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Topic: Dermott J. Mullan: Probabilities of randomly assembling a primitive cell on Earth
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Cre8ionist
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Member # 140
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posted 26. November 2002 08:09
Well, Yersinia, you make a strong circumstantial case, and a jury might well convict on such testimony, too bad you weren't able to show it with the scientific rigor needed to
put it with scientific fact, which, if you remember is what we're debating here.
The simple fact that it's similar does not establish evolutionary descent as scientific fact. Further, so called vestigial connections don't establish it as scientific fact either. We've been through this many times with many creatures, it wasn't long ago when lucy was man's ancestor, and this too was declared as scientific fact, I wouldn't be so hasty. Perhaps an actual recreation of said events in the lab, would do more to convert the skeptical, same with the origin of DNA/protein, life, organelles, organs and the like. Scientifically speaking, repetition would be the key to converting me, that I can say with some certainty.......Cre8
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posted 26. November 2002 16:38
Let us get this thread back on topic. Please focus on Mullan's paper and not what constitutes scientific fact or not.
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Kirk Durston
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posted 27. November 2002 13:37
Charlie D. stated: "no matter how accurate your estimates of information content/aa residue are, no one is claiming that a minimal genome (of 12, 150, or 250 protein-encoding genes) was assembled randomly. Thus, how much information it may have contained, vis-a-vis the chances of such information being generated randomly, is irrelevant to current understanding of OoL."
Since the functional information content of a protein is inextricably tied to its function, I don't see how the generation of information/function is irrelevant to the current understanding of Ool. In order to qualify for the position of the first living cell, the genetic machinery has to be functional. If it is functional, it is such in virtue of the information it contains. No information, no function. So to put it another way, we could discuss the problem of the first organic life as a problem of function, rather than information, since the two concepts are inseparable. Information is just an objective, quantifiable way of measuring the difficulty of achieving a particular function. So if we are thinking about how the first cell became functional, the challenge is in figuring out how the first cell accumulated the amount of information required to achieve that level of function.
Re. 'no one is claiming that a minimal genome … was assembled randomly': Good. That is obviously the most rational position to hold (non-random assembly). However, Nf/N ratio still applies for non-random assembly. The Nf/N ratio is an objective measure of the size of the target the non-random assembly process must connect with. It is an empirical fact that human ID can produce sequences and configurations with an extremely small Nf/N ratio. If one does not want to invoke ID, then what one must do is to lay out a rigorous process by which a particular functional protein can be achieved. For simplicity sake, let's not worry about achieving an entire minimal genome. Let's just pick a particular protein of approximately 300 amino acids, with a particular function (which has an objective, quantifiable Nf/N), and come up with a rigorous explanation as to how we got that function via a non-random process. A key factor in such a rigorous explanation is the Nf/N ratio. For most scenarios I read about, and all computer simulations I've seen, including Schneider's, the Nf/N ratios are unrealistically large, by many, many orders of magnitude, or they are not even considered.
I am sincerely willing to be persuaded. Why don't you start with a rigorous, non-random process for the pre-biotic achievement of just one ~300 residue protein of your choice, with a very liberal Nf/N of 10^-75? If you prefer to go the RNA world/pre-RNA world route, be sure to show how that particular functional protein can be achieved from the self-replicating machinery.
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Frances
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posted 27. November 2002 19:34
Hi Kirk
I believe that we are making some very important progress here in that we seem to have ruled out scenarios which presume a minimal genome to have formed in one random swoop.
The question now is, can one show credible/plausible pathways? That is a question which will be the focus of some interesting research and I would suggest that at present our understanding of plausible pathways have led us to explore RNA-world and proto-RNA/PNA precursors.
I have been reading some interesting papers on this topic. Function driven protein evolution. A possible proto-protein for the RNA-binding proteins. by Fetrow and Godzik. They propose proto-proteins as precursors, small 15-20 residue peptides to which over time structural elements are added. They discuss how structural similarities of small fragments of large proteins show evidenc of this common ancestry.
Additionally Distinct Stages of Protein Evolution as Suggested by Protein Sequence Analysis. Trifonov et al argue that present day peptides are known to be small 20-40 residues and even as small as 2 codons. Their paper presents some evidence for the stages of evolution.
Btw when discussing Schneider, you mentioned the absence or of too high Nf/N. Could you please explain your statement?
[ 27. November 2002, 19:38: Message edited by: Frances ]
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Kirk Durston
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posted 28. November 2002 14:01
Francis, I will have to read those two papers you cite before I can comment on them. That may take me a few days or even longer, so I fear I may not be able to get back with my comments in time to be relevant (I'm going on vacation in 2 weeks time and struggling to finish all the urgent stuff before I leave).
Re. Schneider and Nf/N: Schneider's program might be a worthy discussion on its own. Anyway, in his program, virtually any sequence at all starts off as being functional to some extent, which requires that Nf/N ~ 1. What changes is the efficiency with which a sequence performs its function.
I have a great interest in Schneider's program ... to the extent that I am working on a paper in response. When I have gotton far enough along, I think I'd like to put it up as a subject for discussion on its own ISCID discussion, where everyone can critique it accordingly.
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Frances
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posted 02. December 2002 12:54
Kirk:
quote:
Re. Schneider and Nf/N: Schneider's program might be a worthy discussion on its own. Anyway, in his program, virtually any sequence at all starts off as being functional to some extent, which requires that Nf/N ~ 1. What changes is the efficiency with which a sequence performs its function.
That half of the population dies every cycle hardly argues for Nf/N ~ 1 I would argue.
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posted 02. December 2002 13:39
Response to Art
Dermott Mullan has replied to Art (a Brainstorms participant) via a PDF file because certain formatting could not be performed in the Bulletin Board.
To read the reply, please click here.
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Art
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posted 05. December 2002 21:13
Hi Dermott,
You remarked, concerning my “review” of your submission (I am going to try and make this post here, rather than make a new pdf file to link to; hence, exponents will be denoted with the symbol ^ e.g., 100 = 10^2):
quote:
This is a response to Art (Member No. 179) who posted a criticism of my paper on 23 Nov 2002 at 19.28.
Art’s criticism is based on an incomplete reading of my paper. He seems to have read only as far as p. 20, where there is the phrase “f12 is roughly (1/10)^y where y = 15.6 Na”. Art uses this formula to arrive at the following conclusion: the probability of random assembly of long peptide chains (large Na) should be much smaller than random assembly of small chains (small Na). Clearly, if the above formula for y was the only important factor, then two peptide chains which differed by (say) 40 in their Na values, would differ in probability by 10^624. Art quotes two published papers which show that when small and large chains are assembled randomly in the laboratory, the differences in probability are nowhere near as large as this.
Art concludes that my formula for f12 leads to results which are inconsistent with experiments. If the above formula for f12 were the final derivation of my paper, I would agree with Art’s conclusion.
However, a key point in which my article differs from a lot of earlier work (such as that described in the thread Art refers to) is that, in the next paragraph but one after the formula cited by Art, I proceed to a quantitative discussion of protein specificity. This discussion is couched in terms of the index q, and it leads to a crucial revision of the above expression for y: the revision appears as eq. 1 on p. 22: the probability of random assembly of 12 proteins is not (1/10)^y but (1/10)^z, where z = 15.6Na - 12q. And there is analogous equation for random assembly of RNA (eq. 3).
I fail to see the distinction here. This is because, as I read your paper, Dermott, I gather than q is a constant that reflects some sort of specificity. Thus, eq. 1 on p. 22 can be reduced:
(1/10)^z -> [(1/10)^-12q] [(1/10)^15.6Na] -> A(1/10)^15.6Na
This relation suffers from the same flaw as that given on p.20.
But this conclusion depends on an impression of the nature of q that the rest of the response has clarified. I did not gather these details in the initial paper, and the clarification is appreciated.
quote:
What is essential here is that the probability depends now NOT on a single term (as in the equation for y quoted by Art), but on the algebraic DIFFERENCE between two terms.
