Optimization of Non-Equilibrium Self-Assembly Protocols Using Markov State Models

TL;DR

This paper introduces a method combining Markov state models and optimal control theory to design non-equilibrium assembly protocols that improve the yield of target structures within finite times, addressing kinetic trapping issues.

Contribution

The authors develop an efficient framework using MSMs and gradient descent to optimize time-dependent assembly protocols, reducing simulation needs and enhancing structure yield.

Findings

Optimized protocols significantly increase target structure yield.

The approach effectively avoids kinetic traps during assembly.

Demonstrated on polymer folding and capsid assembly models.

Abstract

The promise of self-assembly to enable bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite-time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach on two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.