Figure 1.
A. Schematic of a tissue cross section. B. Compartment model. The vascular system is separated from the rest of the body. The blood compartment comprises the plasma (available to VEGF), the blood elements (blood cells, fibrin, clotting elements, etc.), as well as the luminal side of the basement membranes of the endothelial cells. The tissue compartment is composed of the parenchymal cells that secrete VEGF, the interstitium as well as the abluminal surface of the endothelial cells lining the capillaries. The fraction that is not accessible to VEGF is represented as a hatched area. The arrows illustrate inter-compartment and intra-compartment exchanges: secretion, vascular permeability, internalization of the receptors, lymphatic drainage, and clearance from the plasma. C. Schematic of the chemical interactions. Two isoforms of VEGF are considered: VEGF121 and VEGF165. Free receptors (VEGFR1, VEGFR2 and NRP1) and free VEGF isoforms are located in the gray areas. VEGF121 and VEGF165 both bind VEGFR1 and VEGFR2. VEGF165 also binds glycosaminoglycan chains (GAG) as well as the co-receptor NRP1. VEGF165 can serve as a bridge for the formation of VEGFR2-NRP1 complex. Finally, VEGF121 can bind to VEGFR1-NRP1 complex.
Table 1.
Geometric parameters for the tissue (human vastus lateralis muscle).
Table 2.
Kinetic parameters of VEGF in the tissue (human vastus lateralis muscle).
Table 3.
VEGF concentration and receptor densities for the tissue (human vastus lateralis).
Table 4.
Geometric parameters of the compartments [9].
Table 5.
Kinetic parameters between the compartments and in the blood.
Figure 2.
Effects of VEGF secretion, vascular permeability, lymph flow rate and clearance.
A. Three scenarios are studied: scenario (a) our previous configuration from [9] (clearance rate cv = 0.0206 min−1); scenario (b) new clearance cv = 0.0648 min−1 in the absence of lymphatic drainage; scenario (c) introduction of the lymphatic drainage of VEGF kL = 2 cm3/min (120 mL/hour [15]) with the new clearance cv = 0.0648 min−1. B. Effect of VEGF secretion. Free VEGF concentration in the tissue is illustrated in blue. The purple curve corresponds to scenario (a) and the red curves to scenarios (b) and (c) for the plasma VEGF concentration. We consider two permeability rates kp = 4×10−8 cm/s (dotted curve) and 4×10−7 cm/s (dashed curve). C. Effect of vascular permeability to VEGF. Scenarios (a), (b) and (c) are represented as the dashed, dashed-dotted-dotted and solid curves respectively. The blue curve corresponds to the tissue while the red curve corresponds to the blood. D. Effect of lymph flow rate. We only consider scenarios (b) and (c) to look at the effect of adding the lymphatics to our model. We consider two permeability rates kp = 4×10−8 cm/s (dotted curve) and 4×10−7 cm/s (dashed curve). The blue curve corresponds to the tissue while the red curve corresponds to the blood. E. Effect of clearance rate. We consider two permeability rates kp = 4×10−8 cm/s (dotted curve) and 4×10−7 cm/s (dashed curve). The blue curve corresponds to the tissue. The pink curve corresponds to scenarios (a) and (b) and the red curve corresponds to the scenario (c) of Figure 2A for the plasma VEGF concentration.
Figure 3.
Free VEGF concentrations in tissue and blood as a function of the receptor density.
The secretion rate is fixed so that, at a vascular permeability of 4×10−8 cm/s, 1 pM of free VEGF is present in the plasma (no luminal receptors; 10,000 abluminal receptors of each species per endothelial cell). VEGF secretion rate is 0.2390 molecule/cell/s. The density of abluminal and luminal receptors was varied from 0 to 10,000 receptors per endothelial cell surface. Note that no steady state could be reached at such secretion rate in the absence of abluminal receptors. The free VEGF concentration in the available interstitial fluid was constant over the range of luminal receptor density and decreased exponentially with the density of abluminal receptors. The free VEGF concentration in the plasma was significantly changed when the density of receptors was low.
Figure 4.
Flow diagrams for a fixed concentration of free VEGF in the plasma.
A. The inflows and outflows are expressed in pmoles/s. The density of luminal and abluminal receptors was varied from 0 to 10,000 per endothelial cell. Free VEGF concentration in the plasma was fixed at 1 pM for a vascular permeability of 4×10−8 cm/s. From top left, counter-clockwise: i. VEGF secreted per parenchymal cell; ii. free VEGF concentration in the tissue (in pM); iii. VEGF intravasating; iv. VEGF disappearing through internalization of the luminal receptors to which it binds; v. VEGF drained through the lymphatics; vi. VEGF disappearing through internalization of abluminal receptors to which it binds. VEGF extravasating and VEGF cleared from the plasma are constant over the course of the simulations due to the fixed free VEGF concentration in the plasma and equal to 2.65×10−4 and 2.94×10−3 pmoles/s respectively. The yellow dot corresponds to the configuration of 10,000 abluminal receptors and no luminal receptors. The purple dot identifies an equal density of receptors on luminal and abluminal surfaces of the endothelial cells (5,000 receptors on each side per endothelial cell). The green dot corresponds to the case of 10,000 luminal receptors and no abluminal receptors. B. Flows normalized to VEGF secretion for different luminal receptor densities: i. no abluminal receptors; ii. 500 abluminal receptors per EC; iii. 1,000 abluminal receptors per EC; iv. 10,000 abluminal receptors per EC. EC = endothelial cell.
