Consider two examples. First, as has been pointed out repeatedly on PS, it is fairly routine to identify functional sequences using methods such as phage display and other random combinatorial mutagenesis (in the context of antibody backbones, for example). Certainly, ATP-binding, protein-protein interactions, and DNA-binding are among the functionalities that can be identified. Typically, the sizes of the domains range from 10-30 amino acids or so. Given the experiments, this means that the fraction of functional sequences in all of sequence space is about 1 in 10^10 (we will use very round numbers for now, to make things easy).
Now, this is for a 10-30 mer. In a collection of random polypeptides of, say, 100 amino acids, this frequency will be 10-fold greater – 1 in 10^9 or so random 100-mers will have at least one such functionality. 1 in 10^18 will have two different functionalities, 1 in 10^27 will have three, etc.
How does this relate to the “real world”? The second example recalls another oft-mentioned (on PS) protein, a gated ion channel with (at least) three functionalities – two protein-protein binding sites and a site for binding a smaller molecule. Given the history of this protein, we can assign a (very generous, for ID proponents) upper limit of about one in 10^28 for the frequency of co-occurrence of this collection of functionalities in a set of 100-mers. (This is very, very generous, and probably off by as many as 10 or more orders of magnitude, but we will use this unrealistic limit to make the point that follows.)
Now, look at the helicase video. One can see four functionalities – two protein-protein binding interfaces, an ATP-binding site, and a DNA-binding site. It isn’t hard to see that the frequency with which these four functionalities might occur in a 100-mer is going to be about 1 in 10^36 (using the most generous of assumptions here). For added context, recall that there are around 10^30 bacteria at any moment in the biosphere. Given the mechanisms by which we know new proteins arise, this means every bacterial generation gives is 10^30 or so new proteins. Depending on the growth rates (averaged across all species), this means that a 100-mer with the four functionalities described above will occur once every 10^4-10^5 years. That is for the most optimistic (for IDers) cases. It may be as often as once every day.
For a different perspective, consider a pond of dilute 100-mers – say, 1 nM in concentration. A (vey large) pond, one percent of the size of the Atlantic Ocean, will have enough 100-mers to include at least one proto-helicase.
Compare these numbers with those that Sal and other anti-evolutionists bandy about. There are more (many more) than 100 orders of magnitude of difference. Basically, Sal’s numbers are vastly different from what we see in direct and indirect measurement of the frequencies of function in sequence space. Which means that the appeal to the “Law of Large Numbers” is inappropriate, incorrect, just plain wrong. (The same goes for all the other ill-conceived attempts, from Axe to Behe to Meyer, to cast protein evolution in some vastly improbable light.)
To answer the question in the title of the thread - when it comes to evidence for design, helicases are indeed a house of cards.
