxyl group in hydrogen bonding with the lipids. The NH2+ group may
be involved in electrostatic interactions with the negatively charged
phosphate group of the lipid bilayers.
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 7998 of file /home/orsi/biblio.bib.bib
+ :
+ : % doi = {10.2277/0511192320},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8045 of file /home/orsi/biblio.bib.bib
+ :
+ : %ISSN = {{0011-9075}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8327 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote = "{\scriptsize The organization of the lipid headgroups in a
neutral model membrane is studied by atomistic simulations in the fluid
lamellar phase, L$_\alpha$. The headgroup dipoles lie approximately
parallel, within 30$^\circ$, to the membrane plane, pointing toward the
water region.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8561 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Three-to-one mapping of water into Lennard-Jones
sites, parameterised to give the correct bulk density and air/liquid
surface tension. Headgroups potential tabulated to reproduce RDFs (using an
iterative adjustment starting from an approximation based on potentials of
mean force). Explicit treatment of long-range electrostatics, but all
interactions are screened using a dielectric constant of 78.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8648 of file /home/orsi/biblio.bib.bib
+ :
+ : % OPTnote="{\scriptsize Marrink's CG model is used to simulate
a 1:1 DPPC/DPPE lipid mixture at the liquid-gel phase coexistence
condition. The only (slight) difference between the two lipids is that
$\epsilon^{head-site}_{DPPE}>\epsilon^{head-site}_{DPPC}$}.",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8657 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize 10\,ns NVT, $\Delta t=2$\,fs, $rCCut=13$\,\AA,
7\,times faster than corresponding AA.}.",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 8782 of file /home/orsi/biblio.bib.bib
+ :
+ : %ISSN = {{0950-382X}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 9187 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize \index{Gaussian curvature modulus!estimate
by~\cite{templer98b}} In this paper the Helfrich ansatz for bending an
amphiphilic monolayer is re-expressed in terms of the deviations in
curvature away from a preferred value. Using this expression and a simple
model of the response of amphiphiles to interfacial bending, it is
demonstrated that there are strict limits to the value of the ratio of the
Gaussian curvature modulus to the mean curvature modulus
$(\kappa_G/\kappa)$. We have made an estimate of $(\kappa_G/\kappa)$ from
measurements of the swelling behavior in water of inverse bicontinuous
cubic mesophases in a system composed of MO, DOPC, and DOPE. The estimate,
$-0.75 \pm 0.08$, is in agreement with the limits set by our model of -1 <
K-G/K < 0. This determination is the first to be made on an inverse
bicontinuous cubic phase which is sufficiently swollen to be in a regime
where first-order curvature elastic energetics should be sufficient to
describe the state of the mesophase and hence provide a reliable estimate
of K-G/K.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 9495 of file /home/orsi/biblio.bib.bib
+ :
+ : %ISSN = {{1433-7851}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+"}" immediately follows an entry type---line 9504 of file
/home/orsi/biblio.bib.bib
+ : Author-Email = {{wf...@igc.phys.chem.ethz.ch
+ : }},
+I'm skipping whatever remains of this entry
+You're missing a field name---line 9835 of file /home/orsi/biblio.bib.bib
+ :
+ : %ISSN = {{0099-2240}},
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 9946 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Surface areas and fluctuations evaluated from
50\,ns molecular dynamics simulations of DPPC bilayers in a 1:2
trehalose:lipid ratio carried out at selected surface tensions are compared
with those of pure bilayers under the same conditions. Trehalose increases
the surface area, as consistent with the surface tension lowering observed
in simulations at constant area. The system bulk elastic modulus
\index{elastic moduli!bulk modulus!simulation study by~\cite{venable06}}
$K_b = 1.5 +/- 0.3 x 10(10) dyn/cm(2)$. is independent of bilayer surface
area and trehalose content within statistical error. In contrast, the area
elastic modulus $K_A$ shows a strong area dependence: trehalose lowers
$K_A$, i.e. it increases fluidity of the bilayer.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 10087 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize Dipole potential ~ 500-850 mV"It is further
important to realize that it is much easier to induce changes in the area
that are coupled to thickness changes, and therefore occur at constant
volume, rather than to induce volume changes". "Most molecules, although
they have zero net charge, have a distribution of charges which gives rise
to dipole-dipole and higher multipole interactions at long distances. This
is represented by fractional charges distributed on the atoms. Usually,
nearby atoms are grouped together into groups of zero net charge, and
electrostatic interactions are calculated as Coulomb interactions between
these charges. Applying a simple cutoff would lead to a situation where
some of the atoms in one group would interact only with some of the atoms
of another group. This would give strong interactions of Coulomb type close
to the cutoff, clearly an artifact of the cutoff itself. Therefore, one
usually uses a group-based cutoff where either all or none of the
interactions between the atoms in two charge groups are included. This
works well when the charge groups are small but may lead to incorrect
results when charge groups are large and nonspherical. This is indeed the
problem with phospholipids which are neutral but have a huge dipole moment
that may be represented by two unit charges of opposite sign ~0.5-nm apart.
