Over at Evolution News, Dr. Douglas Axe argues that merely by using very simple math, we can be absolutely certain that life was designed: it’s an inescapable conclusion. To illustrate his case, he uses the example of a rugged block of marble being transformed by natural weather processes into a statue of a human being. Everyone would agree that this simply can’t happen. And our conclusion wouldn’t change, even if we (i) generously allowed lots and lots of time for the statue to form; (ii) let each body part have a (discrete or continuous) range of permitted forms, or shapes, instead of just one permitted shape; (iii) relaxed the requirement that all body parts have to form simultaneously or in sync, and allowed the different parts of the statue to form at their own different rates; and (iv) removed the requirement that the different parts have to each form independently of one another, and allowed the formation of one part of the statue to influence that of another part.
In his post, Axe rhetorically asks: if we’re so sure that a rugged block of marble could never be transformed by the weather into a human statue, then aren’t we equally entitled to conclude that “blind natural causes” could never have “converted primitive bacterial life into oaks and ostriches and orangutans”? In each case, argues Axe, the underlying logic is the same: when calculating the probability of a scenario which requires many unlikely things to happen, small fractions multiplied by the dozens always result in exceedingly small fractions, and an event which is fantastically improbable can safely be regarded as physically impossible.
In an attempt to persuade Dr. Axe that his logic is faulty on several grounds, I’d like to put eight questions to Dr. Axe, and I sincerely hope that he will be gracious enough to reply.
My first question relates to the size and age of the universe. As I understand it, Dr. Axe, you define “fantastically improbable” as follows: something which is so improbable that its realization can only be expected to occur in a universe which is much bigger (or much older) than our own. Indeed, on page 282 of your book, Undeniable, you further stipulate that “fantastically improbable” refers to any probability that falls below 1 in 10116, which you calculate to be the maximal number of atomic-scale physical events that could have occurred during the 14-billion-year history of the universe. You calculation requires a knowledge of the age of the universe (14 billion years), the amount of time it takes for light to traverse the width of an atom, and the number of atoms in the universe. So here’s my first question for Dr. Axe: how is the design intuition supposed to work for an ordinary layperson who knows none of these things? Such a person will have no idea whether to set the bar at one in a million, one in a billion, one in 10116 , or even one in (10116)116. I should also point out that the figure you use for the number of atoms in the universe refers only to the observable universe. Astronomers still don’t know whether the size of the universe as a whole is finite or infinite. And it gets worse if we go back a few decades, in the history of astronomy. Until the 1960s, the Steady State Theory of the universe was a viable option, and many astronomers believed the universe to be infinitely old. How would you have argued for the design intuition back then?
My second question relates to functional coherence. You make a big deal of this in your book, Undeniable, where you managed to distill the case for Intelligent Design into a single sentence: “Functional coherence makes accidental invention fantastically improbable and hence physically impossible” (p. 160), where functional coherence is defined as a hierarchical arrangement of parts contributing in a coordinated way to the production of a high-level function (p. 144). The problem with your statue illustration should now be apparent. A statue has no functions. It just sits there. Consequently, whatever grounds we may have for rejecting the supposition that ordinary meteorological processes could transform a block of marble into a statue, they obviously have nothing to do with the argument you develop in your book, relating to functional coherence and whether living things could possibly be the product of unguided natural processes. So my question is: will you concede that the marble block is a bad illustration for your argument relating to functional coherence?
My third question relates to the identity of the object undergoing transformation. In your statue illustration, you ask whether “a rugged outcrop of marble would have to be altered by weather in only a few reasonably probable respects in order to convert it into a sculpted masterpiece.” Obviously, the answer is no: the number of steps would be extremely large, and the steps involved would be fantastically improbable. You then compare this case with the evolutionary claim that “blind natural causes converted primitive bacterial life into oaks and ostriches and orangutans.” But there is an obvious difference in the second case: the primordial bacterium itself is not being changed into an orangutan. Its very distant embryonic descendant, living about four billion years later, is developing into an orangutan. Its ancestors 20 million years ago were not yet orangutans. Self-replication, along with rare copying mistakes (mutations), is required in order for evolution to work. So I’d like to ask: why do you think it’s valid to infer from the fact that A’s changing into B is a fantastically improbable event, that A’s distant descendants gradually mutating into B is also fantastically improbable?
My fourth question relates to chemistry. Let me return to your original example of a block of marble being transformed by weather events into a human statue. I think we can all agree that’s a fantastically improbable event. However, the probability is not zero. I can think of another event whose probability is much, much lower: the likelihood of weather processes transforming a block of diamond, of adamantine hardness, into a human statue. What’s the moral of the story? Chemistry matters a lot, when you’re calculating probabilities. But the average layperson, whom you suppose to be capable of drawing a design inference when it comes to living things, knows nothing about the chemistry of living things, beyond the simple fact that they contain atoms of carbon and a few other elements, arranged in interesting structures. An ordinary person would be unable to describe the chemical properties of the DNA double helix, for instance, even if their life depended on it. So my question to you is: why do you think that a valid design inference can be made, without knowing anything about their underlying chemistry?
My fifth question relates to thermodynamics. I’d like you to have a look at the head of Aphrodite, below (image courtesy of Eric Gaba), known as the Kaufmann head. It’s made of coarse-grained marble from Asia Minor, and it dates back to about 150 B.C.
You’ll notice that her face has worn away quite a bit, thanks to the natural weather processes of weathering and erosion. This is hardly surprising: indeed, one might see weathering and erosion as an everyday manifestation of the Second Law of Thermodynamics: in an isolated system, concentrated energy disperses over time. Living things possess an unusual ability to locally decrease entropy within their
highly organized bodies as they continually build and maintain them, while at the same time increasing the entropy of their surroundings by expending energy, some of which is converted into heat. In so doing, they also increase the total entropy of the universe. But the point I want to make here is that a living thing’s highly useful ability to locally decrease entropy is one which a block of marble lacks: its thermodynamic properties are very different. So my question to you is: why would you even attempt to draw an inference about the transformations which living things are capable of over time, based on your observations of what happens to blocks of marble? And why would you encourage others to do the same?
My sixth question relates to your probability calculations. In your post, you explain the reasoning you employ, in order to justify a design inference: “it takes only a modest list of modestly improbable requirements for success to be beyond the reach of chance.” You continue: “Once again, the reasoning here is that small fractions multiplied by the dozens always result in exceedingly small fractions.” Now, this kind of reasoning makes perfect sense, if we are talking about dozens of improbable independent events: all you need to do is multiply the probability of each event, in order to obtain the probability of the combination of events. But if the events are not independent, then you cannot proceed in this fashion. Putting it mathematically: let us consider two events, A and B. If these events are independent, then P(AB) is equal to P(A) times P(B), and if both individual probabilities are low, then we can infer that P(AB) will be very low: one in a million time one in a million equals one in a trillion, for instance. But if A and B are inter-dependent, then all we can say about P(AB) is that it is equal to P(A) times P(B|A), and the latter probability may not be low at all. Consequently, in an inter-dependent system comprising dozens of events, we should not simply multiply the small probability of each event in order to compute the combined probability of all the events occurring together. That would be unduly pessimistic. And yet in your post, you attempt to do just that, despite your earlier statement: “Do I assume each aspect [of the statue] is strictly independent of the others in its formation? No.” So I’d like to ask: if you’re willing to grant that the even the formation of one aspect of a statue may depend on the formation of other aspects, thereby invalidating the method of calculating the probability of the forming the whole statue by multiplying dozens of “small fractions,” then why do you apply this invalid methodology to the formation of living things?
My seventh question relates to the vast number of possible pathways leading to the formation of a particular kind of living thing (such as an orangutan) from a primordial ancestor, and the even vaster number of possible pathways leading to the formation of some kind of living thing from the primordial ancestor. The point I want to make here is a simple one: this or that evolutionary pathway leading to an orangutan may be vanishingly improbable, yet if we consider the vast ensemble of possible pathways leading to an orangutan, the probability of at least one of them being traversed may not be so improbable. And even if we were to agree (for argument’s sake) that the likelihood of an orangutan evolving from the primordial ancestor is vanishingly low, when we consider the potentially infinite variety of all possible life-forms, the likelihood of evolutionary processes hitting on one or more of these life-forms may turn out to be quite high. It is this likelihood which one would need to calculate, in order to discredit the notion that all life on earth is the product of unguided evolutionary processes. Calculating this likelihood, however, is bound to be a very tricky process, and I doubt whether there’s a scientist alive today who’d have even the remotest idea of how to perform such a calculation. So my question is: what makes you think that an untutored layperson, with no training in probability theory, is up to the task? And if the average layperson isn’t up to it, then why should they trust their intuition that organisms were designed?
