Don Kulasiri - Chemical Master Equation for Large Biological Networks: State-space Expansion Methods Using AI

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Our endeavour to understand the biological phenomena at intra- and inter- cellular levels has now become the studies of biomolecular interactions conceptualized as dynamic networks. There is a large body of literature on the experimental and theoretical research in developing the networks related to genetic regulations, metabolic pathways, protein-protein interactions, membranes to name a few. We also have advancements in mathematical and computational sciences to analyze and to model these networks to understand their behaviours. One of the main research issues in these modelling efforts is the fact that molecular numbers that belong to each species in the network can greatly differ in magnitude making the molecular number landscape of a particular network heterogenous. Further, the time complexity involved in the dynamics of the networks is certainly not trivial in deciphering and conceptualizing the networks. Understanding of these irregular dynamisms of the networks is a challenge not only mathematically but also computationally. Stochastic processes provide us with a deep and sophisticated mathematics to formulate the probabilistic models of the networks and within that probabilistic conceptualization of network dynamics, the Chemical Master Equations (CMEs) bestow us with a solid foundation in understanding these complex dynamics.

In this book, we present our recent research in developing novel algorithms related to the state expansion of CMEs of large biological networks based on artificial intelligence strategies guided by Bayesian theorem. Our work here is rooted in Markovian stochastic processes and graph theory. Our aim is to reduce the time- and space complexities in algorithms when CMEs are applied to large networks. We introduce the CMEs and roles of molecular fluctuations in biological networks in Chap. deals with one of the largest networks, which has been deterministically modelled in the literature. It is seen that probabilistic interpretations of the network behaviours show very complex patterns which encapsulate the deterministic behaviours as well.

We acknowledge the Centre for Advanced Computational Solutions (C-fACS), Lincoln University, New Zealand for the facilitation of this research.

The author (DK) is also thankful to Prof. Philip Maini, Director of Wolfson Centre of Mathematical Biology, Mathematical Institute, Oxford University, United Kingdom for facilitating and supporting DK and hosting him in his numerous study-leave periods over the last 13 years.

The author (RK) expresses appreciation to OAARs CORP, United Kingdom for providing the packages and tools for this research. RK is also thankful to Mr. Anshul Kosarwal for being great source of inspiration and support throughout all my research projects.

Both of us (DK and RK) acknowledge Prof. Sandhya Samarasinghe, Lincoln University, New Zealand, and Dr. Shamayitri Ghosh, University Hospitals Sussex NHS Foundation trust, United Kingdom for their constant encouragement and support in completing this book.

Canterbury, New Zealand

London, UK

June 2021