E.S.T.
enzo digiulio
Origin of Life on Earth. txt
In the following a note on the possible origin of life on earth is
concisely reported.
1. Enter mathematics.
Recent observations of planet surfaces and comet dust tend to centre on the
possible presence of water (plus ‘organic’ molecules) as a sign of actual or
fossil life. However oxygen and hydrogen must have reacted to form water
since the time planets were just formed into hot solid masses, in which all
sort of atoms collided and generated molecules. The presence of water per se
cannot be taken as conducive to life.
For life to exist there must be an organizing principle, capable of
dictating at every step the way ordered structures arise. This note
discusses how such a principle can be found, first at the level of
molecules, then at the level of cells and organisms, in the properties of
electrically charged molecules and electrostatic fields. Basing on these, a
very simple schematic model can be built for the way living matter arose.
Postponing to further stages of enquiry the electrodynamical interactions
that are the most evident manifestation of life, it is space-charge
electrostatic fields the model makes use of. An essential point is that
the physical properties of electrostatic fields can create order only if
they are not of the dielectric type commonly found in technical applications
, where the potential function psi satisfyes a Laplace-type equation (
Delta(psi) = 0).
In fact, the necessary properties emerge only when the field is of the
space-charge type, in which the potential function follows Poisson’s
equation:
Delta(psi) = k ro,
where ro is the space charge density. While in Laplace solutions (zero
divergence) the potential function cannot have minima (or maxima), potential
functions that solve the Poisson equation can, if certain conditions are
respected, display minima (or maxima). This implies that in a field with
non-zero space charge an electrified body may find an equilibrium position.
On earth a space-charge environment immediately available is the ion
solution that constitutes oceans: here an electric field can act on
molecular clouds selecting ‘compatible’ elements and thus generating
structures.
The above considerations can be applied in particular to clusters of
connected electric charges, as present in heteroatomic molecules: as is
common in living matter, these contain charge accumulations linked to the
different electronegativity of atoms.
For a first look into this matter it can be assumed that the charges are
point-like. Then a ‘molecule’ that satisfies the above quoted conditions
(linking molecular and field parameters) has a definite ‘address’ in the
field, where it sits with a definite orientation. A consequence of this will
be a specific chemical behaviour.
It is thus possible to write a first sketch of the complex order on which
organism-forming molecules (and at a later stage cells) base their
existence. It is a mathematical ‘quality’ that marks the difference between
a living being and a stone.
The ensuing model is called Electro-scalene Theory (E.S.T.)(1) in that it
considers the asymmetric electric (electrostatic) properties of chemical
entities. Most of the cases for which this viewpoint gives useful
indications are indeed ‘irregular’ structures, based on differences of field
potentials or electric charges.
2. Finding a molecule’s address.
In the model long molecules like the polyelectrolytes of living matter are
approximated with sequences of charges at definite intervals d. Each charge
represents a unit. Calling these charges qi , a polymer will be indicated
with S:
S=(q1)d(q2)d(q3)..
or: S= ..[XXX]A B C D E F [XXX] a c d e f...
where A B C D E F is a gene, [XXX] a hinge (start or end of the gene) and
a b c d e f.. a sequence of introns.
Introns are taken to be connecting sequences, that allow ‘exons’ to reach
any position required by electrical interactions.
In the presence of a field, each gene tends to move to its address.
In the simplest way this can be obtained if the polymer can be assumed to
be geometrically linear and subject to an algebraically linear field:
A B C D E F units disposed on a line
E =Eo + ax unidimensional linear field
If Q is the sum of the charges and M the total ‘moment’ of the individual
charges relative to the first element of the sequence, the total force F
acting on the sequence is:
F= q1*(Eo+ax) + q2*(Eo+a*(x+d) + q3*(Eo+a*(x+2*d)) + .....
= (Eo+a*x)*(q1+q2+q3+..) +[ q1 + q2*a*d + q3*a*2*d + ..] =
= (Eo+a*x)*Q + M .
The address is marked by the equilibrium abscissa xe for which is F = 0:
xe = -Eo/a - M/Q .
For a stable equilibrium it must be : dF/dx <0 and this in the simple
schema above means : Q<0.
In any other case the calculation must be carried out numerically.
