Analysis of a non-Markov transcription model with nuclear RNA export and RNA nuclear retention

Qiqi Deng; Aimin Chen; Huahai Qiu; Tianshou Zhou; Qiqi Deng; Aimin Chen; Huahai Qiu; Tianshou Zhou

doi:10.3934/mbe.2022392

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 8426-8451. doi: 10.3934/mbe.2022392

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Research article

Analysis of a non-Markov transcription model with nuclear RNA export and RNA nuclear retention

1.
Guangdong Province Key Laboratory of Computational Science, School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
2.
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
3.
School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200, China

Academic Editor: Ulf Schmitz

Received: 07 April 2022 Revised: 23 May 2022 Accepted: 29 May 2022 Published: 09 June 2022

Transcription involves gene activation, nuclear RNA export (NRE) and RNA nuclear retention (RNR). All these processes are multistep and biochemical. A multistep reaction process can create memories between reaction events, leading to non-Markovian kinetics. This raises an unsolved issue: how does molecular memory affect stochastic transcription in the case that NRE and RNR are simultaneously considered? To address this issue, we analyze a non-Markov model, which considers multistep activation, multistep NRE and multistep RNR can interpret many experimental phenomena. In order to solve this model, we introduce an effective transition rate for each reaction. These effective transition rates, which explicitly decode the effect of molecular memory, can transform the original non-Markov issue into an equivalent Markov one. Based on this technique, we derive analytical results, showing that molecular memory can significantly affect the nuclear and cytoplasmic mRNA mean and noise. In addition to the results providing insights into the role of molecular memory in gene expression, our modeling and analysis provide a paradigm for studying more complex stochastic transcription processes.
- transcription,
- RNA nuclear retention,
- molecular memory,
- non-Markov model,
- transcription noise
Citation: Qiqi Deng, Aimin Chen, Huahai Qiu, Tianshou Zhou. Analysis of a non-Markov transcription model with nuclear RNA export and RNA nuclear retention[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 8426-8451. doi: 10.3934/mbe.2022392

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Abstract

Transcription involves gene activation, nuclear RNA export (NRE) and RNA nuclear retention (RNR). All these processes are multistep and biochemical. A multistep reaction process can create memories between reaction events, leading to non-Markovian kinetics. This raises an unsolved issue: how does molecular memory affect stochastic transcription in the case that NRE and RNR are simultaneously considered? To address this issue, we analyze a non-Markov model, which considers multistep activation, multistep NRE and multistep RNR can interpret many experimental phenomena. In order to solve this model, we introduce an effective transition rate for each reaction. These effective transition rates, which explicitly decode the effect of molecular memory, can transform the original non-Markov issue into an equivalent Markov one. Based on this technique, we derive analytical results, showing that molecular memory can significantly affect the nuclear and cytoplasmic mRNA mean and noise. In addition to the results providing insights into the role of molecular memory in gene expression, our modeling and analysis provide a paradigm for studying more complex stochastic transcription processes.

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