CMMB Seminar: Modelling and analysis of filopodia extension regulated by VEGF-Delta-Notch signalling in angiogenic tip cell selection

Sunny Modhara

Abstract: 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 growth factors such as Vascular Endothelial Growth Factor (VEGF), that are produced in surrounding tissues, 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 juxtacrine (direct cell-to-cell) Delta-Notch signalling.  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 Delta-Notch 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 can generate spatial instabilities (corresponding to tip cell selection) not present in the absence of filopodial elongation.

Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia.  Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth, considered previously, is an excellent approximation to the PDE model.  However, for smaller diffusivity, the existing bifurcation structure becomes modified and the model predicts that larger VEGF gradients may be required for cells to pattern and thus sprout. In such cases, the PDE model provides valuable insight into the pattern forming potential of the system which the ODE model cannot account for.