Team dracula

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Section: New Results

Mathematical models of erythropoiesis

Mathematical study of feedback control roles and relevance in stress erythropoiesis

Participants : Fabien Crauste, Olivier Gandrillon, Vitaly Volpert.

In collaboration with Ivan Demin (PhD student, now modeler at Novartis Pharma in Basel, Switzerland).

We proposed in [10] a new multi-scale model of erythropoiesis. This model describes erythroid progenitor dynamics and intracellular regulatory network that determines erythroid cell fate (self-renewal, differentiation, death by apoptosis). All erythroid progenitors are divided into several sub-populations according to their maturity. Two intracellular proteins, Erk and Fas, are supposed to be determinant for the regulation of self-renewal, differentiation and apoptosis. Two growth factors, erythropoietin and glucocorticoids, are also taken into account in the modelling, as well as a membrane protein, Fas-ligand, playing an active role in erythroid progenitor death. The model consists of a nonlinear system of ordinary differential equations, with several feedback controls. We studied existence of biologically relevant steady states and their stability. We carried out computer simulations of anaemia and compared the obtained results with available experimental data on induced anaemia in mice. The main objective of this work was to evaluate the roles of the feedback controls in order to provide more insights into the regulation of erythropoiesis. Feedback by Epo on apoptosis was shown to be determinant in the early stages of the response to anaemia, whereas regulation through intracellular regulatory network, based on Erk and Fas, appeared to operate on a long-term scale.

Keywords: anaemia, intracellular regulatory network, growth factor, bistability.

Multi-scale model of erythropoiesis

Participants : Fabien Crauste, Olivier Gandrillon, Vitaly Volpert.

In collaboration with Ivan Demin (Novartis Pharma in Basel, Switzerland).

We investigated in [11] a multi-scale mathematical model of erythropoiesis. Erythroid progenitors were supposed to be able to self-renew. Three cellular processes were supposed to control erythropoiesis: self-renewal, differentiation and apoptosis. We described these processes and regulatory networks that govern them. Two proteins (ERK and Fas) were considered as the basic proteins participating in this regulation. All erythroid progenitors were divided into several sub-populations depending on their maturity level. Feedback regulations by erythropoietin, glucocorticoids and Fas ligand (FasL) were introduced in the model. The model consisted of a system of ordinary differential equations describing intracellular protein concentration evolution and cell population dynamics. We studied steady states and their stability. We carried out computer simulations of an anaemia situation and analysed the results.

Keywords: erythropoiesis, multi-scale model, self-renewal, differentiation, bistability.

Spacial distribution of cell populations in the processes of erythropoiesis

Participant : Vitaly Volpert.

In collaboration with I. Demin (Novartis Pharma in Basel, Switzerland), A. Ducrot (University of Bordeaux).

We studied in [16] spatial cell distribution in the bone marrow taking into account cell self-renewal, differentiation and apoptosis as well as cell motion resulting from cell proliferation. The model consisted of reaction-diffusion equations in a porous medium. The existence of stationary solutions corresponding to normal erythropoiesis was proved. In the leukemic case, this stationary solution becomes unstable. Malignant cells propagate as a travelling wave filling the marrow. We studied this phenomenon numerically in the 2D case. An analytical approximation for the wave speed was compared with the numerical solution of the full problem.

Keywords: cell population, reaction-diffusion equations, porous medium, traveling waves.

Hybrid model of erythropoiesis and leukemia treatment with cytosine arabinoside

Participants : Samuel Bernard, Fabien Crauste, Polina Kurbatova, Vitaly Volpert.

In collaboration with N. Bessonov (St. Petersburg, Russia), I. Demin (Novartis Pharma in Basel, Switzerland), Ch. Dumontet (Hospital E. Herriot, University of Lyon 1) and S. Fischer (University of Lyon 1).

A hybrid model of cell population dynamics, where cells are discrete elements whose dynamics depend on continuous intracellular and extracellular processes, was developed in [21] to simulate the evolution of immature red blood cells in the bone marrow. Cell differentiation, self-renewal or apoptosis were determined by an intracellular network, based on two proteins Erk and Fas and described by ordinary differential equations, and by local extracellular regulation performed by Fas-ligand, a protein produced by mature cells whose concentration evolution was represented by a partial differential equation. The model was used to study normal and leukemic red blood cell production (erythropoiesis), and treatment of leukemia. Normal cells were supposed to have a circadian rhythm, that influences their cell cycle durations, whereas leukemic cells, appart from being characterized by excessive proliferation and insufficient differentiation and apoptosis, were supposed to escape circadian rhythms. We considered a treatment based on periodic administration of Ara-C, an anti-cancer agent targeting cells in DNA synthesis. A pharmacodynamic/pharmacokinetic model of Ara-C was then proposed, and used to simulate the treatment. Influences of the period of the treatment and the day delivery time on the outcome of the treatment were investigated and stressed the relevance of considering chronotherapeutic treatments to cure leukemia.

Keywords: hybrid model, leukemia treatment, chronotherapy, regulatory networks, cell cycle.


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