The presence of this algebraic difference makes a great difference. In fact I will show that, contrary to Art’s conclusion, my formulas are in quantitative agreement with some results which appear in the paper by Ekland, Szostak, and Bartel Science 269, 364, 1995 (hereafter ESB).
To prove this, I refer to the value which q must have if random assembly (subscript ra) of the first cell RNA occurred: the answer is given by the solution of eq. 7 (p. 29). The value I obtain for q(RNA)ra is 22.8 (p. 30). And the question which is central to the physics of cell assembly is: how does this value of qra compare with the available volume in phase space? I address this on p. 31, where I revert to the quantity qmax (introduced on p. 21).
This leads to the key formula in eq. (11): the probability of random assembly is 1 in 10^b
where b depends on the DIFFERENCE qra - qmax. The occurrence of this difference is crucial for my discussion.
Now, I need to note here that the expressions in my paper are all for the case of a 12-protein cell, in which each of 12 proteins must be assembled randomly. However, to make a proper comparison with the experiments in the laboratory, we need to consider the case of a single protein. In that case, the chance of random assembly 1 in 10^b reduces essentially to b = ra(1) - qmax(1) where the term (1) denotes the value appropriate to a single protein.
My response to the essential aspect of Art’s criticism is the following: how does qra(1) depend on Na, the number of amino acids in the protein, and how does qmax(1) depend on Na ? Answer: both factors depend linearly on Na, but the coefficient of the linear dependence is different in qra(1) from what it is in qmax(1).
Basically, this removes the dependence on Na from the relationships - a big improvement over what was proposed before.
(The response goes into much more detail, and tries to work in a less stringent length dependence than was originally suggested; I won’t recapitulate it here, since I have many problems with the basic model under discussion, and it’s not my place to re-write Dermott’s ideas.)
I’d add one more comment for now, and think on the more fundamental matter of the model itself. Basically, it is implied in the original paper that f1, f12, or whatever, is an estimate of the probability of origination of a particular protein or group of (12) proteins. More properly, though, this term is the ratio of functional sequences to all sequences in the relevant sequence space. It is not a probability, although it can be used to help estimate one. For example, suppose f1 were 10^-16. The probability of the corresponding protein arising in some event would be governed by this value, but also by the size of the population of randomly-occurring sequences. Thus, if only one sequence arose, then 10^-16 is a rough approximation of the probability that the random sequence would have the desired functionality. However, if the population size were, say, 10^18 (approximately the number of molecules in 1 liter of a 1 micromolar solution), then the probability of obtaining the relevant sequence is essentially 1. Moreover, in the latter case, the probability of obtaining 12 peptides would also be about 1.
This is not to say that Dermott intends f12 to be a formal equivalent of probability, but it helps to make this clarification from time to time.
One more note - the work I cited that deals with small peptides suggests even less of a length dependence for f1 in peptides than does the ESB paper for RNA. It may be necessary to work this into a fnalized model.
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Dermott J. Mullan
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posted 06. December 2002 23:14
Second part of reply to Art
In his original criticism of my paper, Art referred to two published papers
as examples of research results which (in Art's opinion) contradicted my
results. In my first reply to Art, I dealt with one of those papers (Ekland et al. Science 1995), and demonstrated that the experimental results do not contradict my calculations.
Now, I would like to turn to Art's second reference, a paper by Wilson et al. (PNAS, 98, 3750,2001). In this paper, the aim is to start with an enormous library of random peptides and determine if any of them have significant affinities for a particular protein (streptavidin). The work of Wilson et al. is
very different from that of Ekland et al. in a sense which is highly pertinent to my results. In the experiment of Ekland et al (as I pointed out in my first reply to Art), information was transmitted from RNA to RNA. As a result,
the formal entropy difference between source and receiver is zero. Therefore,
there should be no formal dependence on Na (the number of amino acids in the
equivalent peptide chain).
