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Am J Physiol Heart Circ Physiol 288: H2851-H2860, 2005. First published February 11, 2005; doi:10.1152/ajpheart.01218.2004
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Differential binding of VEGF isoforms to VEGF receptor 2 in the presence of neuropilin-1: a computational model

Feilim Mac Gabhann and Aleksander S. Popel

Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland

Submitted 3 December 2004 ; accepted in final form 2 February 2005


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A comprehensive, biophysically accurate, computational model of vascular endothelial growth factor (VEGF) family member interactions with endothelial cell surface receptors was developed to study angiogenesis. Neuropilin-1 (NRP1) and the signaling VEGF receptor, VEGFR2, do not interact directly but are bridged by one VEGF isoform, VEGF165. Using the model and published experimental data, we estimated the kinetic rate of this VEGFR2-NRP1 coupling in vitro. With the use of this rate, our model gives predictions in good quantitative agreement with several independent in vitro experiments involving VEGF121 and VEGF165 isoforms, confirming that VEGFR2-NRP1 coupling through VEGF165 can fully explain the observed differences in receptor binding and phosphorylation in response to these isoforms. Model predictions also determine the mechanism of action of a commonly used NRP1 antibody and predict the results of potential future experiments. This is the first model to include VEGF isoforms or NRPs, and it is a necessary step toward a quantitative molecular level description of VEGF that can be extended to in vivo situations. The model has applications for both proangiogenic and antiangiogenic therapies, such as for heart disease and cancer, as well as in tissue engineering.

mathematical model; receptor coupling; angiogenesis; endothelial cell

ANGIOGENESIS (or neovascularization) is a vital process for the growth of tumors and is involved in many other diseases as well as in physiological development. Hypovascularized tissues secrete growth factors as angiogenic signals that bind to endothelial cell surface receptors and initiate vessel sprouting. Vascular endothelial growth factor (VEGF) is a secreted, dimeric glycoprotein that acts by binding cognate receptor tyrosine kinases VEGF receptor 1 and 2 (VEGFR1 and VEGFR2) on endothelial and other cells, resulting in receptor autophosphorylation and intracellular signaling. For endothelial cells in vitro, VEGF induces migration, proliferation, and increased survival (43). In vivo, in addition to these effects, VEGF overexpression results in increased permeability of blood vessels and upregulation of proteases for the breakdown of the extracellular matrix, providing a path for the sprouting vessel (7, 17).

The VEGF family of proteins is large and includes VEGF-A, which is expressed, through alternate splicing, as multiple isoforms of varying lengths. Two of the most prevalent isoforms in the human body are VEGF121 and VEGF165. VEGF121 is shorter by 44 amino acids due to the omission of a heparin-binding domain encoded by exon 7. Thus VEGF165 binds to and can be sequestered by the extracellular matrix; VEGF121 does not bind to the extracellular matrix and diffuses freely. The exon 7-encoded domain also contains a binding site for neuropilin-1 (NRP1), making that receptor selective for VEGF165. NRP1 was originally identified on neurons with a role in cell guidance. It binds the repulsion cue molecules of the semaphorin family but has a short cytoplasmic domain and does not signal directly, coupling with signaling plexins on the cell surface (2). It has been shown in vitro that NRP1 can likewise couple to VEGFR2 in the presence of VEGF165; this potentiates the signal that VEGF transduces through VEGFR2 (35, 42). The extracellular domain of VEGFR2 does not interact directly with NRP1 (12), and the VEGFR2 and NRP1 binding sites on VEGF165 are distinct (22, 34). Complexes are thus formed due to bridging, when VEGF165 is binding to both receptors simultaneously (Fig. 1A). NRP1 has not been shown to directly transduce VEGF signals on endothelial cells, although a recent study demonstrated that a chimeric NRP receptor, with an epidermal growth factor-binding extracellular domain, caused migration of human umbilical vein endothelial cells (HUVECs) in response to epidermal growth factor addition (41).



