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Publications of Eduardo D. Sontag jointly with J. K. Kim
Articles in journal or book chapters
  1. H. Hong, J. Kim, M.A. Al-Radhawi, E.D. Sontag, and J. K. Kim. Derivation of stationary distributions of biochemical reaction networks via structure transformation. 2020. Note: Submitted.Keyword(s): stationary distribution, chemical reaction networks, network translation, biochemical reaction networks, chemical master equation, stochastic, probabilistic.
    Abstract:
    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.


  2. J. K. Kim and E.D. Sontag. Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation. PLoS Computational Biology, 13:13(6): e1005571, 2017. [PDF] Keyword(s): systems biology, biochemical networks, stochastic systems, chemical master equation, chemical reaction networks, moments, molecular networks, complex-balanced networks.
    Abstract:
    Biochemical reaction networks in cells frequently consist of reactions with disparate timescales. Stochastic simulations of such multiscale BRNs are prohibitively slow due to the high computational cost incurred in the simulations of fast reactions. One way to resolve this problem is to replace fast species by their stationary conditional expectation values conditioned on slow species. While various approximations schemes for this quasi-steady state approximation have been developed, they often lead to considerable errors. This paper considers two classes of multiscale BRNs which can be reduced by through an exact QSS rather than approximations. Specifically, we assume that fast species constitute either a feedforward network or a complex balanced network. Exact reductions for various examples are derived, and the computational advantages of this approach are illustrated through simulations.



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Last modified: Thu Sep 24 12:35:48 2020
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