Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
J Chem Phys. 2018 Dec 21;149(23):234105. doi: 10.1063/1.5064856.
Spectral gap optimization of order parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. , 2839 (2016)] is a method for constructing the reaction coordinate (RC) in molecular systems, especially when they are plagued with hard to sample rare events, given a larger dictionary of order parameters or basis functions and limited static and dynamic information about the system. In its original formulation, SGOOP is designed to construct a 1-dimensional RC. Here we extend its scope by introducing a simple but powerful extension based on the notion of conditional probability factorization where known features are effectively washed out to learn additional and possibly hidden features of the energy landscape. We show how SGOOP can be used to proceed in a sequential and bottom-up manner to (i) systematically probe the need for extending the dimensionality of the RC and (ii) if such a need is identified, learn additional coordinates of the RC in a computationally efficient manner. We formulate the method and demonstrate its utility through three illustrative examples, including the challenging and important problem of calculating the kinetics of benzene unbinding from the protein T4L99A lysozyme, where we obtain excellent agreement in terms of dissociation pathway and kinetics with other sampling methods and experiments. In this last case, starting from a larger dictionary of 11 order parameters that are generic for ligand unbinding processes, we demonstrate how to automatically learn a 2-dimensional RC, which we then use in the infrequent metadynamics protocol to obtain 16 independent unbinding trajectories. We believe our method will be a big step in increasing the utility of SGOOP in performing intuition-free sampling of complex systems. Finally, we believe that the utility of our protocol is amplified by its applicability to not just SGOOP but also other generic methods for constructing the RC.
序参量谱隙优化（SGOOP）[P. Tiwary 和 B. J. Berne，美国国家科学院院刊，2839（2016）]是一种在分子系统中构建反应坐标（RC）的方法，特别是在存在难以采样的罕见事件且有更大的序参量字典或基函数和有限的系统静态和动态信息的情况下。在其原始形式中，SGOOP 被设计用于构建一维 RC。在这里，我们通过引入一种简单但强大的扩展来扩展其范围，该扩展基于条件概率因子化的概念，其中已知特征被有效地消除，以学习能量景观的其他可能隐藏特征。我们展示了 SGOOP 如何用于以顺序和自底向上的方式进行操作：（i）系统地探测扩展 RC 维数的必要性，以及（ii）如果需要扩展，则以计算有效的方式学习 RC 的其他坐标。我们制定了该方法，并通过三个说明性示例演示了其效用，包括计算苯从 T4L99A 溶菌酶中解吸的动力学这一具有挑战性和重要的问题，我们在离解途径和动力学方面与其他采样方法和实验获得了极好的一致性。在后一种情况下，从适用于配体解吸过程的 11 个序参量的更大字典开始，我们展示了如何自动学习二维 RC，然后我们在不频繁的元动力学方案中使用它来获得 16 个独立的解吸轨迹。我们相信，我们的方法将在增加 SGOOP 在进行复杂系统无直觉采样方面的效用方面迈出一大步。最后，我们相信，我们的协议的效用通过其不仅适用于 SGOOP 而且适用于构建 RC 的其他通用方法而得到放大。
