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Estimation of the infinitesimal generator by square-root approximation.

Luca Donati¹, Martin Heida², Bettina G Keller¹

¹Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, 14195 Berlin, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|September 8, 2018

Summary

Estimating molecular transition rates is crucial for analyzing molecular processes. This study introduces a novel method using Voronoi tessellation to project molecular dynamics onto a low-dimensional rate matrix, linking potential energy surfaces to transition rates.

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Area of Science:

Computational Chemistry
Molecular Dynamics
Statistical Mechanics

Background:

Accurate estimation of time-scales and transition rates is fundamental for molecular process analysis.
Determining transition rates between molecular conformations is a complex mathematical problem involving invariant subspace projection.

Purpose of the Study:

To present a novel method for projecting the infinitesimal generator onto a low-dimensional rate matrix.
To establish a direct relationship between the potential energy surface of molecular structures and their conformational transition rates.

Main Methods:

Discretization of conformational space using Voronoi tessellation.
Approximation of transition rates between adjacent cells via the geometric average of Boltzmann weights.
Projection of the infinitesimal generator acting on function space to a low-dimensional rate matrix.

Main Results:

Demonstrated a direct correlation between potential energy surfaces and molecular conformational transition rates.
Validated the approximation's correctness and convergence to the Smoluchowski equation generator in the limit of small Voronoi cells.
Presented results for both a 2D diffusion process and the high-dimensional alanine dipeptide system.

Conclusions:

The proposed method effectively links molecular structure's potential energy landscape to dynamic transition rates.
This approach offers a computationally tractable way to estimate transition rates for complex molecular systems.
The method provides a robust framework for understanding and predicting molecular conformational changes.