Optimization of non-equilibrium self-assembly protocols using Markov State Models

The promise of self-assembly to enable bottom-up formation of novel materials with prescribed

architectures has sparked a quest to uncover rational design principles for maximizing the yield

of a target structure. Despite a number of successful examples of self-assembly, ensuring the kinetic accessibility of

the target structure remains an unsolved problem in many cases. In particular, long-lived kinetic

traps can result in assembly times that vastly exceed experimentally accessible timescales. One

proposed solution is to develop a non-equilibrium assembly protocol in which system

parameters change over time to avoid such kinetic traps. Here, we develop a framework to use

Markov State Model (MSM) analysis to construct an optimal time-dependent protocol that

maximizes yield of the target structure at a finite time. MSMs are a powerful tool for coarse-

graining the dynamics of complex molecular systems into a reduced-order representation that is

tractable to analysis. By constructing an MSM for a system as a function of its control

parameters, an adjoint-based gradient descent method can be used to efficiently optimize the

assembly protocol. We show that the resulting protocols give improved yields compared to

equilibrium assembly protocols in several model systems.