Monte Carlo Algorithm for Simulating Reversible Aggregation of Multisite Particles

TL;DR

This paper introduces an efficient, exact Monte Carlo algorithm utilizing a dynamic bond tree data structure to simulate reversible aggregation of multisite particles, significantly improving computational speed and memory efficiency.

Contribution

The paper presents a novel Monte Carlo algorithm with a dynamic bond tree for simulating reversible particle aggregation, reducing computational complexity and memory usage.

Findings

Constant time cluster association processing

Sublinear scaling of bond dissociation in acyclic clusters

Reduced memory requirements compared to standard methods

Abstract

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.