Linear conjugacy of chemical reaction networks

A Linear Programming Approach to Weak Reversibility and Linear Conjugacy of Chemical Reaction Networks

Piecewise linear models of chemical reaction networks

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in n...

Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation

Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populatio...

Piecewise linear and Boolean models of chemical reaction networks.

Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [F...

Inference of chemical reaction networks using mixed integer linear programming

The manual determination of chemical reaction networks (CRN) and reaction rate equations is cumbersome and becomes workload prohibitive for large systems. In this paper, a framework is developed that allows an almost entirely automated recovery of sets of reactions comprising a CRN using experimental data. A global CRN structure is used describing all feasible chemical reactions between chemica...