The Density of Beneficial Functions
Sean Pitman
complexity? It depends upon what happens to the density of beneficial
functions in sequence space as the level of functional complexity
increases. The following is a recent exchange I had with Ian Musgrave
concerning this issue.
Link: http://groups.google.com/groups?q=g:thl3152600197d&dq=&hl=en&lr=&ie=UTF-8&selm=80d0c26f.0310151952.5f30b23e%40posting.google.com&rnum=54
_________________
> > Sean
> Ian
Sean
_________________
> >The
> >blind random walk of random mutation simply cannot sort through this
> >pile of junk sequences in what anyone would consider to be a
> >reasonable amount of time (even given trillions upon trillions upon
> >trillions of years).
>
> In fact, this is not so. The question is, can one go from any given
> functional sequence to another given functional sequence via steps of
> one mutation.
Yes, this is the question. Please then Ian, explain to me why ebg
negative E. coli cannot go from anything that they have in their
collective genomes in a large colony with over 4 million base pairs
each, to the lactase function? - if this lactase function is truly
only one step away from some other beneficial sequence or series of
one-step beneficial sequences in these creature's DNA? Hmmmmmmm?
That *is* the question!
> This is similar to the game where you try to get from
> say, CAT to DOG, changing one letter at a time going in steps of real
> english words. For proteins, this is a hard question, given we have
> proteins with a number of different sequence lengths, and 20 possible
> amino acids, but it turns out to have been solved exactly for proteins
> of length 128.
Hmmmmm . . . This is most interesting since proteins of 128aa in
length are relatively short for proteins.
> If the density of functional proteins is one in every
> 10^11 sequences, then we can form such a pathway (see Yockey, H.
> Information Theory and Molecular biology).
Yes, *if* the density were really this high I would agree with you.
Bacterial populations have more than this many individuals so they
could cover this sort of sequence space between stepping stones quite
easily and rapidly.
> So what is the density of
> functional sequences compared to non-functional sequences?
>
> Well it turns out to be somewhere between 1 in 10^9 and 1 in 10^11
> (recent experiments, like evolving structural proteins from random
> sequences, suggests that the density is around 1 in 10^9, evolution of
> catalytic antibodies suggests a similar density, evolution of enolase
> activity suggests that around 1 in a million random sequences is
> enolase)
A potential problem I see with this estimate is that not all proteins
that are beneficial in a "structural or catalytic way, etc" for this
or that creature in this or that environment are beneficial for a
particular colony of creatures in a particular environment. Also, one
particular function, such as the enolase function, might be very easy
to evolve. If the enolase function were as common as 1 in a million
sequences, this would make 10e160 enolases in 128aa sequence space
(far more than your usual 10e90 sequence with a particular function –
such as the cytochrome c function). However, this is just one
function, beneficial or not. The question is, what is the average
density of all beneficial functions in sequence space? Is the average
absolute number really 10e90 in 128aa sequence space? If so, your
density estimate seems to be just a bit off. For example, lets say we
have a function that 1 in 2 protein sequence share as well as another
function that is only shared by 10 different proteins in all of
sequence space. The ratio of the common function in sequence space
would be 1 in 2 while the ratio of the rare function in sequence space
would only be 1 in 10e165. The average density of beneficial
sequences so far is still only 1 in 10e165. You catch my point here?
Just because you quickly evolve an enolase does not mean that you will
just as easily evolve from the enolase that you have to any other
function since all the other beneficial sequences might be relatively
rare. It won't really help you to evolve from one enolase to another
enolase either, since this will be just as neutral with regard to
selection as wandering between completely non-functional sequences.
