Dynamics of Polymerization of Macromolecules with Multiple Binding Sites

In Nature, there are many examples of biological polymerizations in which the monomers possess multiple binding sites. Under certain circumstances, such branched polymerizations may produce a large macroparticle that constitutes a significant fraction of the monomers. In this paper, we show that the polymerizations of antibodies with antigens and the polymerization of fibrin are of this type. We then present the results of stochastic simulations for the time-evolutions of these processes, and characterize their gel transitions. Finally, we relate the innate fluctuations of these processes to the gel transition, and demonstrate the necessity of using a stochastic approach to quantify polymerization kinetics