Locating Transition States for Biomolecular Dynamics via Invertible Dimensionality Reduction

Locating the transition states (TS) for the conformational changes of biomacromolecules is among the major tasks of biomolecular simulations, as they are the bottlenecks of motion encoding key mechanistic insights. However, identifying the short-lived TSs from (even abundant) simulation data has been a long-standing challenge due to the high dimensionality of the molecules. Gentlest ascent dynamics (GAD) is an effective approach that searches for saddle points but only within spaces of small number of (typically <20) dimensions. Such a restriction of GAD may in principle be relieved by dimensionality reduction (DR) that reduces the high-dimensional configurational space of the molecules to a low-dimensional manifold. However, the vast majority of DR algorithms are built to focus on only high-density regions and have therefore distorted the TS regions, disabling a subsequent GAD search. The recently introduced reaction coordinate flows (RCF) is among the few exceptions. As RCF learns an invertible mapping between the configurational space and the reduced RC space through a loss function incorporating both density and transition pair information, it shall be able to preserve kinetics and therefore TS during DR. GAD can then be readily applied to locate the TS candidates in the RCF-learned RC space, which can be validated rigorously through reverse RCF mapping and committor analysis in the original space. Here, we demonstrate the effectiveness of this RCF-GAD integration through alanine dipeptide and the ground-to-excited transition of the T4 lysozyme L99A variant (T4L-L99A) in explicit solvents. For alanine dipeptide, GAD managed to identify three TSs with the RCF reduction to four RCs, but only two TSs with a reduction to two RCs, due to the merging of two low density stable states in the 2RC representation, indicating the necessity of a priori evaluation of the number of intrinsic dimensions for RCF. For T4L-L99A, the TSs located by GAD in a 4RC RCF reduction successfully resembled those found previously via automated path searching, demonstrating the feasibility of our approach for realistic biomolecular systems.