Abstract
In this chapter we generalize the birth–death process analyzed in the previous chapter to account for enzymatic molecule synthesis, rather than simple Poissonian production. To facilitate the analysis we assume a time-scale separation in the enzymatic reactions, and use it to reduce the complexity of the complete system. With this simplification the generalized birth–death process can be separated into two different subsystems that can be studied separately, and correspond to the systems studied in Chaps. 3 and 4. The simplification procedure, introduced in Sect. 5.1, is a very useful mathematical tool way beyond the scope of the present chapter.
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References
Houston P (2001) Chemical kinetics and reaction dynamics. McGraw-Hill, New York
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Santillán M, Qian H (2011) Irreversible thermodynamics in multiscale stochastic dynamical systems. Phys Rev E 83:041,130
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Santillán, M. (2014). Enzymatic Reactions. In: Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-06689-9_5
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DOI: https://doi.org/10.1007/978-3-319-06689-9_5
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Online ISBN: 978-3-319-06689-9
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