So, given this position of mine, I am betting that the density of
beneficial sequences in 128aa space is far less than 1 in 10e9
sequences. For example, about how many uniquely functional proteins
does an E. coli bacterium have? - around 4,200? Each of these
uniquely functional proteins has a degree of flexibility. When asked
this question you have generally come back with a flexibility of
between 10e60 to 10e90 for proteins even larger than 128aa in minimum
length. If each of these 4,200 proteins had at least 10e90 different
proteins that could perform the same function to at least some degree
of benefit, how many total proteins would be beneficial to this
particular bacterium in its current environment? Well, so far, there
would be at least 4,200 times 10e90 or 10e93 different beneficial
proteins - right? How many other proteins, if this bacterium could
make them, would it be able to use in a beneficial way if they were
added to its genome? Perhaps a few, but probably not all that many in
its current environment. But, lets say that this bacterium could use
another 10,000 new single protein functions in at least some
beneficial way (Which begs the question, if it needed them why hasn't
it evolved them by now?). Each of these functions, of course, would
have around 10e90 other protein sequences with the same beneficial
function to at least some degree for a total of 10e94 beneficial
sequences. This would give us a grand total of 10e93 plus 10e94,
which would equal 10e95 beneficial sequences in our sequence space of
potential options. Now, what is the sequence density of all these
beneficial proteins in the potential space of 128aa sequences? It is
only 1 in 10e71. Certainly this is a far smaller number than 10e9.
So, one of us isn't doing our thinking and/or math properly. I'm sure
that must be me. So, please do explain where I went wrong.
> So the density of functional sequences is such that we can find
> pathways from one functional sequence to any other functional
> sequence, without having to hunt for trillions of years (the very fact
> that single mutations can cause profound change of function should be
> a clue).
>
> The standard anti-evolutionary metaphor is that functional sequences
> are sharp peaks, isolated from each other by broad seas of
> non-functional sequences. In fact functional sequences are broad
> messas, connected to other messas of function by ridges of
> transitional sequences, no functional sequence is truly isolated.
Please explain this statement in the light of my previous question
concerning your estimate of 1 in 10e9 for the beneficial sequence
density of 128aa space. Also, even if your density calculations
happened to be a true reflection of reality, which I cannot fathom at
this time, you would still be in a huge mess. Going from a sequence
space of 128aa to an average sized protein of at least 250aa increases
the potential space from 10e166 to 10e325. What do you think happens
to the density of beneficial sequences in this massively increased
potential space? Do you think it stays the same? If so, how do you
figure this?
> >The main problem here is the
> >issue of neutral gaps that do seem to exist and grow exponentially
> >between functions of higher and higher levels of complexity.
>
> There are no neutral gaps. The metaphor of functional sequences for
> one function being broad messas of sequences connected by neutral
> mutation, in turn connected to other broad messas of sequences of a
> different function by narrow ridges of transitional sequences. While
> this is a helpful metaphor, it is misleading, as it suggests that very
> few sequences are near the ridge connecting the two functional messas,
> and a given sequence would have to have many neutral mutations before
> it reached the ridge.
>
> However, we have imposed 3D imagery on a system that can actually only
> be represented in hyperspatial dimensions. Imagine trying to write
> down all the three letter English words that are one letter away from
> CAT on a sheet of paper, such that each word is next to CAT. You cant
> do it on a 2D sheet of paper, you need at least three dimensions.
> Similarly for proteins, a 3D representation doesn't allow you to show
> all the proteins that are one step away as touching each other, you
> need more spatial dimensions. It turns out in the appropriate number
> of spatial dimensions, no sequence is very far from the "edge" that
> connects it to another set of sequences with a different function
> (Yockey again). This is illustrated by the ease with which we can
> evolve proteins with new functions (eg see Gerlt JA, and Babbitt PC.
> (1998 Oct). Mechanistically diverse enzyme superfamilies: the
> importance of chemistry in the evolution of catalysis. Curr Opin Chem
> Biol , 2, 607-12.).
You are correct in your point that a 3D imagery is not actually
correct. There are a huge number of dimensions in the actual problem.
However, you can quickly see as words and phrases get longer, that
they are indeed separated from other beneficial words and phrases by
more than single mutational steps. This is what makes the 3D imagery
very helpful. It illustrates this point very nicely. A simple
thought experiment should prove this to you. For example, while short
3-letter words are all connected by single mutational steps and make
little mesa clusters, longer words, such as 7-letter words are not so
connected or clustered. Try it and see. Pick an 7-letter word and
then see how many other 7-letter words you can evolve one mutation at
a time. See how many mesas you can evolve between, not to mention
beneficial mesas. Then, once you do this for a while, do the same
thing with a short phrase, like "Methinks it is like a weasel." See
how many functional phrases you can evolve between. How close are
your mesas now?
