Angiogenesis is the process by which new blood vessels form from pre-existing ones during, for example, wound healing or organismal development. Endothelial cells (ECs) that form blood vessels respond to tissue-derived growth factors, such as Vascular Endothelial Growth Factor (VEGF), by forming capillary sprouts.  The sprouts are headed by tip cells which migrate, via chemotaxis, towards the source of the growth factors, followed by proliferative stalk cells which maintain contact with the parent vessel. The process of tip cell selection is regulated by interactions between the VEGF signalling pathway and Delta-Notch juxtacrine signalling with neighbouring cells.  Here we develop dynamic, ordinary differential equation (ODE) models to investigate how these interactions modulate VEGF-induced extension of EC filopodia and how these filopodia in turn, help a population of ECs to sprout.

We begin by neglecting filopodia elongation and focus on the signalling processes alone.  We identify regions of parameter space in which there exist stable, spatially homogeneous solutions (all cells are identical) and others in which alternate cells express high (low) levels of Notch activity and VEGF receptors.  We use linear stability analysis to demonstrate how the strengths of feedbacks in the model influence the patterns that emerge.  We then show that the inclusion of filopodia growth into the model, via a variable representing filopodia length for each cell, can generate spatial instabilities (corresponding to tip cell selection) not present in the absence of filopodial elongation. Thus filopodia can be a crucial ingredient in tip cell selection. On the other hand, our analysis shows that VEGF gradients (as opposed to the absolute VEGF concentration) may not be required for tip cell pattering.

The results of such modelling may have implications in anti-angiogenic therapies used in wound healing or cancer treatment, for example.