Screening Fast-Mode Motion in Collective Variable Discovery for Biochemical Processes

Abstract

Collective variables (CVs) describing slow degrees of freedom (DOFs) in biomolecular assemblies are crucial for analyzing molecular dynamics trajectories, creating Markov models and performing CV-based enhanced sampling simulations. While time-lagged independent component analysis (tICA) and its nonlinear successor, time-lagged autoencoder (tAE), are widely used, they often struggle to capture protein dynamics due to interference from random fluctuations along fast DOFs. To address this issue, we propose a novel approach integrating discrete wavelet transform (DWT) with dimensionality reduction techniques. DWT effectively separates fast and slow motion in protein simulation trajectories by decoupling high-and low-frequency signals. Based on the trajectory after filtering out high-frequency signals, which corresponds to fast motion, tICA and tAE can accurately extract CVs representing slow DOFs, providing reliable insights into protein dynamics. Our method demonstrates superior performance in identifying CVs that distinguish metastable states compared to standard tICA and tAE, as validated through analyses of conformational changes of alanine dipeptide and tripeptide and folding of CLN025. Moreover, we show that DWT can be used to improve the performance of a variety of CV-finding algorithms by combining it with Deep-tICA, a cutting-edge CV-finding algorithm, to extract CVs for enhancedsampling calculations. Given its negligible computational cost and remarkable ability to screen fast motion, we propose DWT as a "free lunch" for CV extraction, applicable to a wide range of CV-finding algorithms.