Miller: Axe Decisively Confirmed?

My recent article address many of the previous comments:

I will be traveling for the next week, so I might not be able to respond to comments for a while.

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What do you think @Mercer and @art?

I have to say I find your writings in this article very dishonest when I have pointed out several of the misconceptions you have about the Tokuriki and Tawfik papers you reference.

Purifying selection is what makes it possible for a protein to accumulate mutations without losing structural integrity. They even show this in the very papers you reference and I linked the graph in my post. You haven’t understood the paper you are relying on.

I suppose it is possible just you didn’t see my response.

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I’m not a molecular biologist or anything of the sort so it’s hard for me digest a lot of this. But from the article:
“all other functions dependent on a stable structure must also cease.”

Not all functions are dependent on a stable structure though. And these that arent can serve as intermediates to new folded proteins:

Please correct any misunderstandings I may have



From the article.

Some of my argument relies on the evidence that novel proteins are exceedingly difficult to evolve.

Except that in your earlier article, you explicitly claimed that ALL of the evidence supported your position, which was not true. Basic ethics calls for a correction of your false claim.

In discussions with critics, several important questions were raised which led me to further research studies addressing the effect of mutations on protein stability.\

But many of the questions were about the relevance of going backwards, when thousands of existing studies go forward, including catalytic antibodies, the direction much more relevant to your conclusion. At no point have you even acknowledged the existence of such studies to your audience of laypeople. That is highly misleading.

I found that the consistent results of key studies decisively confirm the conclusion of Doug Axe that most natural proteins are too rare to evolve through an undirected search.

In scientific writing, “key studies” does not mean “studies I’ve blatantly cherry-picked to barely support the conclusion I wish to be true.”

But at least it’s a tacit acknowledgment that your “all evidence” claim in the previous article was false. :smile:

It’s also telling that you are unwilling to run it by us here in favor of putting it up on a page that allows no comments.

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You are correct and Brian Miller is incorrect.

Some functions are dependent on an unstable structure. Some are dependent on restabilizing a structure. Many regulations of protein activity change stable to unstable or unstable to stable.

This is the problem with viewing proteins as analogous to metal parts of a machine.

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Even the studies he’s cherrypicked don’t support his claims at all. It’s like they’ve been read with an astonishing degree of confirmation bias.

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@mercer, please unpack this slowly for the benefit of observers. For example, what is a forward study? What is a backward study? What was the inferences made by Axe and @bjmiller, and how are you challenging them?

@bjmiller can you please clarify what issues were raised by us that caused you to go back to the literature? Can you please confirm that we are cited linked to for our meaningful contribution to your important work?

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I don’t see the contradiction here @mercer. He depends on that point and is now examining it. This is not an admission of error.

If one wishes to estimate how hard it is for evolution to find new functions in sequence space, mutating an existing wild-type protein makes little sense–but Axe didn’t even do that. He mutated a [temperature-sensitive mutant] protein that had already been selected to be on the edge of stability.

The conclusion that this was done to generate the lowest number is hard to escape. It seems that if Axe really thought that he had globally-relevant data, he would have done the same sort of experiment with many other unrelated proteins in the last 14 years.

I do. If ALL evidence supports your position, you can’t ignore any of it. And if someone brings up evidence (catalytic antibodies) that you haven’t seen, Miller’s hand-waving to dismiss that evidence still falsifies the claim that ALL evidence supports the position.


You going to have to explain this constructively.

It’s really odd. It would have made more sense for Axe to take some specialized enzyme, then grown his bacteria on plates containing a closely related substrate they’re not normally active on, and tested to see if he could select for activity on the related substrate. That would actually go some way towards indicating how far away different functions are from each other. How many mutations and generations would it take to find that other function from the extant one?
Even then, it is difficult to extrapolate from a data point of one to a general case for all proteins.

The conclusion that this was done to generate the lowest number is hard to escape. It seems that if Axe really thought that he had globally-relevant data, he would have done the same sort of experiment with many other unrelated proteins in the last 14 years.

At the very least he could have tested the activity of his enzyme on a host of related substrates that beta-lactamases are known to have some cross-reactivity for.

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As I understand it, he didn’t even do this experiment. It was done by a friend of ours working underneath him :smile:.

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On the topic of @bjmiller’s EN&V post, he writes:

The rarity would then be less than 1/3 to the power of the sequence length. This estimate closely matches the result from Axe’s 2004 β-lactamase experiment that only 1 in 1077 sequences corresponds to a functional fold/domainwithin the protein.

