Briggs, K,,Deeds, E. J.
Many macromolecular machines inside the cell exhibit a ‘‘stacked ring’’ architecture, with multiple uniform-length rings of protein subunits bound to one another. The majority of these machines must adopt their fully assembled quaternary structure in order to function, making the assembly process vital for cellular function and survival. The assembly of protein complexes containing stable substructures has been shown to suffer from a type of kinetic trapping that we term ‘‘assembly deadlock,’’ which occurs when smaller intermediates are exhausted from the system before all of the fully functional structures have formed. Deadlock can result in plateaus in the assembly dynamics, leading to delays in reaching maximum complex assembly and a reduced final complex concentration. While these plateaus have been extensively studied for simple rings, the effect of assembly deadlock on more general structures like stacked rings remains to be fully investigated. In this work, we focused on the case of a stacked homotrimer; this structure contains both three- and four-member rings as substructures, but is simple enough to allow for extensive investigation. Our mathematical models revealed that this structure could suffer from extreme deadlock that significantly reduces the efficiency of assembly. Using a computationally efficient simulation approach, we exhaustively analyzed the parameter space of self-assembly for this case, and found that the number and duration of plateaus in the assembly dynamics depended strongly on the pattern of affinities in this structure. Since these complexes are generally only functional when fully assembled, we hypothesized that existing stacked ring architectures would evolve to utilize the most efficient assembly pathways predicted by our models. Analysis of interfaces in solved crystal structures of stacked homotrimers confirmed this prediction. Our findings have important implications for understanding how assembly dynamics have influenced the structural evolution of large macromolecular machines.