title: Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.
abstract: Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.
authors.affiliation: Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: Shuohao
authors.initials: S
authors.lastname: Liao
authors.affiliation: Institute of Mathematics, Czech Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic.
authors.forename: Tomáš
authors.initials: T
authors.lastname: Vejchodský
authors.affiliation: Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK erban@maths.ox.ac.uk.
authors.forename: Radek
authors.initials: R
authors.lastname: Erban
mesh_terms: D008962:Models, Theoretical; D013269:Stochastic Processes
keywords: gene regulatory networks; high-dimensional computation; parametric analysis; stochastic modelling