The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems.

Area of Science:

• Computational Chemistry
• Biophysical Modeling
• Stochastic Simulation

Background:

• The Inhomogeneous Stochastic Simulation Algorithm (ISSA) simulates chemical reactions in spatially inhomogeneous systems by dividing them into subvolumes.
• ISSA can be computationally inefficient when molecular diffusion occurs more frequently than chemical reactions.

Purpose of the Study:

• To introduce the Multinomial Simulation Algorithm (MSA) as a more efficient alternative to ISSA for systems with high diffusion rates.
• To develop an algorithm that accurately handles small reactant populations, outperforming existing hybrid methods.

Main Methods:

• The MSA adapts the ISSA framework by incorporating reactions within subvolumes.
• It employs conditioned binomial random variables to model the net diffusion of molecules between adjacent subvolumes.
• This approach specifically addresses scenarios where diffusion events significantly outnumber reaction events.

Main Results:

• The MSA demonstrates superior performance compared to ISSA in simulations where diffusive transfers are more frequent than chemical reactions.
• Simulation results indicate enhanced accuracy in handling small reactant populations, a common challenge in hybrid algorithms.
• The algorithm's benefits are illustrated through simulation outcomes, validating its effectiveness.

Conclusions:

• The Multinomial Simulation Algorithm (MSA) provides a significant computational advantage for simulating chemical kinetics in systems dominated by diffusion.
• MSA offers a more accurate approach for modeling systems with sparse molecular populations.
• This new algorithm enhances the efficiency and accuracy of stochastic simulations in computational chemistry and biophysics.