I know I know, protein functions are not like the English language.
This is very interesting coming from you and other evolutionists, like
Dawkins, who use English language and computer code analogies and
experiments constantly to explain evolution when you think it serves
your purposes. The fact of the matter is, proteins work exactly like
the English language or any other information system works. There is
no fundamental difference. If you could show how English information
or computer code could evolve via evolutionary mechanisms, certainly
biological information systems would evolve the same way. You would
have solved all of your problems. But, the fact of the matter is, you
can't explain how the mechanism of evolution works any more than I can
jump over the moon.
> Cheers! Ian
Cheers! ; )
Sean
R. Dunno
IIRC, a dormant gene of unknown function became a lactase function in
E. coli after two mutations when the original lactase gene was removed.
I believe it was you who posted this.
Wayne D. Hoxsie Jr.
Yes, but then he goes on to argue that when that gene is removed,
lactace functionality failed to evolve in a particular amount of time.
I suppose if it had, they would have removed that gene and...
I'm reminded of the scene 9 in Monty Python's Life of Brian: the meeting
of the Peoples' Front of Judea:
All right, but apart from the sanitation, the medicine, education,
wine, public order, irrigation, roads, a fresh water system, and
public health, what have the Romans ever done for us?
--
Wayne D. Hoxsie Jr.
SIUE Dept. of Biological Sciences
who...@siue.edu
PGP Key ID 138BCEE1
Von Smith
The answer is that the premise of the question isn't true. When are
you going to acknowledge and discuss the Matsumura et al. article, in
which the researchers evolved beta-galactosidase function from an E.
coli gene that normally codes for beta-glucuronidase?
Matsumura I, Ellington AD. In vitro evolution of
beta-glucuronidase into a beta-galactosidase proceeds through
non-specific intermediates. J Mol Biol. 2001 Jan 12;305(2):331-9
It has been cited to you several times. I don't think Matsumura et
al. made any point in knocking out the ebg gene to get this function,
but there is no reason to suppose they couldn't have.
So there are, in fact, at least *two* other genes that have been
observed to evolve novel lactase function in E. coli in the lab. How
many more do you think we need to observe?
Von Smith
Fortuna nimis dat multis, satis nulli.
Sean Pitman
> > Yes, this is the question. Please then Ian, explain to me why ebg
> > negative E. coli cannot go from anything that they have in their
> > collective genomes in a large colony with over 4 million base pairs
> > each, to the lactase function? - if this lactase function is truly
> > only one step away from some other beneficial sequence or series of
> > one-step beneficial sequences in these creature's DNA? Hmmmmmmm?
> > That *is* the question!
>
> The answer is that the premise of the question isn't true. When are
> you going to acknowledge and discuss the Matsumura et al. article, in
> which the researchers evolved beta-galactosidase function from an E.
> coli gene that normally codes for beta-glucuronidase?
>
> Matsumura I, Ellington AD. In vitro evolution of
> beta-glucuronidase into a beta-galactosidase proceeds through
> non-specific intermediates. J Mol Biol. 2001 Jan 12;305(2):331-9
PDF link:
If you had read this paper yourself, you may have noticed several
interesting things about the study. For one thing, this study was an
"in vitro" study. The E. coli themselves did not "evolve" the changes
in this enzyme here. Besides this, the wild-type genes products of
both the lacZ as well as the gusA genes (beta-galactosidases and
beta-glucuronides) hydrolysis similar glycoside substrates that differ
only at the C4 and C5 positions. And, the beta-glucuronidase enzyme
(gus) already has some selectable (to the scientists)
beta-galactosidase activity to begin with. Each of the four subsequent
point mutations enhanced the beta-galactosidase efficiency of this
enzyme, in a stepwise manner, while reducing the beta-glucuronidase
efficiency of this enzyme.
