Hierarchical Time-Lagged Independent Component Analysis: Computing Slow Modes and Reaction Coordinates for Large Molecular Systems

Analysis of molecular dynamics, for example using Markov models, often requires the identification of order parameters that are good indicators of the rare events, i.e. good reaction coordinates. Recently, it has been shown that the time lagged independent component analysis (TICA) finds the linear combinations of input coordinates that optimally represent the slow kinetic modes and may serve in order to define reaction coordinates between the metastable states of the molecular system. A limitation of the method is that both computing time and memory requirements scale with the square of the number of input features. For large protein systems, this exacerbates the use of extensive feature sets such as the distances between all pairs of residues or even heavy atoms. Here we derive a hierarchical TICA (hTICA) method that approximates the full TICA solution by a hierarchical, divide-and-conquer calculation. By using hTICA on distances between heavy atoms we identify previously unknown relaxation processes in the bovine pancreatic trypsin inhibitor.