Statistical Mechanics of Protein Multimerization and Aggregation

Understanding the evolution of proteins is vital to explaining the diversification of life. As a majority of cellular proteins function not in isolation, but as part of complexes of two or more proteins, developing an understanding of how these protein- protein interactions originate and evolve is crucial. One intriguing observation is that highly-conserved proteins can exhibit different quaternary structures in different lineages, with no apparent correlation between the number of subunits in a complex and organismal complexity. In this work, we develop a theoretical model to investigate the aggregation of proteins on a cubic lattice using an hydrophobic-polar (HP) model. As most protein complexes are homomeric, composed of subunits derived from the same genetic locus, we focus on aggregates of multiple copies of the same protein as a function of concentration and the free energy of protein-protein binding. We construct a fitness landscape to investigate evolutionary trends by categorizing assemblies as monomers, isologous dimers, heterologous dimers, and higher-order assemblies, each with a corresponding impact on cellular fitness.