Delay chemical master equation: direct and closed-form solutions

Proceedings. Mathematical, Physical, and Engineering Sciences
Andre Leier, Tatiana T Marquez-Lago

Abstract

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

References

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Citations

Jan 21, 2018·Nature Communications·Seong Jun ParkJaeyoung Sung
Nov 7, 2019·Proceedings of the National Academy of Sciences of the United States of America·Jiajun Zhang, Tianshou Zhou
Jul 18, 2021·Physical Review. E·Zhenquan ZhangTianshou Zhou

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Software Mentioned

SSA
DSSA

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