In contrast, the technique of Wilson et al. is to start with DNA and encode for
peptides. Therefore, the full entropy difference of 1.79 bits per amino acid plays a role in their results. As a result, if Wilson et al. were attempting to construct a library containing peptides with varying Na values, the frequencies of random generation should scale as 10^(-0.5Na). But Wilson et al attempt no such thing: they are interested only in creating peptides which are ALL OF PRECISELY THE SAME LENGTH. Each of the peptides in their library is designed to be exactly 88 amino acids long. Therefore Wilson et al are not in a position to test my predicted dependence of 10^(-0.5Na). There is no conflict between my predictions and the results of Wilson et al.
Art points out that Wilson et al. found that long peptides which bind to streptavidin (each binder being of length 88 aa) occur with a frequency
which is not very different from the frequency of much shorter
peptides which also bind to streptavidin. (The shorter peptides contain
from 5 to 38 aa.) This may very well be so, but this is a very different
problem (as far as physics is concerned) from the problem I address in my paper. In my paper, I ask: how easy is to GENERATE RANDOMLY a string of Na amino acids?
In my paper, I simply do not address the question that Art has raised: how easy is it for peptides of differing lengths to bind to a particular molecule? The question as to how a peptide binds to another molecule is an interesting one, but it was not a topic of my paper. As Art points out, functionality in proteins may depend on collections of highly degenerate motifs which operate in a modular fashion.
In this regard, a question of primary interest to my work is: How short might an individual motif be? This is exactly the question I tried to answer in picking my shortest possible protein, with Na = 14. What does the literature say about this topic? Following up on leads provided by Wilson et al. I note that there are reports that, in certain cases, 11 aa might suffice for a protein to do its task (Abedi et al. BMC Mol Biol 2: 10, 2001), or maybe as short as 8 aa (Pollack and Gilman PNAS 94 13388, 1997), or maybe 15 aa (Giniger and Ptashne Nature 330, 670, 1987), or maybe pairs of 11-aa peptides (Blair et al. Mol. Cell Biol. 14, 7226 1994), or maybe triplets of 18-aa peptides (Tanaka and Herr 1994 Mol Cell Biol. 14, 6056).
It is not just the number of aa's that matter for the structural motif,
but also how they are arranged: Hope et al. suggest that the basic unit of activation might be a pair of alpha-helices (1988 Nature 333, 635). And if the helices cannot form, the efficiency of protein function disappears (Giniger and Ptashne). Thus, my idea of taking at least a pair of secondary structures (such as alpha helices) as the minimum construct, remains consistent.
However, the importance of the modular approach is that the efficiency of
protein operation (e.g. activation of transcription) is in many cases found to be
proportional to the OVERALL LENGTH of the activating region. (Art refers to
this effect.) It is as if activation depends on a repeated structure composed
of small units acting additively. In such a case, the level of protein
activity goes up in proportion to the number of copies of the motif are present
(Lu et al. PNAS 97, 1988, 2000). Therefore, longer peptides (such as the 88-aa chains of Wilson et al.) should certainly be more efficient at their task than shorter chains (5-38aa). This explains why Wilson et al. were able to discover some peptides which displayed much stronger binding (with nanomolar affinity) to the target (streptavidin) than did the shorter peptides in previous searches for such aptamers (with micromolar affinity).
But I see no contradiction here with my work. Neither do I see a mystery:
if a protein wants to "grab on" to another molecule, and it has a
short motif which is good for providing a "hand to grab with", then two "hands" will be better than one. (A two-handed person can climb a mountain with an efficiency which is a lot more than twice that of a one-handed person.) Three or more "hands" would be still better. The beneficial effects are additive.
As Wilson et al point out, the very fact that there is room for a 38-aa unit to be "fitted in" to 50 different "slots" in the 88-aa peptide by simply shifting registers provides an immediate expansion of 50 in the sequence space. Therefore, since the peptides created by Wilson et al (88-aa) are each as much as 2-16 times longer than earlier peptides (5-38 aa), it is not surprising that improvements in affinity by factors of 200- to 2200-fold are achieved by Wilson et al. (see their Table 2).
