Popovic, Nikola

Grima, Ramon

Basile, Raffaele

Engineering and Physical Sciences Research Council (EPSRC)

2015-06-22T10:39:50Z

2015-06-22T10:39:50Z

2015-07-01

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.

http://hdl.handle.net/1842/10459

en

The University of Edinburgh

chemical mater equation

graphs

non singular perturbation

Graph-based approach for the approximate solution of the chemical master equation

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy