There may be many functional alternative solutions, but that doesn’t make them all local optima. It actually appears that for ATP synthase no such inescapable “local optimum” has been found, as the sequences of basically all it’s subunits have been diverging for all cellular organisms, continuously for the entire known history of life.
No, that isnt’t the reason I am contesting his calculation. I am contesting his calculation because the method isn’t capable of determining how many functional sequences there are.
It’s not merely that I think he’s wrong that makes me contest his calculation. I am contesting the calculation primarily because:
- The method is based on a sampling process that has extremely high intrinsic bias.
- The fraction of sequence space the process samples is an infinitesimally small one.
His method is not capable of telling us how many functional sequences there are. For reasons explained now so many times it boggles the mind anyone would have still have trouble understanding it.
As stated before, even if Gpuccio’s number is actually correct(which there is no good reason to think), the method he uses is not how that is established, and he would only happen to be coincidentally correct in the number. Sort of like if he had happened to correctly guess the true number of functional sequences, and it was later found to be corroborated in some elaborate experiment, that would not mean that just guessing is how we determine the FI for some protein sequence. No, we really do have to use a method that is capable of telling us that, and for reasons given above many times, sequence conservation used to derive FI isn’t how that is done.
Functional sequences, not just local optima. But yes, how many functional sequences are there? You can’t extract that information from picking extant sequences from living organisms and extrapolating from that.
So an invisible, telepathic, palestinian Columbidae, from classical antiquity, instead of Santa, must have made it?
In all seriousness, you seem to have this weird picture in mind where there was a not-yet-fully-formed ATP synthase molecular machine, that lacked subunit beta of the F1 hexamer, and evolution had to sort of “find” a functional beta-subunit before the system would function. It’s the Hoyle-fallacy all over again.
But of course that’s not how these things happen. The individual proteins that make up ATP synthase have ancestries that go back to times before they became part of the ATP synthase complex. The real question is how frequent is the ultimate ancestral function of the entire superfamily to which the beta subunit belongs?
The beta subunit did not evolve de novo into the ATP synthase complex, rather it belongs to a gigantic superfamily of proteins called P-Loop NTPases(which, ironically, also contains the actin and myosin subfamilies), one of the most divergent and oldest protein superfamilies known. The beta subunit is part of the catalytic hexamer(the one that also contains the Walker-A motif), which is actually functional on it’s own as a DNA and RNA translocase(and as an RNA helicase).
The most basic function of all P-loop NTPase members is nucleotide binding (and hydrolysis). That is the inferred ancestral function and the essential role of them all.
That’s the function they tested for in the Keefe & Szostak 2001 experiment (ATP binding), and found to exist at a frequency of approximately 10^-11(noteworthy here is that they found four different completely dissimilar proteins with the function, which would have been undetectable as being related in any BLAST or other similarity-based search). Later experiments revealed that under certain conditions, the protein also catalyzes ATP hydrolysis to ADP.
A version of the original experiment was repeated by another lab, and results published in 2015. This time they used a smaller subset (15) of the 20 known biological amino acids, biased towards the set of amino acids thought to be prebiotic, and found additional proteins capable of ATP binding and hydrolysis.
The Tawfik lab constructed a super simplified facsimile of the inferred ancestor of the P-loop NTPases, called the Walker-A P-loop motif. The protein is only 55 amino acids long, yet functional, in that it could bind and hydrolyse ATP(and other NTPs), bind RNA and DNA.
That function really does seem to be hyperabundant in protein sequence space.