Parameter estimation and bifurcation analysis of stochastic models of gene regulatory networks: tensor-structured methods

TL;DR

This paper introduces tensor-structured parametric analysis (TPA), a novel computational method that efficiently studies parameter effects and bifurcations in stochastic gene regulatory network models, aiding parameter estimation and robustness analysis.

Contribution

The paper presents a new tensor-structured approach for simultaneous analysis of stochastic models across parameter spaces, improving efficiency in bifurcation and sensitivity studies.

Findings

TPA enables rapid analysis of parameter-dependent stochastic models.

The method facilitates bifurcation detection in biochemical networks.

Implementation in Matlab makes the approach accessible for researchers.

Abstract

Stochastic modelling provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. In practice, the common challenge is to calibrate a large number of model parameters against the experimental data. A related problem is to efficiently 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 presented. 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. This methodology is exemplified to study the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. The TPA has been implemented in Matlab and the codes are available at http://www.stobifan.org .