Figure 5.
Flows of VEGF disappearing upon ligated receptor internalization as a function of the VEGF secreted.
The setup is similar to that in Figure 4. A. Linear relationship between the VEGF secreted and the VEGF disappearing via internalization of VEGF-bound abluminal receptors. B. Non-linear relationship between the VEGF secreted and the VEGF disappearing via internalization of the luminal receptors it has bound to. Black circles: no abluminal receptors; red circles: 2,500 abluminal receptors/endothelial cell; green triangles: 5,000 abluminal receptors/endothelial cell; yellow triangles: 7,500 abluminal receptors/endothelial cell; blue squares: 10,000 abluminal receptors/endothelial cell.
Figure 6.
Flow diagrams for a total receptor density of 10,000 per endothelial cells.
A. The density of total (luminal and abluminal) receptors per endothelial cell is fixed at 10,000 (VEGFR1∶VEGFR2∶NRP1 expression is 1∶1∶1). Scenario (a): all the receptors are located on the endothelial abluminal surface (yellow circle on Figure 4A); scenario (b): the receptors are evenly distributed between the luminal and abluminal endothelial surface (purple circle on Figure 4A); scenario (c): all the receptors are located on the endothelial luminal surface. Numbers represent absolute values of VEGF flows expressed in pmoles/s. Percentages of VEGF secretion in parentheses. B. Generalization of particular cases shown in A. The density of receptors varies between 0 and 10,000 receptors per endothelial cell surface. The total receptor density is fixed at 10,000 receptors per endothelial cell. Left: absolute values; Right: percentages of VEGF secretion.
Figure 7.
VEGF distribution and VEGFR occupancy for a total receptor density of 10,000 per endothelial cells.
The scenarios correspond to those in Figure 6B. A. VEGF distribution. i. tissue; ii. blood. Columns from left to right: total VEGF distribution, VEGF165 distribution, VEGF121 distribution. In the absence of luminal receptors (bottom rows in i. and ii.), most VEGF bridges VEGFR2-NRP1 in the tissue and VEGF165∶VEGF121 in the plasma is 92%∶8% similar to that of the isoforms expressions in the tissue. When abluminal receptor density decreases, VEGF is increasingly sequestered in the extracellular matrix (ECM, PBM, EBM) in the tissue compartment and VEGF165 bridges VEGFR2-NRP1 in the plasma. B. VEGFR occupancy. i. tissue; ii. blood. Columns from left to right: total VEGFR occupancy, VEGFR1 occupancy, VEGFR2 occupancy, NRP1 occupancy. When the receptors are distributed on one side of the endothelial cells (either luminal or abluminal), most of the VEGF receptors are in the form of VEGFR1-NRP1 complex while most of VEGFR2 is in its free state (bottom row in i. and top row in ii.). When the receptors are distributed evenly between the endothelial cells luminal and abluminal surfaces, the luminal receptor occupancy remains unchanged (top and middle rows in ii.) but the VEGF receptor occupancy in the tissue shifts towards VEGF165 bridging VEGFR2-NRP1 (bottom and middle rows in i.).
Figure 8.
VEGF distributions in the tissue and in the blood.
The setup is similar to that in Figure 4. Top row: VEGF distribution in the tissue; bottom row: VEGF distribution in the blood. The first column corresponds to the percentage of free VEGF; the second column the percentage of VEGF bound to the receptors; the third column the percentage of VEGF bound to the extracellular matrix and basement membranes.
Figure 9.
A. Ratio [VEGF bound to abluminal VEGFR1]/[VEGF bound to luminal VEGFR1]. B. Ratio [VEGF bound to abluminal VEGFR2]/[VEGF bound to luminal VEGFR2]. C. Ratio [VEGF bound to VEGFR2]/[VEGF bound to VEGFR1]. Top row: tissue; bottom row: blood.
Figure 10.
Summary of VEGF transport in the body.
VEGF is secreted by parenchymal cells in the tissue. Most of VEGF is sequestered in the extracellular matrix or binds to the abluminal receptors and disappears by VEGF-bound receptor internalization. A small fraction (free VEGF) is transported from the available interstitial fluid to the plasma (mostly through the permeability route rather than by the lymphatics). Upon entering the blood, free VEGF either binds to luminal receptors and disappears by VEGF-bound receptor internalization or is cleared from the plasma.