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  		Fig. 1. Binding of VEGF isoforms to VEGF receptor 2 (VEGFR2) and neuropilin 1 (NRP1). A: VEGF121 (121) binds VEGFR2 (2) but not NRP1 (N); VEGF165 (165) binds to both and can couple the receptors together by binding both simultaneously. The arrows represent the reactions: binding (on rates), unbinding (off rates), and coupling (coupling rates). B: simulation of in vitro VEGF isoform competition experiments. Increasing concentrations of cold VEGF165 (left) and cold VEGF121 (right) are added to wells in which 125I-labeled VEGF165 (125I-VEGF165) binds to COS-1 cells coexpressing VEGFR2 and NRP1. Experimental data ({circ} and {bullet}) are from Ref. 42. Results of numerical simulations (lines) are shown for theoretical diffusion-limited coupling rates (solid line) and decreasing coupling rates 10-fold (dotted line), 100-fold (dashed line) and 1,000-fold (dashed-dotted line) lower that the diffusion-limited rate. All lines are coincident for cold VEGF165.

 
The importance of NRP receptors in the vasculature has been shown by genetic studies. Homozygous inactivation of NRP1 in mice caused disorganization of neural pathways, as expected, and also caused embryonic vascular defects involving both the macro- and microvasculature, including insufficient neural vascularization, great vessel transposition, and impaired vascular network development in the yolk sac (20). Inactivation of both NRP1 and another family member, NRP2, was more severe than NRP1 alone and was embryonic lethal at embryonic day 8.5 (37). Yolk sacs lacked capillary beds and many branching arteries and veins. Embryos exhibited large avascular regions and hemorrhages and were 50% shorter than wild type. Mice that lacked NRP1 specifically in endothelial cells had a defective systemic vasculature lacking small vessels and showed reduced branching as well as heart defects (15). In contrast, chimeric mice overexpressing NRP1 demonstrated hypervascularization and blood vessel dilation as well as heart malformation (23).

In the present study, we constructed a computational model of the interactions between NRP1 and VEGFR2 that incorporates parameters from the experimental literature to describe the distinct formation of signaling complexes by the isoforms VEGF121 and VEGF165. We characterized the NRP1-VEGFR2 coupling rate from experiments and validated the model with binding and phosphorylation data from the literature. We analyzed data from seven sets of in vitro experiments and showed that model predictions are in good quantitative agreement with the experimental results. We incorporated a NRP1 antibody into the model, confirmed its mechanism of action, and described a method for improving estimation of the receptor coupling rate and of receptor populations on endothelial cells. VEGFR1 is excluded from the analysis as the experimental data used here are for cells without significant VEGFR1. Heparan sulfate proteoglycans (HSPGs) are not included explicitly in the model; the kinetic rates of binding to VEGFR2 and NRP1 instead are effective rates that include the impact of the presence of HSPGs on the cell surface.

Therapies are being developed both to inhibit ectopic vascularization and to stimulate vascular growth where it may ameliorate disease. To aid in the design of these therapies, we are constructing computational models of endothelial cell behavior in in vitro assays as a basis for developing computational models of angiogenesis in vivo. Use of models such as the one presented here complements experimental research and can lead to increased understanding of the molecular mechanisms of angiogenesis-related diseases and therapies as well as aiding clinical translation of this information in a way that may be difficult or impossible experimentally, for example, in the determination of effective or therapeutic concentrations of drugs or predicting how perturbations in endogenous secretion or in the microenvironment can result in observed effects.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Computational model. To simulate the interactions of VEGF family ligands with endothelial cell surface receptors, we constructed a model that reflects the geometry of the in vitro situation where endothelial cells are plated as confluent monolayers in cell culture chambers (wells) and bathed in cell culture medium, into which the growth factors are added. Thus, while growth factors diffuse in solution in three dimensions, they bind to receptors restricted to the surface of the cells. The model explicitly includes the kinetics of all ligand-receptor interactions, which allows us to examine both short-term and long-term behavior of the system. The concentration of cell surface receptors VEGFR2 and NRP1 and the growth factor-receptor complexes they form are described by partial differential equations that include the processes of diffusion, binding reactions, and coupling on the cell surface. These equations are described in the APPENDIX. The equations were discretized with an implicit, finite-difference scheme and simulated on a personal computer.