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Dermott J. Mullan
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posted 23. December 2002 16:43
Reply to Frances (member No. 169) who posted a comment about my paper on 23 November 2002
Thank you for your comments.
First let me say that the end of your first paragraph appears to be missing: my version of that paragraph ends with the words "It pleases me to..." May I ask what follows?
Next, I appreciate your clarifying comments on mRNA, tRNA, and rRNA. I am indeed interested in the RNA world hypothesis.
You claim that my calculations do not reflect the latest ideas on how life may have started. You refer to work by Orgel and Miller on peptide nucleic acids (PNA's) which are "much simpler than RNA". I'm not sure what you mean by much simpler: the PNA molecule consists of a "ladder" in which the rungs are bases, but the sides of the ladder (to which the rungs are attached) are peptide chains. Thus, PNA is like RNA except that the sides of the ladder in RNA are not peptides but ribose-phosphate chains.
Is this "much simpler"? I do not see it as such. My calculation of the RNA world hypothesis actually specified nothing whatsoever about the sides of the ladder. I simply assumed that (given enough bases in the primordial soup), each time one base collided with another base, the two would bond (somehow) and serve as a piece of the RNA (whether mRNA or tRNA is irrelevant: I'll take whichever one I can get, so as to optimize chances for life to form).
As you can see, my calculation really involves processes in RNA at the most primitive possible level. Assuming that the primordial soup provides the sides of a ladder, I can calculate the chances that a string of bases will be able to combine. My calculation will yield the same numerical answer (for the overall probability) whether the sides of the ladder are peptides or ribose-phosphates.
Your reference to the article where Orgel describes his work is helpful: that article is a remarkably frank discussion of what has and has not been achieved in OoL experiments. The suggestion in that article that minerals might have catalyzed not only the creation of nucleotides but also their polymerization is an interesting point. But once again, it has no effect on my numerical estimates: I assume that N bases will combine into a RNA molecule EVERY TIME there is a collision between two constituents. As I remark in my paper, catalysis may speed up a reaction, but it cannot make the reaction faster than the collision rate: the latter sets a firm and absolute upper limit on reaction rates. And I have used that absolute upper limit in my calculations in order to optimize the chances of as sembling life. Catalysts, even perfect ones, will serve only to reach closer to the limit I have assumed in my calculation. In the absnece of catalysts, the chance sof assembling the first cell are certainly SMALLER than I have calculated.
As regards your quote about Szostak's work on RNA reolication of RNA, I have already disucssed this point in numerical detail in my first response to Art.
Thanks for the referenece to the paper by Saito, Kourouklis and Suga (EMBP 20, 7, 2001). The possibility of RNA-based catalysis is clearly of great interest in the OoL problem. But I reiterate my comments above: I am already assuming that I am working with perfect catalysts when I do my calculations. If no such catalysts exist, then chances of life forming randomly are LESS than I calculate. But even if the catalysts DO exist, and they are perfect, this will NOT improve the chacnes of randomly assembling the first cell above my estimates.
Finally, your reference to a Powerpoint Presnetation on problems with RNA world hypothesis is an incorrect link: when i click on it, it leads me back to the paper by Saito et al.
I would appreciate if you could inform me about the correct link.
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Dermott J. Mullan
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posted 24. December 2002 12:00
reply to message posted by Yersinia (member No. 324) on Nov. 23 2002 21.48
I accept your advice that the way I wrote about the endosymbiotic theory was garbled and/or outdated. I was relying on what Yockey wrote. I view of your comments, I have sent some time on the web updating my information on mitochondria.
As far as I can tell, the ideas are the folllwing:
The first life was in the form of anaerobic prokaryotes (such as the cyano bacteria I discuss in my article), which appeared about 3.5 GYr ago. Later, aerobic prokaryotes appeared, and eventually (about 1.5 Gyr ago) the anaerobic eukaryotes. The latter at some point absorbed the aerobic prokaryotes, which became the mitochondria.
