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Table 4 Pre-determined parameters in the mathematical model

From: Combining experimental and mathematical modeling to reveal mechanisms of macrophage-dependent left ventricular remodeling

Symbol

Biological meaning

Value

Units

Ref

d

Macrophage removal rate**(eqn 1)

0.6

day-1

[29]

ρ

maximal macrophage density (eqn 2)

2500

cells/mm3

[28]

ρF

maximal fibroblast density(eqn 2)

1250

cells/mm3

[28]

ρC

maximal collagen density (eqn 2)

3300

μg/mm3

[28]

kF

Fibroblast growth rate* (eqn 3)

0.924

day-1

[62]

dF

Fibroblast apoptosis rate (eqn 3)

0.12

day-1

[33]

kMΦT

Macrophage TGF-β production rate (eqn 4)

0.07

pg/cell/day

[34]

kFT

Fibroblast TGF-β production rate (eqn 4)

0.004

pg/cell/day

[35]

d

TGF-β degradation rate¥(eqn 4)

15

day-1

[36]

KMφM9

Macrophage secretion MMP9 rate (eqn 5)

3

pg/cell/day

estimated

dM9

MMP-9 degradation rate(eqn 5)

0.875

day-1

[6365]

kon

Kinetic reaction speed (eqn 5)

3 × 10-4

1/(μg/mm3)s-1

[42, 66, 67]

koff

Kinetic reaction speed (eqn 5)

4 × 10-4

s-1

[42, 66, 67]

konc

Kinetic reaction speed (eqn 6)

0.004

s-1

[42, 66, 67]

kFC

Fibroblast collagen production rate (eqn 6)

20

μg/cell/day

[41]

  1. *The growth rate of cells was determined by the population doubling time (T2) via equation k = ln 2/T2 [68].
  2. ** Since macrophages emigrate from the scar tissue to lymph node system instead of dying locally in the scar tissue, the removal rate of macrophage, dMA, was used in our model.
  3. ¥ The decaying rate of chemical factors was calculated from their half-life (T1/2) via the equation d = ln 2/T1/2 [68].