This model builds on our previous simulations of VEGF-VEGFR interactions (26) by adding NRP1 and receptor coupling. All the parameters for the model were obtained from the experimental literature and are described in detail in the APPENDIX. The only parameter not known a priori for the model is the coupling rate, that is, the rate at which VEGF-VEGFR2 or VEGF-NRP1 complexes bind unligated NRP1 or VEGFR2 to form the ternary complex VEGF-VEGFR2-NRP1. This rate is not known for VEGFR or other cell surface receptors. A theoretical diffusion-limited rate is estimated in the APPENDIX (see Fig. 7). We used this estimate as a reference and examined a range of coupling rates. We estimated the actual coupling rate using experimental data (see RESULTS) and used this to explain the binding and phosphorylation of VEGFR2 by VEGF in the presence of NRP1.



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  		Fig. 7. Diffusion-limited coupling rate calculated using the theory developed in Refs. 10 and 11. A: coupling rate (kc). B: coupling rate multiplied by free (unbound) receptor concentration (kcR). The rates for varying surface kinetics (solid line), the best power law approximation (dashed line), and the best constant coupling rate approximation (dotted line) are shown.

 

   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
VEGF isoforms: binding and competition experiments. VEGF121 and VEGF165 exhibit similar affinity for VEGFR2 when the receptor is expressed alone on the surface of COS-1 cells (42). For COS-1 cells expressing both VEGFR2 and NRP1, nonradiolabeled ("cold") VEGF165 can compete with 125I-labeled VEGF165 for cell surface binding; results from these competition experiments (42) are shown as closed circles in Fig. 1B. The experimental binding results are predicted well by the model using known binding kinetics (Fig. 1B); in this case, the results are not coupling rate dependent and all other parameters were available in the literature (none have been "fitted"). However, the presence of NRP1 prevents cold VEGF121 from displacing the radiolabeled ("hot") VEGF165 from the cell surface (Fig. 1B, open circles). Model simulations with a range of coupling rates show that the best fit for the experimental binding is obtained with the predicted diffusion-limited rate (Fig. 1B, solid line). Coupling rates 10-fold, 100-fold, and 1,000-fold lower (Fig. 1B, dotted, dashed, and dashed-dotted lines) allow competition in this concentration range, although the 10-fold lower rate does not give a significantly distinct result. It should also be noted that any further increase in the coupling rate would have little effect over this range of concentrations. To the best of our knowledge, this is the first experiment-based estimate of the coupling rate involving cell surface receptor tyrosine kinases and the first for the bridging of two distinct receptor populations. This coupling rate will now be used to analyze the behavior of VEGF isoforms binding to cells expressing these receptors. Although Fig. 1B does not permit us to pinpoint the coupling rate, we investigated coupling rates 10-fold higher and 10-fold lower than the theoretical prediction for each of the analyses to follow, and no significant effects were noted.

Formation of VEGFR2 signaling complexes. Intracellular autophosphorylation of VEGFR2 is the major pathway of VEGF signaling; NRP1 is not known to induce signaling by itself, and VEGFR1 has significantly lower phosphorylation rates. Thus VEGF bound to VEGFR2 is used as a marker for the strength of the signal transduced to intracellular pathways. It has been shown experimentally that the presence of NRP1 increases the binding of VEGF165 to VEGFR2 (35). Our model demonstrates this behavior, as the coupling of NRP1-bound VEGF165 to VEGFR2 drives formation of ligated VEGFR2-NRP1 complexes. The model correctly predicts VEGF121 binding to these porcine aortic endothelial (PAE) cells coexpressing VEGFR2 and NRP1 (PAEVEGFR2 + NRP1) to be identical to VEGF165 binding to cells in the absence of NRP1. The increase in VEGF165 binding to VEGFR2 on PAEVEGFR2 + NRP1 cells over binding to VEGFR2 on PAEVEGFR2 cells was measured at two concentrations in two experimental studies on the same cell type (35, 36); the increases predicted by the model are similar to those measured experimentally (Fig. 2). A significantly lower (<2-fold) increase in VEGF165 bound to NRP1 on PAEVEGFR2 + NRP1 cells over that bound to NRP1 on PAENRP1 cells was found at 5 ng/ml (111 pM) (35); model predictions are also in agreement with this finding (Fig. 2). Although this is the binding after a 2-h exposure to VEGF, there was also a significant increase in VEGF-VEGFR2 binding, attributable to NRP1, at short times associated with peak phosphorylation. A 2.3-fold increase in phosphorylation of VEGFR2 attributable to NRP1 was seen 7 min after the addition of 1 nM VEGF (4), in good agreement with the model (Fig. 2, open square and dashed line).



