Table 3 Rules and related experimental references for endothelial cell sprouting.

Tip Cell Activation

[VEGF] > 0.5 ng/ml, and vacancy in environment surrounding the tip cell

VEGF gradient, global ∇VEGF

Variable.

-

Default gradient: [VEGF] (ng/ml) in each voxel is uniform, except within a restricted volume. Within this volume, it is randomly generated at the start of each model, and dependent on location.The probability distribution for [VEGF] at location X(i,j,k) is defined by:

$\varphi ({[\text{VEGF}]}_{\text{j}})=\{\frac{1}{\sqrt{2\pi \sigma }}\exp \left[-{\left(\frac{{[\text{VEGF}]}_{\text{j}}-{[\text{VEGF}]}_{\text{mean},\text{j}}}{\sqrt{2}\sigma }\right)}^2\right]$

   • where g_w/W2 < i < g_w/W1   ${[\text{VEGF}]}_{\text{meanj}}=\left|\text{j}\cdot \frac{\text{C}1}{{\text{g}}_{\text{h}}}-\text{C}2\right|$

   • where j > g_h/H1

   • where g_l·L2 < k < g_l·L1

   • σ = C3·[VEGF]_mean,j

Unrestricted Tip Cell Migration Rate with VEGF, M _tip

T1·[VEGF (in ng/ml)] + migNoVEGF μm/hr

Cell Migration Rate without VEGF, migNoVEGF

Default: 6.2 μm/hr

Physiological Range: 5–11 μm/hr¹

Tip Cell Migration Rate as a Function of Extracellular Matrix Composition and VEGF, M _tip

T2·[VEGF (in ng/ml)] + T3·K (fraction collagen content) + migNoVEGFMatrix μm/hr

Cell Migration Rate without VEGF and minimal/no Matrix, migNoVEGFMatrix

Default: 1.2 μm/hr

Physiological Range: 1.2–30 μm/hr (collagen IV, 2D to glass, 2D)

Stalk Cell Proliferation with VEGF, P _stalk

% Cell Proliferation vs. Control = P1·[VEGF (in ng/ml)]+ proNoVEGF after 48 to 72 hours (approximate average = 60 hrs)

Initial Tip Cell Growth

If tip cell is < tipMin in length and no stalk cells are present, tip cell grows to tipMin in current timestep. Thereafter it follows default rules for migration, elongation and proliferation.

Tip Cell Proliferation and Dll4 ^+/- Effect on Tip Proliferation, P _tip

For Dll4 +/+, tip cell proliferates at a rate of P_stalk with 3% probability

For Dll4 +/-, tip cell proliferates at a rate of P_stalk with 8% probability

Tip Cell Division

If tip cell is > tipMax in length, tip cell divides into two cells. The leading cell remains a tip cell, while the cell adjacent to the stalk cells takes on the stalk cell phenotype and rules.

Dll4 ^+/- Effect on Tip Cell Formation

For Dll4^+/-, maximum number of tip cells formed per existing capillary of 400 μm length is 2.

For Dll4^+/+, maximum number of tip cells formed per existing capillary of 400 μm length is 1.

Dll4 ^+/- Effect on Branching

For Dll4^+/-, branchCells = 0.4 and branchTipCells = 0.4. [VEGF] threshold for new tip cell does not need to be crossed. VEGF_branch = 0 ng/ml.

For Dll4^+/+, branchCells = 0.2 and branchTipCells = 0. VEGF_branch = 0.5 ng/ml.

Persistence as a Function of [VEGF]

Weight for a cell's local search is biased in the direction of the global [VEGF] gradient.

• When local [VEGF] gradients are equal in all directions, the weighing range explored: dirBias/denomBias·[VEGF], where dirBias = 0 to 10 in one direction, where there are eight restricted directions. See Figure 6.