Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

Stochastic modeling techniques have emerged as a powerful tool to study the time evolution of processes in many research fields including (bio)chemical engineering and biology. One of the most applied techniques is kinetic Monte Carlo (kMC) modeling according to the stochastic simulation algorithm (SSA) as pioneered by Gillespie, in which MC channels and time steps are discretely sampled from probability distributions. In the last decades, the SSA algorithm, as originally developed for systems with elemental species (e.g., A, B, C, etc.), has been further adapted (i) to also tackle systems with distributed species, therefore, populations and (ii) to enable faster algorithm execution. In the present contribution, we highlight the most important developments, taking bulk/solution polymerization as the reference distributed chemical process. We address SSA principles based on conventional array data structures, common acceleration methods (e.g., tau leaping and the scaling method), and the strength of tree- and matrix-based data structures for detailed storage of molecular information per distribution type and even individual population member. In addition, we report advancement regarding array programming and MC sampling methods complemented by the introduction of the use of higher-order trees and root-finding sampling tools. The contribution gives thus a detailed overview of the available main kMC algorithm steps to study kinetics, irrespective of the specific field of application due to their generic nature.