My eighth and final question relates to algorithms. Scientific observation tells us that every living thing, without exception, is put together by some kind of biological algorithm: a sequence of steps leading to the formation of an individual of this or that species. The algorithm can thus be viewed as a kind of recipe. (Contrast this with your illustration of a statue being formed by blind meteorological processes, which bears little or no relevance to the way in which a living thing is generated: obviously, there’s no recipe in the wind and the rain; nor is there any in the block of marble.) In order for “blind natural processes” (as you call them) to transform a bacterial ancestor into an orangutan, the algorithm (or recipe) for making an ancient bacterial life-form needs to be modified, over the course of time, into an recipe for making an orangutan. Can that happen?
At first blush, it appears fantastically unlikely, for two reasons. First, one might argue that any significant alteration of a recipe would result in an unstable hodgepodge that’s “neither fish nor fowl” as the saying goes – in other words, a non-viable life-form. However, this intuition rests on a false equivalence between human recipes and biological recipes: while the former are composed of letters which need to be arranged into meaningful words, whose sequence of words has to conform to the rules of syntax, as well as making sense at the semantic level, so that it is able to express a meaningful proposition, the recipes found in living things aren’t put together in this fashion. Living things are made of molecules, not words. What bio-molecules have to do is fit together well and react in the appropriate way, under the appropriate circumstances. Living things don’t have to mean anything; they simply have to function. Consequently, the recipes which generate living things are capable of a high degree of modification, so long as the ensembles they produce are still able to function as organisms. (An additional reason why the recipes found in living things can withstand substantial modification is that the DNA found in living organisms contains a high degree of built-in redundancy.)
Second, it might be argued that since the number of steps required to transform a bacterial ancestor into an orangutan would be very large, the probability of nature successfully completing such a transformation would have to be fantastically low: something could easily go wrong along the way. But while the emergence of an orangutan would doubtless appear vanishingly improbable to a hypothetical observer from Alpha Centauri visiting Earth four billion years ago, it might not seem at all improbable, if the Alpha Centaurian also knew exactly what kinds of environmental changes would befall the Earth over the next four billion years. The probability of evolution traversing the path that leads to orangutans might then appear quite high, notwithstanding the billions of steps involved, given a suitably complete background knowledge of the transformations that the Earth itself would undergo during that period. In reality, however, such a computation will never be technically feasible: firstly, because we’d probably need a computer bigger than the cosmos to perform the calculation; and second, because we’ll never have the detailed knowledge of Earth’s geological history that would be required to do such a calculation. So my concluding question to you is: given that the probability of nature generating an orangutan from a bacterial ancestor over a four-billion-year time period is radically uncomputable, why should we trust any intuitive estimate of the probability which is based on nothing more than someone eyeballing a present-day bacterium and a present-day orangutan?
Over to you, Dr. Axe. Cheers.
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Now Bill Cole comes along. “omg, the two genes have differences, this is evidence against they evolved”.
This is where we are. Ladies and gentlemen, I rest my case.
colewd,
Well, I’m not supporting Entropy, because he is being waaay too nice to you. He highlighting the idiocy of the P(all alpha helix) calculation, which is a (relatively) small source of error in your calculations.
Allan and I have (on different occasions) pointed out the hilarity that ensues from your bogus 20^L calculation.
Here’s more ridicule:
Consider your 2500 amino acid protein.
According to YOU, if there were only 19 amino acids, then it would be 55 orders of magnitude more likely.
It’s deranged.
Rumraket,
Because with long sequences even 50% substitutability (hydrophobic and hydrophilic AAs) create a huge combinatorial problem. With 2500 AAs it is 2^2500. The empirical evidence show cases with substitutability much worse then this. In the case of PRPF8 the protein in very highly conserved.
DNA_Jock,
Jock now you are distorting claims. Maybe its time to lay down your sword. You are facing a combinatorial problem there is no way out of this.
Rumraket,
You and Jock are resorting to logical fallacies. Its time to lay down your sword.
