Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 172

Table 1 Default parameters for the sprouting model

Property Value

Contact energy J stalk ; medium ¼ 1 ; J stalk ; tip ¼ 1 ; J tip ; BM ¼ 100

J stalk ; border ¼ 10 7 ; J stalk ; pressure ¼ 10 7 ; J tip ; border ¼ 10 7 ; J tip ; pressure ¼ 10 7

Area A target ; ð tip ; stalk Þ¼ 50 ; k ð tip,stalk Þ¼ 70

Perimeter P target ; ð tip, stalk Þ¼ 30 ; k ð tip Þ¼ 25 ; k ð stalk Þ¼ 5

k ð tip, stalk Þ¼ 1000

Haptotaxis

k ð tip, stalk Þ¼ 0 : 1 Chemotactic pressure

D ¼ 10 2 ; k ¼ 0 : 01 ; s ¼ 1 ; 000 Pressure field

MMP and u-PA field

D ¼ 10 6 ; k ¼ 0 : 01 ; s ¼ 500

Fibrin degradation Type: n =4,k = 1.9, initial concentration = 2

Field: 10 7 ½ u-PA ½ fibrin

BM degradation type: n =3,k = 1, initial concentration = 2

field: 5 10 8 ½ MMP ½ BM

3.2 Integration of the Experimental and Computational Model

In Sect. 3.1 , we showed how a conceptual model of tube formation translates to a
computational model. Basic cell behaviors and properties are included in the
computational and the default parameters can be found in Table 1 . First, the model
is used to test a hypothesis concerning the relation of proteolytic enzyme secretion
and sprout morphology. Subsequently, the model will be extended, mainly
focusing on matrix interactions, to differentiate between forces that drive migra-
tion. With these examples, we emphasize how computational and experimental
biologists can benefit from each other's models in their quest to understand
angiogenesis.

3.2.1 Matrix Degradation and Sprout Morphology

To induce sprouting experimentally, endothelial cells are stimulated with an
angiogenic factor, VEGF and/or bFGF, in combination with the inflammatory
mediator TNFa [ 1 , 43 ]. Both the angiogenic factors as well as TNFa induce
proteolytic enzyme activity. The growth factors are suggested to stimulate
secretion of a soluble form of plasminogen activators, t-PA (tissue plasminogen
activator), which becomes active upon contact with fibrin and degrades fibrin in a
diffuse manner. TNFa is suggested to induce u-PA (urokinase-type plasminogen
activator) production and thereby stimulate receptor-bound u-PA activity [ 24 ].
u-PA is inactive until it is bound to its membrane-bound receptor, which localizes
proteolytic activity to the membranes of the receptor expressing cells. Besides
u-PA, TNFa can also induce the plasminogen activator inhibitor, PAI-1, which
inhibits u-PA and t-PA. Proteolytic activity during sprouting is closely regulated
by endothelial cells and results from a balance between the proteolytic enzymes
and their inhibitors. Endothelial cells secrete MMPs (matrix metalloproteinases) to