Parameters of proteome evolution from histograms of amino-acid sequence   identities of paralogous proteins
  The evolution of the full repertoire of proteins encoded in a given genome is mostly driven by gene duplications, deletions, and sequence modifications of existing proteins. Indirect information about relative rates and other intrinsic parameters of these three basic processes is contained in the proteome-wide distribution of sequence identities of pairs of paralogous proteins. We introduce a simple mathematical framework based on a stochastic birth-and-death model that allows one to extract some of this information and apply it to the set of all pairs of paralogous proteins in seven model organisms. It was found that the histogram of sequence identities p generated by an all-to-all alignment of all protein sequences encoded in a genome is well fitted with a power-law form ~p^(-gamma) with the value of the exponent gamma around 4 for the majority of organisms used in this study. This implies that the intra-protein variability of substitution rates is best described by the Gamma-distribution with the exponent alpha ~ 0.33. We separately measure the short-term (``raw'') duplication and deletion rates r*_dup, r*_del which include gene copies that will be removed soon after the duplication event and their dramatically reduced long-term counterparts r_dup, r_del. Systematic trends of each of the four duplication/deletion rates with the total number of genes in the genome were analyzed. All but the deletion rate of recent duplicates r*_del were shown to systematically increase with N_genes. Abnormally flat shapes of sequence identity histograms observed for yeast and human are consistent with lineages leading to these organisms undergoing one or more whole-genome duplications. 
Jacob Bock Axelsen, Koon-Kiu Yan and Sergei Maslov