Is Doug Axe Right about the Rarity of Proteins?

Over at Evolution News, physicist Brian Miller has posted an article titled, A Dentist in the Sahara: Doug Axe on the Rarity of Proteins Is Decisively Confirmed (February 18, 2019). Dr. Miller claims that recent studies support Dr. Douglas Axe’s contention that “most natural proteins are too rare to evolve through an undirected search.” A few brief excerpts will suffice to convey the tenor of the article:

As a specific example, the Tokuriki and Tawfik study demonstrated the following effects of accumulating mutations:

  • After only a few random mutations (1-2) under weak selection, around a third of subsequent changes to a protein completely disable it.
  • After several more mutations accumulate (5-6), the protein is inactivated by slightly under two-thirds of subsequent changes.
  • After random alteration of less than 10 percent of the protein’s initial sequence, it becomes permanently nonfunctional (fitness approaches zero)…

In the study, after 5-10 mutations, roughly 2 in 3 mutations inactivate a protein. Therefore, 1 in 3 amino acids at each position on average would correspond to a functional sequence. 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 10^77 sequences corresponds to a functional fold/domainwithin the protein. The actual rarity is much more extreme, since almost no sequences are functional after 10 percent of a protein randomly changes…

The authors demonstrate that their results apply generally to globular proteins (e.g., enzymes and components of molecular machines). The reason is that the stability of a protein’s structure decreases on average with each added mutation. As a result, increasingly small percentages of sequences in the local region of sequence space are functional. The drop in stability can be slow at first, but after a certain threshold is reached, the structure rapidly destabilizes. The corresponding region of sequence space then becomes almost entirely devoid of functional sequences. Axe came to the same conclusions previously, but the authors neglected to give him due credit…

This definitive evidence refutes one of the most common criticisms of Axe’s protein research. Namely, critics often complain that he did not consider the possibility that the protein he studied might have performed some other function than the one for which he tested. In reality, since the functional loss is due to the loss of structural stability, all other functions dependent on a stable structure must also cease…

A common response to such probabilistic analyses is that vast numbers of different proteins might serve some particular function. Therefore, finding a specific protein might be quite unlikely, but finding any one of a multitude that perform a particular task could be a tractable problem. This objection fails as a result of studies examining the distribution of proteins in all of nature, for they determined that known proteins reside within only a few hundred thousand protein families

…As I mentioned, after fewer than 10 mutations in the Tokuriki and Tawfik experiment, the rarity of functional sequences approximates to 1/3 to the power of the sequence length. The HisA article reported an even faster drop in fitness, indicating even greater rarity. And several other studies demonstrated a corresponding rarity that was similar. Using Tokuriki and Tawfik’s results, the probability of a trial finding a protein the size of that forming the flagellar filament (L=498) would equate to less than 1 in 10^200.

What do readers think? Is Dr. Miller’s argument valid, and if so, is it sound? I’d be interested in hearing from @swamidass, @Art, @Rumraket, and other contributors. Thoughts?

P.S. I should point out that the Tokuriki and Tawfik study cited by Dr. Miller is by no means a new one: it actually goes back to 2006!

@vjtorley, we are covering this right here: Miller: Axe Decisively Confirmed?

It seems clear that despite the titling of the article, there are some large concessions being made, and large gaps in the science.

See the thread for more discussion.

Much of what comes out of ENV is theatre, but they sometimes have science embedded within it. The best thing to do is just tune out the theatrical parts of the paper. They are always going to claim grand success, no matter what. They essentially never (though individuals have done better) directly concede. So it takes work to understand what to really make of it.

The main issue is that even if Axe’s claims are correct, the Tokuriki and Tawfik papers cannot support that conclusion. The results of the experiments detailed in that paper simply are not capable of lending support to it.

I would even go so far as to say that had fitness actually declined in the two populations under more stringent selection, that would still not have been able to lend support to Axe’s conclusions when many key mechanisms of molecular evolution were explicitly excluded from possibility in the experimental setup.


Hi @swamidass and @Rumraket,

Thanks very much for your kind responses. After reading @Rumraket’s takedown, it appears to me that Dr. Miller (who is a physicist, not a biochemist) has failed to understand the role of purifying selection.

Yeah, that’s what happens in the absence of purifying selection. If deleterious mutations aren’t weeded out, they invariably accumulate. If no compensatory effects are allowed, fitness will decline. This is a surprise to exactly no evolutionary biologist ever.

In another comment in response to Dr. Miller, @Rumraket adds:

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.

I was also interested to read @Mercer’s remark over on the other post:

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.

All in all, not such a convincing paper, after all. @swamidass sums it up well:

The best thing to do is just tune out the theatrical parts of the paper. They are always going to claim grand success, no matter what.


The only puzzle for me on this one is how much of it @bjmiller knows is theatre, and how much he does not know is theatre.

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A take down is a big exaggeration. I am not in the detail here but Rum over stated his criticism of Axe in the past. This is a very complicated argument and you need to make sure your are listening to both sides carefully if you want to sort this out. I would start with a very carefully read summation of Hunts article.Axe (2004) and the evolution of enzyme function

There is a RANGE of rareness in sequence space at that first needs to be understood.

Second we are not yet looking a novel eukaryotic proteins with much longer sequences and historic preservation.

I’m going to make a premature comment, since I haven’t yet read the article in question or the work of Tokuriki and Tawfik. It just seems contradictory for DI writers to use orphan genes as evidence for design, then ignore them when discussing the rarity of protein evolution.


No, the data are very clear. We can get beta-lactamase activity from an unselected library of immunoglobulin genes by screening less than 10^8 clones.

That addresses the prevalence of that particular function in sequence space quite clearly.

Bill, why aren’t those data cited anywhere?