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

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.