A dynamical low-rank approach to the chemical master equation

Bulletin of Mathematical Biology
Tobias Jahnke, Wilhelm Huisinga

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.

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Citations

Jul 4, 2012·BMC Systems Biology·Steffen Waldherr, Bernard Haasdonk
Mar 15, 2014·PLoS Computational Biology·Vladimir KazeevChristoph Schwab
Mar 14, 2012·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Ranadip Pal, Sonal Bhattacharya
Jan 5, 2014·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Mehmet Umut Caglar, Ranadip Pal
Dec 17, 2014·Computational and Structural Biotechnology Journal·Tamás Székely, Kevin Burrage
Aug 16, 2016·Bulletin of Mathematical Biology·Christopher LesterChristian A Yates
Sep 24, 2015·Scientific Reports·David Gelbwaser-KlimovskyGershon Kurizki
Sep 18, 2020·PLoS Computational Biology·Daniel J LaydonBecca Asquith
Jul 24, 2021·The Journal of Chemical Physics·Ion Gabriel IonHerbert De Gersem

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