Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure

Xiyan Yang; Zihao Wang; Yahao Wu; Tianshou Zhou; Jiajun Zhang; Xiyan Yang; Zihao Wang; Yahao Wu; Tianshou Zhou; Jiajun Zhang

doi:10.3934/mbe.2022153

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 3313-3336. doi: 10.3934/mbe.2022153

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Research article

Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure

1.
School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, China
2.
Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, China
3.
School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Academic Editor：Ulf Schmitz

Received: 20 November 2021 Revised: 04 January 2022 Accepted: 18 January 2022 Published: 24 January 2022

While transcription often occurs in a bursty manner, various possible regulations can lead to complex promoter patterns such as promoter cycles, giving rise to an important question: How do promoter kinetics shape transcriptional bursting kinetics? Here we introduce and analyze a general model of the promoter cycle consisting of multi-OFF states and multi-ON states, focusing on the effects of multi-ON mechanisms on transcriptional bursting kinetics. The derived analytical results indicate that burst size follows a mixed geometric distribution rather than a single geometric distribution assumed in previous studies, and ON and OFF times obey their own mixed exponential distributions. In addition, we find that the multi-ON mechanism can lead to bimodal burst-size distribution, antagonistic timing of ON and OFF, and diverse burst frequencies, each further contributing to cell-to-cell variability in the mRNA expression level. These results not only reveal essential features of transcriptional bursting kinetics patterns shaped by multi-state mechanisms but also can be used to the inferences of transcriptional bursting kinetics and promoter structure based on experimental data.
- transcription bursting,
- promoter cycle,
- multi-ON mechanism,
- noise,
- timing
Citation: Xiyan Yang, Zihao Wang, Yahao Wu, Tianshou Zhou, Jiajun Zhang. Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3313-3336. doi: 10.3934/mbe.2022153

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Abstract

While transcription often occurs in a bursty manner, various possible regulations can lead to complex promoter patterns such as promoter cycles, giving rise to an important question: How do promoter kinetics shape transcriptional bursting kinetics? Here we introduce and analyze a general model of the promoter cycle consisting of multi-OFF states and multi-ON states, focusing on the effects of multi-ON mechanisms on transcriptional bursting kinetics. The derived analytical results indicate that burst size follows a mixed geometric distribution rather than a single geometric distribution assumed in previous studies, and ON and OFF times obey their own mixed exponential distributions. In addition, we find that the multi-ON mechanism can lead to bimodal burst-size distribution, antagonistic timing of ON and OFF, and diverse burst frequencies, each further contributing to cell-to-cell variability in the mRNA expression level. These results not only reveal essential features of transcriptional bursting kinetics patterns shaped by multi-state mechanisms but also can be used to the inferences of transcriptional bursting kinetics and promoter structure based on experimental data.

References

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