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Effective Markovian Dynamics Method for Solving Non-Markovian Dynamics of Stochastic Gene Expression
Open accessPublished version of a preprint
Abstract
Experiments have shown that over 10% of proteins are degraded nonexponentially. Gene expression models for nonexponentially degraded proteins are notoriously difficult to solve since the underlying stochastic dynamics is non-Markovian. Here we develop an effective Markovian dynamics (EMD) method which converts a large class of non-Markovian models into effective Markovian ones so that they have the same mRNA and protein distributions at any fixed time. Using the EMD approach, we analytically solve some classical gene expression models with nonexponential or delayed protein decay, whose exact distributions are previously unknown and fail to be obtained using conventional queueing theory. Our theory successfully explains why nonexponentially degraded proteins on average have smaller mRNA-protein correlation than exponentially degraded proteins, and it predicts that bimodality is significantly enhanced in the presence of delayed protein degradation.
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Cites
Global quantification of mammalian gene expression control
Schwanhäusser, B., Busse, D., Li, N., Dittmar, G., Schuchhardt, J., Wolf, J., Chen, W., & Selbach, M. (2011) · Nature · doi:10.1038/nature10098 · Cited by 6,566
Quantifying E. coli Proteome and Transcriptome with Single-Molecule Sensitivity in Single Cells
Taniguchi, Y., Choi, P. J., Li, G.-W., Chen, H., Babu, M., Hearn, J., Emili, A., & Xie, X. S. (2010) · Science · doi:10.1126/science.1188308 · Cited by 1,982
Stochastic protein expression in individual cells at the single molecule level
Cai, L., Friedman, N., & Xie, X. S. (2006) · Nature · doi:10.1038/nature04599 · Cited by 1,145
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Metadata
- Authors
- Li, Y., & Jia, C.
- Affiliations
- University of Electronic Science and Technology of China (CN)
- Beijing Computational Science Research Center (CN)
- Corresponding author
- Jia, Chen
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2025-07-22
- Volume
- 135
- Issue
- 4
- Pages
- 048401-048401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W4411647927
- Cited by
- 7
- References
- 3
- Citations by year
- 2026: 5 · 2025: 2
- FWCI
- 2.11
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
- PubMed (publishedVersion)
- Funders
- National Natural Science Foundation of China (12401629, 12271020)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- stochastic gene expression, non-Markovian dynamics, mRNA-protein correlation, bimodal gene expression, queueing theory, protein degradation kinetics
- MeSH terms
- Markov Chains, Models, Genetic, Proteins, RNA, Messenger, Stochastic Processes, Gene Expression
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