Automatic error control during forward flux sampling of rare events in master equation models

Abstract

Enhanced sampling methods, such as forward flux sampling (FFS), hold a great deal of promise for accelerating stochastic simulations of nonequilibrium biochemical systems involving rare events. However, the description of the tradeoffs between simulation efficiency and error in FFS remains incomplete. We present a novel and mathematically rigorous analysis of the errors in FFS that, for the first time, covers the contribution of every phase of the simulation. We derive a closed form expression for the optimally efficient count of samples to take in each FFS phase in terms of a fixed constraint on sampling error. We introduce a new method, forward flux pilot sampling (FFPilot), that is designed to take full advantage of our optimizing equation without prior information or assumptions about the phase weights and costs along the transition path. In simulations of both singleand multi-dimensional gene regulatory networks, FFPilot is able to completely control sampling error. Higher dimensional systems have additional sources of error and we show that this extra error can be traced to correlations between phases due to roughness on the probability landscape. Finally, we show that in sets of simulations with matched error, FFPilot is on the order of tens-to-hundreds of times faster than direct sampling, in a fashion that scales with the rarity of the events. a) Correspondence to:

Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook

“…This method is due to Klein and Roberts, 131 who use a nonlinear optimization approach to identify M k 's that minimize the computational cost of FFS subject to a user-defined level of statistical uncertainty in the mean first passage time, i.e., the inverse of the rate constant given by Eq. (3).…”

“…[119][120][121] Also, several new variants of FFS have been developed to expand its applicability, 67,76,[122][123][124][125] optimize reaction coordinates, 126 extract free energy profiles, 79,[127][128][129] and improve its efficiency. 130,131 These recent developments call for an updated overview of FFS, both to discuss newer variants and extensions, as well as the types of systems and rare events that have been studied using FFS-like approaches. This paper is organized as follows.…”

Reconstructing an epigenetic landscape using a genetic ‘pulling’ approach

“…Fig. 4a+b shows a comparison of the inferred and true PDFs, which we calculated for a given set of parameters using an enhanced sampling technique [78]. The agreement is again excellent and shows that by using only ∼35 perturbation data points we are able to successfully reconstruct the epigenetic landscape of the model.…”

Segmentation for Human Motion Injury Ultrasound Medical Images Using Deep Feature Fusion

“…According to the determined image features and high-resolution CT scanning algorithm, the high-resolution information sampling equation of medical ultrasound image is obtained [16]. e process is as follows:…”