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  		Fig. 2. Binding of VEGF165 to receptors on transfected porcine aortic endothelial (PAE) cells. The predicted fold increase in binding to VEGFR2 due to the presence of NRP1 (left) and the predicted fold increase in binding to NRP1 due to the presence of VEGFR2 (right) at 2 h (solid line) and at 7 min (dashed line) is compared with experimental data on the increase in steady-state binding ({bullet}, Ref. 35; and {blacktriangleup}, Ref. 36) and phosphorylation ({square}, Ref. 4).

 
It is of note that by setting the coupling rate to zero, NRP1 binding VEGF acts as a "sink" for VEGF at the cell surface. The presence of this VEGF sink does not increase VEGF binding to VEGFR2, and in fact binding to both VEGFR2 and NRP1 is decreased relative to that receptor being expressed alone (data not shown). Thus coupling is required for the increased binding to be observed. At all VEGF165 concentrations, binding to the signaling receptor VEGFR2 on cells coexpressing NRP1 is always increased by coupling, but the total amount of VEGF bound to such a cell is increased by coupling only at low VEGF concentrations, up to 550 pM for these transfected PAE cells (data not shown). On noncoupling cells, one receptor (either VEGFR2 or NRP1) is bound per VEGF molecule, whereas on coupling cells, two receptors (NRP1 and VEGFR2) are bound per VEGF molecule. At high VEGF concentrations, this results in a decreased total binding capacity for the coupling cells.

Note that the increases in complex formation are not the result of increased stability of each complex due to coupling. If NRP1 and VEGFR2 interacted directly, this would be true, but here, the off rate of VEGF165 from VEGFR2 is unchanged by the presence of NRP1 bound to VEGF165 (and vice versa). The average lifetime of each VEGF-VEGFR2 complex is the same in the presence of NRP1; rather, the formation of the complexes is increased due to the presentation of VEGF165 by NRP1 on the surface.

The increase in VEGF bound at low concentrations can be seen in coculture experiments, where populations of untransfected PAE cells (PAE0) and PAE cells expressing either VEGFR2 (PAEVEGFR2) or NRP1 (PAENRP1) are plated together (35). PAE0-PAEVEGFR2 or PAE0-PAENRP1 cocultures bind VEGF predictably and in agreement with the model (Fig. 3, simulation: solid lines; in vitro experimental data: circles). If we sum the VEGF binding to each of these two cocultures, the total (Fig. 3, dashed line and squares) is almost equal to the predicted binding of VEGF to a coculture of PAEVEGFR2 and PAENRP1 cells in the absence of NRP1-VEGFR2 coupling (data not shown). However, this binding is considerably less than that observed for these PAEVEGFR2-PAENRP1 cocultures in in vitro experiments (Fig. 3, triangles). The model predictions with VEGFR2-NRP1 coupling via VEGF165 shows some increased binding to the cells, i.e., the predicted values are above the values given by the dashed line; however, the values obtained under the assumption of no internalization of the VEGF165-VEGFR2, VEGF165-NRP1, and VEGF165-VEGFR2-NRP1 complexes, kint = 0, are still lower than the experimental values represented by the triangles at higher VEGF concentrations (Fig. 3, dotted lines). A better fit is obtained by assuming that the internalization rate of the receptors and complexes is nonzero. In this case, the internalization rate of the VEGF165-VEGFR2-NRP1 complex must still be zero because each receptor is on a different (but apposing) cell and thus the complex cannot be internalized unless this event is preceded by dissociation. We see that an internalization rate of 10–4 s–1 improves the agreement with the experiment substantially (Fig. 3, dotted lines). Note that at higher initial VEGF concentrations (above 450 pM for kint = 0 or above 2.2 nM for kint = 10–4 s–1), the model predicts that the sum of binding to the two single receptor cocultures (Fig. 3, dashed line) will be greater than the binding to the two receptor cocultures (Fig. 3, dotted lines), in contrast with the lower initial VEGF concentrations shown here (data not shown). This is a prediction that could be tested experimentally.



