Landmark Kernel tICA For Conformational Dynamics

Abstract

Molecular dynamics simulations of biomolecules produce a very high dimensional time-series dataset. Performing analysis necessarily involves projection onto a lower dimensional space. A priori selection of projection coordinates requires (perhaps unavailable) prior information or intuition about the system. At best, such a projection can only confirm the intuition. At worst, a poor projection can obscure new features of the system absent from the intuition. Previous statistical methods such a time-structure based independent component analysis (tICA) and Markov state modeling (MSMs) have offered relatively unbiased means of projecting conformations onto coordinates or state labels, respectively. These analyses are underpinned by the propagator formalism and the assumption that slow dynamics are biologically interesting. Although arising from the same mathematics, tICA and MSMs have different strengths and weaknesses. We introduce a unifying method which we term \"landmark kernel tICA\" (lktICA) which uses a variant of the Nystrom kernel approximation to permit approximate non-linear solutions to the tICA problem. We show that lktICA is equivalent to MSMs with \"soft\" states. We demonstrate the advantages of this united method by finding improved projections of (a) a 1D potential surface (b) a peptide folding trajectory and (c) an ion channel conformational change.