Solving chemical master equation for large biological networks: Novel state-space expansion algorithm based on artificial intelligence and Bayesian standards: A thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy at Lincoln University

Abstract

Numerical solutions of the chemical master equation (CME) are gaining increasing attention with the need to understand the stochasticity of biochemical systems. In this thesis, we aim to develop the intelligent state projection (𝐼𝑆𝑃) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment to describe the dynamic behaviour of the system. 𝐼𝑆𝑃 is based on a state-space search and the data structure standards of artificial intelligence (𝐴𝐼) to explore and update the states of a biochemical system. To support the expansion in 𝐼𝑆𝑃, we also develop a Bayesian likelihood node projection (𝐵𝐿𝑁𝑃) function to predict the likelihood of the states. The proposed algorithm systematically expands the projection space based on predefined inputs, which are useful in providing accuracy in the approximation (Ӕ) and an exact analytical solution at the time of interest. We also discuss the applications of the 𝐼𝑆𝑃 algorithm for realistic models and compare this with other existing, and latest, domain expansion methods based on the r-step reachability of the finite state projection (𝐹𝑆𝑃) and the stochastic simulation algorithm (𝑆𝑆𝐴). In all examples, our proposed methods perform better in terms of speed and accuracy of the expansion, the accuracy of the solution, and provide a better understanding of the state-space of the system.