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The Linear Noise Approximation for Spatially Dependent Biochemical Networks.

Per Lötstedt1

  • 1Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-75105, Uppsala, Sweden. perl@it.uu.se.

Bulletin of Mathematical Biology
|April 13, 2018
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Summary

A new algorithm significantly reduces computational work for the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) used in biochemical modeling. This method enhances efficiency for analyzing complex reaction networks.

Keywords:
Fast algorithmLinear noise approximationSpatially dependent

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Area of Science:

  • Computational biology
  • Biochemical reaction modeling
  • Stochastic processes

Background:

  • Reaction-diffusion master equation (RDME) models biochemical networks.
  • Linear noise approximation (LNA) is crucial for analyzing RDME, but computationally intensive.
  • Spatial discretization is often required for RDME, increasing complexity.

Purpose of the Study:

  • Develop and test a novel algorithm for computing the LNA of the RDME.
  • Improve computational efficiency for LNA calculations.
  • Analyze the accuracy of the proposed LNA algorithm.

Main Methods:

  • Derived LNA for a general spatial discretization of the RDME.
  • Developed a new algorithm to compute LNA approximations.
  • Estimated accuracy analytically and validated with numerical experiments.

Main Results:

  • The new LNA algorithm reduces computational work from O(N^3) to O(N M^2), where N is spatial nodes and M is species.
  • This represents a significant computational saving when N > M.
  • Analytical and numerical results confirm the algorithm's accuracy.

Conclusions:

  • The developed algorithm provides a computationally efficient method for LNA of RDME.
  • This advancement aids in the analysis of complex spatial biochemical reaction networks.
  • The findings offer a practical tool for computational biologists and modelers.