Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM). We develop a mathematical model in order to simulate the relocation of VEGFR2 on the cell membrane during the mechanical adhesion of cells onto a ligand-enriched substrate. Co-designing the in vitro experiments with the simulations allows identifying three phases of the receptor dynamics, which are controlled respectively by the high chemical reaction rate, by the mechanical deformation rate, and by the diffusion of free receptors on the membrane. The identification of the laws that regulate receptor polarization opens new perspectives toward developing innovative anti-angiogenic strategies through the modulation of EC activation.

This contribution describes a computational homogenization approach to model the multi-physics processes\ud in Li-ion batteries in a multi-scale view. The adopted approach originates from the fundamental\ud balance laws (of mass, momentum, charge) at both scales and the multi scale analysis roots itself on\ud an energy-based weak formulation of the balance laws, which allows to extend the Hill–Mandel energy\ud averaging theorem to the problem at hand. Electroneutrality assumption has been taken into account.\ud Maxwell’s equations are considered in a quasi-static sense in a rigorous setting. Time dependent scale\ud transitions are formulated, as required by the length/time scales involved in Li-ion batteries processes,\ud while scale separation in time is argued. Constitutive assumptions, computational procedures and\ud simulations will be collected in a companion paper

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