3. Geoelectrical fields.
On planet Earth ions in seas and oceans provide the space charge
environment in which the properties of electrostatic fields can exert their
influence. In the exploration of other planets for signs of life it isn’t
enough for water to be there: available waters must be salt solutions.
An effective organizer can then be an electrostatic field vast enough to
cover masses of sea water. On Earth this means a ‘geoelectric’ field, such
as is often generated in catastrophic events in the planet crust. These
events produce, along with eruptions and earthquakes, triboelectricity
phenomena linked to the mutual sliding of land masses, as observed in the
neighbourhood of faults. A cataclysm, then, can be a means of destruction,
but can also act as the promoter of new molecular ordering.
Modern chemistry knows how specific reactions are driven by means of ionic
catalysts, that impose localized electrical fields. Even with complex
architectures, isotactic (following Nobel Giulio Natta’s language) polymers
can be ‘built’ by means of special classes of catalysts.
In the model it is assumed that the hot, radiation perfuse cauldron of the
original atmosphere gave rise through the eons to fractional precipitation
of a variety of molecules: reduced ones progressively rained to impregnate
rocks (as seems true of hydrocarbons of today’s oil fields), oxidated ones
dissolved after
the liquefaction of water vapour. In what can be called ‘first selection’,
primitive seas must have contained ?organic? molecules with hydrophilic
groups like -OH, -COOH, -NH2, etc. ready to interact. At the first
‘opportunity’ (a cataclysm), while the more complex structures were
disrupted, a number of molecules were pushed to their addresses and orderly
settled. This was the origin of specific types of polymers. It was a first
manifestation of order.
Quite independently, lipid molecules are per se prone to roll up in
spherical shells, in which small semi-polar molecules dissolve, creating a
charged corona. Inside the shell a ‘hole’ of zero field (a ‘crater’) is
born. This will attract the electrically charged high molecular weight
polymers offering them a shelter against disrupturing factors.
With polymers like polypeptides and polynucleotides safely incorporated,
the closed shell initiates a frenzy of chemical activity. The specific
character of electrostatic interactions causes protein active sides
(enzymes) to attract specific substrates, in a continuous sort of selection
that gradually turns the shell into a cell.
At a later stage the growth of organisms can be taken to follow a route of
electrical interactions similar to what happens at molecular level, except
that the field is an electrochemical one. Across the membrane of the cell
the partial solubility of environmental oxygen (or other oxidant) sets up a
concentration difference: the corresponding Nernst potential difference
supplies both the space-organizing capacity and the energy required by
subsequent reactions. This dual-type action of oxygen (or other oxidant) is
an essential aspect of a model representing living organisms.
4. Cells’ reproduction.
The schematic cell here discussed is an empty sphere with a layer of
surface charges. This creates an electric field inside, characterized, as
above mentioned, by a ‘crater’ of zero intensity(2). In the above delineated
environment this becomes the seat of an entangled mass of polyelectrolytes.
The character the cell will acquire depends on the properties of these
polimers, particularly from their addresses in the cell’s field (within the
cell, outside the crater). The model can give a schematic interpretation of
what happens making use of a simple mathematical treatment.
Thanks to the enzymes it contains, the cell produces matter, progressively
encreasing its volume. While the cell’s radius encreases, the radius of the
crater encreases too, and the electrostatic pressure on the inside polymers
decreases, to the point that polynucleotides come to expand freely: the
whole ‘chromosome’ becomes open to the action of duplication enzymes. This
marks the starting of a new cell. As long as the growth process is continued
duplication proceeds. This is what normally happens with unicellular
organisms, that proliferate with no apparent limit.
Multicellular organisms are different, in that the elements present on
their surfaces tend to adhere. In so doing, on a cell’s surface the surface
elements of surrounding cells become operative and so, when the number of
inhibiting elements are sufficient, they extinguishe duplication. A cell
surrounded by cells of similar type is blocked in its expansion: a ‘tissue’
is formed.
5. Cell differentiation.
As a further example of how the model can schematically interpret life
phenomena, the problem of cell differentiation can be sketched.
As shown above, a chromosome can be represented by a necklace of ‘active’
sequences of pearls (exons, capital letters) linked by long sequences of
no-meaning sequences (introns, small letters). ‘Compatible’ exons tend to
occupy their address in the field, incompatile ones being used as introns.
