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Join Date: Mar 2002
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Posts: 1,976
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ISCID 'publishes' another probability argument
I read the whole damn thing, and to save you guys the trouble, here are what I thought were the key ... uh, flaws:
From <a href="http://www.iscid.org/ubbcgi/ultimatebb.cgi?ubb=get_topic&f=6&t=000233&p=1" target="_blank">here</a>:
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In view of these bare-bones requirements, it is hard to imagine how any cell could function without at least the following six types of proteins: (i) those that help to digest food, (ii) those that generate energy for cell operations, (iii) those that carry away waste products, (iv) those that preserve and repair the cell membrane, (v) those that determine when reproduction is to occur, and (vi) those which actually catalyze the tasks of reproduction. Corresponding to each of these six, there must be a regulatory protein which ensures that the corresponding protein does not "express itself" in the wrong location in the cell. It is hard to imagine how a living cell would exist at all if it failed to contain at least these 12 proteins.
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--pg. 15
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In view of this, we can derive an absolutely firm (and probably very generous) upper limit on the number of two-body reactions n2 that occurred between two amino acids during any time interval by calculating the number of collisions ncoll that occurred between those two amino acids during that interval. In practice, n2 is probably orders of magnitude smaller than ncoll. The purpose of a catalyst is of course to increase n2 as much as possible: however,even with a *perfect* catalyst, n2 can never exceed ncoll. So let us turn to estimating ncoll. This number, which is *large* but finite, will provide us with a firm piece of quantitative evidence that will allow us to test the assertion that the first cell was assembled randomly.
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--pg. 25
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13.3. Total number of collisions between amino acids in 1.11 b.y.
Finally, we ask: what was the total number of reactions between amino acids that occurred in the primeval soup before the first cell appeared? The answer is again straightforward: since each amino acid experienced nr(1) in that time, and since there were ntotal amino acids in the primeval soup, the total number of reactions nr between amino acids was about 10^65 before the first cell appeared.
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--pg. 28
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With f=1.08m, and qra . qmax = 4.6, the chance Pr is about one in 10^(15m+64.4). Since m cannot be less than 1, Pr is certainly less than one in 10^79. If m takes on its average value mav = 9, Pr decreases to 1 in 10^200. Even if m takes on values that are much smaller than mav (say 2-3), the probability Pr amounts to only one in 10^(94-109).
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--pg. 32
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23. Conclusion
We have numerically evaluated the probability Pr that, in the first 1.11 billion years of Earth.s existence, random processes were successful in putting together the RNA for the first cell. In estimating Pr, we initially assumed that the first cell follows the rules which guide modern life-forms. That is, we assume there are Naa = 20 distinct amino acids in proteins, and triplet codons in the genetic code.
In calculating Pr, we consider only the random assembly of RNA: we assume that once the RNA is present, it will generate the proteins for the cell. (Thus, we are not requiring that the proteins be assembled randomly: if we were to impose such a requirement, the probabilities of random assembly of the first cell would be even smaller than the results we obtain here.) Furthermore, we consider a cell which is much smaller than those which exist in the modern world. The latter contain at least 250 proteins. By contrast, we have reduced the requirements of the first living cell to a bare minimum: we assume that that cell was able to function with only 12 proteins. Compared to the smallest known living cell, our choice of 12 proteins seems almost absurdly reductionist. Our "cell" looks more like a modern virus (which cannot reproduce itself) than a bona fide cell. But we proceed anyway.
Moreover we also assume that each protein consists of a chain of no more than 14 amino acids. We refer to this as a (12-14) cell. Again, a chain with only 14 amino acids is considerably shorter than the smallest known protein in the modern world (which contains a few dozen amino acids). It is not clear that a protein with only 14 acids would be subject to the 3-dimensional folding which is essential to protein functioning. Nevertheless, we make these reductionist assumptions about a cell with the aim of optimizing the probability of assembling the first cell.
In this spirit, we start with the assumption that the only amino acids which existed in the primitive Earth were the 20 (or so) distinct types of amino acids which occur in the proteins of modern living cells. Also in the spirit of optimization, we assume that the entire pre-biomass of the Earth was in the form of proteinous amino acids. We specifically exclude the non-biological amino acids (numbering more than one hundred) which may have been produced in the primitive Earth. Moreover, we also assume that all 20 of the proteinous amino acids were present solely in the L-isomer form so that the growth of a protein chain is not ended prematurely by unintentional inclusion of a D-isomer. Furthermore, we assume that the initial cell occurred in the physical conditions which are most commonly cited in textbooks, i.e. in a "primeval soup". This allows us to obtain a firm (and generous) upper limit on the number of chemical reactions which could have occurred before the first cell appeared on Earth.