What is especially interesting here is that this potential lactase
evolution of the gus gene did not happen in the "in vivo" experiments
done by Barry Hall and others - even over the course of tens of
thousands of generations. In any case, the point of my argument and
use of experiments like Hall's is not to show that there is only one
or two potential lactase enzymes in sequence space. I believe that
there are literally trillions upon trillions of potential lactase
sequences out there. The point is that even this seemingly large
number of potential lactase enzymes and/or other beneficial sequence
of at this level of complexity (i.e., at least 400aa in length), is
nothing compared to the number of meaningless nonfunctional sequences
that occupy the sequence space at this level of complexity. The ratio
is what is important here. What is the ratio of potential benefit
compared with potential junk? Ask Ian Musgrave how many potential
lactase enzymes there are in sequence space. If he tells you the same
thing that he told me, he will give you 10e90 as the total number of
lactase enzymes in sequence space. The problem is that the lactase
function seems to require a chain of at least 400 amino acids to
achieve the lactase function. Of course, this translates into a
sequence space of over 10e520 different sequences. So tell me, what
is 10e90 when compared to 10e520? If Ian is right in this his
estimates, each functional lactase enzyme would be surrounded, on
average, by 10e430 non-lactase sequences. This is an absolutely
miniscule ratio. I believe that it is this ratio that limited Hall's
mutant E. coli from evolving the lactase function without the lacZ or
ebg genes - regardless of the presence of the gus gene. Even if the
gus gene had evolved the lactase function to a beneficial level in
vivo, this would not help you. Many other bacterial do not have the
lacz, gus, or ebg genes, or any other genetic sequences close enough
to evolve the lactase function even given millions of observed
generations. We have hospital records going back over 50 years with
many species of bacteria remaining lac negative that entire time. Why
do these bacteria have such apparently "limited evolutionary
potential" if not for the relatively low ratio of lactase enzymes in
sequence space?
> It has been cited to you several times.
This is the first time I've seen it. I don't read everything that is
addressed to me in this forum you know . . .
> I don't think Matsumura et
> al. made any point in knocking out the ebg gene to get this function,
> but there is no reason to suppose they couldn't have.
The reason why Matsumura did not need to knock out the ebg gene was
that this study was an "in vitro" study, not an "in vivo" study. The
mutations were introduced into the wild-type gusA "via mutagenic PCR".
> So there are, in fact, at least *two* other genes that have been
> observed to evolve novel lactase function in E. coli in the lab. How
> many more do you think we need to observe?
Most likely there are trillions of potential lactase genes out there
in sequence space. A demonstration of two of them is nothing. The
ratio of beneficial sequences vs. non-beneficial sequences is the
issue here. What is the density of beneficial sequences in sequence
space *at a given level of functional complexity*? A lower levels of
functional complexity, such as the level of antibiotic resistance
and the like, the beneficial density of sequences is relatively high.
At the higher level of single protein functions the density of
beneficial functions becomes much much less. This is evident from the
fact that the evolution of single protein enzymes is much harder to
achieve than the evolution of antibiotic resistance in these same
bacteria. Even those bacteria that cannot evolve the lactase function
are easily able to evolve antibiotic resistance to all kinds of
different antibiotics. Moving up one more level to multi-protein
functions were all the proteins work together at the same time in a
specific orientation with each other, there simply are no examples of
evolution in action - period. Now, why is that?
> Von Smith
Sean
Von Smith
> drea...@hotmail.com (Von Smith) wrote in message news:<8d74ec45.03101...@posting.google.com>...
>
> > > Yes, this is the question. Please then Ian, explain to me why ebg
> > > negative E. coli cannot go from anything that they have in their
> > > collective genomes in a large colony with over 4 million base pairs
> > > each, to the lactase function? - if this lactase function is truly
> > > only one step away from some other beneficial sequence or series of
> > > one-step beneficial sequences in these creature's DNA? Hmmmmmmm?
> > > That *is* the question!
> >
> > The answer is that the premise of the question isn't true. When are
> > you going to acknowledge and discuss the Matsumura et al. article, in
> > which the researchers evolved beta-galactosidase function from an E.
> > coli gene that normally codes for beta-glucuronidase?
