PT  - JOURNAL ARTICLE
AU  - Prugger, Martina
AU  - Einkemmer, Lukas
AU  - Lopez, Carlos F.
TI  - A dynamical low-rank approach to solve the chemical master equation for biological reaction networks
AID  - 10.1101/2022.05.04.490585
DP  - 2022 Jan 01
TA  - bioRxiv
PG  - 2022.05.04.490585
4099  - http://biorxiv.org/content/early/2022/05/04/2022.05.04.490585.short
4100  - http://biorxiv.org/content/early/2022/05/04/2022.05.04.490585.full
AB  - Solving the chemical master equation is an indispensable tool in understanding the behavior of biological and chemical systems. In particular, it is increasingly recognized that commonly used ODE models are not able to capture the stochastic nature of many cellular processes. Solving the chemical master equation directly, however, suffers from the curse of dimensionality. That is, both memory and computational effort scale exponentially in the number of species. In this paper we propose a dynamical low-rank approach that enables the simulation of large biological networks. The approach is guided by partitioning the network into biological relevant subsets and thus avoids the use of single species basis functions that are known to give inaccurate results for biological systems. We use the proposed method to gain insight into the nature of asynchronous vs. synchronous updating in Boolean models and successfully simulate a 41 species apoptosis model on a standard desktop workstation.Competing Interest StatementThe authors have declared no competing interest.