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Adaptively Biased Sequential Importance Sampling for Rare Events in Reaction Networks with Comparison to Exact Solutions from Finite Buffer dCME Method

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posted on 19.02.2014, 00:00 by Youfang Cao, Jie Liang
Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlogl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Funding

This work was supported by NSF DBI 1062328 and DMS-0800257, and National Institutes of Health Grants GM079804 and GM086145.

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Publisher Statement

Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Chemical Physics and may be found at http://scitation.aip.org/content/aip/journal/jcp/139/2/10.1063/1.4811286.

Publisher

American Institute of Physics

Language

en_US

issn

0021-9606

Issue date

01/07/2013

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