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Publications about 'moments'
Articles in journal or book chapters
  1. 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.


  2. E.D. Sontag and A. Singh. Exact moment dynamics for feedforward nonlinear chemical reaction networks. IEEE Life Sciences Letters, 1:26-29, 2015. [PDF] Keyword(s): systems biology, biochemical networks, stochastic systems, Chemical Master Equation, chemical reaction networks.
    Abstract:
    Chemical systems are inherently stochastic, as reactions depend on random (thermal) motion. This motivates the study of stochastic models, and specifically the Chemical Master Equation (CME), a discrete-space continuous-time Markov process that describes stochastic chemical kinetics. Exact studies using the CME are difficult, and several moment closure tools related to "mass fluctuation kinetics" and "fluctuation-dissipation" formulas can be used to obtain approximations of moments. This paper, in contrast, introduces a class of nonlinear chemical reaction networks for which exact computation is possible, by means of finite-dimensional linear differential equations. This class allows second and higher order reactions, but only under special assumptions on structure and/or conservation laws.


Internal reports
  1. E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. Technical report, arXiv:1612.02393, 2016. [PDF] Keyword(s): systems biology, biochemical networks, stochastic systems, Chemical Master Equation, chemical reaction networks, moments, molecular networks, complex-balanced networks.
    Abstract:
    We review in a unified way results for two types of stochastic chemical reaction systems for which moments can be effectively computed: feedforward networks and complex-balanced networks.



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Last modified: Thu Nov 23 10:40:56 2017
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