Table 4 

Predetermined parameters in the mathematical model 

Symbol 
Biological meaning 
Value 
Units 
Ref 


d_{MΦ} 
Macrophage removal rate**(eqn 1) 
0.6 
day^{1} 
[29] 


ρ_{MΦ} 
maximal macrophage density (eqn 2) 
2500 
cells/mm^{3} 
[28] 


ρ_{F} 
maximal fibroblast density(eqn 2) 
1250 
cells/mm^{3} 
[28] 


ρ_{C} 
maximal collagen density (eqn 2) 
3300 
μg/mm^{3} 
[28] 


k_{F} 
Fibroblast growth rate* (eqn 3) 
0.924 
day^{1} 
[62] 


d_{F} 
Fibroblast apoptosis rate (eqn 3) 
0.12 
day^{1} 
[33] 


k_{MΦT} 
Macrophage TGFβ production rate (eqn 4) 
0.07 
pg/cell/day 
[34] 


k_{FT} 
Fibroblast TGFβ production rate (eqn 4) 
0.004 
pg/cell/day 
[35] 


d_{Tβ} 
TGFβ degradation rate^{¥}(eqn 4) 
15 
day^{1} 
[36] 


K_{MφM9} 
Macrophage secretion MMP9 rate (eqn 5) 
3 
pg/cell/day 
estimated 


d_{M9} 
MMP9 degradation rate(eqn 5) 
0.875 
day^{1} 



k_{on} 
Kinetic reaction speed (eqn 5) 
3 × 10^{4} 
1/(μg/mm^{3})s^{1} 



k_{off} 
Kinetic reaction speed (eqn 5) 
4 × 10^{4} 
s^{1} 



k_{onc} 
Kinetic reaction speed (eqn 6) 
0.004 
s^{1} 



k_{FC} 
Fibroblast collagen production rate (eqn 6) 
20 
μg/cell/day 
[41] 


*The growth rate of cells was determined by the population doubling time (T_{2}) via equation k = ln 2/T_{2 }[68]. ** Since macrophages emigrate from the scar tissue to lymph node system instead of dying locally in the scar tissue, the removal rate of macrophage, d_{MA}, was used in our model. ¥ The decaying rate of chemical factors was calculated from their halflife (T_{1/2}) via the equation d = ln 2/T_{1/2 }[68]. 

Jin et al. BMC Systems Biology 2011 5:60 doi:10.1186/17520509560 