> >
> > Matsumura I, Ellington AD. In vitro evolution of
> > beta-glucuronidase into a beta-galactosidase proceeds through
> > non-specific intermediates. J Mol Biol. 2001 Jan 12;305(2):331-9
>
> PDF link:
>
> http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WK7-457D7X4-17-1&_cdi=6899&_orig=search&_coverDate=01%2F12%2F2001&_qd=1&_sk=996949997&view=c&wchp=dGLbVzb-zSkzS&_acct=C000048963&_version=1&_userid=945456&md5=915397a94ffdbd4dc4b46db386154676&ie=f.pdf
>
> If you had read this paper yourself, you may have noticed several
> interesting things about the study. For one thing, this study was an
> "in vitro" study. The E. coli themselves did not "evolve" the changes
> in this enzyme here.
Yes, Dr. Pitman. This is already clear from the title. The question
is: so what? The DNA shuffling techniques Matsumura et al. used are
AFAICT a perfectly standard procedure for simulating in vivo
evolutionary processes. If you think that the scientists "cheated"
somehow by using an in vitro study, please explain how.
> Besides this, the wild-type genes products of
> both the lacZ as well as the gusA genes (beta-galactosidases and
> beta-glucuronides) hydrolysis similar glycoside substrates that differ
> only at the C4 and C5 positions. And, the beta-glucuronidase enzyme
> (gus) already has some selectable (to the scientists)
> beta-galactosidase activity to begin with. Each of the four subsequent
> point mutations enhanced the beta-galactosidase efficiency of this
> enzyme, in a stepwise manner, while reducing the beta-glucuronidase
> efficiency of this enzyme.
In other words, you admit that these functionally distinct genes are
not, in fact, separated from one another by the sort of wide neutral
gaps you contend they should be. ISTM you are trying to have it both
ways: you want to claim that neutral gaps are a pervasive obstacle to
evolving novel functions, but at the same time you wish to minimize
instances of such evolution by saying: "Oh, well the gusA, lacZ, and
ebg genes really aren't all that different."
>
> What is especially interesting here is that this potential lactase
> evolution of the gus gene did not happen in the "in vivo" experiments
> done by Barry Hall and others - even over the course of tens of
> thousands of generations.
It may be interesting, but it does not support your case. The fact is
that Matsumura was able to demonstrate the existence of a *selectable*
pathway between beta-glucuronidase activity and beta-galactosidase
activity with none of your "neutral gaps". Since they are central to
your argument, the burden is on you to demonstrate that they exist.
(Remember,you are not merely expressing skepticism about evolution of
complex functions, you are making the *positive* claim that it cannot
happen). That Hall's plating experiments did not result in this exact
pathway only shows that there is something wrong with your prediction
of how quickly we should expect it to appear in vivo.
> In any case, the point of my argument and
> use of experiments like Hall's is not to show that there is only one
> or two potential lactase enzymes in sequence space.
And yet you seem to put a lot of effort in trying to suggest just
that.
> I believe that
> there are literally trillions upon trillions of potential lactase
> sequences out there. The point is that even this seemingly large
> number of potential lactase enzymes and/or other beneficial sequence
> of at this level of complexity (i.e., at least 400aa in length), is
> nothing compared to the number of meaningless nonfunctional sequences
> that occupy the sequence space at this level of complexity.
The problem with this is that, for any gene that is already doing
something beneficial for the organism, nonfunctional sequences will be
selected *against*. Nonfunctional sequences aren't neutral in such
cases; they are detrimental. This has an immense effect on how
quickly selection works on such sequence spaces.
> The ratio
> is what is important here. What is the ratio of potential benefit
> compared with potential junk? Ask Ian Musgrave how many potential
> lactase enzymes there are in sequence space. If he tells you the same
> thing that he told me, he will give you 10e90 as the total number of
> lactase enzymes in sequence space. The problem is that the lactase
> function seems to require a chain of at least 400 amino acids to
> achieve the lactase function. Of course, this translates into a
> sequence space of over 10e520 different sequences. So tell me, what
> is 10e90 when compared to 10e520? If Ian is right in this his
> estimates, each functional lactase enzyme would be surrounded, on
> average, by 10e430 non-lactase sequences.
And the overwhelming majority of these sequences will be selected
*against*. They aren't neutral gaps. This makes a huge difference.
