We present “on the fly” algorithmic criteria for the accuracy and stability (non-stiffness) of
reduced models constructed with the quasi-steady state and partial equilibrium …

We consider a prototype reaction–diffusion system which models a network of two
consecutive reactions in which chemical components A and B form an intermediate C which …

Reactions with enzymes are critical in biochemistry, where the enzymes act as a catalyst in
the process. One of the most widely used mechanisms for modeling enzyme-catalyzed …

The Michaelis–Menten (MM) rate law has been a fundamental tool in describing enzyme-
catalyzed reactions for over a century. When substrates and enzymes are homogeneously …

Reactions with enzymes are critical in biochemistry, where the enzymes act as catalysis in
the process. One of the most used mechanisms for modeling enzyme-catalyzed reactions is …

The method of slow invariant manifolds (SIMs), applied previously to model the reduced
kinetics of spatially homogeneous reactive systems, is extended to systems with diffusion …

Abstract The Michaelis–Menten mechanism is probably the best known model for an
enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS reductions are …

A class of multi-scale reaction-diffusion systems is introduced which possess exact, low-
dimensional, invariant manifolds. These manifolds are given in closed form by elementary …

Deterministic models of bacterial genetic circuits commonly assume a well-mixed ensemble
of species. This assumption results in ordinary differential equations (ODEs) describing the …

We investigate the convergence of an implicit Voronoi finite volume method for reaction–
diffusion problems including nonlinear diffusion in two space dimensions. The model allows …