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Continuous Time Markov Chain Models for Chemical Reaction

Summary: Chapter 7
Continuous Time Markov Chain
Models for Chemical Reaction
7.1 Chemical reaction networks: basic construc-
Some of this material is adapted from the survey article [8]. We will begin in Sec-
tion 7.1.1 by developing the basic stochastic equations for chemical systems. Next,
in Section 7.1.2 we describe the most common choice for intensity (or propensity)
function: mass-action kinetics. In Section 7.1.3 we give a series of models for gene
transcription and translation. In Section 7.1.4 we derive both the generator and the
forward equations, which is also called the chemical master equation in this context.
Finally, in Section 7.1.5 we point out that the model developed here is, in fact, quite
general and not confined to the chemical setting.
7.1.1 The stochastic equations and basic terminology
We begin our study of chemical systems by considering a system consisting of three
"species," denoted A, B, and C, and one reaction,
A + B C,
in which one molecule of A and one molecule of B are consumed to produce one
molecule of C. The intuition for the model for the reaction is that the probability of


Source: Anderson, David F. - Department of Mathematics, University of Wisconsin at Madison


Collections: Mathematics