Markov State Model Optimization of Self-Assembly Protocols for Finite Subunit Pool Systems

A large body of recent theoretical and experimental work in self-assembly has shown that designing time-dependent protocols for system parameters can greatly boost assembly yields and target state selectivity, as well as structure reconfigurability. We recently developed a gradient-based optimization algorithm that combines Markov state model (MSM) analysis with optimal control theory to efficiently compute time-dependent protocols that maximize the finite time assembly yield of a target structure. Although the method performed well on diverse self-assembly systems, it was limited to systems with approximately constant (or negligible) chemical potential. Here, we describe extending the method to systems where subunit depletion is non-negligible, by constructing MSMs as a function of the free monomer concentration. We test the extended method on a system of triangular subunits designed to assemble into icosahedral capsids.