On the analysis of the inverse problem of metabolic pathways using artificial neural networks

Here we develop the use of artificial neural networks for solving the inverse metabolic problem, in other words, given a set of steady-state metabolite levels and fluxes in a pathway of known structure to obtain the parameters of the system, in this case the enzymatic limiting rate and Michaelis constants. This requires two main procedures: first the development of a computer program with which one can model metabolism in the forward direction (i.e. given the internal and parameters to determine the steady-state fluxes and metabolite concentrations), and second, given arrays of associated parameters and variables thereby obtained, to exploit artificial neural networks to form a model capable of obtaining the parameters from the variables. We studied 2-step pathways exhibiting first-order kinetics, 2-step pathways exhibiting reversible Michaelis-Menten kinetics and then 3-step pathways (again exhibiting reversible Michaelis-Menten kinetics), modelled using the program Gepasi. Whilst it was fairly easy for the networks to learn most of the parameters in the 2-step pathway, it was found helpful for the Michaelis-Menten case to vary the concentration of the starting pathway substrate for each set of internal parameters, and to train separate networks for each parameter. Some parameters were much easier to learn than others, reverse K(m) and V(max) values normally being the most difficult. For the 3-step pathway learning sometimes required as much as 3 days, and occasionally convergence was not obtained. Overall, neural networks of the present type, with fully interconnected feedforward architectures and trained according to the backpropagation algorithm, scaled poorly as the problem size was increased.