Understanding the observed variability in the number of homologs of a gene is a very important unsolved problem that has broad implications for research into coevolution of structure and function, gene duplication, pseudogene formation, and possibly for emerging diseases. Here, we attempt to define and elucidate some possible causes behind the observed irregularity in sequence space. We present evidence that sequence variability and functional diversity of a gene or fold family is influenced by quantifiable characteristics of the protein structure. These characteristics reflect the structural potential for sequence plasticity, i.e., the ability to accept mutation without losing thermodynamic stability. We identify a structural feature of a protein domain-contact density-that serves as a determinant of entropy in sequence space, i.e., the ability of a protein to accept mutations without destroying the fold (also known as fold designability). We show that (log) of average gene family size exhibits statistical correlation (R(2) > 0.9.) with contact density of its three-dimensional structure. We present evidence that the size of individual gene families are influenced not only by the designability of the structure, but also by evolutionary history, e.g., the amount of time the gene family was in existence. We further show that our observed statistical correlation between gene family size and contact density of the structure is valid on many levels of evolutionary divergence, i.e., not only for closely related sequence, but also for less-related fold and superfamily levels of homology.

During protein evolution, amino acids change due to a combination of functional constraints and genetic drift. Proteins frequently contain pairs of amino acids that appear to change together (covariation). Analysis of covariation from naturally occurring sets of orthologs cannot distinguish between residue pairs retained by functional requirements of the protein and those pairs existing due to changes along a common evolutionary path. Here, we have separated the two types of covariation by independently recombining every naturally occurring amino acid variant within a set of 15 subtilisin orthologs. Our analysis shows that in this family of subtilisin orthologs, almost all possible pairwise combinations of amino acids can coexist. This suggests that amino acid covariation found in the subtilisin orthologs is almost entirely due to common ancestral origin of the changes rather than functional constraints. We conclude that naturally occurring sequence diversity can be used to identify positions that can vary independently without destroying protein function.