Data-driven computation of molecular reaction coordinates

Abstract

The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics are characterized by rare or slow transition events. In a recent publication, precise defining characteristics of such reaction coordinates were identified and linked to the existence of a so-called transition manifold. This theory gives rise to a novel numerical method for the pointwise computation of reaction coordinates that relies on short parallel MD simulations only, but yields accurate approximation of the long time behavior of the system under consideration. This article presents an extension of the method towards practical applicability in computational chemistry. It links the newly defined reaction coordinates to concepts from transition path theory and Markov state model building. The main result is an alternative computational scheme that allows for a global computation of reaction coordinates based on commonly available types of simulation data, such as single long molecular trajectories or the push-forward of arbitrary canonically distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, which computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a small protein system.

Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds

“…There is however no formal guarantee that maps of form (9) fall into the prevalent set of maps predicted by Theorem 2.6, and for general manifolds K ⊂ L 2 1/ρ , this is indeed not the case. 2 However, there is empirical evidence that transition manifolds in real-world systems, specifically molecular dynamical systems, are "sufficiently regular" for (9) to preserve their features well (Bittracher et al 2018). Still, this necessary restriction to a finite-dimensional class of embedding functions represents a significant deficit of the framework described here.…”

“…The intermediate lag time τ = 20 ps falls between the slow and fast time scales of the system, which have been explicitly computed in Bittracher et al (2018). In cases where a full time scale analysis is not available, the type and size of the molecule can often x i .…”

“…At the heart of this approach is the insight that good reaction coordinates can be found by parameterizing a certain transition manifold M in the function space L 1 . For metastable systems, this manifold has strong connections to the aforementioned transition pathway (Bittracher et al 2018), but the two concepts are not equivalent. Its defining property is that for times τ that fall between the fastest and slowest time scales, the transition density functions with relaxation time τ concentrate around M. Hence, M can be seen as the "backbone" of the slowly equilibrating parts of the dynamics.…”

“…The existence of three eigenvalues close to 1 (not counting the eigenvalue 1 itself) indicates a three-dimensional reaction coordinate. b Test points in the space of the three sub-dominant diffusion map eigenvectors, i.e., the final three-dimensional reaction coordinate hint at a suitable τ , as estimates for the time scales of certain common physiochemical reactions, such as dihedral angle reconfigurations or formation of secondary motifs, are well-known(Bittracher et al 2018). For each test point x i , M = 96 Gromacs MD simulations of length τ were performed, which took 40 h on a 96 core compute cluster.…”

A kernel-based approach to molecular conformation analysis

“…It has recently been demonstrated in Ref. 29 how more evenly distributed test points can be generated. However, as the distribution of the test points directly influences the form of the transfer operator, and only the eigenpairs of transfer operators associated with the Lebesgueor the Gibbs measure possess physical interpretations in the context of metastability, a reweighting, for example by importance sampling techniques, has to be introduced to preserve the correct statistics.…”