The mean and noise of stochastic gene transcription with cell division

Qi Wang; Lifang Huang; Kunwen Wen; Jianshe Yu; Qi Wang; Lifang Huang; Kunwen Wen; Jianshe Yu

doi:10.3934/mbe.2018058

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1255-1270. doi: 10.3934/mbe.2018058

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The mean and noise of stochastic gene transcription with cell division

1.
Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
2.
College of Science, Guangxi University of Science and Technology, Liuzhou 545006, China
3.
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510275, China

Received: 31 January 2018 Revised: 16 April 2018 Published: 01 October 2018
MSC : Primary: 37H10; Secondary: 34F05, 60J10, 92C40

Life growth and development are driven by continuous cell divisions. Cell division is a stochastic and complex process. In this paper, we study the impact of cell division on the mean and noise of mRNA numbers by using a two-state stochastic model of transcription. Our results show that the steady-state mRNA noise with symmetric cell division is less than that with binomial inheritance with probability 0.5, but the steady-state mean transcript level with symmetric division is always equal to that with binomial inheritance with probability 0.5. Cell division except random additive inheritance always decreases mean transcript level and increases transcription noise. Inversely, random additive inheritance always increases mean transcript level and decreases transcription noise. We also show that the steady-state mean transcript level (the steady-state mRNA noise) with symmetric cell division or binomial inheritance increases (decreases) with the average cell cycle duration. But the steady-state mean transcript level (the steady-state mRNA noise) with random additive inheritance decreases (increases) with the average cell cycle duration. Our results are confirmed by Gillespie stochastic simulation using plausible parameters.
- Asymmetric cell division,
- cell cycle,
- partition,
- mean and noise
Citation: Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu. The mean and noise of stochastic gene transcription with cell division[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1255-1270. doi: 10.3934/mbe.2018058

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Abstract

Life growth and development are driven by continuous cell divisions. Cell division is a stochastic and complex process. In this paper, we study the impact of cell division on the mean and noise of mRNA numbers by using a two-state stochastic model of transcription. Our results show that the steady-state mRNA noise with symmetric cell division is less than that with binomial inheritance with probability 0.5, but the steady-state mean transcript level with symmetric division is always equal to that with binomial inheritance with probability 0.5. Cell division except random additive inheritance always decreases mean transcript level and increases transcription noise. Inversely, random additive inheritance always increases mean transcript level and decreases transcription noise. We also show that the steady-state mean transcript level (the steady-state mRNA noise) with symmetric cell division or binomial inheritance increases (decreases) with the average cell cycle duration. But the steady-state mean transcript level (the steady-state mRNA noise) with random additive inheritance decreases (increases) with the average cell cycle duration. Our results are confirmed by Gillespie stochastic simulation using plausible parameters.

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