7065
2018
eng
425201
425201
42
30
article
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Estimation of the infinitesimal generator by square-root approximation
In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.
J. Phys.: Condens. Matter
10.1088/1361-648X/aadfc8
yes
2018-09-07
Luca Donati
Marcus Weber
Martin Heida
Bettina G. Keller
Marcus Weber
Numerical Mathematics
Weber, Marcus
SFB1114-A5