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A dynamical low-rank approach to the chemical master equation. (English) Zbl 1169.92021
Summary: 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.

MSC:
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C37 Cell biology
60H30 Applications of stochastic analysis (to PDEs, etc.)
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