Exact solutions of reversible dimerization and trimerization kinetics

We revisit the dimerization kinetics problem and obtain exact solutions for the reversible trimerization rate equation. The homologous and hybrid cases are analyzed and for the trimerization both the concerted and stepwise mechanisms were considered. We present a full analysis of the solutions. We compared the time evolution of the species concentrations with the corresponding irreversible process and highlighted the differences. We show in detail the correct mathematical limiting procedure to pass from reversible to irreversible kinetics. We also obtain the corresponding expressions for the half-life to reach equilibrium concentrations. We checked all these equations against numerically exact results and the agreement was found to be perfect. We fitted experimental kinetics data corresponding to the tubulin-GDP heterodimer dissociation and found an excellent match. Finally, we provide some practical hints on how to estimate rate constants from these oligomerization processes. It is hoped that the expressions offered in this comprehensive study will be helpful in the time analysis and modelling of reversible oligomerizations in (bio)chemical contexts.