Evolution of interface binding strengths in simplified model of protein quaternary structure

The self-assembly of proteins into protein quaternary structures is of fundamental importance to many biological processes, and protein misassembly is responsible for a wide range of proteopathic diseases. In recent years, abstract lattice models of protein self-assembly have been used to simulate the evolution and assembly of protein quaternary structure, and to provide a tractable way to study the genotype-phenotype map of such systems. Here we generalize these models by representing the interfaces as mutable binary strings. This simple change enables us to model the evolution of interface strengths, interface symmetry, and deterministic assembly pathways. Using the generalized model we are able to reproduce two important results established for real protein complexes: The first is that protein assembly pathways are under evolutionary selection to minimize misassembly. The second is that the assembly pathway of a complex mirrors its evolutionary history, and that both can be derived from the relative strengths of interfaces. These results demonstrate that the generalized lattice model offers a powerful new idealized framework to facilitate the study of protein self-assembly processes and their evolution.