In the following LONDON, BERLIN, PARIS, STOCKHOLM are genes in their
address, madrid and rome are incompatible sequenses. The cell will be
defined as LONDON-BERLIN-PARIS-STOCKHOLM.
...shcndkdkdn LONDON nnsjmsmslofkajah BERLIN ukdhdbddmfjfjfggfjfb
hdhdhd PARIS hsjssksksksks madrid mbdhsjckflfnng rome khsggshdhdhdbb
ngshdjdkdklflflffff STOCKHOLM bsshshsssjsjjsj.
If the field changes, some of the compatibles will slip down as
incompatibles and some incompatibles will become compatibles , so as to turn
the cell in a different type, say LONDON-ATHENS-BERLIN-STOCKHOLM .
This modulation is the consequence of new electrically active molecules
coming to modify the environment and interacting with the cell’s surface
elements.
Using imagination it can be said that the environment plays like a pianist
on the cell’s surface keyboard.
If the polymer is a polynucleotide, the sequence may represent a
chromosome, with a number of genes, each one marked by a figure giving its
address in the cell’s field. This field is non null only outside of the
central mass, and here the single ‘addressable’ sequences will be
‘expressed’, that is orderly disposed along the lines of force and exposed
to enzymes.
According to what has been said of addresses of molecules, in a long linear
polyelectrolyte single segments may have individual addresses. Calling
A,B,C,.. the units that compose the polymer, it may happen that the sequence
of n units X,Y,Z , in a given fields satifies in itself the conditions for
equilibrium.
6. Uniqueness of planet Earth.
A consequence of possibly deep significance can be drawn from the above.
Earth is, from the point view of life, a special, maybe unique kind of
planet. The formation of specialized macromolecules in ion-rich waters could
not happen if there weren?t geoelectric fields around. These fields are
possible only when the
the plastic properties of the planet produce crustal plates floating on a
magmatic mass. These properties depend on age, size, total mass and distance
from the sun, that determine its ‘plasticity’and therefore how surface
plates grind their way through eons1.
Earth is the result of a very special combination of values in its physical
properties and Life appears to be is a unique consequence of this.
(1). The model can easily include Stephen J.Gould?s hypothesis on
Punctuated equilibrium (2002). If one cataclysm destroyed, a second
cataclysm
can restore.
(1) See: E. R.Caianiello- E.Di Giulio, energetics versus communicationtion
in the nervous system, Cybernetics and Systems, An international Journal,
13:187-196, 1982.
(2) A superficially charged empty sphere of a conducting material has a
null field inside. The same is true of an empty sphere of insulating
material. A cell with a definite number of surface charges is half-way
between: the field inside is zero in the neighboorhod of the center,
different from zero elsewhere. In the model the existence of this ‘crater’
is an essential feature of living cells.
Origin of Life on Earth. txt
In the following a note on the possible origin of life on earth is
concisely reported.
1. Enter mathematics.
Recent observations of planet surfaces and comet dust tend to centre on the
possible presence of water (plus ‘organic’ molecules) as a sign of actual or
fossil life. However oxygen and hydrogen must have reacted to form water
since the time planets were just formed into hot solid masses, in which all
sort of atoms collided and generated molecules. The presence of water per se
cannot be taken as conducive to life.
For life to exist there must be an organizing principle, capable of
dictating at every step the way ordered structures arise. This note
discusses how such a principle can be found, first at the level of
molecules, then at the level of cells and organisms, in the properties of
electrically charged molecules and electrostatic fields. Basing on these, a
very simple schematic model can be built for the way living matter arose.
Postponing to further stages of enquiry the electrodynamical interactions
that are the most evident manifestation of life, it is space-charge
electrostatic fields the model makes use of. An essential point is that
the physical properties of electrostatic fields can create order only if
they are not of the dielectric type commonly found in technical applications
, where the potential function psi satisfyes a Laplace-type equation (
Delta(psi) = 0).
In fact, the necessary properties emerge only when the field is of the
space-charge type, in which the potential function follows Poisson’s
equation:
Delta(psi) = k ro,
where ro is the space charge density. While in Laplace solutions (zero
divergence) the potential function cannot have minima (or maxima), potential
functions that solve the Poisson equation can, if certain conditions are
respected, display minima (or maxima). This implies that in a field with
non-zero space charge an electrified body may find an equilibrium position.
