Thursday, November 23, 2006

Evolutionary history of cytochrome c

This post is a little provocative, and is based in part on my earlier posts about the specification of cytochrome c. If this analytical process is fair, then it should make possible the sort of explanation outlined below. Note that, in my opinion, this is substantially more detailed than the traditional evolutionary explanations offered. However, I would be interested in other people's thoughts on the numbers involved, or pointers to other places where similar analysis has been carried out.

Cytochrome c is genetically coded. Other forms of electron transport are possible, but this one could not have predated the genetic code and transcription mechanisms. This means that it is likely that cytochrome c would not have substantially predated the appearance of prokaryotic life. On the other hand, the gene that became cytochrome c was established in prokaryotic life by the time it became dominant – say 3500 Myr. The reason for this conclusion is that we don't see any forms of life that don't utilize cytochrome c, with the exception of parasitic forms which would not have predated this point.

We can determine how many possible events there were that might have led to the first appearance of cytochrome c, and thus the “probabilistic resources” available for this evolutionary step. The total time available is (let's say) of the order of 1000 Myr. Assuming that there are biochemical processes that can occur 100 times per second (I suspect that there are very few biochemical processes that are energetically neutral to such an extend that they could oscillate at this frequency – the mechanisms that allow cells to tick “more rapidly” are dependent upon the sort of systems that we are seeking to explain), this represents of the order of 1018 biochemical “ticks”. There are of the order of 1022 moles of organic carbon available – that is, of the order of 1046 atoms in total, of which let's say 1% is in an appropriate environment to be a resource for finding proto-cytochrome c, and proto-cytochrome c requires of the order of 100 carbon atoms.

Thus, the total number of reconfigurations of hundreds of carbon atoms available to try and find proto-cytochrome c is about 1060. If proto-cytochrome c was substantially more specified (less probable) than this, then there would not have been sufficient probabilistic resources available to consider its appearance to be a likely event in this timescale. Note also that this says nothing about the requirement of existing genetic systems.

By the time of the appearance of multicellular, eukaryotic life – say 600 Myr: 100 Myr in either direction has little effect on the argument – cytochrome c was already well specified. The reason for this conclusion is that all modern life has a similar high specification – there aren't any substantially different forms in different phyla. It would be possible that the convergence to a generally single form of cytochrome c took place in different phyla after the Cambrian era – but with prokaryotic organisms having faster generation times, asexual reproduction and being dominated for selection by fewer factors, it seems more likely that a highly specified form would have been established before this point in time.

Based on the list of 113 versions of cytochrome c referenced earlier, the probability of a random sequence of DNA coding for one of these versions of cytochrome c is about 10-85. It was observed that going from 103 to 113 different versions increased this probability by two orders of magnitude (from about 10-87). It is pretty arbitrary, but for the sake of argument, let's say that the probability of a random sequence of DNA coding for any version of cytochrome c (which today would be well-specified) is of the order of 10-70. This is then a measure of the specification of cytochrome c today, following all the years of natural selection on the earlier forms.

If these figures (or ones like it) are accepted, then we can see the scale of the work done by natural selection from the time random mutation produced proto-cytochrome c to today. Cytochrome c has evolved from requiring a DNA sequence no less probable than 1 in 1060 to having a DNA sequence that we are saying has a probability of 1 in 1070, in around 3 Myr.

Note that arguing for a lower specification for proto-cytochrome c increases the demand placed on natural selection to arrive at its modern specification. Arguing for too high a specification for proto-cytochrome c runs the risk of exhausting reasonable probabilistic resources for its initial appearance.