Dependency Between Protein–Protein Interactions and Protein Variability and Evolutionary Rates in Vertebrates: Observed Relationships and Stochastic Modeling

Recent developments in sequencing and growth of bioinformatics resources provide us with vast depositories of protein network and single nucleotide polymorphism data. It allows us to re-examine, on a larger and more comprehensive scale, the relationship between protein–protein interactions and protein variability and evolutionary rates. This relationship has remained far from unambiguously resolved for quite a long time, reflecting shifting analysis approaches in the literature, and growing data availability. In this study, we utilized several public genomic databases to investigate this relationship in human, mouse, pig, chicken, and zebrafish. We observed strong non-linear relationship patterns (tending towards convex decreasing function shapes) between protein variability and the density of corresponding protein–protein interactions across all five species. To investigate further, we carried out stochastic simulations, modeling the interplay between protein connectivity and variability. Our results indicate that a simple negative linear correlation model, often suggested (or tacitly assumed) in the literature, as either a null or an alternative hypothesis, is not a good fit with the observed data. After considering different (but still relatively simple, and not overfitting) simulation models, we found that a convex decreasing protein variability–connectivity function (specifically, exponential decay) led to a much better fit with the real data. We conclude that simple correlation models might be inadequate for describing protein variability–connectivity interplay in vertebrates; they often tend towards false negatives (showing no more than marginal linear or rank correlation where there are in fact strong non-random patterns). ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s00239-019-09899-z) contains supplementary material, which is available to authorized users.