1. M. Chaves, E.D. Sontag, and R. J. Dinerstein. Steady-states of receptor-ligand dynamics: A theoretical framework. J. Theoret. Biol., 227(3):413-428, 2004. [PDF] Keyword(s): zero-deficiency networks, systems biology, biochemical networks, receptor-ligand models, dynamical systems. Abstract:

   This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, and, as an application, a minimal parametrization is provided for models for two- or multi-state receptor interaction with ligand. In addition, an "affinity quotient" is introduced, which allows an elegant classification of ligands into agonists, neutral agonists, and inverse agonists.




2. M. Chaves and E.D. Sontag. State-Estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type. European J. Control, 8:343-359, 2002. [PDF] Keyword(s): observability, zero-deficiency networks, systems biology, biochemical networks, observers, nonlinear stability, dynamical systems. Abstract:

   This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.




3. E.D. Sontag. Correction to: ``Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction'' [IEEE Trans. Automat. Control 46 (2001), no. 7, 1028--1047; MR1842137 (2002e:92006)]. IEEE Trans. Automat. Control, 47(4):705, 2002. [PDF] Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems. Abstract:

   errata for Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction




4. E.D. Sontag. Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction. IEEE Trans. Automat. Control, 46(7):1028-1047, 2001. [PDF] Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems, kinetic proofreading, T cells, immunology. Abstract:

   This paper deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The results given here extend, but are also heavily based upon, certain previous work by Feinberg, Horn, and Jackson, of which a self-contained and streamlined exposition is included. The theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by McKeithan for T-cell receptor signal transduction.

1. M. Chaves and E.D. Sontag. An alternative observer for zero deficiency chemical networks. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 575-578, 2001. Keyword(s): observability, observers, zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems.



2. M. Chaves and E.D. Sontag. Observers for certain chemical reaction networks. In Proc. 2001 European Control Conf., Sep. 2001, pages 3715-3720, 2001. Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems, observability, observers.

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