Determining the influence of complex, molecular-system dynamics on the evolution of proteins is hindered by the significant challenge of quantifying the control exerted by the proteins on system output. We have employed a combination of systems biology and molecular evolution analyses in a first attempt to unravel this relationship. We employed a comprehensive mathematical model of mammalian phototransduction to predict the degree of influence that each protein in the system exerts on the high-level dynamic behaviour. We found that the genes encoding the most dynamically sensitive proteins exhibit relatively relaxed evolutionary constraint. We also investigated the evolutionary and epistatic influences of the many nonlinear interactions between proteins in the system and found several pairs to have coevolved, including those whose interactions are purely dynamical with respect to system output. This evidence points to a key role played by nonlinear system dynamics in influencing patterns of molecular evolution.

This work was supported by the Ministerio de Economia y Competitividad, Spain (grant no. BFU2013-43726-P, subprogram BMC) and the María de Maez to Program for Units of Excellence in R&D (MDM-2014-0370); the Departament d'Economia i Coneixement de la Generalitat de Catalunya (Grup de Recerca Consolidat GRC 2014 SGR 866); AGAUR, Generalitat de Catalunya (2011 FI BI 00275 to B.M.I.); and the Spanish Ministry of Science and Innovation (MICINN) (Juan de la Cierva Program to L.M.)