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Modélisation mathématique de l'impact de la dynamique des microtubules sur la migration cellulaire

Abstract : The cell motility (or migration), capacity of the cell to generate its own movement, plays an important role on numerous biological process like embryogenesis, but also in the development of pathologies like cancer. The aim of this work is to model and better understand the impact and the role of microtubules, which are dynamics elements of the cytoskeleton, on migration. To our knowledge, the action of microtubules on migration has never been studied by mathematical models. The work for this phd thesis is splitted into two parts. The first one is dedicated to the development of a model that takes into account microtubules action and second part dedicated to the development and implementation of the numerical schemes needed to solve the equations of the model. The approach that has been used couple a biomechanical model and a biochemical one proposed by Edelstein and al in 2011. The biochemical part of our model describe both the action of a Rho-GTPase protein on migration and the action of the dynamic instability of microtubules on these protein. The system proposed thus couple Stokes equations describing biomechanical aspects, reaction-diffusion equations on a moving domain for the proteins and ODE for the MT dynamics. We use a Level-Set method to describe the displacement of this moving domain. In order to use a large diversity of meshes and mostly locally refined grids, we choose to use Discrete Duality Finite Volume (DDFV). If the DDFV discretization of Stokes equations has already been studied, the resolution of transport equations induced by the Level-Set method has led to the development of a DDFV approach for WENO schemes. A description of the scheme and numerical simulations allowing to highlight its convergence and robustness are proposed. A splitting method for the diffusion on a moving domain has been improved, allowing to handle large deformations. The implementation of the schemes has been done with Fortran 90, only using previous codes allowing the computation of geometrical information for a DDFV mesh. The calibration of the parameters has been done with biological data of the literature and those obtained by the group of S. Honoré in the CRO2 lab in the hospital La Timone. The first numerical results concerning the impact of the vincristine, a drug that destabilize microtubules, on migration are presented and illustrate the using of the model.
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Submitted on : Thursday, January 4, 2018 - 3:40:32 PM
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Rémi Tesson. Modélisation mathématique de l'impact de la dynamique des microtubules sur la migration cellulaire. Mathématiques [math]. Aix-Marseille Université (AMU), 2017. Français. ⟨tel-01675563⟩



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