Sure. 20 amino-acids that have tendencies towards forming alpha-helices, beta-strands, loops, and turns. Four kinds of structures, rather than heads and tails, the analogy should still help you understand the problem with your all-alpha-helix scenario.
Really? So we should not expect coins to land in combinations of heads and tails, nor should we expect protein sequences to “land” in combinations of alpha-helices, beta-strands, loops and turns? Did you know that these secondary structures were predicted based on the basic physical-chemical properties of proteins?
I don’t need that at all. All I need is to understand that their combinations will have tendencies towards either of those secondary structures to predict that a 2500 aa-long protein will show a combination of alpha-helices, beta-strands, loops and turns. That it won’t be just a very long alpha-helix. How far off do you think I’m in that prediction?
I know this is a devastating blow to your misguided use of alpha-helix probabilities, but that’s life.
It’s like Bill just doesn’t understand the difference between the total size of the landscape, and the shape of it.
And he thinks that sequences observed in living organisms constitute, roughly, almost the entirety of selectable function. We see some sequences, and so we must infer those are the only possible selectable functions.
When it comes to unprobed areas of the landscape, he becomes a radical skeptic, and inferences about these areas having been traversed over geological time become, in his mind, a kind of wishful thinking.
Pardon the mspaint, but he effectively sees landscape A, and thinks B is unreasonable conjecture, because the total landscape is 20^L.
What logical fallacies? Point them out.
Bill at this point I suspect even you must know what you’re saying isn’t true.
Entropy,
This I agree with this but at the end of the day you have a combinatorial problem that can be reduced by substitutability to create the secondary fold. 2500 amino acids is a large mountain to climb.
You have not yet made the case that you can reduce it from the alpha helix estimate based on Jocks numbers as the other folds maybe less probable then the alpha helix.
Rumraket,
You both are creating straw-men. I was arguing about a 2500 AA sequence and you changed the argument to a 6 AA sequence. One has 20^6 possible sequences the other has 20^2500 possible sequences. I am going to be charitable and not accuse you of dishonesty as you accused me.
Why? You have just repeated the claim that there is a huge combinatorial problem. You have not shown what the problem is. Saying “even if you increase substitutability there is still a huge problem” doesn’t show that there actually is a problem. Bill it’s like you don’t understand the difference between INSISTING that there is a problem, and DEMONSTRATING that there is a problem.
Try this for an analogy: I say there’s a problem with crossing some island on foot, you ask me why? I say “there are 10^500 trees on the island”. You ask “why is that a problem?” I respond “Even if we reduce that by 50%, there’s still 5^500 trees on the island”.
At this stage, I have yet to actually show that one cannot walk across the island.
It doesn’t matter how many trees there are, what matters is how they are arranged and how tightly they are packed. If they form a giant wall that can’t be climbed or squeezed through somewhere, then yes the island can’t be crossed. But no amount of me talking about how many trees there are constitutes any sort of information about how, or how densely, they are arranged.
What empirical evidence?
Yes they are, but how does that tell you how the unprobed areas of the landscape look?
You see the red dots in this landscape below, and you say “look, they’re highly similar” and so you infer the landscape must look like A. Why? How do you know that?
We say “but there’s also the orange dots, how do you know they didn’t evolve from some common ancestral sequence somewhere in the lower area between them?”
So, how do you know that? You seem to be claiming that you DO know that. And your argument is “the red dots are conserved”. And “the orange dots, and the red dots have dissimilarities, this is evidence against them having evolved”. How do you know that?
HOW do you know that?
The size of the landscape is 20^L
The red dots are conserved.
The orange dots are conserved, and dissimilar from the red dots.
How do you get from those three facts, to “there is a huge combinatorial problem”? What problem?
How
do
you
know
that?
Rumraket,
What is the shape of the PRPF8 landscape Rum? What is the substitutability of the AA’s considering it is highly conserved? What did it take to go from a disordered protein to the ordered protein we are observing? What function was it performing as a disordered protein?
Bill, I was addressing your claim that sequence differences is evidence against evolution. It would be trivial, but boring, to sit there and type out 2500 letter-long sequences and mutate them incrementally. But the argument would remain unaltered. How the hell would the fact that there are sequence differences, somehow constitute evidence against them having evolved incrementally from some common ancestor?