With all of these assumptions, we find that the probability of assembling the RNA required for even the most primitive (12-14) cell by random processes in the time available is no more than one in 10^79.
In order to improve on the probability that random processes assembled the RNA for the first cell, we make the (unproven but likely) assumption that proteins in the earliest cells were constructed from a smaller set of distinct amino acids than those which occur in modern cells. In order to ensure that the primitive life forms had a similar level of error protection in their genetic code as that which exists in the modern world, we consider a case in which the early proteins consisted of only Naa = 5 distinct amino acids. For these, the genetic code can operate with doublet codons. In such a world, the probability of randomly assembling the RNA for the first cell in the time available is certainly larger than in our modern (triplet codon) world. But the probability is still small, no more than one part in about 10^63.
We have identified a region in parameter space where, once the genetic code exists, the probability of random assembly of the first cell could have reached formally large values in optimal conditions. These conditions include the following: (i) the first cell contained 12 proteins; (ii) each protein in the cell contained 14 amino acids; (iii) there were 4 bases in DNA; (iv) the protein specificity index was no larger than 2.5 (far below its average value); and (v) conditions in the primitive pre-biosphere were such that chemical reactions occurred at their maximum possible rates. (The last of these conditions almost certainly involves an optimization which is unrealistic by as much as 10 orders of magnitude.)
(Note that we have said nothing about how the genetic code came into existence. We merely assume that it is already in operation. The origin of the code is a more formidable problem than the one we have addressed here.) If mathematics were the only consideration, our conclusions would suggest that the RNA for the first cell could have been assembled randomly in the primeval soup in 1.11 b.y. once there was a code and abundant supplies of between 11 and 14 distinct proteinous amino acids. However, when we take into account considerations of coding theory (especially the necessity to protect the proteins from errors of transcription), it appears that this region of parameter space is hostile to protein production. And the genetic code has to pass through a "bottleneck" in order to enter into the modern world, with its 20 proteinous amino acids. As a result, the first cell might have had serious difficulties surviving as an autonomous biological system.
Finally, the extreme nature of our assumptions regarding the first cell (12 proteins, each containing 14 amino acids) can hardly be overstated. If a cell is to fulfil even the minimum requirements of a Von Neumann self-replicating machine, it probably needs at least 250 proteins. Even with multiple optimizations in our assumptions about the primeval soup, the window of opportunity for creating such a cell in 1.11 b.y. narrows down to a very restricted region in phase space: (I) there must have been exactly 14 distinct amino acids in the cell proteins, (II) the protein specificity index must have been between 1.0 and 1.17, and (III) at least 10^58 chemical reactions must have occurred between the bases (or amino acids) in 1.11 b.y. The "fine tuning" of such conditions presents a problem. However, there are more serious problems than fine tuning: error protection in the genetic code fails altogether in these conditions. Even the Central Dogma of biology breaks down. A cell formed under these conditions would truly be subject to serious uncertainties not only during day-to-day existence but especially during replication. The cell could hardly be considered robust.
Nevertheless, as Yockey (p. 203) points out, the possibility that an organism from the doublet-codon world might have survived the "bottleneck" may have some empirical support. According to the endosymbiotic theory (L. Margulis 1970, Origin of Eukaryotic Cells, Yale Univ. Press, New Haven CT), mitochondria might have been at one time free-living bacteria which now survive in a symbiotic relationship with the cytoplasma of other cells. In mitochondria, the genetic code differs somewhat from the code in other cells. Perhaps mitochondria are representative of organisms which originated in the doublet-codon world, but which could not survive on their own because of the difficulties associated with the hostile zone of parameter space where they originated.
In summary, if the first cell actually originated by random processes, the genetic code must already have existed, and conditions must have been "finely tuned" in order to trace a path through a narrow (and hostile) region of parameter space. The idea that some of the constants of the physical world have been subject to "fine tuning" in order to allow life to emerge, has been widely discussed in recent years (e.g. in the book by J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle, Oxford University Press, 1994, 706 pp). If we are correct in concluding that "fine tuning" is also required in order to assemble the first cell, we might regard this conclusion as a biological example of the Anthropic Principle.
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--pg. 44-47
[ November 23, 2002: Message edited by: Principia ]</p>
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11-23-2002, 05:37 PM
