Computational modeling of angiogenesis: towards a multi-scale understanding of cell-cell and cell-matrix interactions

Combined with in vitro and in vivo experiments, mathematical and computational modeling are key to unraveling how mechanical and chemical signaling by endothelial cells coordinates their organization into capillary-like tubes. While in vitro and in vivo experiments can unveil the effects of, for example, environmental changes or gene knockouts, computational models provide a way to formalize and understand the mechanisms underlying these observations. This chapter reviews recent computational approaches to model angiogenesis, and discusses the insights they provide into the mechanisms of angiogenesis. We introduce a new cell-based computational model of an in vitro assay of angiogenic sprouting from endothelial monolayers in fibrin matrices. Endothelial cells are modeled by the Cellular Potts Model, combined with continuum descriptions to model haptotaxis and proteolysis of the extracellular matrix. The computational model demonstrates how a variety of cellular structural properties and behaviors determine the dynamics of tube formation. We aim to extend this model to a multi-scale model in the sense that cells, extracellular matrix and cell-regulation are described at different levels of detail and feedback on each other. Finally we discuss how computational modeling, combined with in vitro and in vivo modeling steers experiments, and how it generates new experimental hypotheses and insights on the mechanics of angiogenesis.