There wouldn’t be an exact border between any two things if you just assume one can change incrementally into the other, but it’s just an assumption that occurs inside your head, as you say.
That isn’t true. It is a random sample, just not a uniformly random sample.
Turns out, with this information, we can actually compute precisely how much larger of a library they’d need it was uniformly random. Good news is that it isn’t that much larger. Would you like to try computing it?
However, the uniform distribution isn’t nearly as important as the distribution sampled in actual biological systems, which is not uniform, and matches more closely what they used.
Yeah his response basically consists of speaking about the readability of english sentences instead of the physics and biochemistry of proteins.
But the question being assessed here is to what extent functional proteins are rare and isolated in sequence space.
He writes:
Both Hunt and Venema seem to think the outcome would have been more favorable (i.e., functional sequences would have been more prevalent) had I used the highly proficient natural enzyme as a starting point rather than the handicapped version. Actually, as a demonstration will show, the opposite is true.
But the analogy Axe goes on to employ using english grammar and spelling is simply irrelevant to protein biophysics and chemistry, and no demonstration using actual protein biophysics follows. Axe just talks about grammar and spelling and the discernability of meaning of sentences.
But ironically his analogy’s relevance to the very point Hunt brings up(the mutational oversensitivity of the enzyme he constructs) is undermined by Axe’s own words in his paper:
Most studies using a biological screen or selection method to score variants of a natural sequence as active or inactive employ a threshold that requires only a small fraction of wild-type activity for an active score to be assigned.11 Coupled with the fact that natural proteins are typically folded with stabilities well in excess of the bare minimum under the conditions of selection, this means that variants scored active may actually carry significant structural disruption. As an illustration, consider an experiment in which random substitutions are introduced into a small region within a natural enzyme, with functional selection applied in the usual way (Figure 2a). Because the wild-type protein is well stabilized by favourable side-chain interactions throughout the fold (Figure 2a, left), it has some capacity to absorb the destabilizing effects of disruptive substitutions in small numbers (Figure 2a, right). In essence, the relatively high quality of interactions throughout the unchanged portion of the protein can compensate for, or buffer, the effects of unfavourable interactions within the changed portion. This accounts for the observation that substitutions having little functional effect alone or in modest numbers have very substantial disruptive effects when combined in numbers large enough to exhaust that initial buffering capacity.
So here Axe basically says that he knows that by constructing a mutationally sensitive version of the enzyme, this will decrease the pass rates he later uses to calculate how many functional sequences there are. Mutants that the natural enzyme could tolerate because the increased buffering capacity of it’s excess stability, are much more likely to fail for this sensitive thing Axe constructed. And that’s for an extant TEM-1 beta-lactamase. Imagine if he’d used the even more highly stable, and conformationally flexible, reconstructed ancestor of all class A beta-lactamases, which would have had an even higher buffering capacity than extant beta-lactamases.
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It is random, as @swamidass discusses above. You might as well say the lottery is not random because you only get numbers between 1 and 50 in the drawing.
They stated right there in the abstract that it was a random sampling. All they did was use about the same ratios of amino acids as those found in biological proteins within those random sequences.
Collapsing into secondary structures from a linear peptide is folding. It doesn’t take much for folds to appear in peptides, and they certainly aren’t as difficult to produce as ID/creationists let on.
I don’t think so. Axe’s response was more to other criticisms, and do not address the key point that I reiterate here. Specifically, the flaw in Axe’s argument is that he equates the bases of the hills I illustrate in Figures 1 and 2 of my post.
The points Axe responds to are:
Objection 1: Axe’s paper doesn’t claim to support intelligent design or challenge Darwinism, so it’s a mistake to use it for those purposes.
This is completely unrelated to my argument.
Objection 2: Although Axe makes a case that functional sequences are rare in sequence space, this has no bearing on whether new protein folds can evolve. The evolution of new protein folds simply requires that functional sequences not be isolated in sequence space, which has nothing to do with how rare functional sequences are.
This is also completely unrelated to my criticism.
Objection 3: Because Axe measured mutational sensitivity from a weakly functional starting sequence rather than the fully functional natural enzyme, the mutants he generated were inappropriately disadvantaged, and this is why he arrived at such a low value for the prevalence of functional sequences.
The Objection is either a misunderstanding or misrepresentation of my criticism. I do mention that he used a weakly-functional starting sequence, and I illustrate (in Fig. 2 of my post here on PS) what this means for Axe’s conclusions. But my remarks have nothing to do with a mutant being disadvantaged (whatever that means). Furthermore, as @Rumraket has stated, Axe’s word games do absolutely nothing to rescue the 2004 study from my criticism. The main point remains unaddressed.
Objection 4: Axe’s experiment doesn’t reflect how evolution really works. He mutated amino acids in groups of ten, whereas evolution sifts mutations one at a time. Consequently, Axe’s results tell us nothing about whether protein folds can or cannot evolve.
This has nothing to do with my critique.
So, @BenKissling, as can be seen, Axe really has not addressed the fundamental weakness in his study, or, more precisely, the conclusions he and other ID proponents draw from it. He does not accurately represent my argument, and his attempted response is not relevant to the matter of proteins, activity, and sequence space.
I would remind you that two DI scientists - @Agauger and @bjmiller - have both chosen to avoid this issue completely, even when given ample opportunity to discuss this matter. That speaks volumes to me and should give you pause as well.
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That is the most ridiculous thing I’ve ever heard.
Are you dropping the claim about peptidase activity invalidating Axe’s study then?
While on the subject of things that speak volumes, consider how among all the things Ben could have chosen to respond to out of all the issues brought up between Art and myself, that is the response Ben produced.
Interesting tidbit: We now know with some precision what that “buffering capacity” is. It’s likely about 15 kcal/mol of thermodynamic stability associated with the fold. About 2/3s of mutations will reduce the stability by 1 kcal/mol or more.
So you tell me, @Rumraket, will there be more sequences closer to 15 kcal/mol stability or closer to 0 kcal/mol stability? And which is the more likely to be closer to the sequence which is actually ancestral to the moderm TEM-1?
Which version of it? It’s not the same.
The reconstructed ancestor is more thermodynamically stable than any extant one. But this is all totally besides the point, because there’s zero reason to think the only way a protein such as one exhibiting a serine beta-lactamase fold can evolve is by de novo emergence of that fold in one fell swoop, as opposed to gradually from from something simpler, or gradually from another fold, or by fusions of domains from other proteins.
??? I have no idea what you are talking about, @BenKissling. Surely you are not debating that the serine beta lactamases and dd peptidases are related.
@Art I was contesting this statement. I found no evidence that TEM-1, the enzyme Axe actually studied, shows peptidase activity. I found evidence that other beta-lacatamases show weak peptidase activity, just not TEM-1.