Table 3.

Rules and related experimental references for endothelial cell sprouting.

Rule	Logical or Mathematical Statement	Reference
Tip Cell Activation	[VEGF] > 0.5 ng/ml, and vacancy in environment surrounding the tip cell	[44]
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 gw/W2 < i < gw/W1   ${[\text{VEGF}]}_{\text{meanj}}=\left|\text{j}\cdot \frac{\text{C}1}{{\text{g}}_{\text{h}}}-\text{C}2\right|$
	• where j > gh/H1
	• where gl·L2 < k < gl·L1
	• σ = C3·[VEGF]mean,j
Unrestricted Tip Cell Migration Rate with VEGF, Mtip	T1·[VEGF (in ng/ml)] + migNoVEGF μm/hr	[54,56,57,96]
Cell Migration Rate without VEGF, migNoVEGF	Default: 6.2 μm/hr	[62,97]
	Physiological Range: 5–11 μm/hr1
Tip Cell Migration Rate as a Function of Extracellular Matrix Composition and VEGF, Mtip	T2·[VEGF (in ng/ml)] + T3·K (fraction collagen content) + migNoVEGFMatrix μm/hr	[46,57,59,62,98]
Cell Migration Rate without VEGF and minimal/no Matrix, migNoVEGFMatrix	Default: 1.2 μm/hr	[52]
	Physiological Range: 1.2–30 μm/hr (collagen IV, 2D to glass, 2D)
Stalk Cell Proliferation with VEGF, Pstalk	% Cell Proliferation vs. Control = P1·[VEGF (in ng/ml)]+ proNoVEGF after 48 to 72 hours (approximate average = 60 hrs)	[10,44,57-59,99,100]
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, Ptip	For Dll4 +/+, tip cell proliferates at a rate of Pstalk with 3% probability	[10,13,69,88]
	For Dll4 +/-, tip cell proliferates at a rate of Pstalk 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.	[13]
	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.	[13]
	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.	[96] The effects of EGF (epithelial growth factor) on persistence was studied in this reference.
	• 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.