On earth a space-charge environment immediately available is the ion
solution that constitutes oceans: here an electric field can act on
molecular clouds selecting ‘compatible’ elements and thus generating
structures.
The above considerations can be applied in particular to clusters of
connected electric charges, as present in heteroatomic molecules: as is
common in living matter, these contain charge accumulations linked to the
different electronegativity of atoms.
For a first look into this matter it can be assumed that the charges are
point-like. Then a ‘molecule’ that satisfies the above quoted conditions
(linking molecular and field parameters) has a definite ‘address’ in the
field, where it sits with a definite orientation. A consequence of this will
be a specific chemical behaviour.
It is thus possible to write a first sketch of the complex order on which
organism-forming molecules (and at a later stage cells) base their
existence. It is a mathematical ‘quality’ that marks the difference between
a living being and a stone.
The ensuing model is called Electro-scalene Theory (E.S.T.)(1) in that it
considers the asymmetric electric (electrostatic) properties of chemical
entities. Most of the cases for which this viewpoint gives useful
indications are indeed ‘irregular’ structures, based on differences of field
potentials or electric charges.
2. Finding a molecule’s address.
In the model long molecules like the polyelectrolytes of living matter are
approximated with sequences of charges at definite intervals d. Each charge
represents a unit. Calling these charges qi , a polymer will be indicated
with S:
S=(q1)d(q2)d(q3)..
or: S= ..[XXX]A B C D E F [XXX] a c d e f...
where A B C D E F is a gene, [XXX] a hinge (start or end of the gene) and
a b c d e f.. a sequence of introns.
Introns are taken to be connecting sequences, that allow ‘exons’ to reach
any position required by electrical interactions.
In the presence of a field, each gene tends to move to its address.
In the simplest way this can be obtained if the polymer can be assumed to
be geometrically linear and subject to an algebraically linear field:
A B C D E F units disposed on a line
E =Eo + ax unidimensional linear field
If Q is the sum of the charges and M the total ‘moment’ of the individual
charges relative to the first element of the sequence, the total force F
acting on the sequence is:
F= q1*(Eo+ax) + q2*(Eo+a*(x+d) + q3*(Eo+a*(x+2*d)) + .....
= (Eo+a*x)*(q1+q2+q3+..) +[ q1 + q2*a*d + q3*a*2*d + ..] =
= (Eo+a*x)*Q + M .
The address is marked by the equilibrium abscissa xe for which is F = 0:
xe = -Eo/a - M/Q .
For a stable equilibrium it must be : dF/dx <0 and this in the simple
schema above means : Q<0.
In any other case the calculation must be carried out numerically.
3. Geoelectrical fields.
On planet Earth ions in seas and oceans provide the space charge
environment in which the properties of electrostatic fields can exert their
influence. In the exploration of other planets for signs of life it isn’t
enough for water to be there: available waters must be salt solutions.
An effective organizer can then be an electrostatic field vast enough to
cover masses of sea water. On Earth this means a ‘geoelectric’ field, such
as is often generated in catastrophic events in the planet crust. These
events produce, along with eruptions and earthquakes, triboelectricity
phenomena linked to the mutual sliding of land masses, as observed in the
neighbourhood of faults. A cataclysm, then, can be a means of destruction,
but can also act as the promoter of new molecular ordering.
Modern chemistry knows how specific reactions are driven by means of ionic
catalysts, that impose localized electrical fields. Even with complex
architectures, isotactic (following Nobel Giulio Natta’s language) polymers
can be ‘built’ by means of special classes of catalysts.
In the model it is assumed that the hot, radiation perfuse cauldron of the
original atmosphere gave rise through the eons to fractional precipitation
of a variety of molecules: reduced ones progressively rained to impregnate
rocks (as seems true of hydrocarbons of today’s oil fields), oxidated ones
dissolved after
the liquefaction of water vapour. In what can be called ‘first selection’,
primitive seas must have contained ?organic? molecules with hydrophilic
groups like -OH, -COOH, -NH2, etc. ready to interact. At the first
‘opportunity’ (a cataclysm), while the more complex structures were
disrupted, a number of molecules were pushed to their addresses and orderly
settled. This was the origin of specific types of polymers. It was a first
manifestation of order.
