Explicit modelling of metabolic networks relies on well-known mathematical tools and specialized computer programs. However, identifying and estimating the values of the very numerous enzyme parameters inherent to the models remain a tedious and difficult task, and the rate equations of the reactions are usually not known in sufficient detail. A way to circumvent this problem is to use 'non-mechanistic' models, which may account for the behaviour of the systems with a limited number of parameters. Working on the first part of glycolysis reconstituted in vitro, we showed how to derive, from titration experiments, values of effective enzyme activity parameters that do not include explicitly any of the classical kinetic constants. With a maximum of only two parameters per enzyme, this approach produced very good estimates for the flux values, and enabled us to determine the optimization conditions of the system, i.e. to calculate the set of enzyme concentrations that maximizes the flux. This fast and easy method should be valuable in the context of integrative biology or for metabolic engineering, where the challenge is to deal with the dramatic increase in the number of parameters when the systems become complex.