Statistical mechanics of protein evolution

Alexandre V. Morozov (Rutgers University)

Understanding non-equilibrium transport on networks and in other complex media is crucial for quantitative analysis of numerous biological, physical, social and technological systems, from protein-protein interactions in biology to the World Wide Web. While transport on networks with unweighted edges can be described using scaling and other analytical techniques, few closed-form results are available for weighted networks, which appear naturally in considering evolutionary dynamics on fitness landscapes, chemical reactions, and protein folding. I will describe an efficient recursive approach for studying random walks on weighted networks, as well as fitness or energy landscapes of arbitrary complexity. After demonstrating the approach on some simple examples, I will apply it to the problem of protein evolution. Specifically, I will investigate how structural coupling between protein folding and binding (the fact that most proteins can only function when folded) gives rise to evolutionary coupling between the traits of folding stability and binding strength, facilitating emergence of evolutionary "spandrels" (features that appear through adaptation even though the feature itself does not contribute to the organism's fitness).