Monte Carlo Algorithm for Simulating Reversible Aggregation of Multisite Particles

We present an efficient and exact Monte Carlo algorithm to simulate reversible aggregation of particles with dedicated binding sites. This method introduces a novel data structure of dynamic bond tree to record clusters and sequences of bond formations. The algorithm achieves a constant time cost for processing cluster association and a cost between $\mathcal{O}(\log M)$ and $\mathcal{O}(M)$ for processing bond dissociation in clusters with $M$ bonds. The algorithm is statistically exact and can reproduce results obtained by the standard method. We applied the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtained an average scaling of $\mathcal{O}(M^{0.45})$ for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods. The algorithm also demands substantially less memory than the conventional method.