Pharmacokinetic/pharmacodynamic model of a methionine starvation based anti-cancer drug

A new therapeutic approach against cancer is developed by the firm Erytech. This approach is based on starved cancer cells of an amino acid essential to their growth (the L-methionine). The depletion of plasma methionine level can be induced by an enzyme, the methionine-γ-lyase. The new therapeutic formulation is a suspension of erythrocytes encapsulating the activated enzyme. Our work reproduces a preclinical trial of a new anti-cancer drug with a mathematical model and numerical simulations in order to replace animal experiments and to have a deeper insight on the underlying processes. With a combination of a pharmacokinetic/pharmacodynamic model for the enzyme, substrate, and co-factor with a hybrid model for tumor, we develop a “global model” that can be calibrated to simulate different human cancer cell lines. The hybrid model includes a system of ordinary differential equations for the intracellular concentrations, partial differential equations for the concentrations of nutrients and drugs in the extracellular matrix, and individual based model for cancer cells. This model describes cell motion, division, differentiation, and death determined by the intracellular concentrations. The models are developed on the basis of experiments in mice carried out by Erytech. Parameters of the pharmacokinetics model were determined by fitting a part of experimental data on the concentration of methionine in blood. Remaining experimental protocols effectuated by Erytech were used to validate the model. The validated PK model allowed the investigation of pharmacodynamics of cell populations. Numerical simulations with the global model show cell synchronization and proliferation arrest due to treatment similar to the available experiments. Thus, computer modeling confirms a possible effect of treatment based on the decrease of methionine concentration. The main goal of the study is the development of an integrated pharmacokinetic/pharmacodynamic model for encapsulated methioninase and of a mathematical model of tumor growth/regression in order to determine the kinetics of L-methionine depletion after co-administration of Erymet product and Pyridoxine.