Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth - PubMed (original) (raw)

Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth

Roeland M H Merks et al. PLoS Comput Biol. 2008.

Erratum in

Abstract

Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of fully formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting or splitting of existing blood vessels (angiogenesis). Although they are closely related biologically, no current model explains both phenomena with a single biophysical mechanism. Most computational models describe sprouting at the level of the blood vessel, ignoring how cell behavior drives branch splitting during sprouting. We present a cell-based, Glazier-Graner-Hogeweg model (also called Cellular Potts Model) simulation of the initial patterning before the vascular cords form lumens, based on plausible behaviors of endothelial cells. The endothelial cells secrete a chemoattractant, which attracts other endothelial cells. As in the classic Keller-Segel model, chemotaxis by itself causes cells to aggregate into isolated clusters. However, including experimentally observed VE-cadherin-mediated contact inhibition of chemotaxis in the simulation causes randomly distributed cells to organize into networks and cell aggregates to sprout, reproducing aspects of both de novo and sprouting blood-vessel growth. We discuss two branching instabilities responsible for our results. Cells at the surfaces of cell clusters attempting to migrate to the centers of the clusters produce a buckling instability. In a model variant that eliminates the surface-normal force, a dissipative mechanism drives sprouting, with the secreted chemical acting both as a chemoattractant and as an inhibitor of pseudopod extension. Both mechanisms would also apply if force transmission through the extracellular matrix rather than chemical signaling mediated cell-cell interactions. The branching instabilities responsible for our results, which result from contact inhibition of chemotaxis, are both generic developmental mechanisms and interesting examples of unusual patterning instabilities.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1

Figure 1. Anti-VE-cadherin antibody treatment inhibits de novo blood-vessel growth in mouse allantois cultures.

Endothelial cells fluorescently labeled in red with endothelium-specific CD34-Cy3 antibody. DIC/fluorescent image overlays. (A–C) Control. (D–F) Anti-VE-cadherin-treated cell cultures.

Figure 2

Figure 2. Endothelial cell aggregation; simulation initiated with 1000 scattered cells.

(A) After 10 Monte Carlo steps (MCS) (∼5 min). (B) After 1000 MCS (∼8 h). (C) After 10,000 MCS (∼80 h). (D) Contact-inhibited chemotaxis drives formation of vascular networks. Scale bar: 50 lattice sites (≈100 µm). Contour levels (green) indicate ten chemoattractant levels relative to the maximum concentration in the simulation. Grey shading indicates absolute concentration on a saturating scale.

Figure 3

Figure 3. Sprout formation in the absence of contact inhibition.

(A–C) Cell-autonomous cell elongation; (A) Λ = 22 µm; (B) Λ = 24 µm; (C) Λ = 32 µm; (D–F) Adhesion-driven sprouting. (D) J(c,c) = 1; (E) J(c,c) = 5; (F) J(c,c) = 10; (G–I) Passive cell elongation at short diffusion lengths; (G) D = 1·10−14 m2 s−1; (H) D = 2·10−14 m2 s−1; (I) D = 3·10−14 m2 s−1.

Figure 4

Figure 4. Sprouting instability in a simulation initiated with a cluster of endothelial cells.

(A) After 10 MCS (5 min). (B) After 1,000 MCS (∼8 h). (C) After 10,000 MCS (∼80 h). (D) No sprouting in a simulation without contact inhibition of chemotaxis (Χ(c,c)/Χ(c,M) = 1) at 10,000 MCS (∼80 h). Scale bar: 50 lattice sites (≈100 µm).

Figure 5

Figure 5. Compactness (C = A cluster/A hull) of 128-cell clusters after 10,000 MCS (∼80 h) as a function of the relative chemotactic response at cell-cell vs. cell-ECM interfaces.

Error bars show standard deviations over ten simulations.

Figure 6

Figure 6. Cell trajectories of simulated endothelial cells in 128-cell clusters in a contact-inhibited, sprouting cluster (A,B) and in a non-contact-inhibited, non-sprouting cluster (C,D).

