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Title: Graph-based approach for the approximate solution of the chemical master equation
Author: Basile, Raffaele
ISNI:       0000 0004 5347 631X
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2015
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The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution – which gives the corresponding probability density function – is possible only in very simple cases, there is a clear need for approximation techniques. Here, we propose a novel perturbative three-step approach which draws heavily on graph theory: (i) we expand the eigenvalues of the transition state matrix in the CME as a series in a non-dimensional parameter that depends on the reaction rates and the reaction volume; (ii) we derive an analogous series for the corresponding eigenvectors via a graph-based algorithm; (iii) we combine the resulting expansions into an approximate solution to the CME. We illustrate our approach by applying it to a reversible dimerization reaction; then, we formulate a set of conditions, which ensure its applicability to more general reaction networks. We follow attempting to apply the results to a more complicated system, namely push-pull, but the problem reveals too complex for a complete solution. Finally, we discuss the limitations of the methodology.
Supervisor: Popovic, Nikola; Grima, Ramon Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: chemical master equation ; graphs ; non singular perturbation