Accumulation pattern of amino acid substitutions in protein evolution

A simple method for the evolutionary analysis of amino acid sequence data is presented and used to examine whether the number of variable sites (NVS) of a protein is constant during its evolution. The NVSs for hemoglobin and for mitochondrial cytochrome c are each found to be almost constant, and the ratio between the NVSs is close to the ratio between the unit evolutionary periods. This indicates that the substitution rate per variable site is almost uniform for these proteins, as the neutral theory claims. An advantage of the present analysis is that it can be done without knowledge of paleontological divergence times and can be extended to bacterial proteins such as bacterial c-type cytochromes. It is suggested that the NVS of cytochrome c has been almost constant even over the long period (ca. 3.0 billion years) of bacterial evolution but that at least two different substitution rates are necessary to describe the accumulated changes in the sequence. This "two clock" interpretation is consistent with fossil evidence for the appearance times of photosynthetic bacteria and eukaryotes.