This is a typical impression ID proponents have got from Axe’s work, as that is how it is normally sold to them in the ID literature, which is the idea that Axe has shown the prevalence of any protein with a functional domain(or worse, any functional protein at all), as we can see here: Imagine: 60 Million Proteins in One Cell Working Together

This paper is interesting because it relates to the work of Douglas Axe that resulted in a paper in the Journal of Molecular Biology in 2004. Axe answered questions about this paper earlier this year, and also mentioned it in his recent book Undeniable (p. 54). In the paper, Axe estimated the prevalence of sequences that could fold into a functional shape by random combinations. It was already known that the functional space was a small fraction of sequence space, but Axe put a number on it based on his experience with random changes to an enzyme. He estimated that one in 10^74 sequences of 150 amino acids could fold and thereby perform some function — any function.

But this is of course wrong. Very very wrong. Even Ann Gauger says this is not what Axe has shown, as we can see here:

Doug’s paper showed the rarity of a functional protein with a particular activity (B-lactam) and a particular structure ( TEM-1 B-lactam) (that’s what he and I mean by a functional fold BTW). Out all possible protein structures only 1 in 10^77 will have that structure and that enzymatic activity. It’s a way of answering the question, how many ways are there to make a protein that has that particular structure with that particular chemistry out of all possible proteins.


I’ll just copy-paste the relevant parts of my previous response to @bjmiller’s invoking the Tokuriki and Tawfik paper (Bershtein et al 2006) paper here:

No, they don’t. One of them (Bershtein et al 2006) was deliberately set up to exclude several well-characterized mechanisms of evolutionary change in order to better understand, in isolation, the consequences of a single mechanism of change in the absense of the effects of the others. It only allowed the effects of mutations within the reading frame of the protein. Potentially compensatory chromosomal mutations were avoided by deliberately only mutating the plasmid genes with PCR, and then transforming competent cells to measure the fitness effects of those mutations.

The TEM-1 gene was cloned into a plasmid (as it occurs in nature) under its endogenous promoter. Recloning after each round of mutagenesis confined the mutational drift to the open reading frame of TEM-1. Our in vitro random mutagenesis protocol was optimized for high reproducibility and was calibrated to obtain, on average, two mutations per gene per round of mutagenesis. We maintained three populations of randomly drifting TEM-1 genes: one population under no selection (Lib0), and the rest under purifying selection at ‘high’ and ‘low’ stringencies. Each population, or plasmid library, was separately mutated, ligated into an empty vector and transformed into E. coli host cells; it then underwent purifying selection: ‘high’ selection pressure (250 mg ml21 ampicillin; Lib250; Supplementary Fig. 2), and ‘low’ selection pressure (12.5 mg ml21 ampicillin; Lib12.5). After growth on selection plates, plasmid DNA was extracted from the surviving E. coli colonies, and the TEM-1 genes were subjected to the next round of mutagenesis. Altogether, ten successive rounds of mutagenesis and purifying selection were performed. Loss of diversity was less than 50% per round, and a diversity of at least 10^6 variants per library was maintained throughout.
As expected, a rapid fitness decline was observed in Lib0 (no selection). The fitness of the selected populations (Lib12.5 and Lib250) remained unchanged under the threshold of selection, and decreased above that threshold (Supplementary Fig. 3).

This figure is from supplementary materials of Bershtein et al 2006.

This completely rules out the possibility of compensatory duplications, other forms of regulation of gene dosage, compensatory chromosomal mutations, and so on.

And even then, it is noteworthy that the aspect of the protocol that involved purifying selection was still able to maintain structural integrity of the protein against the prevalence of deleterious mutations.

Fig. 3. The fitness ‘landscape’ of the TEM-1 gene.
The fitness dynamics of the different TEM-1 libraries is presented as a function of mutational input. The average fitness (W) of a given population was defined as the fraction of β-lactamase variants that confer resistance at a given concentration of ampicillin (see Methods). Wild-type TEM-1 exhibited W=1 for all ampicillin concentrations ≤ 2500 µg/ml. All fitness measurements are detailed in Supplementary Table 1.The rapid fitness decline of the unselected library Lib0 is shown at 12.5 μg/ml of ampicillin (○). The fitness of the libraries subjected to purifying selection remained unchanged at concentrations under the applied selection thresholds, as exemplified here by Lib12.5 at 50 μg/ml ampicillin (∆), and Lib250 at 500 μg/ml (F). At concentrations exceeding the selection thresholds, constant decreases in fitness were observed, exemplified by Lib12.5 at 500 μg/ml ampicillin (◊). Note that the impact of ampicillin is much higher on freshly transformed cells (as in the purifying selections) than on ongrowing, replicated colonies (as in the fitness measurements). Thus, the threshold ampicillin concentration for the fitness measurements was found to be ≤100μg/ml for Lib12.5 (selected with freshly transformed cells at 12.5 μg/ml ampicillin), and ≤1000 μg/ml for Lib250 (selected at 250 μg/ml).

