# Particle-based simulation of non-elementary bimolecular kinetics

Source: [Particle-based simulation of non-elementary bimolecular kinetics](<https://www.sota2.com/research/paper/68fa4b541e209131ce945266>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T04:40:56.407Z

Authors: Taylor Kearney, Mark B. Flegg

Published: 2025-07-31T08:03:32.000Z

## Abstract

Particle-based simulations are an essential tool for the study of biochemical systems for scales between molecular/Brownian dynamics and the reaction-diffusion master equation. These simulations utilise proximity-based reaction conditions and are typically limited to elementary (mass-action) kinetics. We present a novel framework for directly simulating non-elementary bimolecular kinetics in a particle-based framework. By mimicking the behaviour of a third implicit reactant, we adapt non-elementary reaction conditions, previously restricted to trimolecular chemical interactions, to biomolecular reactions for the first time. We implement our approach in an event-driven simulation, which we validate by reproducing Michaelis-Menten kinetics. We then demonstrate its utility by simulating the classical Goldbeter model of circadian oscillations completely at the level of individual molecules. This model features multiple non-elementary reactions and requires the incorporation of several existing simulation techniques. Our method accurately reproduces the target non-elementary kinetics, without simulating the implied underlying fast elementary reactions, thereby significantly reducing the computational cost. This work expands the class of reaction networks accessible to particle-based simulations and provides a practical alternative to explicitly simulating all elementary steps in systems where quasi-steady-state approximations are applicable.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2508.10909>)

[PDF](<https://arxiv.org/pdf/2508.10909.pdf>)