Sequence-related human proteins cluster by degree of evolutionary conservation

Gene duplication followed by adaptive evolution is thought to be a central mechanism for the emergence of novel genes. To illuminate the contribution of duplicated protein-coding sequences to the complexity of the human genome, we study the connectivity of pairwise sequence-related human proteins and construct a network $\left(\mathcal{N}\right)$ of linked protein sequences with shared similarities. We find that (i) the connectivity distribution $P\left(k\right)$ for $k$ sequence-related proteins decays as a power law $P\left(k\right)\sim k^{-\gamma }$ with $\gamma \approx 1.2$, (ii) the top rank of $\mathcal{N}$ consists of a single large cluster of proteins $(\approx 70\%)$, while bottom ranks consist of multiple isolated clusters, and (iii) structural characteristics of $\mathcal{N}$ show both a high degree of clustering and an intermediate connectivity (“small-world” features). We gain further insight into structural properties of $\mathcal{N}$ by studying the relationship between the connectivity distribution and the phylogenetic conservation of proteins in bacteria, plants, invertebrates, and vertebrates. We find that (iv) the proportion of sequence-related proteins increases with increasing extent of evolutionary conservation. Our results support that small-world network properties constitute a footprint of an evolutionary mechanism and extend the traditional interpretation of protein families.

Figure 1

Connectivity distribution of human protein sequences. Shown is a double logarithmic representation of the probability $P\left(k\right)$ that a given human protein is sequence-related with $k$ other proteins. $P\left(k\right)$ is shown with $k=1$ linear (small circles) as well as with logarithmic bin sizes (full circles) to reduce noise. The decay of $P\left(k\right)$ can be approximated by a power law, $P\left(k\right)\sim k^{-\gamma }$, with a decay exponent $\gamma \approx 1.2$ (best-fit regression on double-logarithmic scales). The inset shows $P\left(k\right)$ for a numerical simulation of a random network ${\mathcal{N}}_{\mathrm{rand}}$, with the same overall number of proteins and connections as observed in the original empirical network. The connectivity distribution for ${\mathcal{N}}_{\mathrm{rand}}$ can be approximated by $P{\left(k\right)}_{\mathrm{rand}}\sim e^{-⟨k⟩}({⟨k⟩}^k∕k\text{!})$, with the average connectivity $⟨k⟩\approx 70$.

Figure 2

Highly sequence-related human proteins are increasingly conserved throughout evolution. Left-hand side: schematically a phylogenetic tree with the taxonomic classes of the species C. elegans, S. cerevisiae, A. thaliana, and M. genitalium as compared to H. sapiens. Right-hand side: the average of the connectivity distribution of human proteins and the corresponding degree of evolutionary conservation, defined as the number of species in which the protein is sequence-related. Statistical analysis shows that each subset is significantly different $(p<2.2\times {10}^{-16})$ from the corresponding nonconserved set (data not shown).