One then has the choice either to work with neutral charge groups and
accept the artifacts that the nonspherical cutoff will cause, or to find a
suitable compromise with non-neutral charge groups". "Neutral charge groups
eliminate the peak in the correlation functions at the cutoff and are in
that respect most similar to the PME simulation. The area per lipid from
that simulation is, however, the one that differs most from the PME
simulation, and from experiments. This indicates that large charge groups
and a nonspherical cutoff cause large artifacts". "Cutoff simulations do
not suffer to any great extent from the omission of long-rane
electrostatics".}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 10244 of file /home/orsi/biblio.bib.bib
+ :
+ : % no doi
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 10261 of file /home/orsi/biblio.bib.bib
+ :
+ : % no doi
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+You're missing a field name---line 10293 of file /home/orsi/biblio.bib.bib
+ :
+ : %OPTnote="{\scriptsize The dipole potential of a lipid bilayer
membrane accounts for its much larger permeability to anions than cations
and affects the conformation and function of membrane proteins. The
absolute value of the dipole potential has been very difficult to measure,
although its value has been estimated to range from 200 to 1,000 mV from
ion translocation rates, the surface potential of lipid monolayers, and
molecular dynamics calculations. Here, a point charge probe method was used
to investigate the dipole potentials of both ester and ether lipid
membranes. The interactions between electrons and lipid molecules were
recorded by phase-contrast imaging using cryo-EM. The magnitude and the
profile of the dipole potential along the bilayer normal were obtained by
subtracting the contribution of the atomic potential from the cryo-EM image
intensity. The peak dipole potential was estimated to be 510 and 260 mV for
diphytanoylphosphatidylcholine and diphytanylphosphatidylcholine,
respectively.}",
+(Error may have been on previous line)
+I'm skipping whatever remains of this entry
+Reallocated wiz_functions (elt_size=4) to 6000 items from 3000.
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=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.dvi Wed Dec 21 02:20:08 2011
Binary file, no diff available.
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.idx Wed Dec 21 02:20:08 2011
@@ -0,0 +1,5 @@
+\indexentry{file!input data}{4}
+\indexentry{file!output data}{16}
+\indexentry{area\_volume.dat}{16}
+\indexentry{summary.dat}{16}
+\indexentry{CTP}{46}
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.ilg Wed Dec 21 02:20:08 2011
@@ -0,0 +1,6 @@
+This is makeindex, version 2.14 [02-Oct-2002] (kpathsea + Thai support).
+Scanning input file main.idx....done (5 entries accepted, 0 rejected).
+Sorting entries....done (17 comparisons).
+Generating output file main.ind....done (19 lines written, 0 warnings).
+Output written in main.ind.
+Transcript written in main.ilg.