Quite independently, lipid molecules are per se prone to roll up in
spherical shells, in which small semi-polar molecules dissolve, creating a
charged corona. Inside the shell a ‘hole’ of zero field (a ‘crater’) is
born. This will attract the electrically charged high molecular weight
polymers offering them a shelter against disrupturing factors.
With polymers like polypeptides and polynucleotides safely incorporated,
the closed shell initiates a frenzy of chemical activity. The specific
character of electrostatic interactions causes protein active sides
(enzymes) to attract specific substrates, in a continuous sort of selection
that gradually turns the shell into a cell.
At a later stage the growth of organisms can be taken to follow a route of
electrical interactions similar to what happens at molecular level, except
that the field is an electrochemical one. Across the membrane of the cell
the partial solubility of environmental oxygen (or other oxidant) sets up a
concentration difference: the corresponding Nernst potential difference
supplies both the space-organizing capacity and the energy required by
subsequent reactions. This dual-type action of oxygen (or other oxidant) is
an essential aspect of a model representing living organisms.
4. Cells’ reproduction.
The schematic cell here discussed is an empty sphere with a layer of
surface charges. This creates an electric field inside, characterized, as
above mentioned, by a ‘crater’ of zero intensity(2). In the above delineated
environment this becomes the seat of an entangled mass of polyelectrolytes.
The character the cell will acquire depends on the properties of these
polimers, particularly from their addresses in the cell’s field (within the
cell, outside the crater). The model can give a schematic interpretation of
what happens making use of a simple mathematical treatment.
Thanks to the enzymes it contains, the cell produces matter, progressively
encreasing its volume. While the cell’s radius encreases, the radius of the
crater encreases too, and the electrostatic pressure on the inside polymers
decreases, to the point that polynucleotides come to expand freely: the
whole ‘chromosome’ becomes open to the action of duplication enzymes. This
marks the starting of a new cell. As long as the growth process is continued
duplication proceeds. This is what normally happens with unicellular
organisms, that proliferate with no apparent limit.
Multicellular organisms are different, in that the elements present on
their surfaces tend to adhere. In so doing, on a cell’s surface the surface
elements of surrounding cells become operative and so, when the number of
inhibiting elements are sufficient, they extinguishe duplication. A cell
surrounded by cells of similar type is blocked in its expansion: a ‘tissue’
is formed.
5. Cell differentiation.
As a further example of how the model can schematically interpret life
phenomena, the problem of cell differentiation can be sketched.
As shown above, a chromosome can be represented by a necklace of ‘active’
sequences of pearls (exons, capital letters) linked by long sequences of
no-meaning sequences (introns, small letters). ‘Compatible’ exons tend to
occupy their address in the field, incompatile ones being used as introns.
In the following LONDON, BERLIN, PARIS, STOCKHOLM are genes in their
address, madrid and rome are incompatible sequenses. The cell will be
defined as LONDON-BERLIN-PARIS-STOCKHOLM.
...shcndkdkdn LONDON nnsjmsmslofkajah BERLIN ukdhdbddmfjfjfggfjfb
hdhdhd PARIS hsjssksksksks madrid mbdhsjckflfnng rome khsggshdhdhdbb
ngshdjdkdklflflffff STOCKHOLM bsshshsssjsjjsj.
If the field changes, some of the compatibles will slip down as
incompatibles and some incompatibles will become compatibles , so as to turn
the cell in a different type, say LONDON-ATHENS-BERLIN-STOCKHOLM .
This modulation is the consequence of new electrically active molecules
coming to modify the environment and interacting with the cell’s surface
elements.
Using imagination it can be said that the environment plays like a pianist
on the cell’s surface keyboard.
If the polymer is a polynucleotide, the sequence may represent a
chromosome, with a number of genes, each one marked by a figure giving its
address in the cell’s field. This field is non null only outside of the
central mass, and here the single ‘addressable’ sequences will be
‘expressed’, that is orderly disposed along the lines of force and exposed
to enzymes.
