He is extrapolating the results from other work to a protein with a size similar to the one Axe worked on. Specifically (10-24/2093)x(20150) = ~10-59.
Those values are between 14 and 53 orders of magnitude higher than Axe’s number(10-63 to 10-24). So Axe’s number is not within that range(which it appears you are reading Art to say), one of the reasons being that his experiment was fundamentally flawed by Axe working on an enzyme intentionally manipulated to be extra sensitive to mutation. So even the most similar number is still off by a factor of one hundred trillion.
Since the method Axe is using fundamentally is based on extrapolation from how many mutations “pass” (the rate of passing mutants feed directly into his calculation), because the enzyme he used is intentionally created to have fewer passes, this has the effect of reducing the number of sequences he estimates.
Now of course, this is not even an estimation of the amount of sequences that have that enzymatic function in sequence space(it cannot possibly be, since we know of entirely dissimilar protein enzymes with the same activity).
It is an estimation of the number of sequences that simultaneously adopt that particular protein foldand catalyzes the hydrolysis of beta lactam antibodies(as Ann Gauer also agreed here*) well enough for colonies to appear on an agar plate containing the mininum inhibitory concentration(MIC) of antibiotic. This is NOT the limit of adaptive function for an enzyme in a microorganism in the real world.
Italics are her own emphases. That structure and that enzymatic activity. Not an estimation of the true density of the function in question, much much less an estimation of any fitness-enhancing function.
And the deck was deliberately stacked by using a temperature sensitive enzyme and testing it against the MIC.
It’s trash work, all of it, and you don’t even understand it.
@colewd, the comments by @CrisprCAS9 and @Rumraket are spot on. I don’t need to add anything. But I want to thank these two for explaining things so nicely. When I read your comments, @colewd, I worry that my essay was poorly written, too confusing to be of use. It is a relief to see that this is probably not the case.
Hi Art
What assumptions about fixation did you make here?
10^-10 → 10^-63 (or thereabout): this is the range of estimates of the density of functional sequences in sequence space that can be found in the scientific literature. The caveats given in Section 2 notwithstanding, Axe’s work does not extend or narrow the range. To give the reader a sense of the higher end (10^-10) of this range, it helps to keep in mind that 1000 liters of a typical pond will likely contain some 10^12 bacterial cells of various sorts. If each cell gives rise to just one new protein-coding region or variant (by any of a number of processes) in the course of several thousands of generations, then the probability of occurrence of a function that occurs once in every 10^10 random sequences is going to be pretty nearly 1. In other words, 1 in 10^-10 is a pretty large number when it comes to “probabilities” in the biosphere.
My opinion of third party’s restatement of a fourth party’s work is irrelevant to what your assumptions are. Why do you refuse to state your assumptions? Start a sentence with ‘I assume that’ then end it with something that coherently links empirical evidence to some mathematical expression you feel appropriate.
the probability of occurrence of a function that occurs once in every 10^10
If the probability is 1 in 10^10, and there are 10^10 opportunities for the event to occurs, the probability of that event occurring at least once is about 63%. @Art’s liter of pondwater is more than enough to take the probability to 1.0.