Modified Smoluchowski Rate Equations for Aggregation and Fragmentation in Finite Systems

Protein self-assembly into supramolecular structures is important for cell biology. Theoretical methods employed to investigate protein aggregation and analogous processes include molecular dynamics simulations, stochastic models, and deterministic rate equations based on the mass-action law. In molecular dynamics simulations, the computation cost limits the system size, simulation length, and number of simulation repeats. Therefore, it is of practical interest to develop new methods for the kinetic analysis of simulations. In this work we consider the Smoluchowski rate equations modified to account for reversible aggregation in finite systems. We present several examples and argue that the modified Smoluchowski equations combined with Monte Carlo simulations of the corresponding master equation provide an effective tool for developing kinetic models of peptide aggregation in molecular dynamics simulations.