According to what has been said of addresses of molecules, in a long linear
polyelectrolyte single segments may have individual addresses. Calling
A,B,C,.. the units that compose the polymer, it may happen that the sequence
of n units X,Y,Z , in a given fields satifies in itself the conditions for
equilibrium.
6. Uniqueness of planet Earth.
A consequence of possibly deep significance can be drawn from the above.
Earth is, from the point view of life, a special, maybe unique kind of
planet. The formation of specialized macromolecules in ion-rich waters could
not happen if there weren?t geoelectric fields around. These fields are
possible only when the
the plastic properties of the planet produce crustal plates floating on a
magmatic mass. These properties depend on age, size, total mass and distance
from the sun, that determine its ‘plasticity’and therefore how surface
plates grind their way through eons1.
Earth is the result of a very special combination of values in its physical
properties and Life appears to be is a unique consequence of this.
(1). The model can easily include Stephen J.Gould?s hypothesis on
Punctuated equilibrium (2002). If one cataclysm destroyed, a second
cataclysm
can restore.
(1) See: E. R.Caianiello- E.Di Giulio, energetics versus communicationtion
in the nervous system, Cybernetics and Systems, An international Journal,
13:187-196, 1982.
(2) A superficially charged empty sphere of a conducting material has a
null field inside. The same is true of an empty sphere of insulating
material. A cell with a definite number of surface charges is half-way
between: the field inside is zero in the neighboorhod of the center,
different from zero elsewhere. In the model the existence of this ‘crater’
is an essential feature of living cells.
Origin of Life on Earth. txt
In the following a note on the possible origin of life on earth is
concisely reported.
1. Enter mathematics.
Recent observations of planet surfaces and comet dust tend to centre on the
possible presence of water (plus ‘organic’ molecules) as a sign of actual or
fossil life. However oxygen and hydrogen must have reacted to form water
since the time planets were just formed into hot solid masses, in which all
sort of atoms collided and generated molecules. The presence of water per se
cannot be taken as conducive to life.
For life to exist there must be an organizing principle, capable of
dictating at every step the way ordered structures arise. This note
discusses how such a principle can be found, first at the level of
molecules, then at the level of cells and organisms, in the properties of
electrically charged molecules and electrostatic fields. Basing on these, a
very simple schematic model can be built for the way living matter arose.
Postponing to further stages of enquiry the electrodynamical interactions
that are the most evident manifestation of life, it is space-charge
electrostatic fields the model makes use of. An essential point is that
the physical properties of electrostatic fields can create order only if
they are not of the dielectric type commonly found in technical applications
, where the potential function psi satisfyes a Laplace-type equation (
Delta(psi) = 0).
In fact, the necessary properties emerge only when the field is of the
space-charge type, in which the potential function follows Poisson’s
equation:
Delta(psi) = k ro,
where ro is the space charge density. While in Laplace solutions (zero
divergence) the potential function cannot have minima (or maxima), potential
functions that solve the Poisson equation can, if certain conditions are
respected, display minima (or maxima). This implies that in a field with
non-zero space charge an electrified body may find an equilibrium position.
On earth a space-charge environment immediately available is the ion
solution that constitutes oceans: here an electric field can act on
molecular clouds selecting ‘compatible’ elements and thus generating
structures.
The above considerations can be applied in particular to clusters of
connected electric charges, as present in heteroatomic molecules: as is
common in living matter, these contain charge accumulations linked to the
different electronegativity of atoms.
For a first look into this matter it can be assumed that the charges are
point-like. Then a ‘molecule’ that satisfies the above quoted conditions
(linking molecular and field parameters) has a definite ‘address’ in the
field, where it sits with a definite orientation. A consequence of this will
be a specific chemical behaviour.
It is thus possible to write a first sketch of the complex order on which
organism-forming molecules (and at a later stage cells) base their
existence. It is a mathematical ‘quality’ that marks the difference between
a living being and a stone.
The ensuing model is called Electro-scalene Theory (E.S.T.)(1) in that it
considers the asymmetric electric (electrostatic) properties of chemical
entities. Most of the cases for which this viewpoint gives useful
indications are indeed ‘irregular’ structures, based on differences of field
potentials or electric charges.
