Douglas Axe has done experiments to try to determine if there are many possible protein sequences that have functions or only a few. If functioning proteins are very common, then evolution by natural selection might seem to be more probable. But if functioning proteins are very rare, then evolution by natural selection might seem to be less probable. The results of these experiments show that functional proteins are very rare and the possibility that many alternate evolutionary paths exist is not a good explanation for the origin of species.
http://www.toriah.org/articles/axe-2000.pdf
How much of protein sequence space has been explored by life on Earth?
3. Discussion
Protein sequence space is often viewed as a limitless desert of maladjusted sequences with only a few oases of working sequences linked by narrow pathways (Axe 2000, 2004). The navigation over this space by natural selection is difficult and could take many different routes thus resulting in organisms with largely different protein compositions. This idea of contingency, if taken at the level of species, led Gould to suggest that if one was to rerun the ‘tape of life’ then evolution would take a totally different path and we, as a species, would only appear as a highly improbable accident (Gould 1991; Luisi 2003; de Duve 2007a,b). However, if there is any merit to our simple calculation then protein sequence analysis provides no support for the idea of contingency at a molecular level and it provides strong support for the ideas of convergence (Conway Morris 2000, 2004; Dawkins 2005; Vermeij 2006; de Duve 2007a,b). If one was to rerun the tape, then the protein composition of organisms would be similar. Our calculation removes the almost impossibly unrealistic pressure on natural selection to navigate through protein sequence space avoiding the vast number of functionless sequences by simply indicating that most sequences have been tried are useful in some way, and that there are many possible routes to obtain proteins with desirable functions (Nagano et al. 2002; Anantharaman et al. 2003; Holliday et al. 2007).
Finally, we conclude that the number 20100 and similar large numbers (e.g. Salisbury 1969;Maynard Smith 1970; Mandecki 1998; Luisi 2003; Carrier 2004; de Duve 2005) are simply ‘straw men’ advanced to initiate discussion in the same spirit as the ‘Levinthal paradox’ of protein folding rates (Levinthal 1969; Zwanzig et al. 1992). 20100 is now no more useful than the approximate 2×101 834 097 books present in Borges' (1999) fantastical ‘Library of Babel’ and has no connection with the real world of amino acids and proteins. Hence, we hope that our calculation will also rule out any possible use of this big numbers ‘game’ to provide justification for postulating divine intervention (Bradley 2004; Dembski 2004).
Axe (2004) and the evolution of enzyme function
Summary
To summarize, the claims that have been and will be made by ID proponents regarding protein evolution are not supported by Axe’s work. As I show, it is not appropriate to use the numbers Axe obtains to make inferences about the evolution of proteins and enzymes. Thus, this study does not support the conclusion that functional sequences are extremely isolated in sequence space, or that the evolution of new protein function is an impossibility that is beyond the capacity of random mutation and natural selection.
http://bio-complexity.org/ojs/index.php/main/article/download/BIO-C.2010.1/56
These two are from the "Look mam, we have peer reviewed articles too" magazine of self publishing, so we can safely ignore them.