Variable-free exploration of stochastic models: a gene regulatory network example

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 [13], we 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 [9] 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.

26 pages, 9 figures

References in corpus (7)

• Coarse Molecular Dynamics of a Peptide Fragment: Free Energy, Kinetics, and Long-Time Dynamics Computations
• Coarse Brownian Dynamics for Nematic Liquid Crystals: Bifurcation Diagrams via Stochastic Simulation
• Coarse-Grained Kinetic Computations for Rare Events: Application to Micelle Formation
• Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
• Coarse Nonlinear Dynamics and Metastability of Filling-Emptying Transitions: Water in Carbon Nanotubes
• An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
• Apparent hysteresis in a driven system with self-organized drag

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