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.ind Wed Dec 21 02:20:08 2011
@@ -0,0 +1,19 @@
+\begin{theindex}
+
+ \item area\_volume.dat, 16
+
+ \indexspace
+
+ \item CTP, 46
+
+ \indexspace
+
+ \item file
+ \subitem input data, 4
+ \subitem output data, 16
+
+ \indexspace
+
+ \item summary.dat, 16
+
+\end{theindex}
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.lof Wed Dec 21 02:20:08 2011
@@ -0,0 +1,26 @@
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\contentsline {figure}{\numberline {2.1}{\ignorespaces Bilayer
self-assembly}}{14}
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\contentsline {figure}{\numberline {4.1}{\ignorespaces Bilayer
snapshot}}{17}
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\contentsline {figure}{\numberline {7.1}{\ignorespaces The molecular
dynamics algorithm}}{23}
+\contentsline {figure}{\numberline {7.2}{\ignorespaces Periodic boundary
conditions}}{27}
+\contentsline {figure}{\numberline {7.3}{\ignorespaces Cell
subdivision}}{29}
+\contentsline {figure}{\numberline {7.4}{\ignorespaces Verlet neighbour
list}}{29}
+\addvspace {10\p@ }
+\contentsline {figure}{\numberline {8.1}{\ignorespaces The plasma
membrane}}{36}
+\contentsline {figure}{\numberline {8.2}{\ignorespaces Phospholipid
molecule}}{36}
+\contentsline {figure}{\numberline {8.3}{\ignorespaces Lipid
aggregates}}{37}
+\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {}}}{37}
+\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {}}}{37}
+\contentsline {figure}{\numberline {8.4}{\ignorespaces Multi-lamellar
vesicles}}{38}
+\contentsline {figure}{\numberline {8.5}{\ignorespaces Transbilayer
structure}}{39}
+\contentsline {figure}{\numberline {8.6}{\ignorespaces DMPC phase
diagram}}{40}
+\contentsline {figure}{\numberline {8.7}{\ignorespaces Lateral pressure
profile}}{40}
+\contentsline {figure}{\numberline {8.8}{\ignorespaces Charges and dipoles
of lipids and water}}{41}
+\contentsline {figure}{\numberline {8.9}{\ignorespaces Trans-bilayer
electrical potential}}{42}
+\contentsline {figure}{\numberline {8.10}{\ignorespaces Lipid
characteristic motions}}{43}
=======================================
--- /dev/null
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--- /dev/null
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+\addvspace {10\p@ }
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23328 water molecules}}{19}
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512 lipids, 16810 waters}}{19}
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1058 lipids, 16000}}{20}
+\addvspace {10\p@ }
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experimental measurements}}{42}
=======================================
--- /dev/null
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@@ -0,0 +1,168 @@
+%\documentclass[10pt,draft,twoside]{report}
+%\documentclass[10pt,twoside]{article}
+%\documentclass[11pt]{article}
+%\documentclass[12pt]{report} % THESIS
+\documentclass[a4paper,twoside]{report}
+%\documentclass[12pt,draft]{report}
+%\documentclass[11pt,draft]{report}
+%\documentclass[9pt,draft]{book} % 8/8/2005
+%\documentclass[9pt]{book} % 8/8/2005
+
+\usepackage{amsmath,graphicx}
+
+%\usepackage{here}
+%\usepackage{fancy}
+%\usepackage{picins,array,tabularx,multicol,dcolumn,makeidx,times}
+\usepackage{picins}
+\usepackage{makeidx}
+
+%\usepackage{shapepar}
+\usepackage{amssymb}
+ %\usepackage{overcite}%reference number as an exponent NO mario 05
+%\usepackage{upref}
+%\usepackage{float}
+%\usepackage{fancyheadings} % for page headings
+%\usepackage{threeparttable} % allows notes in tabular environment
+%\usepackage{afterpage}
+%\usepackage{ifthen} % used for \ifthenelse control
+\usepackage{setspace} % line spacing package
+\usepackage{rotating} % different line spacing package
+%\usepackage{STY/psboxit} % out for brahms manual
+%\usepackage{STY/colors} % out for brahms manual
+\usepackage{colortbl}
+\usepackage{subfigure}
+\usepackage{enumerate}
+\usepackage{textcomp}
+%\usepackage{natbib}
+\usepackage{xspace}
+\usepackage[perpage,symbol]{footmisc}
+
+% Citation style in the text: numbers in parenthesis, sorted by their
+% order in the list of references.
+% Uses a range if possible: (1-3), not (1,2,3)
+\usepackage[super,numbers,sort&compress]{natbib}
+%\usepackage[super,numbers,sort&compress]{natbib}
+%\usepackage[super,ref]{cite}
+
+% Bibliography style (requires the style file biophysj.bst in the
+% document directory)
+\bibliographystyle{biophysj}
+\renewcommand{\bibnumfmt}[1]{#1}
+% Numbering style in the list of references: a number followed by a period
+%\renewcommand{\bibnumfmt}[1]{(#1)}
+
+%\input{macros}
+%\renewcommand\thefootnote{\fnsymbol{footnote}}
+\newcommand{\de}{\mbox{d}}
+\newcommand\brahms{{\sc{brahms }\xspace}}
+\newcommand{\boldeta}{\mbox{\boldmath$\eta$}}
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+\newcommand{\btau}{\mbox{\boldmath$\tau$}}
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+\newcommand{\xiv}{\mbox{\boldmath$\xi$}}
+
+ % the most trees saved \setlength{\oddsidemargin}{-0.7in}
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{\topmargin}{-0.45in} %less the value, more the text
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+
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+
+\usepackage{fancyhdr}
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+\pagestyle{fancy}
+
+% tight margins
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+
+
+%\setlength{\headheight}{1in}
+%\setlength{\textheight}{9.7in}
+
+%................header definition..............................