There are 20^2500 possible sequences, okay. So what? Why does that imply that when we find two somewhat dissimilar L=2500 sequences that this is evidence against them having evolved? What does the size of the total space hav to do with how they came to exist in their present form? You never connect these dots. You blather over and over again about how big the landscape is. Nothing follows from this alone.
Rumraket,
How
do
you
know
that?
Love this 🙂 We know this because of the preservation over deep time of proteins like PRPF8. It shows a limit to their substitutability. Unless you can show almost unlimited substitutability your theory is toast. The fat lady has been warming up for a while 🙂
Rumraket,
Rum, reproduction will pass along similar sequences and this is a fact. The longer the sequence the more subtle a single substitution will look. This is why your argument was a straw man. Another observed fact is preservation over deep time. This shows a limit to substitutability. All together Axe’s claim is spot on.
So you admit that you don’t actually know this, so you don’t actually know that there is a “huge combinatorial problem”, and by implication, it cannot be the case that dissimilarities in sequence constitutes evidence against them having evolved.
Now that we have conclusively settled that you don’t have a case, and just now have discovered this, you try to switch the burden of proof to me. Hilarious.
To think of all the time you have spent insisting there’s a huge combinatorial problem, because 20^L is huge, only to now realize you can’t actually back that up.
Well it is at least the level of differences we see between the sequences from prokaryotic group II self-splicing intron encoded PRPF8 homologues, and eukaryotic ones. And that is the most conservative estimate I can make. These must have derived from some common ancestral sequence simply because of the fact that there is nesting hierarchical structure in the sequence data. No other explanation meaningfully accounts for that observation.
IIRC reverse transcriptases and PRPF8-like proteins are homologous. Reverse transcriptases probably substantially predate the origin of group II self-splicing introns, so PRPF8-like proteins must derive from them.
I don’t know that PRPF8-like proteins (or reverse transcriptases) ultimately derive from a disordered protein, so insisting on me laying out such a scenario is a red herring.
So why can’t they have evolved from somewhere down lower on a slope, with selection pushing them up to where we find them today?
Yes, and?
That doesn’t follow.
Why does it not merely show that selection has driven them up some local optimum from some other area in sequence space? How do you exclude this possibility simply from the fact that they are relatively conserved?
Also, when you insist that less conserved sequences such as prokaryotic group II self-splicing intron-derived PRPF8-like monologues* don’t share common descent with eukaryotic PRPF8, isn’t that essentially special pleading?
I mean you say that some cluster of sequences called PRPF8 are conserved, and this means they can’t have evolved.
So we show you less conserved PRPF8-like sequences from prokaryotes, and even less conserved reverse transcriptases still exhibiting a similar fold and related function, and then you turn around and say their lack of conservation is somehow evidence against them having evolved.
Having your cake and eating it too? How did the lady get fat when you’re hoarding all the sweets?
*This typo is so hilarious I’ll let it stand.
Rumraket,
We don’t need to know the landscape as long as we observe preservation. Preservation shows a limit to substitutability and thats all you need. Sequence length plus preservation equals design or as Eric would say the existence of a halting oracle.
This is possible but it shows a lack of substitutability that this happened. All we need is a little constraint as per Axe’s argument. Why would we see the same optimization in every animal? If your theory is right then it was some very different sequence that existed in bacteria and then suddenly became optimized in yeast and never moved. This itself appears miraculous.
How does preservation distinguish between these two possibilities?
Is not.
You have not addressed one word that I wrote. Simply repeating your fallacy does nothing to strengthen your argument. Has a mutation ever happened? If so, why is the gross size of the space in which it happened of any relevance?
Rather than someone who denies everything except the maths? What biological process does your maths relate to?
It would be a step up from the usual incontinent estimates.
So what about tandem repeat and transposition? Hmmm? Why are you pretending that proteins cannot lengthen? What’s the shortest catalytic peptide?
Rumraket,
It doesn’t have to. The existence of those hills shows functional constraint.
How does it show that?
First of all I’m not sure what you mean by “same optimization”. I suppose you mean why are they so conserved? Well because at the cellular level, PRPF8 performs pretty much the same function in all eukaryotic cells and has became necessary to splice out introns from pre-mRNA well before the diversification of animalia.
