Correction to "structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction"

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]  Eduardo D. Sontag Global Stability of McKeithan's Kinetic Proofreading Model for T-Cell Receptor Signal Transduction , 1999 .

[2]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[3]  Georges Bastin Issues in modelling and control of mass balance systems , 1999 .

[4]  M. Feinberg The existence and uniqueness of steady states for a class of chemical reaction networks , 1995 .

[5]  S. Bhat,et al.  Nonnegativity, reducibility, and semistability of mass action kinetics , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  T. McKeithan,et al.  Kinetic proofreading in T-cell receptor signal transduction. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[7]  R. Jackson,et al.  General mass action kinetics , 1972 .

[8]  M. Feinberg Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems , 1987 .

[9]  Irving R. Epstein,et al.  An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos , 1998 .

[10]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[11]  J. A. Gubner,et al.  Differential Equations , 1991, Nature.

[12]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[13]  Jan F. M. Van Impe,et al.  Nonlinear and Adaptive Control in Biotechnology: A Tutorial , 1995, Eur. J. Control.

[14]  A. I. Vol'pert,et al.  Analysis in classes of discontinuous functions and equations of mathematical physics , 1985 .

[15]  D. Dochain,et al.  On-Line Estimation and Adaptive Control of Bioreactors , 2013 .

[16]  Eduardo D. Sontag,et al.  State-estimators for Chemical Reaction Networks of Feinberg-Horn-Jackson Zero Deficiency Type , 2002, Eur. J. Control.

[17]  Georges Bastin,et al.  On state accessibility in reaction systems , 1993 .

[18]  G. Gavalas Nonlinear Differential Equations of Chemically Reacting Systems , 1968 .