Estimating Reciprocal Partition Functions to Enable Design Space Sampling

Abstract

Reaction rates are a complicated function of molecular interactions, which can be selected from vast chemical design spaces. Seeking the design that optimizes a rate is a particularly challenging problem since the rate calculation for any one design is itself a difficult computation. Toward this end, we demonstrate a strategy based on transition path sampling to generate an ensemble of designs and reactive trajectories with a preference for fast reaction rates. Each step of the Monte Carlo procedure requires a measure of how a design constrains molecular configurations, expressed via the reciprocal of the partition function for the design. Though the reciprocal of the partition function would be prohibitively expensive to compute, we apply Booth's method for generating unbiased estimates of a reciprocal of an integral to sample designs without bias. A generalization with multiple trajectories introduces a stronger preference for fast rates, pushing the sampled designs closer to the optimal design. We illustrate the methodology on two toy models of increasing complexity: escape of a single particle from a Lennard-Jones potential well of tunable depth and escape from a metastable tetrahedral cluster with tunable pair potentials.

arXiv comment16 pages, 6 figures

References in corpus (18)

• Statistically optimal analysis of samples from multiple equilibrium states
• The pseudo-marginal approach for efficient Monte Carlo computations
• A Novel Path Sampling Method for the Calculation of Rate Constants
• Sampling rare switching events in biochemical networks
• Forward Flux Sampling for rare event simulations
• Simulating rare events in equilibrium or non-equilibrium stochastic systems
• Elaborating Transition Interface Sampling Methods
• Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis
• Rate constants for diffusive processes by partial path sampling
• Event-chain Monte Carlo algorithms for hard-sphere systems
• On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
• The Penalty Method for Random Walks with Uncertain Energies
• Near-optimal protocols in complex nonequilibrium transformations
• Precision shooting: Sampling long transition pathways
• A Noisy Monte Carlo Algorithm
• Sampling diffusive transition paths
• Preserving Correlations Between Trajectories for Efficient Path Sampling
• Path sampling with Stochastic Dynamics: Some new Algorithms

Cited by in corpus (2)

• Simulating a Chemically-Fueled Molecular Motor with Nonequilibrium Molecular Dynamics
• Sterically Driven Current Reversal in a Model Molecular Motor