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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 6: 1431-1448. doi: 10.3934/mbe.2014.11.1431
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Effects of elongation delay in transcription dynamics

  • 1.
    School of Mathematics and Systems Science, Beihang University, Beijing 100191
  • 2.
    Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084
  • 3.
    School of Mathematics and System Sciences and LMIB, Beihang University, Beijing, 100191
  • 4.
    Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084
  • Received: 01 June 2014 Accepted: 29 June 2018 Published: 01 September 2014

  • MSC : 92C45, 34F05.

  • In the transcription process, elongation delay is induced by the movement of RNA polymerases (RNAP) along the DNA sequence, and can result in changes in the transcription dynamics. This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. We show that the average transcription level approaches to a periodic dynamics over cell cycles at homeostasis, and the elongation delay can reduce the transcription level and increase the transcription noise. Moreover, the transcription elongation can induce bimodal distribution of mRNA levels that can be measured by the techniques of flow cytometry.

    Citation: Xuan Zhang, Huiqin Jin, Zhuoqin Yang, Jinzhi Lei. Effects of elongation delay in transcription dynamics[J]. Mathematical Biosciences and Engineering, 2014, 11(6): 1431-1448. doi: 10.3934/mbe.2014.11.1431

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  • In the transcription process, elongation delay is induced by the movement of RNA polymerases (RNAP) along the DNA sequence, and can result in changes in the transcription dynamics. This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. We show that the average transcription level approaches to a periodic dynamics over cell cycles at homeostasis, and the elongation delay can reduce the transcription level and increase the transcription noise. Moreover, the transcription elongation can induce bimodal distribution of mRNA levels that can be measured by the techniques of flow cytometry.


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