Deflation reveals dynamical structure in nondominant reaction coordinates

Abstract

The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions into lower-dimensional representations that model the system dynamics. These dynamical models have been developed to optimally approximate the system's global kinetics. However, the separate aims of optimizing global kinetics and modeling a process of interest diverge when the process of interest is not the slowest process in the system. Here, we introduce deflation into state-of-the-art methods in molecular kinetics in order to preserve the use of variational optimization tools when the slowest dynamical mode is not the same as the one we seek to model and understand. First, we showcase deflation for a simple toy system and introduce the deflated variational approach to Markov processes (dVAMP). Using dVAMP, we show that nondominant reaction coordinates produced using deflation are more informative than their counterparts generated without deflation. Then, we examine a protein folding system in which the slowest dynamical mode is not folding. Following a dVAMP analysis, we show that deflation can be used to obscure this undesired slow process from a kinetic model, in this case a VAMPnet. The incorporation of deflation into current methods opens the door for enhanced sampling strategies and more flexible, targeted model building.arXiv:1907.04101v1 [q-bio.BM]

Unsupervised Learning Methods for Molecular Simulation Data

“…In early developments of kinetic models for molecular simulation data (see section 6 ); when pairwise RMSD was used, k -centers and regular space clustering were frequently employed for clustering steps of kinetic modeling algorithms. 20 , 21 , 251 − 254 Other—and especially more recent—applications are mostly based on k -means or its minibatch variant 29 , 40 , 255 − 259 and, less frequently, k -medoids 260 ).…”

“…Then, the variationally optimal latent coordinates are obtained by a singular value decomposition of a modified propagation matrix where the latent coordinates { u α } for the data are stored in the columns of , the latent coordinates { v α } for the time-lagged data are the columns of , and the singular values σ̂ α comprise the diagonal of Σ̂ . 259 , 330 Note that the singular value decomposition in eq 55 reduces to a standard eigendecomposition when C 0τ is symmetric.…”

“… 4 , 330 For reversible data, eq 55 is equivalent to eq 44 . 259 Furthermore, MSMs are a special case of Koopman models when the data is both reversible and represented by a basis of indicator functions. 330 The interested reader is further referred to ref ( 259 ), which demonstrates the equivalence of TICA and TCCA under reversible conditions, as well as the relationship of both algorithms to CCA in general.…”

Molecular latent space simulators

“…One may eliminate these modes from the slow subspace a posteriori by simply discarding the SRV eigenfunctions identied to correspond to these processes, orif they are known beforehand as a result of a previous analysisa priori by subtracting them out of the system featurization using deation. 52…”

Computational methods for exploring protein conformations

“…VAMPnets [ 73 ]), these methods map directly from molecular coordinates to Markov states, and so are not useful for identifying CVs for other purposes. Additionally, the slowest modes are not always the modes of interest [ 45 , 78 ], although a solution to this problem was recently provided by the d eflated v ariational a pproach to M arkov p rocesses (dVAMP) [ 79 ].…”