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  		Fig. 3. Binding of VEGF165 to cocultures of PAE cells transfected with different VEGFRs. The experimental data (symbols, Ref. 35) and simulation results (lines) are normalized to the VEGF binding predicted at a VEGF concentration of 10 ng/ml (222 pM) to PAE0-PAENRP1 cocultures. VEGF binding to PAE0-PAEVEGFR2 (solid line and {circ}), PAE0-PAENRP1 (solid line and {bullet}), and PAEVEGFR2-PAENRP1 cocultures (dotted line and {blacktriangleup}) are shown. The sum of VEGF binding to PAE0-PAEVEGFR2 and PAE0-PAENRP1 is also shown (dashed line and {square}). kint, Internalization rate of cell surface receptors and complexes.

 
Phosphorylation of VEGFR2. NRP1 has also been shown to increase the VEGF165-induced phosphorylation of VEGFR2 on endothelial cells in vitro (42). To demonstrate that this can be fully explained by our model as being a result of increased binding, we simulated the experiments performed. Short-term binding (5 min post-VEGF addition) is used as the marker for VEGFR2 phosphorylation in our model. Four experiments were simulated in which HUVECs were exposed to VEGF165 or VEGF121 alone or in combination with a fragment of placental growth factor-2 (PlGF2), which was shown to bind NRP1 but not VEGFR2, and thus is used in excess to block VEGF binding to NRP1.

Using the results of competition experiments (42), we calculated the affinity of this PlGF2 fragment for NRP1 on COS-1 cells expressing only NRP1 to be 11.9 µM based on a VEGF-NRP1 affinity of 2.1 nM on that cell type (data not shown). Note that the receptor populations on HUVECs are variable. The cells used in this experiment were found to have 49,500 total VEGF receptors with an average affinity of 169 pM (42). It was also found, in experiments similar to those shown in Fig. 1B, that VEGF121 at concentrations up to 100 nM could not compete with 287 pM radiolabeled VEGF165 for the binding sites (42). For this to hold, NRP1 must be in excess over the VEGFR2 (data not shown); thus we examined a range of ratios of NRP1 to VEGFR2 of 1–10.

With the use of the same PlGF2 fragment affinity, the IC50 (VEGF concentration for half-maximal binding/phosphorylation at 5 min) was calculated for each isoform with and without the PlGF2 fragment present, and the ratios of VEGF121 IC50 to VEGF165 IC50 were plotted as a function of the ratio of NRP1 to VEGFR2 numbers (Fig. 4). The experimentally observed ratios are indicated (arrows), 6.5-fold and 2.2-fold increases in IC50 for VEGF121 over VEGF165 in the absence and presence of the PlGF2 fragment, respectively (42). An NRP1-to-VEGFR2 ratio of 5.3 exhibits good agreement for the experimentally observed IC50 ratios. In the case of a 10-fold lower coupling rate, the ratio was 7.4; a higher coupling rate showed no variation.



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  		Fig. 4. Differential phosphorylation of VEGFR2 on human umbilical vein endothelial cells (HUVECs) by VEGF165 and VEGF121. Ratio of predicted IC50s on HUVECs for VEGF165 and VEGF121 in the absence (solid line, simulation results; top arrow, experimental data) and presence (dotted line, bottom arrow) of a placental growth factor 2-derived peptide are shown. Experimental data are taken from Ref. 42.

 
The average affinity calculated may not be the same for both receptors; we examined the effect of affinity on the results. With NRP1 in excess, we kept its affinity constant and increased that of VEGFR2 (in agreement with the higher IC50 for VEGF121). At up to a twofold higher affinity, good agreement with the experiment was maintained (data not shown).