2. Finding a molecule’s address.
In the model long molecules like the polyelectrolytes of living matter are
approximated with sequences of charges at definite intervals d. Each charge
represents a unit. Calling these charges qi , a polymer will be indicated
with S:
S=(q1)d(q2)d(q3)..
or: S= ..[XXX]A B C D E F [XXX] a c d e f...
where A B C D E F is a gene, [XXX] a hinge (start or end of the gene) and
a b c d e f.. a sequence of introns.
Introns are taken to be connecting sequences, that allow ‘exons’ to reach
any position required by electrical interactions.
In the presence of a field, each gene tends to move to its address.
In the simplest way this can be obtained if the polymer can be assumed to
be geometrically linear and subject to an algebraically linear field:
A B C D E F units disposed on a line
E =Eo + ax unidimensional linear field
If Q is the sum of the charges and M the total ‘moment’ of the individual
charges relative to the first element of the sequence, the total force F
acting on the sequence is:
F= q1*(Eo+ax) + q2*(Eo+a*(x+d) + q3*(Eo+a*(x+2*d)) + .....
= (Eo+a*x)*(q1+q2+q3+..) +[ q1 + q2*a*d + q3*a*2*d + ..] =
= (Eo+a*x)*Q + M .
The address is marked by the equilibrium abscissa xe for which is F = 0:
xe = -Eo/a - M/Q .
For a stable equilibrium it must be : dF/dx <0 and this in the simple
schema above means : Q<0.
In any other case the calculation must be carried out numerically.
3. Geoelectrical fields.
On planet Earth ions in seas and oceans provide the space charge
environment in which the properties of electrostatic fields can exert their
influence. In the exploration of other planets for signs of life it isn’t
enough for water to be there: available waters must be salt solutions.
An effective organizer can then be an electrostatic field vast enough to
cover masses of sea water. On Earth this means a ‘geoelectric’ field, such
as is often generated in catastrophic events in the planet crust. These
events produce, along with eruptions and earthquakes, triboelectricity
phenomena linked to the mutual sliding of land masses, as observed in the
neighbourhood of faults. A cataclysm, then, can be a means of destruction,
but can also act as the promoter of new molecular ordering.
Modern chemistry knows how specific reactions are driven by means of ionic
catalysts, that impose localized electrical fields. Even with complex
architectures, isotactic (following Nobel Giulio Natta’s language) polymers
can be ‘built’ by means of special classes of catalysts.
In the model it is assumed that the hot, radiation perfuse cauldron of the
original atmosphere gave rise through the eons to fractional precipitation
of a variety of molecules: reduced ones progressively rained to impregnate
rocks (as seems true of hydrocarbons of today’s oil fields), oxidated ones
dissolved after
the liquefaction of water vapour. In what can be called ‘first selection’,
primitive seas must have contained ?organic? molecules with hydrophilic
groups like -OH, -COOH, -NH2, etc. ready to interact. At the first
‘opportunity’ (a cataclysm), while the more complex structures were
disrupted, a number of molecules were pushed to their addresses and orderly
settled. This was the origin of specific types of polymers. It was a first
manifestation of order.
Quite independently, lipid molecules are per se prone to roll up in
spherical shells, in which small semi-polar molecules dissolve, creating a
charged corona. Inside the shell a ‘hole’ of zero field (a ‘crater’) is
born. This will attract the electrically charged high molecular weight
polymers offering them a shelter against disrupturing factors.
With polymers like polypeptides and polynucleotides safely incorporated,
the closed shell initiates a frenzy of chemical activity. The specific
character of electrostatic interactions causes protein active sides
(enzymes) to attract specific substrates, in a continuous sort of selection
that gradually turns the shell into a cell.
At a later stage the growth of organisms can be taken to follow a route of
electrical interactions similar to what happens at molecular level, except
that the field is an electrochemical one. Across the membrane of the cell
the partial solubility of environmental oxygen (or other oxidant) sets up a
concentration difference: the corresponding Nernst potential difference
supplies both the space-organizing capacity and the energy required by
subsequent reactions. This dual-type action of oxygen (or other oxidant) is
an essential aspect of a model representing living organisms.
4. Cells’ reproduction.
The schematic cell here discussed is an empty sphere with a layer of
surface charges. This creates an electric field inside, characterized, as
above mentioned, by a ‘crater’ of zero intensity(2). In the above delineated
environment this becomes the seat of an entangled mass of polyelectrolytes.
