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.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

The role of spatial organization of cells in erythropoiesis

Erythropoiesis, the process of red blood cell production, occurs mainly in the bone marrow. The functional unit of mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells (CFU-E/Pro-EBs) and their differentiating progeny, the erythroblasts. Central macrophages display on their surface or secrete various growth or inhibitory factors that influence the fate of the surrounding erythroid cells. CFU-E/Pro-EBs have three possible fates: (a) expansion of their numbers without differentiation, (b) differentiation into reticulocytes that are released into the blood, (c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex molecular network, that is highly dependent upon environmental conditions in the erythroblastic island. In order to assess the functional role of space coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A model was developed in which cells are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations and extracellular concentrations by partial differential equations. We used the model to investigate the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, whereas early-stage erythroblasts produce the most Fas-ligand in mice. Although the global behaviors of the erythroblastic islands in both species were similar, differences were found, including a relatively slower response time to acute anemia in humans. Also, our modeling approach was very consistent with in vitro culture data, where the central macrophage in reconstituted erythroblastic islands has a strong impact on the dynamics of red blood cell production. The specific spatial organization of erythroblastic islands is key to the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling cell decision provides a realistic functional unit of mammalian erythropoiesis that integrates multiple microenvironmental influences within the erythroblastic island with those of circulating regulators of erythropoiesis, such as EPO and glucocorticosteroids, that are produced at remote sites.

Hybrid model of erythropoiesis

A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.