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PreprintCited by 19Gene Regulatory Network Analysisstochastic dynamics and bifurcationStochastic processes and statistical mechanics

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Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition

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Wu, Bingjie, Holehouse, James, Grima, Ramon, Jia, Chen·2023·The Journal of Chemical Physics
DOI 10.1101/2023.11.21.568174

Preprint — published as 10.1063/5.0188455

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Abstract

In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [“Exact time-dependent solutions for a self-regulating gene.” Phys. Rev. E 83: 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate.

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Cites

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    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 · cited 2×

    “Bursty protein synthesis is often due to rapid translation of protein from a single, short-lived mRNA molecule [15, 16]; if the mRNA lifetime is quite long (as common in mammalian cells [17]), then protein synthesis may appear non-bursty.”
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Metadata

Authors
Wu, B., Holehouse, J., Grima, R., & Jia, C.
Affiliations
  • Beijing Computational Science Research Center (CN)
  • Santa Fe Institute (US)
  • University of Edinburgh (GB)
ORCID
Venue
The Journal of Chemical Physics
Publisher
openRxiv
Published
2023-11-22
Volume
160
Issue
7
ISSN
0021-9606 (ISSN-L)
DOI
10.1101/2023.11.21.568174
OpenAlex
W4391876285
Cited by
19
References
1
Citations by year
2026: 8 · 2025: 8 · 2024: 3
FWCI
2.59
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • The Journal of Chemical Physics (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
  • PubMed (publishedVersion)
  • Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, cc-by)
Funders
  • National Science Foundation (2133863)
  • Leverhulme Trust (RPG-2020-327)
  • National Natural Science Foundation of China (U1930402,, U2230402, 12271020, U12271020)
  • Division of Materials Research
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
chemical master equation, protein expression, autoregulation, negative feedback, positive feedback, spectral decomposition, Heun functions, generating functions, continued fractions, time-dependent solutions, synthetic gene circuits
MeSH terms
Proteins, Stochastic Processes, Gene Expression, Gene Regulatory Networks

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