Computing committors via Mahalanobis diffusion maps with enhanced sampling data

What is it about?

Molecular dynamics (MD) is a computer simulation technique where the movement of atoms is calculated according to Newton's laws of motion. These simulations can provide trustworthy atomistic-level detail otherwise unavailable from experiments in various fields including materials science and chemical physics. However, each computed MD “snapshot” corresponds to roughly 10^-15 seconds of atomic motion, while significant chemical reactions and transitions in bio-molecules are very rare events on this scale and can happen from milliseconds to hours, requiring weeks or years-long simulations. Further, each “snapshot” is very high-dimensional for even small molecules and difficult to process with statistical techniques. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales and describe them in a visual and comprehensive manner. In this work, we deal with the timescale issue via accelerated simulations with robust statistical reweighting, and we combat the dimensionality issue with physically-motivated model reduction. The accelerated simulations come from “metadynamics”, a robust sampling method that forces an MD simulation to explore new regions. The model reduction is through “collective variables” such as dihedral angles that give a coarse-grained description of the geometric arrangement of the considered molecule. We combine these techniques as a facet of our proposed method “Target Measure Mahalanobis Diffusion Map”, which analyzes the collection of MD snapshots as a network and successfully extracts rare event statistics. We prove that the proposed algorithm correctly approximates the dynamics of interest and test it on benchmark examples. Finally, we apply the proposed algorithm to quantify transitions in alanine dipeptide described in four dihedral angles. The resulting transition rate between its two metastable states separated by a high free energy barrier is in good agreement with the one obtained by a very long unbiased all-atom simulation.

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Photo by Terry Vlisidis on Unsplash

Photo by Terry Vlisidis on Unsplash