Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

Abstract

During angiogenesis, new blood vessels sprout and grow from existing ones. This processplays a crucial role in organ development and repair, in wound healing and in numerouspathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importanceof mechanical, chemical and cellular cues. Endothelial cells proliferate and move over anextracellular matrix by following external gradients of Vessel Endothelial Growth Factor,adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite elementdescription of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1ligands determines tip cell selection and vessel branching. Through their production rates,competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may befavored or impeded depending on the mechanical configuration of strain vectors in the ECMnear tip cells. Numerical simulations demonstrate that increasing Jagged production resultsin pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.