Screening Fast-Mode\nMotion in Collective Variable\nDiscovery for Biochemical Processes

Collective variables (CVs) describing slow degrees of\nfreedom (DOFs)\nin biomolecular assemblies are crucial for analyzing molecular dynamics\ntrajectories, creating Markov models and performing CV-based enhanced\nsampling simulations. While time-lagged independent component analysis\n(tICA) and its nonlinear successor, time-lagged autoencoder (tAE),\nare widely used, they often struggle to capture protein dynamics due\nto interference from random fluctuations along fast DOFs. To address\nthis issue, we propose a novel approach integrating discrete wavelet\ntransform (DWT) with dimensionality reduction techniques. DWT effectively\nseparates fast and slow motion in protein simulation trajectories\nby decoupling high- and low-frequency signals. Based on the trajectory\nafter filtering out high-frequency signals, which corresponds to fast\nmotion, tICA and tAE can accurately extract CVs representing slow\nDOFs, providing reliable insights into protein dynamics. Our method\ndemonstrates superior performance in identifying CVs that distinguish\nmetastable states compared to standard tICA and tAE, as validated\nthrough analyses of conformational changes of alanine dipeptide and\ntripeptide and folding of CLN025. Moreover, we show that DWT can be\nused to improve the performance of a variety of CV-finding algorithms\nby combining it with Deep-tICA, a cutting-edge CV-finding algorithm,\nto extract CVs for enhanced-sampling calculations. Given its negligible\ncomputational cost and remarkable ability to screen fast motion, we\npropose DWT as a “free lunch” for CV extraction, applicable\nto a wide range of CV-finding algorithms.