Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA deficiency-based approach to parametrizing positive equilibria of biochemical reaction systems
128
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (ii) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness (ACR), as we demonstrate for the EnvZ-OmpR pathway.
rate research
Read More
This work introduces a novel approach to study properties of positive equilibria of a chemical reaction network $mathscr{N}$ endowed with Hill-type kinetics $K$, called a Hill-type kinetic (HTK) system $left(mathscr{N},Kright)$, including their multiplicity and concentration robustness in a species. We associate a unique positive linear combination of power-law kinetic systems called poly-PL kinetic (PYK) system $left( {mathscr{N},{K_text{PY}}} right)$ to the given HTK system. The associated system has the key property that its equilibria sets coincide with those of the Hill-type system, i.e., ${E_ + }left( {mathscr{N},K} right) = {E_ + }left( {mathscr{N},{K_text{PY}}} right)$ and ${Z_ + }left( {mathscr{N},K} right) = {Z_ + }left( {mathscr{N},{K_text{PY}}} right)$. This allows us to identify two novel subsets of the Hill-type kinetics, called PL-equilibrated and PL-complex balanced kinetics, to which recent results on absolute concentration robustness (ACR) of species and complex balancing at positive equilibria of power-law (PL) kinetic systems can be applied. Our main results also include the Shinar-Feinberg ACR Theorem for PL-equilibrated HT-RDK systems (i.e., subset of complex factorizable HTK systems), which establishes a foundation for the analysis of ACR in HTK systems, and the extension of the results of Muller and Regensburger on generalized mass action systems to PL-complex balanced HT-RDK systems. In addition, we derive the theory of balanced concentration robustness (BCR) in an analogous manner to ACR for PL-equilibrated systems. Finally, we provide further extensions of our results to a more general class of kinetics, which includes quotients of poly-PL functions.
We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same result is conjectured but as yet unproved for general endotactic networks. The algorithms we present are the first capable of verifying endotacticity of chemical reaction networks for systems with greater than two constituent species. We implement the algorithms in the open-source online package CoNtRol and apply them to several well-studied biochemical examples, including the general $n$-site phosphorylation / dephosphorylation networks and a circadian clock mechanism.
In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.
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.
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
