(111d) Systematic Identification of Coarse Variables in Biomolecular Systems through Dimensionality-Reduction Tools: Reconstruction and Navigation of Free-Energy Landscapes

Molecular simulation methods such as molecular dynamics (MD) can be used to study macroscopic phenomena associated with biomolecular processes by generating information with atomic resolution and at fine time scales. In particular, obtaining free-energy landscapes is of fundamental importance as it enables the characterization of stable/unstable states and their corresponding transition rates, which can then be used to gain insight into key biological processes. However, constructing free-energy landscapes for complex molecular systems of interest, e.g., proteins, can be difficult as it requires (i) identification of relevant order parameter/s and (ii) proper sampling of the corresponding space. In this talk, we address those challenges using two model systems: the alanine dipeptide molecule and the helix-forming pentapeptide protein in water undergoing a temperature-induced coil-to-helix folding process. Here we focus on the development of methods that exploit a novel class of manifold-learning techniques to identify good coarse variables, i.e., order parameters, and on methods that accelerate the slow dynamics associated with such variables.

Coarse variables are obtained through the use of a nonlinear dimensionality-reduction technique known as diffusion maps [1, 2]. It relies on the construction of a Markov transition matrix, which defines a random walk over the data. The probability of reaching any point (or molecular configuration in this case) from another depends on an appropriate pairwise affinity metric. The similarity between any two points is expressed by a diffusion distance, which is based on their dynamic proximity. The eigenvectors of this Markov matrix establish the mapping from the original high-dimensional 3N space to a low-dimensional coarse-variable space in which the Euclidean distance between points corresponds to their diffusion distance in the original space. We also present candidate, equation-free based [3-5] tools, linked with stochastic estimation techniques, to construct and navigate the underlying effective free-energy landscapes and to coarse-grain slow and otherwise difficult-to-access dynamics.

References:

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