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. 2011 Oct 4:2:62.
doi: 10.3389/fphys.2011.00062. eCollection 2011.

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Yasmin L Hashambhoy  1 , John C Chappell, Shayn M Peirce, Victoria L Bautch, Feilim Mac Gabhann
Affiliations

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Yasmin L Hashambhoy et al. Front Physiol. .

Abstract

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF-Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF-Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.

Keywords: VEGF; angiogenesis; capillary sprouting; computational model; mathematical model; sFlt-1; vascular development.

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Figures

Figure 1
Figure 1
Schematics. (A,B) Schematics of the 2-D computational model space. In (A), sFlt-1 is secreted from an opposing wall of parenchymal cells. In (B), sFlt-1 is secreted from a layer of parenchymal cells below the interstitial space. Diffusion in the z direction is assumed to be instantaneous, and both cases (A,B) are essentially 2-D models. (C) Schematic of the molecular species and the cell surface signaling and non-signaling receptor complexes. (D) Schematic showing non-signaling (top) and signaling (bottom) receptor complexes.
Figure 2
Figure 2
Volumetric Gradients of VEGF and sFlt-1. (A–D) Gradients of VEGF, sFlt-1, and their complexes along a line from the sprout leading edge to the parenchymal cell wall. (E–H) Gradients of VEGF, sFlt-1, and their complexes along a transverse line in front of the sprout leading edge. (B,F) VEGF gradients in the absence (dotted line) and presence (solid line) of sFlt-1 (C,G), sFlt-1 (red) and VEGF–sFlt-1 complex (purple) gradients, (D,H), ECM-bound gradients: ECM–VEGF in the absence (dotted blue line) and presence (solid blue line) of sFlt-1 and ECM–VEGF–sFlt-1 (purple line). All results are from 10 h after the start of simulation.
Figure 3
Figure 3
sFlt-1 can alter both absolute and relative levels of active Flk-1 on the sprout. (A–C) local VEGF and sFlt-1 gradients near the sprout for the scenario with sFlt-1 secretion from both the base vessel and the sprout. Note that the y-axis is stretched compared to the x-axis to emphasize the area local to the sprout. See the text and Figure 2 for more on the gradients in the x- and y-directions. (D) Active distribution across the endothelial surface. Flk-1 is considered active if both subunits in a dimerized Flk-1 complex are bound to VEGF. The results of three different scenarios are displayed: no sFlt-1 secretion from the sprout; sFlt-1 secretion only from the endothelial cells making up the base vessel; sFlt-1 secretion from both vessel and sprout. sFlt-1 secretion decreases the absolute amount and relative gradient of Flk-1 activation on the surface of sprouts. (E) As free sFlt-1 increases (due to increased sFlt-1 secretion) so does relative Flk-1 activation along the sprout. (F) Average receptor complex concentrations along the sprout for three cases: no sFlt-1 secretion (red), base and sprout sFlt-1 secretion (black), and base and sprout sFlt-1 secretion without any sFlt-1 binding to surface receptors mFlt-1 or Flk-1 (green). Active VEGF surface complexes are shown on the left, and inactive surface complexes are on the right. The removal of sFlt-1 heterodimerization barely affects active VEGF surface receptor complex levels.
Figure 4
Figure 4
Decreased tip cell sFlt-1 secretion results in increased Flk-1 activation on the sprout. (A,B) Active Flk-1 levels on 10 μm long (A) or 30 μm long (B) sprouts in which tip cell sFlt-1 secretion is the same or lower than that of base vessel cells. The difference in Flk-1 activation on the leading edge of the sprout (due to decreased sFlt-1 secretion) compared to Flk-1 activation on the base vessel is more pronounced in short sprouts than in longer sprouts.
Figure 5
Figure 5
Active Flk-1 levels show that sprout directionality is partially governed by proximity to neighboring sprouts. All panels are for the scenario with both base and sprout sFlt-1 secretion. (A,B) Active Flk-1 levels on sprouts that are closer to (A) or farther away from (B) each other. (C) Free VEGF and (D), free sFlt-1 in the vicinity of the pair of sprouts that are close together. (E) Free VEGF and (F), free sFlt-1 in the vicinity of the pair of sprouts that are farther apart. Note that for panels (C–F), the y-axis is stretched compared to the x-axis, and the geometry of the sprouts is outlined on the x–y plane.
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