The other paper you cited (Lundin et al 2018) explored the fitness effects of mutations and found, completely unsurprisingly that most mutations are deleterious. They didn’t find anything which supports the view that protein evolution can only go downhill as mutations accumulate. Their protocol did not even include a lineage evolving under purifying selection. All mutations were created directly in DNA by PCR and then inserted in the bacterial chromosome and their fitness effects were tested. When the effects of multiple mutations in combination were tested, it was again the in absence of purifying selection.


The contortions are interesting. Behe ignores neutral evolution, while Axe, @bjmiller, and @Agauger ignore selection.


Since Axe first published his paper, critics have consistently raised certain key issues which have been repeated on this forum:

  1. Were other functions present in the protein even after the tested activity ceased?
  2. Is beta-lactamase rarity representative of most proteins?
  3. Could many other proteins perform the same function?

The cited research addresses all of these questions:

  1. The loss of function corresponds to the destabilizing of the protein, so all functions related to a stable protein must cease.

  2. The 21 studied proteins all show the same distribution of stability reduction for mutations, so nearly all globular proteins would have a similar minimum rarity in sequence space near an optimized sequence. And, nearly all would become entirely nonfunctional with nearly any random combination of mutations leading to a 10% sequence change.

  3. The number of “sequence families”/single domain architectures (SDAs) is increasing very slowly/“becoming saturated”, and the few hundred thousand “close families” which have been identified are typically combinations of the small number of SDAs. Therefore, a search through sequence space would never even enter the neighborhood of any protein families. The number of SDAs is far too small to find even one.

According to the standard model, at some point in the past, the first representative of an entirely new fold had to appear through a nonfunctional sequence exploring sequence space through random mutations. Natural selection cannot differentiate two nonfunctional sequences, so the search had to be fairly close to random.

All of the key criticisms of Axe’s research have been overturned, and his estimates of rarity are exceedingly optimistic. Yet, they still demonstrate the implausibility for evolution to produce even one novel protein of modest size with a distinctly different fold in the entire history of the earth. The research studies cited as counterexamples almost always relate to the challenge of slightly modifying an existing protein fold, not generating an entirely new one.

Rajendrani Mukhopadhyay, “Close to a miracle”
Also, see Ann Gauger
“Once you have identified an enzyme that has some weak, promiscuous activity for your target reaction, it’s fairly clear that, if you have mutations at random, you can select and improve this activity by several orders of magnitude,” says Dan Tawfik at the Weizmann Institute in Israel. “What we lack is a hypothesis for the earlier stages, where you don’t have this spectrum of enzymatic activities, active sites and folds from which selection can identify starting points. Evolution has this catch-22: Nothing evolves unless it already exists.” (Emphasis added).

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@bjmiller thank you for your response. You did not yet confirm we were properly attributed.

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Wow. So much theater, Brian!

This is hilarious! You’re now misrepresenting Axe’s paper completely, because he never assayed activity at all! If I had reviewed the paper, I would have rejected it immediately for that reason alone, regardless of the results.

Why can’t you even acknowledge the existence of that major problem with the paper? Is it a good idea to turn a continuous variable (activity) into a binary one? Even a physicist can answer that.

The paper didn’t establish that beta-lactamase activity is rare. That was a huge extrapolation.

Catalytic antibodies with measurable beta-lactamase activity are found in less than 10^8 samples of an unimmunized library. That ain’t rare.

But not the criticisms actually made, and it even misses the few you deem worthy of acknowledgement.

Perhaps you should read Axe’s paper. He was in no way looking at space near an optimized sequence, because he chose a temperature-sensitive mutant. Or perhaps you meant “optimized for near-instability”?

That’s directly addressed by 32 years of the catalytic antibody literature.

Both of those claims are simply false.

Why do you repeatedly misrepresent an extrapolation from an N of 1 as a global demonstration?

You’re not addressing catalytic antibodies, which do represent entirely new ones. And you are really missing a basic understanding of folds. Folds are structural classifications that typically encompass many different functions.