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Relating Reaction Mechanisms
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Particle-based simulation of non-elementary bimolecular kinetics.

Taylor Kearney1, Mark B Flegg1

  • 1Monash University, Victoria, Australia.

Mathematical Biosciences
|November 26, 2025
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Summary

Particle-based simulations now directly handle complex biochemical reactions. This novel framework efficiently simulates non-elementary kinetics, reducing computational cost for systems biology research.

Keywords:
Circadian oscillationsMichaelis-Menten kineticsNon-elementary bimolecular kineticsParticle-based simulationProximity-based reaction conditionsQuasi-steadystate approximation

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Area of Science:

  • Biochemistry
  • Computational Biology
  • Chemical Kinetics

Background:

  • Particle-based simulations are crucial for biochemical systems, bridging scales between molecular dynamics and reaction-diffusion models.
  • Current methods are limited to elementary (mass-action) kinetics, restricting the simulation of complex biological processes.

Purpose of the Study:

  • To develop a novel framework for directly simulating non-elementary bimolecular kinetics in particle-based simulations.
  • To adapt non-elementary reaction conditions, typically for trimolecular interactions, to biomolecular reactions.

Main Methods:

  • Implemented a novel approach using a third implicit reactant to mimic non-elementary kinetics.
  • Utilized an event-driven simulation framework.
  • Validated the method by reproducing Michaelis-Menten kinetics and simulating the Goldbeter circadian rhythm model.

Main Results:

  • Successfully simulated non-elementary bimolecular kinetics without explicitly modeling underlying fast elementary reactions.
  • Accurately reproduced Michaelis-Menten kinetics and the Goldbeter model dynamics.
  • Significantly reduced computational cost compared to simulating all elementary steps.

Conclusions:

  • The developed framework expands the scope of reaction networks accessible to particle-based simulations.
  • Offers a practical and computationally efficient alternative for simulating systems with non-elementary kinetics where quasi-steady-state approximations apply.