Table S4. Kinetic Parameters

Table S4. Kinetic parameters

Measured parameters / Model parameters*
Value / Unit / Value / Unit / Reference
TSP1 binding to CD36
kon / 5 × 105 / M-1s-1 / 9.5 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 1
koff / 1.15 × 10-1 / s-1 / Calculated
Kd / 230 / nM / 2
TSP1 binding to CD47
kon / 5 × 105 / M-1s-1 / 9.5 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 1
koff / 5 × 10-3 / s-1 / Calculated
Kd / 10 / nM / 3
TSP1 binding to LRP1
kon / 2.1 × 105 / M-1s-1 / 4.0 × 108 / (mol/cm3 tissue)-1 s-1 / 4
koff / 2.5 × 10-3 / s-1 / 4
Kd / 12 / nM / 4
TSP1 binding to β1
kon / 5 × 105 / M-1s-1 / 9.5 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 1
koff / 5 × 10-2 / s-1 / Calculated
Kd / 100 / nM / Assumed to be 10x lower than TSP1-CD47, based on 3
TSP1 binding to VEGF
kon / 5 × 105 / M-1s-1 / 9.5 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 3
koff / 5 × 10-3 / s-1 / Calculated
Kd / 10 / nM / 5
Coupling of CD36 and β1
kc, on tumor cells / 3.1 × 1013 / (mol/cm2)-1 s-1 / 2.0 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on VEGF receptor coupling
kc, on endothelial cells / 3.1 × 1013 / (mol/cm2)-1 s-1 / 3.0 × 109 / (mol/cm3 tissue)-1 s-1 / Assumed, based on VEGF receptor coupling
koff / 10-3 / s-1
Coupling of CD36 and VEGFR-2
kc, on tumor cells / 3.1 × 1011 / (mol/cm2)-1 s-1 / 2.0 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed to be 100x lower than VEGF receptor coupling
kc, on endothelial cells / 3.1 × 1011 / (mol/cm2)-1 s-1 / 3.0 × 109 / (mol/cm3 tissue)-1 s-1 / Assumed to be 100x lower than VEGF receptor coupling
koff / 10-3 / s-1 / Assumed, based on VEGFR dissociation
Coupling of CD47 and VEGFR-2
kc, on tumor cells / 3.1 × 1011 / (mol/cm2)-1 s-1 / 2.0 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed to be 100x lower than VEGF receptor coupling
kc, on endothelial cells / 3.1 × 1011 / (mol/cm2)-1 s-1 / 3.0 × 109 / (mol/cm3 tissue)-1 s-1 / Assumed to be 100x lower than VEGF receptor coupling
koff / 10-3 / s-1 / Assumed, based on VEGFR dissociation
TSP1 binding to GAGs
kon / 5 × 105 / M-1s-1 / 9.5 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 3
koff / 1 × 10-1 / s-1 / Calculated
Kd / 200 / nM / 6
MMP3 binding to proMMP9
kon / 1.0 × 104 / M-1s-1 / 1.9 × 107 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 1,7
koff / 1.0 × 10-3 / s-1 / Assumed, based on 1,7
Kd / 100 / nM / Calculated
MMP3 activating proMMP9
kact / 1.9 × 10-3 / s-1 / 8
TSP1 binding to MMP3
kon / 1.0 × 105 / M-1s-1 / 1.9 × 108 / (mol/cm3 tissue)-1 s-1 / Assumed, based on 1,7
koff / 2.1 × 10-3 / s-1 / Estimated by fitting data, see text
Kd / 22 / nM / Calculated
Proteolysis of VEGF165 via MMPs
kp / 631 / M-1s-1 / 1.2 × 106 / (mol/cm3 tissue)-1 s-1 / Estimated in 9 by fitting data from 10
TSP1 cleavage
kp / 3.9 × 10-3 / s-1 / Assumed†
MMP9 binding to LRP1
kon / 9.2 × 103 / M-1s-1 / 1.8 × 107 / (mol/cm3 tissue)-1 s-1 / 11
koff / 4.9 × 10-4 / s-1 / 11
Kd / 53 / μM / 11
VEGF binding to VEGFR-1
kon / 3 × 107 / M-1s-1 / 5.7 × 1010 / (mol/cm3 tissue)-1 s-1 / Calculated
koff / 10-3 / s-1 / Assumed‡
Kd / 33 / pM / 12
VEGF binding to VEGFR-2
kon / 107 / M-1s-1 / 1.9 × 1010 / (mol/cm3 tissue)-1 s-1 / Calculated
koff / 10-3 / s-1 / Assumed‡
Kd / 100 / pM / 13,14
VEGF165 binding to NRP1
kon / 3.2 × 106 / M-1s-1 / 6.1 × 109 / (mol/cm3 tissue)-1 s-1 / Calculated
koff / 10-3 / s-1 / Assumed‡
Kd / 312.5 / pM / 15,16
VEGF165 binding to NRP2
kon / 1 × 106 / M-1s-1 / 1.9 × 109 / (mol/cm3 tissue)-1 s-1 / Calculated
koff / 10-3 / s-1 / Assumed‡
Kd / 1 / nM / 17–19, ~3–50-fold less tight than VEGF165-NRP1 binding
VEGF binding to GAGs
kon / 8.6 × 103 / M-1s-1 / 1.6 × 107 / (mol/cm3 tissue)-1 s-1 / 20–22
koff / 6.9 × 10-4 / s-1 / 20–22
Kd / 80 / nM / 20–22
Coupling of NRP and VEGFR-2
kcV165R2,N, on tumor cells / 3.1 × 1013 / (mol/cm2)-1 s-1 / 2.0 × 1010 / (mol/cm3 tissue)-1 s-1. / Estimated in 23 using data from 24
kcV165R2,N, on endothelial cells / 3.1 × 1013 / (mol/cm2)-1 s-1 / 3.0 × 1011 / (mol/cm3 tissue)-1 s-1. / Estimated in 23 using data from 24
koffV165R2,N / 10-3 / s-1 / Assumed‡
kcV165N,R2, on tumor cells / 1014 / (mol/cm2)-1 s-1 / 6.5 × 1010 / (mol/cm3 tissue)-1 s-1. / Estimated in 23 using data from 24
kcV165N,R2, on endothelial cells / 1014 / (mol/cm2)-1 s-1 / 9.5 × 1011 / (mol/cm3 tissue)-1 s-1. / Estimated in 23 using data from 24
koffV165N,R2 / 10-3 / s-1 / Assumed‡
Coupling of NRP and VEGFR-1
kc, on tumor cells / 1014 / (mol/cm2)-1 s-1 / 6.5 × 1010 / (mol/cm3 tissue)-1 s-1. / Assumed to be the same as VEGFR2 coupling to NRP
kc, on endothelial cells / 1014 / (mol/cm2)-1 s-1 / 9.5 × 1011 / (mol/cm3 tissue)-1 s-1. / Assumed to be the same as VEGFR2 coupling to NRP
koff / 10-2 / s-1 / Assumed to be slower dissociation than VEGFR2-NRP

* The konand kcvalues are converted to units used in the model: kon, (mol/cm3 tissue)-1 s-1 and kc, (mol/cm3 tissue)-1 s-1.The association rates (kon) are converted using the volume fraction of interstitial space relative to the total volume of the tumor tissue: 5.22 × 10-4 (mol/cm3 tissue)/M. The receptor-coupling rate(kc) represents the rate of association for receptors on a specific cell surface. Thus, there are differentconversions for receptors on tumor cells and endothelial cells (ECs), as the cells have different surface areas: 1534 cm2 tumor cell/cm3 tissue; 105 cm2 EC/cm3 tissue. The geometric factors are based on breast tumor xenografts. We assume the same tissue structure and geometry as in previous work25, where the derivation of these parameters can be found.

† Given a lack of quantitative measurements for TSP1 cleavage, we assumed the proteolysis rate to be the same as VEGF and multiply by the total concentration of species who act to proteolyze TSP1 (plasmin, elastase, and thrombin), ~4.5 nM26,27, accounting for the unbound, extracellular portions. This is similar to a rate estimated in a recent mathematical model28.

‡ For reactions whose dissociation rate constants were not directly known, we assumed a koff of 1 × 10-3 sec-1, which is consistent with measured off rates for the VEGF family14,29.

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