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Reaction rates for mesoscopic reaction-diffusion kinetics.

Stefan Hellander1, Andreas Hellander2, Linda Petzold3

  • 1Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA.

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|March 14, 2015
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Summary
This summary is machine-generated.

This study derives mesoscopic reaction rates for the reaction-diffusion master equation (RDME) by matching it to Brownian dynamics (BD) simulations. It identifies optimal mesh sizes for accurate mesoscopic modeling in systems biology.

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Area of Science:

  • Computational Systems Biology
  • Biophysics
  • Chemical Kinetics

Background:

  • The reaction-diffusion master equation (RDME) is widely used for modeling stochastic reaction-diffusion processes in biological systems.
  • RDME assumptions may fail, leading to unphysical results, necessitating more comprehensive models like Brownian dynamics (BD).

Purpose of the Study:

  • To derive scale-dependent mesoscopic reaction rates for the RDME by approximating a microscopic BD model.
  • To establish fundamental limits on mesh resolution for accurate RDME simulations.
  • To determine the optimal mesh size for accurate mesoscopic dynamics.

Main Methods:

  • Matching RDME solution statistics to statistics from a microscopic Smoluchowski Brownian dynamics model.
  • Utilizing a Robin boundary condition at the molecular reaction radius.
  • Theoretical analysis and numerical examples to validate results.

Main Results:

  • Derived scale-dependent reaction rates for the RDME.
  • Established fundamental limits on mesh resolution for accurate mesoscopic modeling.
  • Demonstrated that mesoscopic dynamics approach microscopic dynamics as mesh resolution approaches the lower limit.
  • Showed decreased accuracy for mesh sizes below this fundamental limit.

Conclusions:

  • The derived mesoscopic reaction rates enable more accurate RDME simulations by bridging the gap with microscopic BD models.
  • Identifying the fundamental lower limit of mesh resolution is crucial for optimizing accuracy in mesoscopic modeling.
  • This work provides a framework for selecting appropriate mesh sizes for reliable RDME applications in systems biology.