# Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

## TL;DR

This paper introduces a novel adaptive and heterogeneous scaling algorithm called partial scaling to accelerate kinetic Monte Carlo simulations of chemical reaction networks, reducing computational cost while maintaining accuracy.

## Contribution

The paper presents a new partial scaling method that adaptively adjusts reaction rates without prior classification of species, implemented in BioNetGen, enhancing simulation efficiency.

## Key findings

- Significantly accelerates biological system models
- Maintains accuracy with reduced reaction events
- Applicable to diverse biological models

## Abstract

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a sub-volume $\lambda \Omega$ ($0<\lambda<1$) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor $1/\lambda$ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an \emph{a priori} classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, $N_c$, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.