Evolutionary drivers of protein shape

Diffusional motion within the crowded environment of the cell is known to be crucial to cellular function as it drives the interactions of proteins. However, the relationships between protein diffusion, shape and interaction, and the evolutionary selection mechanisms that arise as a consequence, have not been investigated. Here, we study the dynamics of triaxial ellipsoids of equivalent steric volume to proteins at different aspect ratios and volume fractions using a combination of Brownian molecular dynamics and geometric packing. In general, proteins are found to have a shape, approximately Golden in aspect ratio, that give rise to the highest critical volume fraction resisting gelation, corresponding to the fastest long-time self-diffusion in the cell. The ellipsoidal shape also directs random collisions between proteins away from sites that would promote aggregation and loss of function to more rapidly evolving nonsticky regions on the surface, and further provides a greater tolerance to mutation.