Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling - PubMed (original) (raw)

Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling

Roeland M H Merks et al. Dev Biol. 2006.

Abstract

Vasculogenesis, the de novo growth of the primary vascular network from initially dispersed endothelial cells, is the first step in the development of the circulatory system in vertebrates. In the first stages of vasculogenesis, endothelial cells elongate and form a network-like structure, called the primary capillary plexus, which subsequently remodels, with the size of the vacancies between ribbons of endothelial cells coarsening over time. To isolate such intrinsic morphogenetic ability of endothelial cells from its regulation by long-range guidance cues and additional cell types, we use an in vitro model of human umbilical vein endothelial cells (HUVEC) in Matrigel. This quasi-two-dimensional endothelial cell culture model would most closely correspond to vasculogenesis in flat areas of the embryo like the yolk sac. Several studies have used continuum mathematical models to explore in vitro vasculogenesis: such models describe cell ensembles but ignore the endothelial cells' shapes and active surface fluctuations. While these models initially reproduce vascular-like morphologies, they eventually stabilize into a disconnected pattern of vascular "islands." Also, they fail to reproduce temporally correct network coarsening. Using a cell-centered computational model, we show that the endothelial cells' elongated shape is key to correct spatiotemporal in silico replication of stable vascular network growth. We validate our simulation results against HUVEC cultures using time-resolved image analysis and find that our simulations quantitatively reproduce in vitro vasculogenesis and subsequent in vitro remodeling.

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Figures

Fig. 1

Typical time sequence of in vitro vasculogenesis at 4 h (h), 9 h, 12 h, 24 h and 48 h after incubation. Scale bar is 500 μm.

Fig. 2

Morphometry of experimental photographs and simulation results (see Supplementary methods). Red: detected vessels. Green: detected branch points.

Fig. 3

Connectivity constraint. Double arrows indicate “Collisions,” where the central site _x⃗_’s neighbors x′i→ have the same index as x⃗ while the next or previous location clockwise around x⃗ has an index different from that of x⃗ (i.e., site pairs for which δσx→,σx→i′(1−δσx→,σx→i+1′)=1orδσx→,σx→i′(1−δσx→,σx→i−1′)=1. (a) For precisely two collisions, we accept the proposed update. (b) For more than two collisions, we reject the proposed update, unless rule c applies. (c) For more than two collisions, with precisely two non-ECM cells involved, we accept the proposed update. (d) For more than two collisions with only one non-ECM cell involved, we reject the proposed update. (e) Incorrect rejection of a proposed update. The constraint detects a local connectivity violation for cell “b,” which actually would remain connected via the gray sites of “b”.

Fig. 4

Typical in silico vasculogenesis time sequence. Each lattice site represents an area of 2 μm × 2 μm. We randomly distributed 282 virtual endothelial cells over a 333 × 333 pixel area, which we positioned in a 500 × 500 lattice to minimize boundary effects. This cell density corresponds to that in the in vitro experiments. The total simulated area is 1000 μm × 1000 μm. Isolines (green) indicate ten chemoattractant levels relative to the maximum concentration in the simulation The grayscale indicates absolute concentration on a logarithmic scale.

Fig. 5

Number of lacunae (a, c) and number of branch points (b, d) over time for in vitro (a, b) and in silico vascular-like morphogenesis (c, d). Error bars and stippled lines give standard deviations (n = 28 and n = 10 for in vitro and in silico experiments respectively).

Fig. 6

Changes of patterns in in silico cell cultures with increasing endothelial cell length. (a) 20 μm, (b) 40 μm, (c) 60 μm, (d) 80 μm and (e) 100 μm. Isolines (green) indicate ten chemoattractant levels relative to the maximum concentration in the simulation. Greyscale indicates absolute concentration on a logarithmic scale.

Fig. 7

In silico vasculogenesis in simulations with increasing intercellular adhesion. (a) Jc,c = 20, (b) Jc,c = 15, (c) Jc,c = 10, (d) Jc,c = 5, (e) Jc,c = 1. Other settings as in standard model. Isolines (green) indicate ten chemoattractant levels relative to the maximum concentration in the simulation. Greyscale indicates absolute concentration on a logarithmic scale.

Fig. 8

In silico vasculogenesis in simulations with increasing cell length and area; number of cells is adjusted to keep the total area covered by cells constant. (a) L = 200 μm, A = 800 μm2, 141 cells; (b) L = 300 μm, A = 1200 μm2, 94 cells; (c) L = 400 μm, A = 1600 μm2, 70 cells; (d) L = 500 μm, A = 2000 μm2, 56 cells. Other settings as in standard model. Isolines (green) indicate ten chemoattractant levels relative to the maximum concentration in the simulation. Grayscale indicates absolute concentration on a logarithmic scale.

Fig. 9

Alternative mechanisms of vasculogenesis which assume steep chemoattractant gradients (α = ε = 1.25 × 10−3 s−1; _λ_L = 0; 415 cells; other parameters as in main text). (a) Without shape constraints, steep gradients stretch the large (A = 100 pixel) cells, promoting the formation of stable, polygonal patterns resembling vascular networks. Enforcing round cells (L = 10, _λ_L = 50) suppresses this mechanism. (b) Smaller cells (A = 50) do not stretch for these parameter values and do not form vascular networks. We have reported elsewhere (Merks et al., 2004) that cell adhesion (Jc,c = 1) can drive formation of vascular-like networks. Parameters are those in reference (Merks et al., 2004) (rescaled): 1000 cells, ε= 1.25 × 10−3 s−1, α = 2.5 × 10−3 s−1. Round cells (L = 0, _λ_L = 50) suppress this mechanism. (c) Contact inhibition of motility drives in silico formation of polygonal patterns by round cells (L = 10, _λ_L = 50). Here, we suppress formation of chemotactic filopodia and lamellipodia at endothelial cell contacts, e.g., through vascular endothelial cadherin-binding-dependent, conditional VEGF-A signaling (Dejana, 2004).

Fig. 10

Alternative vascular development mechanisms do not show correct pattern coarsening (i.e., lacunar growth): (a) steep morphogen gradients (compare Fig. 7a), (b) adhesion (compare Fig. 7b) and (c) contact inhibition of motility (compare Fig. 7c). Mechanisms (a) and (b) depend on cell elongation; constraining cells to be round suppresses these mechanisms. Stippled lines indicate standard deviations over ten simulations.

Fig. 11

Random walks of round (solid line) and elongated (stippled line) virtual cells in the absence of chemotactic cues. Elongated cells migrate fastest along their long axis, while rounded cells undergo an isotropic random walk. Scale bar, 10 μm (5 lattice sites).

Fig. 12

Reproduced with permission of the authors from Drake et al. (2000). (a) Control, showing untreated endothelial cells’ formation of a normal capillary plexus. (c) Injecting soluble VEGFR-1 into chick embryos blocks VEGF-signaling, causing clusters of rounded, vascular progenitor cells to form. (b, d) Stained nuclei of vascular progenitor cells. Scale bar, 15 μm.

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Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling - PubMed (original) (raw)