1. E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. In R. Tempo, S. Yurkovich, and P. Misra, editors, Emerging Applications of Control and Systems Theory, volume 473 of Lecture Notes in Control and Inform. Sci., pages 295-312. Springer-Verlag, Berlin, 2018. [PDF] Keyword(s): chemical master equations, stochastic systems, moments, reaction networks, reaction networks, incoherent feedforward loop, feedforward, IFFL, systems biology. Abstract:

   The study of stochastic biomolecular networks is a key part of systems biology, as such networks play a central role in engineered synthetic biology constructs as well as in naturally occurring cells. This expository paper reviews in a unified way a pair of recent approaches to the finite computation of statistics for chemical reaction networks.




2. E.D. Sontag. A technique for determining the signs of sensitivities of steady states in chemical reaction networks. IET Systems Biology, 8:251-267, 2014. Note: Code is here: https://github.com/sontaglab/CRNSeSi. [PDF] Keyword(s): sensitivity, retroactivity, biomolecular networks, systems biology, stoichiometry, reaction networks, systems biology. Abstract:

   This paper studies the direction of change of steady states to parameter perturbations in chemical reaction networks, and, in particular, to changes in conserved quantities. Theoretical considerations lead to the formulation of a computational procedure that provides a set of possible signs of such sensitivities. The procedure is purely algebraic and combinatorial, only using information on stoichiometry, and is independent of the values of kinetic constants. Two examples of important intracellular signal transduction models are worked out as an illustration. In these examples, the set of signs found is minimal, but there is no general guarantee that the set found will always be minimal in other examples. The paper also briefly discusses the relationship of the sign problem to the question of uniqueness of steady states in stoichiometry classes.




3. E.D. Sontag and D. Zeilberger. A symbolic computation approach to a problem involving multivariate Poisson distributions. Advances in Applied Mathematics, 44:359-377, 2010. Note: There are a few typos in the published version. Please see this file for corrections: https://drive.google.com/file/d/0BzWFHczJF2INUlEtVkFJOUJiUFU/view. [PDF] Keyword(s): probability theory, stochastic systems, systems biology, reaction networks, chemical master equation. Abstract:

   Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing WZ Theory and associated algorithms. A symbolic computation package has been developed and is made freely available. A discussion of motivating biomolecular problems is also provided.

1. E.D. Sontag. Quantifying the effect of interconnections on the steady states of biomolecular networks. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 5419-5424, 2014.



2. D. Del Vecchio and E.D. Sontag. Dynamics and control of synthetic bio-molecular networks. In Proceedings American Control Conf., New York, July 2007, pages 1577-1588, 2007. Keyword(s): systems biology, reaction networks, synthetic biology. Abstract:

   This tutorial paper presents an introduction to systems and synthetic molecular biology. It provides an introduction to basic biological concepts, and describes some of the techniques as well as challenges in the analysis and design of biomolecular networks.

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