Combining multi-target regression deep neural networks and kinetic modeling to predict relative fluxes in reaction systems

The strong nonlinearity of large and highly connected reaction systems, such as metabolic networks, hampers the determination of variations in reaction fluxes from variations in species abundances, when comparing different steady states of a given system. We hypothesize that patterns in species abundance variations exist that mainly depend on the kernel of the stoichiometric matrix and allow for predictions of flux variations. To investigate this hypothesis, we applied a multi-target regression Deep Neural Network (DNN) to data generated via numerical simulations of an Ordinary Differential Equation (ODE) model of yeast metabolism, upon Monte Carlo sampling of the kinetic parameters. For each parameter configuration, we compared two steady states corresponding to different environmental conditions. We show that DNNs can predict relative fluxes impressively well even when a random subspace of input features is supplied, supporting the existence of recurrent variation patterns in abundances of chemical species, which can be recognized automatically.