ArticleProceedings. Mathematical, physical, and engineering sciences2015
Delay chemical master equation: direct and closed-form solutions.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- Solving stochastic gene-expression models using queueing theory: A tutorial review.Biophysical journal · 2024Review
- Stochastic modeling of the mRNA life process: A generalized master equation.Biophysical journal · 2023Article
- Article
- Parameter identification of a delayed infinite-dimensional heat-exchanger process based on relay feedback and root loci analysis.Scientific reports · 2022Article
- Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number.Science advances · 2022Article
- Modeling bursty transcription and splicing with the chemical master equation.Biophysical journal · 2022Article
- Effects of noise and time delay on E2F's expression level in a bistable Rb-E2F gene's regulatory network.IET systems biology · 2021Article
- Neural network aided approximation and parameter inference of non-Markovian models of gene expression.Nature communications · 2021Article
- Markovian approaches to modeling intracellular reaction processes with molecular memory.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- The Chemical Fluctuation Theorem governing gene expression.Nature communications · 2018Article
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2 authors.
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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.
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