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

Bingjie Wu, James Holehouse, Ramon Grima*, Chen Jia*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 [Ramos et al., 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.

Original languageEnglish
Article number074105
JournalThe Journal of Chemical Physics
Volume160
Issue number7
Early online date16 Feb 2024
DOIs
Publication statusPublished - 21 Feb 2024

Keywords / Materials (for Non-textual outputs)

  • Stochastic Processes
  • Proteins/genetics
  • Gene Regulatory Networks
  • Gene Expression

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