Functions are not so rare at all, and definitely not isolated, in sequence space of biopolymers

[Rumraket (Mikkel R.)]

@Giltil

Not all functions are rare in sequence space, only complex ones.

I should add that I don’t think you’re wrong to say that some functions are more, or even considerably more rare, than others. I don’t think it would be sensible to extend the hyperabundance of some specific function in sequence space, to basically all protein functions. That would be an unwarranted extrapolation, and also doesn’t make biochemical sense.

But some functions being much more rare than others does not in and of itself imply they are too rare to evolve. It might imply they’re unlikely to evolve by de novo evolution from non-coding DNA, but there are other mechanisms available to evolution for novel gene evolution than that. I wrote a post about that here:

@Rumraket

@colewd

I would argue if you traced its origin back to the first enzyme of a similar type the design inference becomes a viable explanation for the origin of catalytic activity in an enzyme containing hundreds of amino acids.

There doesn’t appear to be any need of that hypothesis.

While I think Axe’s estimate of frequency of sequences that adopt the structure and function of beta-lactamases is an extremely skewed underestimate (in part because of numerous shortcomings of his experimental approach), there does appear to be some evidence that comparatively speaking enzyme sequences are considerably more rare in protein sequence space, than things like ligand/molecule binding proteins, transmembrane transporters, or transcriptional regulators and the like.
In this respect I don’t think it would be wrong to say that you’d expect de novo protein evolution (from non-coding DNA) to yield enzymes much more rarely than, for example, proteins with structural or regulatory roles.

However, I think it is a mistake to take this to imply that de novo enzyme evolution is so rare as to be essentially impossible. One problem is there are numerous ways to get a de novo enzyme sequence than just the spontaneous emergence of an ORF in some stretch of non-coding DNA. And while on the subject of non-coding DNA, even this is more likely to yield something functional, than the sort of spontaneous polymerization “tornardo-in-a-junkyard” picture one gets from reading IDcreationist material. We have to be mindful that a lot of non-coding DNA is actually previously functional, protein coding DNA that has been carried along by selfishly expanding transposable elements. That means a lot of non-coding DNA is actually quite near in sequence space to DNA encoding significant secondary structural elements of proteins. Much nearer than just completely random.

That said, I think a more holistic view of protein evolution implies that enzyme functions are most likely to emerge in already existing, stably folding proteins, or (less often) from gene fusion events where pieces of already existing genes are copy-pasted as insertion vents, resulting in shuffled and recombined protein coding gene fragments. Folding proteins are largely modular structures consisting of secondary structural elements, which can in principle be moved around and combined into new structures.

This makes much more sense to me, because pieces of already existing proteins are of course much nearer in protein sequence space to “something potentially functional”, than some arbitrarily picked non-coding DNA sequence that has been blindly accumulating mutations for eons. So when it comes to explaining the ultimately origin of novel catalytic functions, I would rank (from more to less likely) the order of likelihood of explanations like this:

1. Emergence of new catalytic function in an already existing catalytic scaffold (divergence of duplicate enzymes).
2. Emergence of new catalytic function in a non-catalytic scaffold (structural/ligand binding protein becomes an enzyme).
3. Domain or subdomain sized fragments(exon shuffling, insertions, or just gene-gene-fusion) combine to yield a new protein with a catalytic function. (see this and this and this)
4. Oligomerization of smaller protein fragments result in a new protein (repeat-proteins).
5. De novo gain of an open reading frame that codes for a functional enzyme sequence, from non-coding DNA.

I think the vast majority of enzyme function gains in the history of life owe to 1 and 2, with the diversity of all known chemical reactions catalyzed by enzymes reducing to a smaller set of enzyme superfamilies. There’s a nice article showing exactly this here:

journals.plos.org

Exploring the Evolution of Novel Enzyme Functions within Structurally Defined…

Author Summary Enzymes, as biological catalysts, are crucial to life. Understanding how enzymes have evolved to perform the wide variety of reactions found across all kingdoms of life is fundamental to a broad range of biological studies, especially…

Now these families in turn have to have originated somehow, and here I think 3 and 4 provide the best, most likely explanations for the reasons already stated. Pieces of already existing, stably folding proteins are much closer in protein sequence space to something potentially functional, so their shuffling/recombination and fusion into larger structures constitutes a much more efficient, and biased-towards-functional-and-folding “search process” than spontaneous gain of an enzyme fold from non-coding DNA does. And there’s a lot of good evidence that stably folding tertiary structures can be gained by repeating duplications (oligomerization) of smaller fragments.

This is, again, what I consider a more holistic view of protein evolution over the history of life on Earth. It’s the sort of picture I’ve come to hold after 13 years of reading the literature, and trying to follow the evidence and arguments from different camps. To sum up, I think you put too much trust in Axe’s work, and when considering evolution I don’t think you really appreciate the many different “search strategies” are available to evolution besides the sort of “randomly hook amino acids together into longer chains” pop-out-of-a-soup-of-amino-acids view.