Formulation of the protein synthesis rate with sequence information

Wenjun Xia; Jinzhi Lei; Wenjun Xia; Jinzhi Lei

doi:10.3934/mbe.2018023

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 2: 507-522. doi: 10.3934/mbe.2018023

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Formulation of the protein synthesis rate with sequence information

Wenjun Xia ¹,
Jinzhi Lei ^{2
,
,}

1.
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2.
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

Received: 04 June 2016 Accepted: 16 March 2017 Published: 01 April 2018
MSC : 92C45

Translation is a central biological process by which proteins are synthesized from genetic information contained within mRNAs. Here, we investigate the kinetics of translation at the molecular level by a stochastic simulation model. The model explicitly includes RNA sequences, ribosome dynamics, the tRNA pool and biochemical reactions involved in the translation elongation. The results show that the translation efficiency is mainly limited by the available ribosome number, translation initiation and the translation elongation time. The elongation time is a log-normal distribution, with the mean and variance determined by the codon saturation and the process of aa-tRNA selection at each codon binding site. Moreover, our simulations show that the translation accuracy exponentially decreases with the sequence length. These results suggest that aa-tRNA competition is crucial for both translation elongation, translation efficiency and the accuracy, which in turn determined the effective protein production rate of correct proteins. Our results improve the dynamical equation of protein production with a delay differential equation that is dependent on sequence information through both the effective production rate and the distribution of elongation time.
- RNA translation,
- efficiency,
- delay differential equation,
- noncoding RNA
Citation: Wenjun Xia, Jinzhi Lei. Formulation of the protein synthesis rate with sequence information[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 507-522. doi: 10.3934/mbe.2018023

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Abstract

Translation is a central biological process by which proteins are synthesized from genetic information contained within mRNAs. Here, we investigate the kinetics of translation at the molecular level by a stochastic simulation model. The model explicitly includes RNA sequences, ribosome dynamics, the tRNA pool and biochemical reactions involved in the translation elongation. The results show that the translation efficiency is mainly limited by the available ribosome number, translation initiation and the translation elongation time. The elongation time is a log-normal distribution, with the mean and variance determined by the codon saturation and the process of aa-tRNA selection at each codon binding site. Moreover, our simulations show that the translation accuracy exponentially decreases with the sequence length. These results suggest that aa-tRNA competition is crucial for both translation elongation, translation efficiency and the accuracy, which in turn determined the effective protein production rate of correct proteins. Our results improve the dynamical equation of protein production with a delay differential equation that is dependent on sequence information through both the effective production rate and the distribution of elongation time.

References

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