For an extremely slow and geologically broad definition of “suddenly”, pretty much yes. Introns “rapidly” (probably hundreds of millions of years) proliferated in eukaryotes after the split from the prokaryotic ancestors that carried group II self-splicing introns, which increased the selective pressure on keeping the functionality of the splicing apperatus, driving the mean fitness of PRPF8 proteins up some local optimum where it has been unable to leave because so many essential proteins came to carry introns that they previously didn’t, which if unspliced would kill the host organism.
Think of it this way. There was some ancestor of extant eukaryotes before all the genes had acquired introns. If these introns happened in non-essential genes with weak fitness benefits, errors in splicing in these genes would be less likely to be selected against.
But if introns manage to insert in something like core metabolism, or translation, or replication related genes, this is likely very different. These genes are conditionally essential, so errors in splicing were more likely to carry huge if not lethal fitness costs.
So if mutations in the splicing apperatus caused splicing errors, that’s would more likely be tolerable up to a certain level if introns had yet to insert in essential genes.
But once introns, which are known to proliferate like selfish genetic parasites, managed to insert in essential genes, splicing errors would be much more likely to be much more costly.
That means splicing apperatus mutants are suddenly much more costly. Carriers of splicing apperatus mutations that cause splicing errors therefore get eventually outcompeted. So in the end, the conservation of core splicing proteins like PRPF8 was driven by the very selfish element that carried them, group II self-splicing introns. As these genetic parasites gradually invaded all the hosts genes, the fitness cost of splicing errors drove the preservation of the function of the splicing machinery.
How so?
I certainly agree it does, but mere functional constraint in the present does not tell us what happened historically. It does not follow that the observed functional constraint is not a product of some historical process. Yet you seem to be arguing that very thing.
So once again I am left wondering why you conclude what you do.
This is nonsense. If we show you a protein that has barely changed, you argue it shows evolution can’t happen. If we show you proteins varying widely, you say the differences are evidence evolution didn’t happen. That is, there is (in your book) no conceivable evidence for evolution even if it happened.
Allan Miller,
What about…What about… your in the weeds Allan. All we need is minor functional constraint. Everything you are claiming that is random does not explain the observation of thousands of optimized functional sequences in the database that are preserved over time. A tandem repeat of a non functional sequence is a longer non functional sequence.
Allan Miller,
Not by the mechanisms of record.
Ironically that doesn’t follow. It might be too short to perform the function of interest, but tanden repeat could form a catalytic cleft with function.
Neither half of a bridge alone allows a vehicle to pass, but the whole bridge does.
Allan Miller,
I would ask a different question. What is the shortest genome in an organism that can self replicate. Lets call it 500k base pairs. 4^500000 ways to arrange it 🙂
How open minded of you. I guess we can conclude this matter then. You insist it isn’t even possible to show evidence for evolution.
Closely related sequences = they are constrained so can’t have evolved.
Divergent sequences = they’re too different, so can’t have evolved.
Guys, guys, just give up okay? That bridge will never join up. Thank you for playing Bill, merry christmas and happy new year.
What does that mean?
Rumraket,
I agree. Nice catch.
The question is does this help us get to a secondary fold?
Oh, why be so cautious? Let’s just say fifty squillion to the power bibble. I’m sure you think you’re playing a blinder, here.
But what about them? Why are you insisting that the only way to make proteins is to pick random acids one by one?
Allan Miller,
-random mutation natural selection, genetic drift, recombination, endosymbiosis etc. Needs to be deterministic. Best candidate is recombination which maybe deterministic but mostly makes change at the gene level.
Rum and Allan thanks for the exchange. Its late for you guys. Lets re engage after Xmas.
Merry Christmas to both you guys.
Of course. If you can get a short stretch of alpha helix, tandem repeat can make it longer. There’s your secondary fold. It was already there of course; you’ve just made it longer. But this illustrates why your calculation, based on random pick over the full present length, is pure bollocks.
And what does that mean? You are resorting to word salad.
FTFY
No, my 10^55 calculation is a faithful rendition of of your V^N math, because:
20^2500 = 19^2500 x 10^55
Changing the number of amino acids in the repertoire has a 10^55-fold effect on your deluded probability calculations.
Switching from your original “substitutability” claim (2^2500) to the “one based on Jock’s numbers” (31%^(2500/6)) is a 10^540 fold change.
You do not understand what the Chou-Fasman 31% means. Here’s what it does NOT mean: it does NOT mean that that probability that a random six-mer will form an alpha helix is 31% (it is higher). Even if it did, your raising 31% to any power is fallacious.
