A Dynamical Low-Rank Approach to the Chemical Master Equation

Original Article

Abstract

Stochastic reaction kinetics have increasingly been used to study cellular systems, with applications ranging from viral replication to gene regulatory networks and to signaling pathways. The underlying evolution equation, known as the chemical master equation (CME), can rarely be solved with traditional methods due to the huge number of degrees of freedom. We present a new approach to directly solve the CME by a dynamical low-rank approximation based on the Dirac–Frenkel–McLachlan variational principle. The new approach has the capability to substantially reduce the number of degrees of freedom, and to turn the CME into a computationally tractable problem. We illustrate the accuracy and efficiency of our methods in application to two examples of biological interest.

Keywords

Chemical master equation Stochastic reaction kinetics Dirac–Frenkel–McLachlan variational principle Dynamical low-rank approximation Genetic toggle switch Lambda phage 

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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Institut für Angewandte und Numerische MathematikUniversität Karlsruhe (TH)KarlsruheGermany
  2. 2.Hamilton InstituteNUIMMaynoothIreland

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