(A,C) Cell trajectories during initial sprouting, indicating the cells' centers of mass at 100 MCS (∼50 min) intervals from 100 to 5,000 MCS (∼1–40 h). (B,D) Cell trajectories after initial sprouting, indicating the cells' centers of mass at 1,000 MCS (∼8 h) intervals from 4,000 to 20,000 MCS (∼30–170 h). Closed circles indicate initial cell positions; open circles indicate final cell positions. Colors identify individual cells; brightness increases from dark (initial positions) to bright (final positions). Outlines of clusters shown at 1000 MCS (∼8 h) intervals (A,C) or 4000 MCS (∼33 h) intervals (B,D). (E) Average displacement of cells from original positions over time in 10 simulations with 128 cells each, in contact-inhibited (solid curves) and non-contact-inhibited simulations (dashed curves). Grey curves indicate standard deviations. (F) Cell velocity formula image with Δ_t_ = 300 MCS (∼2.5 h) for contact-inhibited (solid curves) and non-contact-inhibited (dashed curves) simulations.

Figure 7

Figure 7. Compactness (C = A cluster/A hull) of 128-cell clusters on 200×200-pixel lattices (∼400 µm×400 µm) after 5,000 MCS (∼40 h) for standard chemotaxis, as a function of the adhesion between endothelial cells, J(c,c).

For J(c,c)<40 (i.e., J(c,c)<2 J(c,M) the cells adhere without chemotaxis. Insets: Representative configurations after 5000 MCS (∼40 h).

Figure 8

Figure 8. Compactness (C = A cluster/A hull) of 128-cell clusters on 200×200-pixel lattices (∼400 µm×400 µm ) after 5000 MCS (∼40 h) for standard chemotaxis as a function of absolute chemotactic strength, Χ(c,M).

Insets: Representative configurations after 5000 MCS (∼40 h).

Figure 9

Figure 9. Compactness (C = A cluster/A hull) of 128-cell clusters on 200×200-lattices (∼400 µm×400 µm) after 5000 MCS (∼40 h) for standard chemotaxis as a function of the saturation of the chemotactic response, s.

Insets: representative configurations after 5000 MCS (∼40 h).

Figure 10

Figure 10. Compactness (C = A cluster/A hull) of 128-cell clusters (solid curve) on 200×200-pixel lattices (∼400 µm×400 µm) and 1,024-cell clusters (dashed-dotted curve) on 400×400-pixel lattices (∼800 µm×800 µm) after 5000 MCS (∼40 h) for Savill-Hogeweg chemotaxis as a function of the chemoattractant diffusion constant D.

Larger diffusion constants have longer diffusion lengths, formula image. Dashed curve shows the compactness of VE-cadherin-inhibited 128-cell clusters. Insets: Representative configurations after 5,000 MCS (∼40 h) of the 128-cell clusters (left panels) and 1,024-cell clusters (right panels; not to scale).

Figure 11

Figure 11. Compactness (C = A cluster/A hull) of 128-cell clusters on 400×400-pixel lattices (∼400 µm×400 µm) after 5,000 MCS (∼40 h) as a function of the cell motility T, for standard Savill–Hogeweg extension–retraction chemotaxis (solid curve), and for extension-only chemotaxis (dashed curve).

Black curves show the mean over 100 simulations for each T (with a _T_-increment of 10). Dotted grey curves indicate one standard deviation. Insets: Representative configurations after 5,000 MCS (∼40 h).

Figure 12

Figure 12. Evolution of the compactness (C = A cluster/A hull) of 256-cell clusters on 500×500-pixel lattices (∼1,000 µm×1,000 µm) vs. time for standard Savill-Hogeweg extension-retraction chemotaxis (solid and dashed curves, for T = 50 and T = 200 respectively), and for extension-only chemotaxis (dash-dotted curve, T = 200), with only extending pseudopods responding to the chemoattractant.

Black curves show the mean of 100 simulations. Dotted grey curves mark one standard deviation. Insets: Representative configurations after 1000 (∼8 h) and 5000 MCS (∼40 h). Videos available online.

Figure 13

Figure 13. Cumulative energy differences for standard Savill–Hogeweg extension_–_retraction chemotaxis (solid and dashed curves, for T = 50 and T = 200, respectively), and for extension-only chemotaxis (dash-dotted curve, T = 200) as a function of time.

Black curves show the mean of 100 simulations. Dotted grey curves mark one standard deviation.

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