The genome of the mitchondria could become smaller because the nuclear genome supplied for many of their needs. As a result, the genome of current mitochondira are small, encoding for as few a 2 and as many as 67 proteins. Since the original free-standing cells could have had (presumably) maybe 1000-2000 proteins, at least 1000 protein-coding segments have vanished from the mitochondria DNA over time.
The segments which are left are the ones of interest to Yockey (and to me) in discussing the possibility of an earlier genetic code. The fact is, as Yockey points out (p. 192), examples of differeces in the mtDNA coding can be found in nature. For example, the combination CUN (where N=a,c,u,g) encodes for Leu in most cells, but in yeast mtDNA, CUN encodes for Thr. And whereas UGA is usually a nonsense codon, this is not the case in mtDNA: there, it encodes for Trp. And whereas AGA and AGG encode for Arg in most cells, they encode for nonsense in mammalian mtDNA.
Other examples are listed by Yockey.
They demonstrate that the mtDNA encodes in a (slightly) different way from the usual code.
These differences are an important way to determine how things might have changed in the gemnetic code with time.
Specifically, I believe that Yockey makes a strong case for a doublet-codon world by pointing out that 8 amino acids are encoded by "words" such as xyN where x and y are a, c, u, or g, while N stands for anything. Thus, Gly is encoded by GGG, GGC, GGA, GGU. This looks to me as if the third member of the codon is superfluous: the codon would work just as well if only the first two members were present. The fact that 8 of the current 20 amino acids have this behavior is remarkable. Also there are six more amino acids which are encoded by xyM where M is one of U or C or one of A or G. Thus, 14 of the amino acids look as if the first two members of the codon are dominat. the fact that a doublet codon world could handle exactly 14 codons (plus one stop and one start) is remarkable, I think.
As you say, these sorts of differneces provide a fertile technical field of study into how the genetic code itself mght have evolved.
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Dermott J. Mullan
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posted 27. December 2002 01:03
Reply to Kirk Durston (member No. 174) posted Nov. 25, 2002 14;13
You point out that I am starting with a very small cell. You question the utility of such a small cell: you think I have gone too far with this. You may be right, but at least it has opened up the possibility of assembling a cell at random in the early Earth. Of course I agree with your sentiments in the last paragraph of your posting: the hard part is to get information into the system. That is, the software is the difficult part.
Nevertheless, I think it is worth seeing if the hardware of a cell can be put together randomly under ANY circumstances. When i started the calculation, I believed that I would be able to prove mathematically that it is impossible to assemble any cell randomly under any circumstances in the early Earth. And I found that this belief was correct as long as only one polypeptide would be able to perform the function of each of the six basic functions of cell operation. That is, under conditions of maximum possible specificity in protein operation, I can prove mathematically that even a 12-14 cell cannot be assembled randomly in the time available.
However, the possibility that more than one polypeptide might be able to perform each of the six basic cell functions is the essential point of my calculation. Now i find that in the triplet codon world, it is still impossible to randomnly assemble a 12-14 cell. But something new appears in the 2-codon world: at least for a 12-14 cell, random assembly of the cell hardware now does appear to be possible, at least in a certain window. This means that my original belief about the total impossibility of assembling the cell hardware randomly was not founded on a solid basis. I now have to admit that in at least one corner of parameter space, random assembly of a cell (however minimalist) was possible in the early (doublet codon) Earth.
Now, you suggest that i should examine the case of a cell with N_p = 150 proteins each having N_a = 300 amino acids. OK. I'll do that, using the formulas in my paper.
The key formula is on p. 32: the chances of random assembly are 1 in 10^b where b=(N_p+2)X(mlog(N_p) + q_(ra) - q_(max)). (Here, I use ^ to denote superscript and _ to denote subscript).
You suggest that i should use N_p = 150: this leads to b=152(2.18m + q_(ra) - q_(max)).
Now, for N_a=14, I found q_(ra) - q_(max) = 4.6.