+
+\pagestyle{headings} % commented out - mario 05
+%...............................................................
+%\lhead[]{}
+%\rhead[]{\fancyplain{}{\leftmark}}
+%..............................................................
+
+
+\makeindex
+% compile with >makeindex main
+
+\title{\Huge \textbf{BRAHMS}\\\bigskip
+{\em User Manual}}
+
+\author{Mario Orsi}
+\begin{document}
+
+\maketitle
+%\raggedright
+
+%\include{title}
+
+%\pagebreak
+%\newpage
+%\onehalfspacing
+\pagenumbering{roman}\setcounter{page}{1}
+
+%\clearpage
+
+
+\include{acknowledgement}
+\tableofcontents
+%\clearpage
+\listoffigures
+\listoftables
+%\newpage
+%\openup=10pt
+\pagenumbering{arabic}\setcounter{page}{1}
+%\include{styleRules}
+\include{introduction}
+\part{Running Brahms}
+
+%\include{gettingStarted}
+\include{input/inputParameters}
+\include{runningSimulations/run}
+\include{output/out}
+\include{visualization/vis}
+\include{analysis/an}
+\include{bench/benchmarks}
+
+\part{Background}
+
+%\include{multiResolution/multi}
+
+%\appendix
+
+\include{md/md}
+\include{biophys/biophys}
+
+%\part*{Appendices}
+
+%\begin{footnotesize}
+\begin{scriptsize}
+\renewcommand{\bibname}{{\large References}}
+\bibliography{/home/orsi/biblio.bib}
+%\end{small}
+%\end{footnotesize}
+%\printindex
+\end{scriptsize}
+%\include{coda}
+\end{document},
=======================================
--- /dev/null
+++ /trunk/doc/latexSource/main.toc Wed Dec 21 02:20:08 2011
@@ -0,0 +1,198 @@
+\contentsline {paragraph}{The Art of Molecular Dynamics Simulation}{2}
+\contentsline {paragraph}{Gromacs manual}{2}
+\contentsline {paragraph}{Life - as a matter of fat\nobreakspace {}\cite
{mouritsen}}{2}
+\contentsline {paragraph}{Membrane force field}{2}
+\contentsline {paragraph}{Rigid-body integration}{2}
+\contentsline {part}{I\hspace {1em}Running Brahms}{3}
+\contentsline {chapter}{\numberline {1}Input parameters}{4}
+\contentsline {section}{\numberline {1.1}{\tt brahms.md}}{4}
+\contentsline {paragraph}{{\tt deltaT}}{4}
+\contentsline {paragraph}{{\tt stepAvg}}{4}
+\contentsline {paragraph}{{\tt stepLimit}}{4}
+\contentsline {paragraph}{{\tt resetTime}}{4}
+\contentsline {paragraph}{{\tt doCheckpoint}}{5}
+\contentsline {paragraph}{{\tt stepCheckpoint}}{5}
+\contentsline {paragraph}{{\tt stepPdb}}{5}
+\contentsline {paragraph}{{\tt runId}}{5}
+\contentsline {paragraph}{{\tt applyThermostat}}{5}
+\contentsline {paragraph}{{\tt extTemperature}}{5}
+\contentsline {paragraph}{{\tt tauT}}{5}
+\contentsline {paragraph}{{\tt applyBarostat}}{5}
+\contentsline {paragraph}{{\tt extPressure}}{5}
+\contentsline {paragraph}{{\tt tauP}}{5}
+\contentsline {paragraph}{{\tt flexBox}}{5}
+\contentsline {paragraph}{{\tt keepTetragonal}}{5}
+\contentsline {paragraph}{{\tt keepSquare}}{5}
+\contentsline {paragraph}{{\tt rCutLipLip}}{5}
+\contentsline {paragraph}{{\tt rCutWatWat}}{5}
+\contentsline {paragraph}{{\tt rCutSolute}}{6}
+\contentsline {paragraph}{{\tt rCutSoluteElse}}{6}
+\contentsline {paragraph}{{\tt rNebrShell}}{6}
+\contentsline {paragraph}{{\tt stepNebr}}{6}
+\contentsline {paragraph}{{\tt nebrTabFac}}{6}
+\contentsline {paragraph}{{\tt removeSystemTranslation}}{6}
+\contentsline {paragraph}{{\tt removeMonolayersTranslation}}{6}
+\contentsline {paragraph}{{\tt nSites}}{6}
