Inferring biochemical reaction pathways: the case of the gemcitabine pharmacokinetics

The representation of a biochemical system as a network is the precursor of any mathematical model of the processes driving the dynamics of that system. Pharmacokinetics uses mathematical models to describe the interactions between drug, and drug metabolites and targets and through the simulation of these models predicts drug levels and/or dynamic behaviors of drug entities in the body. Therefore, the development of computational techniques for inferring the interaction network of the drug entities and its kinetic parameters from observational data is raising great interest in the scientific community of pharmacologists. In fact, the network inference is a set of mathematical procedures deducing the structure of a model from the experimental data associated to the nodes of the network of interactions. In this paper, we deal with the inference of a pharmacokinetic network from the concentrations of the drug and its metabolites observed at discrete time points.

The method of network inference presented in this paper is inspired by the theory of time-lagged correlation inference with regard to the deduction of the interaction network, and on a maximum likelihood approach with regard to the estimation of the kinetic parameters of the network. Both network inference and parameter estimation have been designed specifically to identify systems of biotransformations, at the biochemical level, from noisy time-resolved experimental data. We use our inference method to deduce the metabolic pathway of the gemcitabine. The inputs to our inference algorithm are the experimental time series of the concentration of gemcitabine and its metabolites. The output is the set of reactions of the metabolic network of the gemcitabine.

Time-lagged correlation based inference pairs up to a probabilistic model of parameter inference from metabolites time series allows the identification of the microscopic pharmacokinetics and pharmacodynamics of a drug with a minimal a priori knowledge. In fact, the inference model presented in this paper is completely unsupervised. It takes as input the time series of the concetrations of the parent drug and its metabolites. The method, applied to the case study of the gemcitabine pharmacokinetics, shows good accuracy and sensitivity.