High-dimensional problems in stochastic modelling of biological processes

Thesis

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). This thesis addresses such computational challenges by a tensor-structured computational framework.

After a background introduction in Chapter 1, Chapter 2 derives the order of convergence in volume size between the stationary distributions of the exact chemical master equation (CME) and its continuous Fokker-Planck approximation (CFPE). It also proposes the multi-scale approaches to address the failure of the CFPE in capturing the noise-induced multi-stability of the CME distribution. Chapter 3 studies the numerical solution of the high-dimensional CFPE using the tensor train and the quantized-TT data formats. In Chapter 4, the tensor solutions are applied to study the parameter estimation, robustness, sensitivity and bifurcation structures of stochastic reaction networks.

A Matlab implementation of the proposed methods/algorithms is available at http://www.stobifan.org.

Authors: Liao, S

• DOI: 10.5287/ora-d5yngpod2
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Keywords: Stochastic Modelling; High Dimensional Computing; Tensor Method