A dynamical low-rank approach to the chemical master equation.
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.
Jahnke
Tobias
T
Institut für Angewandte und Numerische Mathematik, Universität Karlsruhe (TH), Englerstr. 2, 76128 Karlsruhe, Germany. jahnke@math.uni-karlsruhe.de
Huisinga
Wilhelm
W
D010582:Bacteriophage lambda / Q000235:genetics / Q000378:metabolism; D004735:Energy Transfer; D005786:Gene Expression Regulation / Q000235:genetics; D007700:Kinetics; D008432:Mathematical Computing; D008956:Models, Chemical; D015398:Signal Transduction / Q000235:genetics*; D013269:Stochastic Processes; D049490:Systems Biology / Q000379:methods*; D013816:Thermodynamics