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Enzyme-catalysed reactions involve two distinct timescales. There is a shorttimescale on which enzymes bind to substrate molecules to produce boundcomplexes, and a comparatively long timescale on which the complex istransformed into a product. The rate at which the substrate is converted intoproduct is characteristically non-linear and is traditionally derived byapplying singular perturbation theory to the system's governing equations.Central to this analysis is the assumption that complex formation iseffectively instantaneous on the timescale over which significant substratedegradation occurs. This prevents accurate modelling of enzyme kinetics by manyparticle-based simulations of reaction-diffusion systems as they rely onproximity-based reaction conditions that do not correctly model the fastreactions associated with the complex on the long timescale. In this paper wederive a new proximity-based reaction condition that correctly incorporates thereactions that occur on the short timescale for a specific enzymatic system. Wepresent proof of concept particle-based simulations and demonstrate thatnon-linear reaction rates typical of enzyme kinetics can be reproduced withoutneeding to explicitly simulate reactions on the short timescale.

Enzyme kinetics simulation at the scale of individual particles