Species connectivities and reaction mechanisms from neutral response experiments

We develop a new method for obtaining connectivity data for nonlinear reaction networks, based on linear response experiments. In our approach the linear response is not the result of an approximation procedure but is due to the appropriate design of the response experiments, that is (1) they are carried out with the preservation of constant values for the total (labeled plus unlabeled) input and output fluxes and (2) the labeled compounds obey a neutrality condition (i.e., they have practically the same kinetic and transport properties as the unlabeled compounds). Under these circumstances the linear response equations hold even though the kinetics of the process is highly nonlinear. On the basis of this linear response law, we develop a method for evaluating reaction connectivities in biochemical networks from stationary response experiments. Given a system in a stationary regime, a pulse of a labeled species is introduced (with conservation of the total flux) and then the response of all the species of the network is recorded. The mechanistic information is contained in a connectivity matrix, K, which can be evaluated from the response data by means of differential as well as integral methods. The approach does not require any prior knowledge of the reaction mechanism. We carried out a numerical study of the method, based on a two-step procedure. Starting from a known reaction mechanism, we generated response data sets, to which we add noise; then, we use the noisy data sets for retrieving the connectivity matrix. The calculations were done with two programs written in Mathematica: the urea cycle and the upper part of glycolysis are used as sample biochemical networks. Given enough computer power, there are no limitations concerning the number of species involved in the response experiments; on current desktop systems processing responses of teens of species would take a few hours. The method is limited by the occurrence of experimental errors: if experimental errors in the evaluation of fluxes are larger than 10%, the method may fail to reproduce the correct values of some elements of the connectivity matrix.