Conveners
Positive equilibria of reaction network models
- Maya Mincheva ()
Description
Multistationarity, or the existence of several positive equilibria, is a common property of biochemical reaction networks' models. The existence of multistationarity can be guaranteed using different approaches. In one of the talks, we explain how degree theory can be used to obtain sufficient conditions for multistationarity. Moreover, using this approach multistationarity regions in parameter space can be computed. In another talk, multistationarity of reaction networks will be characterized in terms of a rational parametrization of the equilibrium solutions. The other two talks concern a generalization of mass action kinetics systems to systems with power law kinetics, where the kinetic orders are real numbers. In one of the talks, an extension of the Deficiency Zero Theorem, which is applicable to systems with power law kinetics, will be presented. In the other talk, the existence of positive equilibria for a special class of systems with power law kinetics will be discussed. Applications to signalling networks will be presented in all of the talks.
In this paper, we study power law kinetics on chemical reaction networks with Independent decompositions, i.e. the network is the union of subnetworks whose reaction sets form a partition of the network's reaction set and the network's stoichiometric subspace is the direct sum of the stoichiometric subspaces of the subnetworks. Our main result is a Deficiency Zero Theorem when the subnetworks...
In this talk, we present our results on power law kinetic systems whose kinetic order vectors (which we call “interactions”) are reactant-determined (i.e. reactions with the same reactant complex have identical kinetic order vectors) and are linear independent per linkage class. In particular, we focus on its subset called PL-TLK systems. Our main result states that any weakly reversible...
Classical results give structural conditions under which the steady state set of a (bio)chemical reaction system has a monomial parametrization. This property has been studied extensively in the context of characterizing a mechanism's capacity for mono- and multi-stationarity. In this talk, we generalize the existing structural framework and derive sufficient conditions for guaranteeing that...
Multistationarity is defined as the existence of several positive equilibria of an ordinary differential equations model. Multistationarity is a required property of biological switches- reaction networks that govern important cellular functions, such as cell differentiation and cell death. This is the case, because biological switches are modelled by differential equations systems whose...
