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Publications of Eduardo D. Sontag jointly with J. Kim
Articles in journal or book chapters
and J. K. Kim.
Derivation of stationary distributions of biochemical reaction networks via structure transformation.
Note: Submitted.Keyword(s): stationary distribution,
chemical reaction networks,
biochemical reaction networks,
chemical master equation,
The 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, the stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically. Here, we develop a method for deriving stationary distributions from deterministic steady states by translating given BRNs to have a special network structure. Specifically, we merge and shift nodes and edges so as to make the deterministic steady states complex balanced, i.e., in- and out-flows of each node are equal. Then, using the complex balanced steady states, the stationary distributions of various autophosphorylation and toggle switch systems are derived. This greatly extends a class of BRNs for which stationary distributions can be analytically derived.
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