Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
J Chem Phys. 2022 Dec 28;157(24):244901. doi: 10.1063/5.0130407.
The promise of self-assembly to enable the 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 with 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 the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.
自组装有望实现具有规定结构和功能的材料的自下而上形成，这促使人们努力揭示最大化目标结构产率的合理设计原则。然而，尽管有许多自组装的成功例子，但在许多系统中，确保目标结构的动力学可达性仍然是一个未解决的问题。特别是，长寿命的动力学陷阱可能导致组装时间大大超过实验可达到的时间尺度。一种建议的解决方案是设计非平衡组装协议，其中系统参数随时间变化以避免这种动力学陷阱。在这里，我们开发了一个框架，将马尔可夫状态模型 (MSM) 分析与最优控制理论相结合，以计算在有限时间内最大化目标结构产率的时变协议。我们提出了一种基于伴随的梯度下降方法，该方法与作为其控制参数函数的系统的 MSM 结合使用，能够有效地优化组装协议。我们还描述了一种插值方法，可大大减少构建 MSM 所需的模拟次数。我们通过两个示例演示了我们的方法；胶体颗粒聚合物折叠的简单半解析模型，以及更复杂的衣壳组装模型。我们的结果表明，优化时变协议可以显著提高所选结构的产率，包括平衡自由能极小值、长寿命亚稳态结构和瞬态状态。
