Publications about 'biochemical reaction networks' |
Articles in journal or book chapters |
This paper deals with the analysis of the dynamics of chemical reaction networks, developing a theoretical framework based only on graphical knowledge and applying regardless of the particular form of kinetics. It paper introduces a class of networks that are "structurally (mono) attractive", by which we mean that they are incapable of exhibiting multiple steady states, oscillation, or chaos by the virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function which we call a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. We study basic motifs, three-body binding, and transcriptional networks. We focus on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, ERK signaling, and the Ribosome Flow Model. |
The long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models, and stationary distributions in stochastic models. Unlike deterministic steady states, the stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically. Here, we develop a method for deriving stationary distributions from deterministic steady states by translating given BRNs to have a special network structure. Specifically, we merge and shift nodes and edges so as to make the deterministic steady states complex balanced, i.e., in- and out-flows of each node are equal. Then, using the complex balanced steady states, the stationary distributions of various autophosphorylation and toggle switch systems are derived. This greatly extends a class of BRNs for which stationary distributions can be analytically derived. |
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. |
This is a short expository article describing how the species-reaction graph (SR graph) can be used to analyze both multistability and monotonicity of biochemical networks. |
Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to biochemical reaction networks with inflows and outflows. Included is also a characterization of exponential stability of general homogeneous switched systems |
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems. |
Conference articles |
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders.
This document was translated from BibT_{E}X by bibtex2html