Exact solutions of reversible dimerization and trimerization kinetics

We review the oligomerization kinetics problem and present exact solutions for the reversible dimerization and trimerization rate equations. The homologous and hybrid cases are analyzed. For the trimerization case, 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 present 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 numerical 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. It is hoped that students will get valuable insight into how concentrations attain their equilibrium values as time goes on. We believe that the expressions presented in this lecture will be helpful in the time analysis and modelling of reversible oligomerizations in (bio)chemical and nanotechnology contexts.