A VEGF reaction-diffusion mechanism that selects variable densities of endothelial tip cells

Abstract

The patterned differentiation of endothelial cells into tip and stalk cells represents an important step in the process of angiogenic sprouting. Vascular biologists hypothesize that changes in the density and overall structure of the vasculature can be traced in part to changes in the number of tip cells selected in the endothelium prior to sprout formation. However, the dominant hypotheses for tip cell selection invoke lateral inhibition via Notch; this juxtacrine mechanism predicts that a fixed fraction of endothelial cells become tip cells through a pattern-forming instability. Here, we present and analyze a hypothetical mechanism for tip cell selection that is based on endothelial competition for diffusible vascular endothelial growth factor (VEGF); this mechanism predicts that variable densities of tip cells emerge depending on the local (paracrine) production rate of VEGF. First, we hypothesize a network of VEGF signaling and trafficking based on previous experimental findings that could allow internalization of VEGF to occur with positive feedback. We formalize the hypothesis into a set of nonlinear ordinary differential equations and perform linear stability analysis to elucidate a general criterion for tip cell pattern formation under the mechanism. We use numerical integration to explore the nonlinear dynamics and final steady-states of tip cell patterns under this mechanism; the observed density of tip cells can be tuned from 10% to 84%. We conclude with proposals of future experiments and computational studies to explore how competitive consumption of diffusible VEGF may play a role in determining vascular structure.\n\nStatement of SignificanceThe patterned differentiation of endothelial cells into tip and stalk cells represents an important step in the process of blood vessel growth. Vascular biologists hypothesize that changes in the density and overall structure of the vasculature can be traced in part to changes in the number of tip cells selected during angiogenesis. However, the dominant hypotheses for tip cell selection predict that a locally fixed fraction of endothelial cells become tip cells following stimulation by vascular endothelial growth factor (VEGF). Here, we present and analyze a hypothetical mechanism for tip cell selection based on endothelial competition for diffusible VEGF; this mechanism predicts that variable densities of tip cells emerge depending on the local production rate of VEGF.