+\contentsline {paragraph}{{\tt nWaters}}{6}
+\contentsline {paragraph}{{\tt nDOPCsDSPCs}}{6}
+\contentsline {paragraph}{{\tt nDOPEs}}{6}
+\contentsline {paragraph}{{\tt nLipids}}{6}
+\contentsline {paragraph}{{\tt nSolutes}}{6}
+\contentsline {paragraph}{{\tt nTypes}}{6}
+\contentsline {paragraph}{{\tt region}}{6}
+\contentsline {paragraph}{{\tt adjustRegion}}{6}
+\contentsline {paragraph}{{\tt regionAdjusted}}{6}
+\contentsline {paragraph}{{\tt randSeed}}{6}
+\contentsline {paragraph}{{\tt initHalfCellWat}}{7}
+\contentsline {paragraph}{{\tt initUcell}}{7}
+\contentsline {paragraph}{{\tt loadStructure}}{7}
+\contentsline {paragraph}{{\tt loadVelocities}}{7}
+\contentsline {paragraph}{{\tt centerInputStruct}}{7}
+\contentsline {paragraph}{{\tt reCenterBilayer}}{7}
+\contentsline {paragraph}{{\tt zConstraint}}{7}
+\contentsline {paragraph}{{\tt insertSolute}}{7}
+\contentsline {section}{\numberline {1.2}{\tt lipid.ff}}{7}
+\contentsline {section}{\numberline {1.3}{\tt water.ff}}{7}
+\contentsline {section}{\numberline {1.4}{\tt brahms.an}}{7}
+\contentsline {subsection}{\numberline {1.4.1}Region dimensions}{7}
+\contentsline {paragraph}{{\tt writeAreaVol}}{7}
+\contentsline {subsection}{\numberline {1.4.2}Lipid lateral diffusion}{7}
+\contentsline {paragraph}{{\tt latDiff}}{7}
+\contentsline {paragraph}{{\tt nBuffLatDiff}}{7}
+\contentsline {paragraph}{{\tt nValLatDiff}}{7}
+\contentsline {paragraph}{{\tt stepLatDiff}}{8}
+\contentsline {paragraph}{{\tt limitLatDiffAv}}{8}
+\contentsline {paragraph}{{\tt writeLipLatMotion}}{8}
+\contentsline {subsection}{\numberline {1.4.3}Transmembrane profiles}{8}
+\contentsline {subsubsection}{Electron density profiles}{8}
+\contentsline {paragraph}{{\tt edp}}{8}
+\contentsline {paragraph}{{\tt sizeHistEdp}}{8}
+\contentsline {paragraph}{{\tt stepEdp}}{8}
+\contentsline {paragraph}{{\tt limitEdp}}{8}
+\contentsline {subsubsection}{Electrostatic potential profiles}{8}
+\contentsline {paragraph}{{\tt epp}}{9}
+\contentsline {paragraph}{{\tt sizeHistEpp}}{9}
+\contentsline {paragraph}{{\tt stepEpp}}{9}
+\contentsline {paragraph}{{\tt limitEpp}}{9}
+\contentsline {subsubsection}{Lateral pressure profile}{9}
+\contentsline {paragraph}{{\tt lpp}}{9}
+\contentsline {paragraph}{{\tt sizeHistLpp}}{9}
+\contentsline {paragraph}{{\tt stepLpp}}{9}
+\contentsline {paragraph}{{\tt limitLpp}}{9}
+\contentsline {subsubsection}{Water polarization profile}{9}
+\contentsline {paragraph}{{\tt wpp}}{9}
+\contentsline {paragraph}{{\tt sizeHistWpp}}{9}
+\contentsline {paragraph}{{\tt stepWpp}}{9}
+\contentsline {paragraph}{{\tt limitWpp}}{9}
+\contentsline {subsection}{\numberline {1.4.4}Radial distribution function
in pure water systems}{9}
+\contentsline {paragraph}{{\tt rdfWat}}{9}
+\contentsline {paragraph}{{\tt rangeWatRdf}}{9}
+\contentsline {paragraph}{{\tt sizeHistWatRdf}}{9}
+\contentsline {paragraph}{{\tt stepWatRdf}}{9}
+\contentsline {paragraph}{{\tt limitWatRdf}}{9}
+\contentsline {subsection}{\numberline {1.4.5}Translational self-diffusion
and rotational diffusion in pure water systems}{9}
+\contentsline {paragraph}{{\tt diffusion}}{9}
+\contentsline {paragraph}{{\tt nBuffDiffuse}}{9}
+\contentsline {paragraph}{{\tt nValDiffuse}}{10}
+\contentsline {paragraph}{{\tt stepDiffuse}}{10}
