PT  - JOURNAL ARTICLE
AU  - Hyukpyo Hong
AU  - Jinsu Kim
AU  - M Ali Al-Radhawi
AU  - Eduardo D. Sontag
AU  - Jae Kyoung Kim
TI  - Derivation of stationary distributions of biochemical reaction networks via structure transformation
AID  - 10.1101/2021.03.23.436681
DP  - 2021 Jan 01
TA  - bioRxiv
PG  - 2021.03.23.436681
4099  - http://biorxiv.org/content/early/2021/03/24/2021.03.23.436681.short
4100  - http://biorxiv.org/content/early/2021/03/24/2021.03.23.436681.full
AB  - Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives symbolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.Competing Interest StatementThe authors have declared no competing interest.