> This is an absolutely
> miniscule ratio. I believe that it is this ratio that limited Hall's
> mutant E. coli from evolving the lactase function without the lacZ or
> ebg genes - regardless of the presence of the gus gene. Even if the
> gus gene had evolved the lactase function to a beneficial level in
> vivo, this would not help you. Many other bacterial do not have the
> lacz, gus, or ebg genes, or any other genetic sequences close enough
> to evolve the lactase function even given millions of observed
> generations. We have hospital records going back over 50 years with
> many species of bacteria remaining lac negative that entire time. Why
> do these bacteria have such apparently "limited evolutionary
> potential" if not for the relatively low ratio of lactase enzymes in
> sequence space?
So either it happens everywhere all the time, or it can never happen?
Why are these my only two possibilities, Dr. Pitman? I've asked you
this question before, and I'm still waiting for your answer.
>
> > It has been cited to you several times.
>
> This is the first time I've seen it. I don't read everything that is
> addressed to me in this forum you know . . .
Ian has cited it at least three times previously, and I have mentioned
it on at least one other occasion. Considering the care with which
you usually respond to Ian Musgrave's posts, I would have expected
better.
>
> > I don't think Matsumura et
> > al. made any point in knocking out the ebg gene to get this function,
> > but there is no reason to suppose they couldn't have.
>
> The reason why Matsumura did not need to knock out the ebg gene was
> that this study was an "in vitro" study, not an "in vivo" study. The
> mutations were introduced into the wild-type gusA "via mutagenic PCR".
So what? The process is still essentially random with respect to
realizing a particular function, and Matsumura was still able to find
a selectable pathway.
>
> > So there are, in fact, at least *two* other genes that have been
> > observed to evolve novel lactase function in E. coli in the lab. How
> > many more do you think we need to observe?
>
> Most likely there are trillions of potential lactase genes out there
> in sequence space. A demonstration of two of them is nothing.
Then what is the point of making such a big deal about Hall's
experiments, and trying to use them to claim that only E. coli with
the ebg gene can re-evolve lactase function?
> The
> ratio of beneficial sequences vs. non-beneficial sequences is the
> issue here.
If the organism has at least two other genes that are known to have
reasonably short evolutionary pathways to the function in question,
then obviously it isn't much of an issue at all. A gene only needs one
ancestor.
The only scenarios evolutionary theories have to be able to explain
are the evolution of *extant* structures from probable ancestors, not
the transformation of *any* arbitrary sequence into any arbitrary
target sequence. The total number of functional sequences that is
ever likely to appear in life on earth is, I am sure, only a tiny
subset of all possible functional sequences. So what? A tiny subset
is all we need, and a key prediction of evolutionary theory is that
that the functions present in that tiny subset will be precisely those
that are connected to one another via viable evolutionary pathways,
rather than separated from one another by hopelessly large gaps, a
prediction that is confirmed by our ability to construct phylogenies
connecting them to one another.
> What is the density of beneficial sequences in sequence
> space *at a given level of functional complexity*? A lower levels of
> functional complexity, such as the level of antibiotic resistance
> and the like, the beneficial density of sequences is relatively high.
> At the higher level of single protein functions the density of
> beneficial functions becomes much much less. This is evident from the
> fact that the evolution of single protein enzymes is much harder to
> achieve than the evolution of antibiotic resistance in these same
> bacteria. Even those bacteria that cannot evolve the lactase function
> are easily able to evolve antibiotic resistance to all kinds of
> different antibiotics. Moving up one more level to multi-protein
> functions were all the proteins work together at the same time in a
> specific orientation with each other, there simply are no examples of
> evolution in action - period. Now, why is that?
Perhaps because you try to define counter-examples, such as the PCP
and 2,4-DNT cascades out of existence? Genes can evolve both novel
functions, novel interactions with other functions, and novel
expression, so there doesn't appear to be any great problem in
principle. In practice, I would imagine that it is difficult to
construct an experiment that would select for a "multi-protein
function where all the proteins work together, etc." How would one
select for such things?
Von Smith
>
> Sean
>
> www.naturalselection.0catch.com