+\contentsline {paragraph}{{\tt limitDiffuseAv}}{10}
+\contentsline {chapter}{\numberline {2}Setting up, running and restarting
simulations}{11}
+\contentsline {section}{\numberline {2.1}System generation}{11}
+\contentsline {subsection}{\numberline {2.1.1}Pure water systems}{11}
+\contentsline {paragraph}{{\tt initUcell}}{11}
+\contentsline {paragraph}{\tt nWaters}{11}
+\contentsline {paragraph}{\tt nSites}{11}
+\contentsline {subsection}{\numberline {2.1.2}Single-component lipid
bilayers}{11}
+\contentsline {paragraph}{\tt nLipids}{11}
+\contentsline {paragraph}{\tt nWaters}{11}
+\contentsline {paragraph}{{\tt initHalfCellWat}}{11}
+\contentsline {paragraph}{\tt nSites}{12}
+\contentsline {paragraph}{\tt region}{12}
+\contentsline {section}{\numberline {2.2}Restarting simulations}{13}
+\contentsline {section}{\numberline {2.3}Self-assembly simulations}{13}
+\contentsline {subsection}{\numberline {2.3.1}``Disassembling'' run}{13}
+\contentsline {subsection}{\numberline {2.3.2}Equilibration run}{13}
+\contentsline {subsection}{\numberline {2.3.3}Self-assembly run}{13}
+\contentsline {chapter}{\numberline {3}Output}{15}
+\contentsline {section}{\numberline {3.1}Screen output}{15}
+\contentsline {paragraph}{\tt step}{15}
+\contentsline {paragraph}{\tt time/ns}{16}
+\contentsline {paragraph}{\tt E/(kJ/mol)}{16}
+\contentsline {paragraph}{\tt U/(kJ/mol)}{16}
+\contentsline {paragraph}{\tt P/atm}{16}
+\contentsline {paragraph}{\tt T\_lip/C}{16}
+\contentsline {paragraph}{\tt T\_H2O/C}{16}
+\contentsline {paragraph}{\tt A\_lip/(A$^2$)}{16}
+\contentsline {paragraph}{\tt V\_lip/(nm$^3$)}{16}
+\contentsline {paragraph}{\tt ST/(dyn/cm)}{16}
+\contentsline {paragraph}{\tt dipHG/D}{16}
+\contentsline {paragraph}{\tt tiltHG/deg}{16}
+\contentsline {section}{\numberline {3.2}Output files}{16}
+\contentsline {paragraph}{\tt area\_volume.dat}{16}
+\contentsline {paragraph}{\tt initialConfiguration.pdb}{16}
+\contentsline {paragraph}{\tt inputParameters.log}{16}
+\contentsline {paragraph}{\tt simulationSetup.log}{16}
+\contentsline {paragraph}{\tt summary.dat}{16}
+\contentsline {paragraph}{\tt tailOrderParameters.dat}{16}
+\contentsline {paragraph}{\tt topology.log}{16}
+\contentsline {paragraph}{\tt trajectory.pdb}{16}
+\contentsline {chapter}{\numberline {4}Visualization}{17}
+\contentsline {chapter}{\numberline {5}Analysis}{18}
+\contentsline {section}{\numberline {5.1}``On-the-fly'' analysis in
Brahms}{18}
+\contentsline {section}{\numberline {5.2}Post-processing analysis}{18}
+\contentsline {chapter}{\numberline {6}Benchmarks}{19}
+\contentsline {section}{\numberline {6.1}Single processor}{19}
+\contentsline {subsection}{\numberline {6.1.1}Water systems}{19}
+\contentsline {subsection}{\numberline {6.1.2}Hydrated lipid bilayers}{19}
+\contentsline {part}{II\hspace {1em}Background}{21}
+\contentsline {chapter}{\numberline {7}The molecular dynamics
methodology}{22}
+\contentsline {section}{\numberline {7.1}Foundations}{22}
+\contentsline {section}{\numberline {7.2}Interaction potentials}{24}
+\contentsline {section}{\numberline {7.3}Rigid bodies}{24}
+\contentsline {section}{\numberline {7.4}Forces and torques}{24}
+\contentsline {section}{\numberline {7.5}Equations of motion}{25}
+\contentsline {paragraph}{Part A}{25}