The character the cell will acquire depends on the properties of these
polimers, particularly from their addresses in the cell’s field (within the
cell, outside the crater). The model can give a schematic interpretation of
what happens making use of a simple mathematical treatment.
Thanks to the enzymes it contains, the cell produces matter, progressively
encreasing its volume. While the cell’s radius encreases, the radius of the
crater encreases too, and the electrostatic pressure on the inside polymers
decreases, to the point that polynucleotides come to expand freely: the
whole ‘chromosome’ becomes open to the action of duplication enzymes. This
marks the starting of a new cell. As long as the growth process is continued
duplication proceeds. This is what normally happens with unicellular
organisms, that proliferate with no apparent limit.
Multicellular organisms are different, in that the elements present on
their surfaces tend to adhere. In so doing, on a cell’s surface the surface
elements of surrounding cells become operative and so, when the number of
inhibiting elements are sufficient, they extinguishe duplication. A cell
surrounded by cells of similar type is blocked in its expansion: a ‘tissue’
is formed.
5. Cell differentiation.
As a further example of how the model can schematically interpret life
phenomena, the problem of cell differentiation can be sketched.
As shown above, a chromosome can be represented by a necklace of ‘active’
sequences of pearls (exons, capital letters) linked by long sequences of
no-meaning sequences (introns, small letters). ‘Compatible’ exons tend to
occupy their address in the field, incompatile ones being used as introns.
In the following LONDON, BERLIN, PARIS, STOCKHOLM are genes in their
address, madrid and rome are incompatible sequenses. The cell will be
defined as LONDON-BERLIN-PARIS-STOCKHOLM.
...shcndkdkdn LONDON nnsjmsmslofkajah BERLIN ukdhdbddmfjfjfggfjfb
hdhdhd PARIS hsjssksksksks madrid mbdhsjckflfnng rome khsggshdhdhdbb
ngshdjdkdklflflffff STOCKHOLM bsshshsssjsjjsj.
If the field changes, some of the compatibles will slip down as
incompatibles and some incompatibles will become compatibles , so as to turn
the cell in a different type, say LONDON-ATHENS-BERLIN-STOCKHOLM .
This modulation is the consequence of new electrically active molecules
coming to modify the environment and interacting with the cell’s surface
elements.
Using imagination it can be said that the environment plays like a pianist
on the cell’s surface keyboard.
If the polymer is a polynucleotide, the sequence may represent a
chromosome, with a number of genes, each one marked by a figure giving its
address in the cell’s field. This field is non null only outside of the
central mass, and here the single ‘addressable’ sequences will be
‘expressed’, that is orderly disposed along the lines of force and exposed
to enzymes.
According to what has been said of addresses of molecules, in a long linear
polyelectrolyte single segments may have individual addresses. Calling
A,B,C,.. the units that compose the polymer, it may happen that the sequence
of n units X,Y,Z , in a given fields satifies in itself the conditions for
equilibrium.
6. Uniqueness of planet Earth.
A consequence of possibly deep significance can be drawn from the above.
Earth is, from the point view of life, a special, maybe unique kind of
planet. The formation of specialized macromolecules in ion-rich waters could
not happen if there weren?t geoelectric fields around. These fields are
possible only when the
the plastic properties of the planet produce crustal plates floating on a
magmatic mass. These properties depend on age, size, total mass and distance
from the sun, that determine its ‘plasticity’and therefore how surface
plates grind their way through eons1.
Earth is the result of a very special combination of values in its physical
properties and Life appears to be is a unique consequence of this.
(1). The model can easily include Stephen J.Gould?s hypothesis on
Punctuated equilibrium (2002). If one cataclysm destroyed, a second
cataclysm
can restore.
(1) See: E. R.Caianiello- E.Di Giulio, energetics versus communicationtion
in the nervous system, Cybernetics and Systems, An international Journal,
13:187-196, 1982.
(2) A superficially charged empty sphere of a conducting material has a
null field inside. The same is true of an empty sphere of insulating
material. A cell with a definite number of surface charges is half-way
between: the field inside is zero in the neighboorhod of the center,
different from zero elsewhere. In the model the existence of this ‘crater’
is an essential feature of living cells.