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A new method for choosing the computational cell in stochastic reaction-diffusion systems.

Hye-Won Kang¹, Likun Zheng, Hans G Othmer

¹School of Mathematics, University of Minnesota, Twin Cities, MN 55455, USA. hkang@math.umn.edu

Journal of Mathematical Biology

|November 11, 2011

Summary

Choosing compartment size for stochastic reaction-diffusion simulations is key. New criteria ensure accurate modeling by relating noise to species numbers and network sensitivity, optimizing computational grids for reliable results.

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Area of Science:

Computational Biology
Biophysics
Mathematical Biology

Background:

Determining optimal computational compartment size for stochastic reaction-diffusion systems remains a challenge.
Existing criteria for cell size selection are varied and not universally applicable.

Purpose of the Study:

To develop robust criteria for selecting computational compartment size in reaction-diffusion simulations.
To ensure accurate representation of molecular noise and species concentrations.

Main Methods:

Applied a generalized noise measure based on the largest eigenvalue of the covariance matrix to discretized reaction-diffusion systems.
Derived a new criterion based on network sensitivity for predicting grid size.
Analyzed convergence to spatially-uniform solutions.

Main Results:

Showed noise measure converges to the reciprocal of the smallest mean species number for first-order networks.
Developed a criterion for maximum compartment volume as cell volume approaches zero.
Derived a network-wide sensitivity criterion applicable to all reaction orders and reduction methods.

Conclusions:

The proposed criteria provide a robust method for optimizing compartment size in stochastic reaction-diffusion simulations.
These criteria ensure accurate modeling of molecular fluctuations and concentration convergence.
The findings are applicable to diverse reaction networks, including those in developmental biology.