Mathematical analysis of synthesis chemical reactions for virus building block polymers in <i>vivo</i>

Yuewu Liu; Yan Peng; Yuewu Liu; Yan Peng

doi:10.3934/mbe.2024279

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 6: 6393-6406. doi: 10.3934/mbe.2024279

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Mathematical analysis of synthesis chemical reactions for virus building block polymers in vivo

Yuewu Liu ^{1
,
,},
Yan Peng ²

1.
College of Information and Intelligence, Hunan Agricultural University, Changsha 410128, China
2.
College of Agronomy, Hunan Agricultural University, Changsha 410128, China

Received: 22 December 2023 Revised: 09 May 2024 Accepted: 28 May 2024 Published: 26 June 2024

For numerous viruses, their capsid assembly is composed of two steps. The first step is that virus structural protein monomers are polymerized to building blocks. Then, these building blocks are cumulative and efficiently assembled to virus capsid shell. These building block polymerization reactions in the first step are fundamental for virus assembly, and some drug targets were found in this step. In this work, we focused on the first step. Often, virus building blocks consisted of less than six monomers. That is, dimer, trimer, tetramer, pentamer, and hexamer. We presented mathematical models for polymerization chemical reactions of these five building blocks, respectively. Then, we proved the existence and uniqueness of the positive equilibrium solution for these mathematical models one by one. Subsequently, we also analyzed the stability of the equilibrium states, respectively. These results may provide further insight into property of virus building block polymerization chemical reactions in vivo.
- synthesis chemical reactions,
- building block,
- existence,
- uniqueness
Citation: Yuewu Liu, Yan Peng. Mathematical analysis of synthesis chemical reactions for virus building block polymers in vivo[J]. Mathematical Biosciences and Engineering, 2024, 21(6): 6393-6406. doi: 10.3934/mbe.2024279

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Abstract

For numerous viruses, their capsid assembly is composed of two steps. The first step is that virus structural protein monomers are polymerized to building blocks. Then, these building blocks are cumulative and efficiently assembled to virus capsid shell. These building block polymerization reactions in the first step are fundamental for virus assembly, and some drug targets were found in this step. In this work, we focused on the first step. Often, virus building blocks consisted of less than six monomers. That is, dimer, trimer, tetramer, pentamer, and hexamer. We presented mathematical models for polymerization chemical reactions of these five building blocks, respectively. Then, we proved the existence and uniqueness of the positive equilibrium solution for these mathematical models one by one. Subsequently, we also analyzed the stability of the equilibrium states, respectively. These results may provide further insight into property of virus building block polymerization chemical reactions in vivo.

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