Validity conditions for stochastic chemical kinetics in diffusion-limited systems

Area of Science:

• Computational chemistry
• Chemical kinetics
• Biophysics

Background:

• The chemical master equation (CME) and stochastic simulation algorithm (SSA) are foundational tools for modeling chemical reactions.
• These models rely on assumptions of molecular "diluteness" and "well-mixedness" within the reaction volume.
• Understanding the physical basis of these assumptions is crucial for accurate simulation results.

Purpose of the Study:

• To clarify the physical meaning and necessity of the "dilute" and "well-mixed" conditions for CME and SSA.
• To investigate the relationship between these two conditions in chemical systems.
• To analyze the implications of these validity conditions for reaction-diffusion extensions of CME and SSA.

Main Methods:

• Mathematical proof establishing the equivalence and interdependence of the "dilute" and "well-mixed" conditions.
• Analysis of spatially inhomogeneous reaction-diffusion models based on CME and SSA.
• Derivation of conditions for the physical validity of molecule transfer between subvolumes (voxels).

Main Results:

• The "dilute" and "well-mixed" conditions are proven to be equivalent and necessary for accurate bimolecular reaction modeling.
• For reaction-diffusion models, a lower bound on voxel edge length is required for physical validity.
• Decreasing voxel size maintains constant bimolecular reaction rates but increases diffusive transfer rates.

Conclusions:

• The "dilute" and "well-mixed" assumptions are critical for the validity of CME and SSA.
• Reaction-diffusion CME and SSA are inherently approximate and cannot be made exact by reducing voxel size.
• Despite approximations, these models remain valuable tools for practical simulations of complex chemical systems.