Derivation of stationary distributions of biochemical reaction networks via structure transformation

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. Hong, Kim and colleagues develop a method for analytically deriving the stationary distributions of stochastic biochemical reaction networks using network structure transformation. They provide this method in a user-friendly computational package, CASTANET, available open-source.

Automated summary

The researchers developed a method to analytically derive the stationary distributions of stochastic biochemical reaction networks by transforming the network structure through complex balancing. They revealed the unique stochastic dynamics of various BRNs and provided the computational package CASTANET to aid in understanding long-term stochasticity.