In order to address your suggestion, we need to know how q_(ra) and q_(max) depend on N_a. I have already pointed out, in my first reply to Art, that both factors increase linearly with N_a, with certain coefficients. The coefficient of N_a in the expression for q_(ra) is essentially log(64) (the number of codons in the triplet world) while the coefficient of N_a in q_(max) is log(20) (the number of distinct amino acids in proteins).
Therefore, the q_(ra)-q_(max) increases as 0.5N_a where 0.5 = log(64) - log(20). As a result, if I change from N_a = 14 to 300, then q_(ra)-q_(max) will increase from 4.6 to about 150. In such a case, even with minimum specificity (m=1), the exponent of random assembly b is then a large positive number of order 10 thousand. The chances of assembling such a cell are very small, consistent with my conclusion about the triplet codon world.
Now let us go to the doublet codon world.
If N_(aa) = 5, the formula for random assembly on p. 34 is 1 in 10^b where b=(N_p+2)[m log(N_p)+q_d-q_(max)], where q_d-q_(max) = 3.4 for N_a = 14. In this case, with doublet codons, there are 16 words in the source vocabulary, and 5 in the receiver vocab, so the coefficient of N_a dependence in the difference q_d-q_(max) is again 0.5N_a (where 0.5 = log(16) - log(5)). Therefore, setting N_a = 300 (as you suggest), I find that b is again of order 10 thousand. Chances of randon assembly are very small.
But now let us consider the case which I find most interesting: suppose the doublet codon world is encoding for N_(aa) = 14 distinct amino acids + one start plus one stop. Then as on p. 36, q_d - q_(max) becomes a negative number (-2.8) if N_a = 14.
You will now ask; What happens as N_a increases from 14 to 300? Answer: since the entropy of source and receiver are equal, the coefficient of N_a in the difference term q_d-q_(max) is formally zero. That is, the value of N_a is irrelevant. The same answer emerges for N_a = 14 as for N_a = 300, namely: the difference q_d-q_(max) = -2.8.
Therefore, my conclusion remains the same: as long as mlog(N_p) remains less than 2.8, the chances of random assembly are of order unity.
For N_p = 150 (as you suggest), this means that as long as m is less than 1.29 (but no less than 1), the cell you favor, namely a (150-300)cell in my notation, has a good chance of being randomly assembled in the early Earth.
Thus, the window of opportunity persists.
Notice that I am not at all setting a lower bound on the probability. In my paper, when i consider the triplet or doublet codon worlds, I come up with probabilities such as 1 in 10^_79 or 1 in 10^63 and simply leave the result as such. Of course, most people will agree that these probabilities are infinitesimally small.
However, something very diffferent happens in the window of opportunity: here, the probabilities are no longer numbers such as 1 in 10^75. In the window, the exponents 75 approach zero! Now the probabilities are actually of order unity. We are no longer talking about highly IMprobable events, but in highly PROBABLE events.
The change in sign from a positive to a negative exponent in the probability is an essential aspect of my calculation. And this whole possibility arises becaiuse in the relevant formulas, I find that there is an algebraic difference term q_d -q_(max). The existence of this algebraic difference is crucial (as I have pointed out in my first reply to Art).
The magnitude of the difference is linearly proportional to N_a, but the coefficient of N_a depends on entropy differences between source and receiver. Does N_p enter? Hardly at all: only as a logarithmic term, the slowest possible functional dependence. Differences in N_a are in general more important than differences in N_p.
It is the presence of the above algebraic differnece, in combination with the specific entropy difference that occurs in whatever example one considers, that makes it possible for the exponent to change sign in certain regions of parameter space. And this change in sign is at the heart of my argument, for it converts what might have been a very improbable event into a near certainty.
Thank you for suggesting that I try a 150-300 cell rather than a 12-14 cell. I hope I have answered your query.
Thank you also for your comments on Art's comments. I appreciate your comments about the length of a protein and the chances of proteins of different length being functional. I have addressed this point also in my second reply to Art.
