The use of mathematical methods for the analysis of chemical reaction systems has a very
long history, and involves many types of models: deterministic versus stochastic, continuous …

Posttranslational modification of proteins is important for signal transduction, and hence
significant effort has gone toward understanding how posttranslational modification …

Mathematical modelling has become an established tool for studying the dynamics of
biological systems. Current applications range from building models that reproduce …

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

Which reaction networks, when taken with mass-action kinetics, have the capacity for
multiple steady states? There is no complete answer to this question, but over the last 40 …

Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with
especially notable applications in optimization. We study the question of certifying …

This work concerns the question of how two important dynamical properties, oscillations and
bistability, emerge in an important biological signaling network. Specifically, we consider a …

We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE)
and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction …

Bistability has important implications in signaling pathways, since it indicates a potential cell
decision between alternative outcomes. We present two approaches developed in the …

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 …