Estimation of the infinitesimal generator by square-root approximation

Abstract

For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.

References in corpus (4)

• Canonical sampling through velocity-rescaling
• Combining simulations and solution experiments as a paradigm for RNA force field refinement
• Girsanov reweighting for path ensembles and Markov state models
• Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

Cited by in corpus (7)

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• A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models
• Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations
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• Assessing transition rates as functions of environmental variables
• The Augmented Jump Chain -- a sparse representation of time-dependent Markov jump processes
• Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies