Table 2 Model Parameters*

R₁(t = 0)

65,000 #/cell

# of VEGFR1 per cell at time zero

R₂(t = 0)

12,000 #/cell

# of VEGFR2 per cell at time zero

N(t = 0)

10,000 #/cell

# of Neuropilin-1 per cell at time zero

E(t = 0)

1,000,000 #/cell

# of ECM sites per cell which can bind

VEGF at time zero

$k_f^{VR1};k_r^{VR1}$

3 × 10⁷ M^-1 s^-1;

1 × 10^-3 s^-1

Association/dissociation rate constant for

VEGF binding to VEGFR1

$k_f^{VR2};k_r^{VR2}$

1 × 10⁷ M^-1 s^-1;

1 × 10^-3 s^-1

Association/dissociation rate constant for

VEGF binding to VEGFR2

$k_f^{VE};k_r^{VE}$

4.2 × 10⁵ M^-1 s^-1;

1 × 10^-2 s^-1

Association/dissociation rate constant for

VEGF binding to ECM (based on HS values from literature)

$k_f^{VN};k_r^{VN}$

3.125 × 10⁶ M^-1 s^-1;

1 × 10^-3 s^-1

Association/dissociation rate constant for

VEGF binding to NP-1

$k_f^{FR1};k_r^{FR1}$

3 × 10⁷ M^-1 s^-1;

1 × 10^-3 s^-1

Association/dissociation rate constant for

VEGFf binding to VEGFR1(modeled the same as VEGF)

$k_c^{C2N};k_{uc}^{C2N}$

3.1 × 10¹³ (mol/cm²)^-1 s^-1;

1 × 10^-3 s^-1

Coupling/uncoupling rate constant for

VEGF-VEGFR2 with NP-1

$k_c^{R1N};k_{uc}^{R1N}$

1 × 10¹⁴ (mol/cm²)^-1 s^-1;

1 × 10^-2 s^-1

Coupling/uncoupling rate constant for

VEGFR1 with NP-1

$k_c^{CNR2};k_{uc}^{CNR2}$

1 × 10¹⁴ (mol/cm²)^-1 s^-1;

1 × 10^-3 s^-1

Coupling/uncoupling rate constant for

VEGF-NP-1with VEGFR2

$k_f^{FX};k_r^{FX}$

$k_f^{FR1};k_r^{FR1}$

Association/dissociation rate constant for

VEGFf binding to VEGFR1-NP-1

$k_c^{DN};k_{uc}^{DN}$

$k_c^{R1N};k_{uc}^{R1N}$

Coupling/uncoupling rate constant for

VEGFf-VEGFR1 with NP-1

k _int

2.8 × 10^-4 s^-1

Internalization rate for unbound receptors

$k_{\mathsf{\text{int}}}^C$

2.8 × 10^-4 s^-1

Internalization rate for VEGF-bound receptors

$k_{\mathsf{\text{int}}}^F$

2.8 × 10^-4 s^-1

Internalization rate for VEGFf-bound receptors

S _I

k _int I ₀

Synthesis rate for species I where I₀ is the initial concentration of I