Work

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

Year: 2024

Type: article

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 [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.

Source: The Journal of Chemical Physics

DOI: 10.1063/5.0188455

Authors: Bingjie Wu, James Holehouse, Ramon Grima, Chen Jia

Institutions: Beijing Computational Science Research Center, Santa Fe Institute, University of Edinburgh

Language: English

Topic: Gene Regulatory Network Analysis

Subfield: Molecular Biology

Field: Biochemistry, Genetics and Molecular Biology

Domain: Life Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: National Science Foundation, Leverhulme Trust, National Natural Science Foundation of China, Division of Materials Research