The complexity of metabolic networks and their regulation renders an intuitive analysis of these biological systems a difficult task. Mathematical modeling approaches help to deal with this complexity, making them an important tool for metabolic engineering. Different methods were developed, ranging from basic stoichiometric models up to fine-grained kinetic models. Kinetic modeling is the most detailed and complex mathematical description of a metabolic network and constitutes an important branch in the growing fields of systems biology. In this update, we provide a guide for the construction, simulation, and analysis of kinetic metabolic models in general, before we describe some recently published models of plant metabolic pathways, giving an overview of the opportunities and challenges of this mathematical method. Furthermore, we evaluate the current strategies and take an outlook to possible and necessary future developments of kinetic modeling.
THE MATHEMATICS BEHIND METABOLIC NETWORKSA metabolic network can be translated in mathematical terms by relatively easy means: The concentration of a metabolite is described by a variable S i . As a result of mass balances (no matter can appear or disappear), the change of this variable over time (dS i / dt) is given by the sum of the rates of the enzymes synthesizing the metabolite minus the sum of the rates of the enzymes utilizing the metabolite. The rate of each enzymatic step can be described by enzymekinetic rate laws, such as the Michaelis-Menten equation, as a function depending on metabolite concentrations and parameters such as the maximal velocity of a reaction, or binding constants. This process yields a system of ordinary differential equations (ODEs) in which dS i /dt is on one side and the metabolitedependent rate laws are on the other side of the equations (see Eqs. 4 and 5 below). With this system of differential equation, the metabolic network can be simulated, and by solving the system of ODEs the steady state can be calculated, in which all reaction rates and metabolite concentrations are constant.The process described above is simplified by considering the cell as a homogenous volume. While for many scenarios this is a valid simplification, for other instances, ODE-based kinetic models will not be the method of choice. For example, if spatial gradients are of importance to address a certain question, partial differential equations would be used instead, which increases the complexity of a model dramatically. Furthermore, if metabolites with very low concentrations are considered (e.g. hormones), stochastic effects are coming into play, so that the model would include stochastic components rather than being deterministic. More details on different methods for metabolic modeling are given in a recent comprehensive overview of computational models of metabolism (Steuer and Junker, 2009).Deterministic, ODE-based enzyme-kinetic models have the longest history in the area of metabolic pathway modeling. The local complexity of kinetic models leads to t...