Multi-dimensional spectral gap optimization of order parameters (SGOOP) through conditional probability factorization

Abstract

Spectral gap optimization of order parameters (SGOOP) (Tiwary and Berne, Proc. Natl. Acad. Sci. 113 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 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 usefulness 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 fairly generic and arbitrarily chosen 11 order parameters, 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 usefulness of SGOOP in performing intuition-free sampling of complex systems. Finally, we believe that the usefulness of our protocol is amplified by its applicability to not just SGOOP but also other generic methods for constructing the RC.