I will try to explain.
Your facts are wrong.
Your logic is wrong.
Your math is wrong.
Facts: the “substitutability” of extant optimized proteins is higher than 50%.
[See McLaughlin et al. Nature 491 138 2012, remembering that you are arguing for the proportion of sequences that have minimal selectable function: about 90% of PDZ’s neighbours have function.]
Logic: As Rumraket has explained, the landscape surrounding a peak is not informative about the landscape in the lowlands. See Hayashi et al. 2006, Keefe & Szostak 2001, etc.
Math: Every time you take a probability and raise it to a power, you are assuming independence. This too is ludicrous. If I have a “one in a million” 20-mer that carries a stable helix-turn-helix motif, what is the probability of a 40-mer that forms a stable helix-turn-helix-loop-helix-turn-helix structure? It is NOT 1 in a million million. A 60-mer that….
Every single one of these errors has been pointed out to you multiple times, yet you make the same errors again and again. When people stop trying to correct you, it is not a sign of the power of your argument, rather of resignation.
DNA_Jock,
Jock you are making straw man arguments again. I have never claimed exact math and thats not the argument. Your statement of bias people correcting me is amusing as they are correcting their own arguments and not mine. What you are unable to do is make a positive claim that evolutionary resources can clear the bar of 10^50 trials to get a secondary fold of 2500 amino acids. I gave you 10^40 for your contingent claims. Show me its greater then that.
Thats exactly (except of the ludicrous part 🙂 ) right and I am giving you a contingency of interdependence of 10^40.
You appear to have a mental block around making estimates. This argument is about estimates that are so large it makes the theory look silly.
Were talking about a secondary fold around here of one of 20000 proteins in a eukaryotic cell and you cannot demonstrate that it can be produced by evolutionary mechanisms. I can show by rough estimates that it is exceedingly unlikely given 10^50 total evolutionary resources. This is Axe’s point.
I know you don’t like the x^n calculation because it falsifies the theory you are defending. At the end of the day it is how you calculate the amount of possible way to arrange a sequence and proteins are arranged in a sequence. For evolution by natural variation and selection to have a chance you need to have exceedingly high substitutability around the AA’s and the empirical evidence around preservation shows this is false.
Au contraire, mon ami, I absolutely LOVE your x^n calculation: you have produced obviously ridiculous results with it, completely destroying any credibility. My personal favorite: colewd’s calculation that, for every single 80-mer that can fold (he claims there are only 10^80 of them), there exist another 10 million million that can bind ATP (we agree there are 10^93 of these)!
Math. You are doing it wrong.
DNA_Jock,
Your assertion is that an estimate is wrong based on method however I am using the same x^n divided by total functional sequences available method everyone else uses except you. Szostak Hazen, Hunt, Axe, Felsenstein etc. Lets call it Jock math. I do admire you as you go down swinging 🙂
Why don’t you try to make a positive argument for random genetic change creating a secondary fold versus being a math denier 🙂
Heh. Bill the problem is you haven’t shown that 10^50 “trials” (whatever you even mean by that) is actually required.
It looks like you keep making this mistake of thinking that the size of the space is somehow synonymous with how many different mutants that must be sampled to reach the top of a hill. It is a complete mystery how you have ended up with that fantastically wrong misconception, and you never seem able to explain why it follows from anything.
It’s like you’re saying that for a primordial sequence to crawl up the slope of a hill and reach some local optimum, for even that to happen, some population of randomly mutating organisms would have to sample literally the entirety of the base and slope of the hill. That makes zero logical sense.
Why doesn’t it merely show that some primordial sequence was pushed to some logical optima by selection? How did you rule that out?
DNA_Jock,
As an admin why don’t you argue within the rules?
You misunderstand.
x^n is the size of the sequence space. No disagreement there.
What colewd does is say “the probability of generating an N-mer is P(N), therefore the probability of generating a polymer Y times longer is P(N)^Y”
THAT is the exponentiation that is ludicrous. As you have demonstrated with your calculation that there are only 10^80 80mers that fold, when we know that there are ~ 10^93 of them that bind ATP. It’s frikking hilarious!
Regarding your demand for a “positive argument”, did you read the paper Rumraket referenced?
Foldability of a natural de novo evolved protein
Did you understand it?