+\contentsline {paragraph}{Part B}{26}
+\contentsline {subsection}{\numberline {7.5.1}Integration timestep: how
long?}{26}
+\contentsline {section}{\numberline {7.6}Periodic boundary conditions}{26}
+\contentsline {subsection}{\numberline {7.6.1}Minimum image convention}{27}
+\contentsline {section}{\numberline {7.7}Truncation of nonbonded
interactions}{27}
+\contentsline {section}{\numberline {7.8}Derivation of forces and
torques}{27}
+\contentsline {subsection}{\numberline {7.8.1}Dipole-dipole interactions:
shifted-force variant}{28}
+\contentsline {subsubsection}{Dipolar potential}{28}
+\contentsline {subsubsection}{Dipolar forces}{28}
+\contentsline {subsubsection}{Dipolar torques}{28}
+\contentsline {section}{\numberline {7.9}Improving the interaction
computations}{28}
+\contentsline {subsection}{\numberline {7.9.1}Cell subdivision}{29}
+\contentsline {subsection}{\numberline {7.9.2}Neighbour List}{29}
+\contentsline {section}{\numberline {7.10}Thermodynamic measurements}{30}
+\contentsline {subsection}{\numberline {7.10.1}Potential energy}{30}
+\contentsline {subsection}{\numberline {7.10.2}Kinetic energy and
temperature}{30}
+\contentsline {paragraph}{Mixtures}{30}
+\contentsline {subsection}{\numberline {7.10.3}Pressure tensor}{31}
+\contentsline {subsubsection}{Virial contribution from nonbonded pair
interactions}{31}
+\contentsline {subsubsection}{Virial contribution from bonded (Hooke) pair
interactions}{31}
+\contentsline {subsubsection}{Virial contribution from angle-bending
interactions}{32}
+\contentsline {subsubsection}{Scalar (hydrostatic) pressure}{32}
+\contentsline {subsubsection}{Surface tension}{32}
+\contentsline {section}{\numberline {7.11}Temperature control}{32}
+\contentsline {subsection}{\numberline {7.11.1}Weak-coupling method -
Berendsen thermostat}{32}
+\contentsline {section}{\numberline {7.12}Pressure (and temperature)
control}{33}
+\contentsline {subsection}{\numberline {7.12.1}Box transformation matrix
and scaled variables}{33}
+\contentsline {subsection}{\numberline {7.12.2}Weak-coupling method -
Berendsen barostat}{33}
+\contentsline {subsubsection}{Isotropic}{33}
+\contentsline {subsubsection}{Anisotropic}{33}
+\contentsline {subsection}{\numberline {7.12.3}Stochastic velocity
rescaling}{34}
+\contentsline {section}{\numberline {7.13}Statistical analysis}{34}
+\contentsline {paragraph}{Standard deviation}{34}
+\contentsline {chapter}{\numberline {8}Lipids and membranes}{35}
+\contentsline {section}{\numberline {8.1}Types of membrane lipids}{35}
+\contentsline {section}{\numberline {8.2}Phospholipid structure and
self-assembly}{35}
+\contentsline {section}{\numberline {8.3}Phospholipid bilayers}{37}
+\contentsline {subsection}{\numberline {8.3.1}Structure}{37}
+\contentsline {subsubsection}{Structure of the hydrocarbon region:
intramolecular order parameters}{38}
+\contentsline {subsection}{\numberline {8.3.2}Phase behaviour of lipid
bilayers}{38}
+\contentsline {subsection}{\numberline {8.3.3}The lateral pressure
profile}{38}
+\contentsline {subsection}{\numberline {8.3.4}The dipole potential}{41}
+\contentsline {subsection}{\numberline {8.3.5}Dynamics}{42}
+\contentsline {section}{\numberline {8.4}Summary}{43}
=======================================
***Additional files exist in this changeset.***