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Dermott J. Mullan
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posted 27. December 2002 14:39
Reply to charlie d. member No. 159 who posted a comment on Nov 25 2002 at 20:05
charlie d wrote:
quote:
"the problem with Mullan's calculations is that NO-ONE is claiming that a minimal genome was assembled randomly...irrelevant to current understanding of OoL"
This is a truly sweeping statement: charlie d says that not a single person in the entire population of 6 billion people claims that the genome of the first cell was assembled randomly. How can charlie d possibly make such a statement with any confidence? How can he speak for 6 billion people?
It is public knowledge that certain evolutionists are atheists. Dawkins is a famous example. Also William Provine who spreads "his darwinian gospel that evolution logically leads to atheism: 'and that's why the vast majority of working evolutionists are in fact atheists'" (Witham: Where Darwin meets the Bible, Oxford Univ press, 2002, p. 8).
Someone who is literally an atheist cannot rely on a designer of the first cell (either its chemical makeup or its information content).
So what will such a person turn to in order to account for the first cell and its genome?
It seems inevitable to me that such people have nowhere else to turn but random assembly of both cell and genome.
Can charlie d say with confidence that Dawkins and Provine do NOT claim that random assembly was at work to bring the first cell into existence? If Dawkins and Provine do not claim such, then I stand corrected. But I still have 5,999,999,998 other people to check up on.
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charlie d.
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Member # 159
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posted 27. December 2002 21:09
LOL. I stand corrected, it is indeed possible that a human being on the planet today may imagine that the first living cell arose complete, in one fell swoop, entirely by chance (and if not today, maybe tomorrow someone will change their mind, who knows?). ![[Big Grin]](biggrin.gif)
Of course, what I meant is that random cell assembly is not the position of modern evolutionary biologists or OoL scientists (indeed, almost certainly, not the position of the overwhelming majority of biologists), and therefore Dr. Mullan's criticism is directed to the wrong people, and the wrong theory. Inasmuch as his paper is criticizing that particular tornado-in-a-junkyard hypothesis, and not modern evolutionary theory or OoL science, Mullan's criticism may even be scientifically sound; alas, it is also an exercise in futility.
As for the specifics, I am actually quite sure that even Dawkins and Provine (die-hard atheists as they are) know enough biology to understand that the current working hypothesis for OoL research is that the first cells arose gradually, after many millions of years of chemical evolution, and that the first replicators were acellular. In reality, however, it is entirely unclear to me why it should matter at all whether Dawkins and Provine are atheists, quakers, or whatever: the point here is not whether life has any trascendental meaning, but how it first arose, mechanistically.
Instead of asking me to account for 6 billion opinions on the OoL, thus, it is probably more appropriate for Dr. Mullan to provide some reasonably recent published reference from the professional relevant literature claiming that the first complete cell must have arisen by random assembly of its components as in the hypothesis criticized in his paper (I noticed any such specific reference is oddly lacking in his manuscript). After all, if this is, as he seems to claim, the current mainstream OoL hypothesis, rather than just another convenient strawman, finding several appropriate references in the literature should be exceedingly easy.
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Dermott J. Mullan
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posted 28. December 2002 22:32
reply to charlie d's comment on Dec. 27 2002
I think you are asking for the impossible. How can I find a published paper in the recent biological literature about random assembly of the first cell if (according to your claim) the vast majority of modern bioogists do not believe in the process? The scientists I know do not write papers on topics they do not believe in.
Apart from that, however, I gather from your comment that you have not read my paper in its entirety. You claim that I am arguing against random assembly of the first cell. But in Sections 19-22 I spell out conditions (in the doublet codon world) where the hardware of the first cell COULD have been assembled with high probability.
I might speculate that the vast majority of biologists today may have abandoned the possibility of random assembly of the first cell because they thought the mathematics would NOT work. And in a triplet codon world, I agree with that conclusion. But what I have shown is that there IS a pathway through phase space where (under the right conditions) the hardware of the first CAN be assembled randomly. Whether it survives or not is another matter which I have not addressed with any completeness.
If my numerics are correct, one might conjecture that the hypothesis of random assembly may have been abandoned prematurely.
Of course, I have not addressed at all the origin of the genetic code. I merely discuss the assembly of hardware.
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