A mechano-biological model of the coupling between cellular con- tractility and VEGFR2/VEGF interactions.

Angiogenesis, the new blood vessel formation from a pre-existing one, is the main mechanism of neovascularization in both physiological and pathological conditions. Angiogenesis is a complex multistep process, which requires the interaction among growth factors, endohelial cell (EC) surface receptors and extracellular matrix (ECM) components. The molecular regulation of these mecha- nisms depends on the most important pro-angiogenic regulator, namely vascular endothelial growth factor (VEGF). VEGF binding its receptors VEGFR2, induces EC activation through the formation of a multi-molecular receptor complex, which includes αvβ3 integrins [1], i.e. transmembrane pro- teins related to cell contractility and focal adhesion. It is well-known that VEFG ligands are released by tumor cell, that need blood vessel for nutriments and oxigen supply to grow and proliferate. The identification of the mechanical laws that regulate these processes could open new perspectives to develop innovative anti-angiogenic strategies through the modulation of EC activation. The model [2], which simulate the relocation of VEGFR2 on the endothelial cell membrane dur- ing the mechanical adhesion of EC onto a ligand-enriched substrate, is mathematically rigorous and self-consistent, in that it stems from continuity equations (for mass, energy, and entropy), standard chemical kinetics, thermodynamic restrictions, and constitutive specifications. The model provides the governing equations in a strong form, stated for dimensionless unknown fields and converted in a weak form prior to the numerical approximation via the Finite Element Method. The partial differ- ential equations of the model have been implemented in a computer code, using parameters from the experimental analyses. The simulations allowed us to identify 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. At a later time, the interaction between low affinity integrins and VEGFR2/ligand complex has been modeled taking into account of large deformations with the ultimate goal to predict conditions for angiogenesis