Variable-free exploration of stochastic models

A gene regulatory network example

Radek Erban, Thomas A. Frewen, Xiao Wang, Timothy C. Elston, Ronald Coifman, Boaz Nadler, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.

Original languageEnglish (US)
Article number155103
JournalJournal of Chemical Physics
Volume126
Issue number15
DOIs
StatePublished - 2007
Externally publishedYes

Fingerprint

Stochastic models
genes
Genes
translating
data simulation
complex systems
Eigenvalues and eigenfunctions
Large scale systems
bursts
constrictions
eigenvectors
diffusion coefficient
coefficients
Processing
simulation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Erban, R., Frewen, T. A., Wang, X., Elston, T. C., Coifman, R., Nadler, B., & Kevrekidis, I. G. (2007). Variable-free exploration of stochastic models: A gene regulatory network example. Journal of Chemical Physics, 126(15), [155103]. https://doi.org/10.1063/1.2718529

Variable-free exploration of stochastic models : A gene regulatory network example. / Erban, Radek; Frewen, Thomas A.; Wang, Xiao; Elston, Timothy C.; Coifman, Ronald; Nadler, Boaz; Kevrekidis, Ioannis G.

In: Journal of Chemical Physics, Vol. 126, No. 15, 155103, 2007.

Research output: Contribution to journalArticle

Erban, R, Frewen, TA, Wang, X, Elston, TC, Coifman, R, Nadler, B & Kevrekidis, IG 2007, 'Variable-free exploration of stochastic models: A gene regulatory network example', Journal of Chemical Physics, vol. 126, no. 15, 155103. https://doi.org/10.1063/1.2718529
Erban, Radek ; Frewen, Thomas A. ; Wang, Xiao ; Elston, Timothy C. ; Coifman, Ronald ; Nadler, Boaz ; Kevrekidis, Ioannis G. / Variable-free exploration of stochastic models : A gene regulatory network example. In: Journal of Chemical Physics. 2007 ; Vol. 126, No. 15.
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