Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical ...

We consider cascades of enzymatic Goldbeter-Koshland loops (Goldbeter and Koshland in Proc Natl Acad Sci 78(11):6840-6844, 1981) with any number n of layers, for which there exist two layers involving the same phosphatase. ...

Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution. Our approach is based on the recent article by Bihan, Santos, ...

The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice ...

Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) ...

We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. ...

We will concentrate on biochemical reaction networks, of interest in systems biology, in particular enzymatic networks, consisting of different types of multisite phosphorylation networks. One source of inspiration for our ...

We develop tools from computational algebraic geometry for the study of steady state features of autonomous polynomial dynamical systems via elimination of variables. In particular, we obtain nontrivial bounds for the ...