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

By Eduardo Sontag. IEEE Transactions on Automatic Control, 2000

311 citations recorded by the source corpus.

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 (1977, 1979, 1987, 1995) and Horn and Jackson (1972), 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 (1995) for T-cell receptor signal transduction.

Subfields: Control and Systems Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/5cad30e10ef55a843a850d2b80d71f11baf8cd61

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Citations in the corpus

Modeling and analysis of mass-action kinetics (2009, background): “Specifically, [14] shows that, for every initial condition in the nonnegative orthant, the positive limit set is a subset of the set of nonnegative equilibria.”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “Since in the theory of chemical reaction networks, see for instance Sontag (2001), the components of F are usually polynomial or rational functions of x 1 , . . . , x d and θ 1 , . . . , θ p , the solution of (3) will be smooth enough in many examples and α ≥ 4 is satisﬁed in a large number of…”
Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property (2005, background): “Also, recent articles address the role of reaction networks in cellular biochemistry [1, 2, 5, 10], in genetics [22, 23, 33], in bioengineering [32], and immunology [34].”
Mathematical Analysis of Chemical Reaction Systems (2018, background): “Mathematical models that use mass-action kinetics (or kinetics derived from the law of mass-action, such as Michaelis-Menten kinetics or Hill kinetics) are ubiquitous in chemistry and biology [1, 16, 28, 30, 36, 40, 45, 47, 67, 69].”
Linear conjugacy of chemical reaction networks (2011, background): “Active theoretical topics within the mathematical literature include determining network conditions which guarantee locally stable dynamics [14,18,19,26,27,32], conditions which prohibit/permit multistability [7,8,11,24], and conditions which ensure the persistence of the chemical species [1, 2, 6, ”
Monotone Chemical Reaction Networks (2007, background): “For example, the seminal work on what today is known as the Feinberg–Horn–Jackson theory [11,19] – and [7,29] for recent results – restricts the reaction rates to mass action kinetics, but considers quite general topologies.”
Toric Differential Inclusions and a Proof of the Global Attractor Conjecture (2015, methodology): “ot; n 1 >0 from the boundary of Rn + . Therefore, for each initial condition x 0 2Rn + we can construct an invariant region Rn 1 n above such that x 0 2R n 1 n . Then we can use LaSalle invariance [19, 20] for the global strict Lyapunov function mentioned above to conclude that, within any linear”