title: The Force at the Tip--Modelling Tension and Proliferation in Sprouting Angiogenesis.
abstract: Sprouting angiogenesis, where new blood vessels grow from pre-existing ones, is a complex process where biochemical and mechanical signals regulate endothelial cell proliferation and movement. Therefore, a mathematical description of sprouting angiogenesis has to take into consideration biological signals as well as relevant physical processes, in particular the mechanical interplay between adjacent endothelial cells and the extracellular microenvironment. In this work, we introduce the first phase-field continuous model of sprouting angiogenesis capable of predicting sprout morphology as a function of the elastic properties of the tissues and the traction forces exerted by the cells. The model is very compact, only consisting of three coupled partial differential equations, and has the clear advantage of a reduced number of parameters. This model allows us to describe sprout growth as a function of the cell-cell adhesion forces and the traction force exerted by the sprout tip cell. In the absence of proliferation, we observe that the sprout either achieves a maximum length or, when the traction and adhesion are very large, it breaks. Endothelial cell proliferation alters significantly sprout morphology, and we explore how different types of endothelial cell proliferation regulation are able to determine the shape of the growing sprout. The largest region in parameter space with well formed long and straight sprouts is obtained always when the proliferation is triggered by endothelial cell strain and its rate grows with angiogenic factor concentration. We conclude that in this scenario the tip cell has the role of creating a tension in the cells that follow its lead. On those first stalk cells, this tension produces strain and/or empty spaces, inevitably triggering cell proliferation. The new cells occupy the space behind the tip, the tension decreases, and the process restarts. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of forces in sprouting, hence underlining the necessary collaboration between modelling and molecular biology techniques to improve the current state-of-the-art.
authors.affiliation: CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal.
authors.forename: Patrícia
authors.initials: P
authors.lastname: Santos-Oliveira
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal.
authors.forename: António
authors.initials: A
authors.lastname: Correia
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal.
authors.forename: Tiago
authors.initials: T
authors.lastname: Rodrigues
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal.
authors.forename: Teresa M
authors.initials: TM
authors.lastname: Ribeiro-Rodrigues
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal; Department of Complementary Sciences, Coimbra Health School (ESTeSC), Instituto Politécnico de Coimbra, Coimbra, Portugal.
authors.forename: Paulo
authors.initials: P
authors.lastname: Matafome
authors.affiliation: Centre for Genomics and Oncological Research: Pfizer/Universidad de Granada/Junta de Andalucía (GENYO), Granada, Spain.
authors.forename: Juan Carlos
authors.initials: JC
authors.lastname: Rodríguez-Manzaneque
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal.
authors.forename: Raquel
authors.initials: R
authors.lastname: Seiça
authors.affiliation: Institute for Biomedical Imaging and Life Sciences (IBILI), Faculty of Medicine, University of Coimbra, Coimbra, Portugal.
authors.forename: Henrique
authors.initials: H
authors.lastname: Girão
authors.affiliation: CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal.
authors.forename: Rui D M
authors.initials: RD
authors.lastname: Travasso
mesh_terms: D000818:Animals; D001808:Blood Vessels / Q000254:growth & development*; D049109:Cell Proliferation / Q000502:physiology*; D019295:Computational Biology; D006801:Humans; D051379:Mice; D008955:Models, Cardiovascular; D009389:Neovascularization, Pathologic / Q000503:physiopathology; D018919:Neovascularization, Physiologic / Q000502:physiology*; D042461:Vascular Endothelial Growth Factor A / Q000378:metabolism
chemical_list: D042461:Vascular Endothelial Growth Factor A