Blocking VEGFR2-NRP1 coupling. PlGF2 inhibits the phosphorylation of VEGFR2 induced by VEGF165 but not that induced by VEGF121. When in excess, it causes the response to VEGF165 to converge to that of VEGF121. The mechanism of PlGF2 inhibition is occupying the binding site on NRP1; another possible method for inhibiting the action of NRP1 is the inhibition of coupling without blocking the VEGF binding to NRP1. To further validate the model under the conditions of more complex receptor-ligand interactions, we modeled another phosphorylation experiment involving the differential effect of VEGF121 and VEGF165 isoforms, where the response of bovine retinal endothelial (BRE) cells to the isoforms was measured in vitro in the presence or absence of a NRP1 antibody (31). This antibody is directed at a domain of NRP1 not involved in binding (14, 24, 28); deletion of this domain does not prevent VEGF binding to NRP1 (13). However, the antibody decreases the response of these BRE cells to VEGF165 but not VEGF121 (31). It is possible that the antibody interacting with that domain causes a conformational change or otherwise affects VEGF binding, but if VEGF binding to NRP1 is not impeded, the remaining possibility is an abrogation of coupling (A. L. Kolodkin and D. D. Ginty, personal communication). We thus hypothesize that rather than interfering with binding, the antibody impedes coupling, possibly due to steric interference; the proposed method of action is shown in Fig. 5A. The antibody binds NRP1, and this complex is permissive for VEGF165 binding but not subsequent VEGFR2 coupling. With excess antibody, the system can be simplified to two noninteracting populations of receptors with zero coupling between them.



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  		Fig. 5. NRP1 antibody (Ab) blocks VEGFR2-NRP1 coupling. A: proposed mechanism of action of NRP1 Ab. Other notations are as in Fig. 1A. B, left: predicted VEGF-VEGFR2 complex formation on bovine retinal endothelial cells 5 min after the VEGF addition for VEGF121 (dotted line) and for VEGF165 in the absence (solid line) or presence (dashed line) of NRP1 Ab. Right, predicted decrease in binding of VEGF165 to VEGFR2 due to NRP1 Ab.

 
The VEGF-VEGFR2 formation predicted by the model under these conditions is shown in Fig. 5B. VEGF121 and VEGF165 produced a similar number of VEGFR2 complexes; NRP1 antibody has no effect on VEGF121-VEGFR2 complex formation; and the antibody significantly decreases the VEGFR2 complex formation by VEGF165, all in agreement with experiment (31). The predicted difference between VEGF165- and VEGF121-induced VEGFR2 complex formation is <11%. The experimentally observed decrease in response to NRP1 antibody was 55% at 25 ng/ml (555 pM); the predicted decrease in our model is about 45% (Fig. 5B); this is reasonably good agreement as the gain between growth factor binding and receptor phosphorylation as well as any baseline level of VEGF secretion, both of which might increase the predicted effect of NRP1 antibody, is unknown.

If, instead of blocking coupling, the antibody were blocking binding to NRP1, then the VEGF165 response would converge with that of VEGF121. The fact that it falls further reflects the fact that the NRP1 is acting as a sink for VEGF165, binding but failing to present it to VEGFR2. This suggests that our hypothesis is correct, that this NRP1 antibody blocks coupling rather than binding. Members of the semaphorin family of neuronal guidance cues act by bridging nonsignaling NRPs and signaling plexins. It is possible that the NRP1 antibody could work to block these coupling plexins (and thus affect neuronal growth cone signaling), but there is no experimental evidence for this yet.

Testable predictions of the model. With agreement between the model and published in vitro experiments, we simulated the results of an experiment that has not yet been performed, investigating the dynamics of VEGF isoform binding; this experiment is similar to that shown in Fig. 1B but uses radiolabeled VEGF121 rather than VEGF165. Cold VEGF121 and VEGF165 compete for binding with hot VEGF121 (Fig. 6, left). VEGF165 competes for the binding sites much more effectively than VEGF121 on these PAEVEGFR2 + NRP1 cells. This result is coupling rate dependent. We then added the NRP1 antibody to the simulation, using the mechanism defined earlier; we added 1 µM of an antibody of nanomolar affinity (the binding characteristics of this antibody have not been published). This antibody can interfere with the VEGFR2-NRP1 coupling, and thus we expect its addition to decrease the difference between VEGF165 and VEGF121 in the competition assay; this is what we see (Fig. 6, right). We note also that the addition of the antibody allows us to distinguish between the theoretical coupling rate (Fig. 6, thin solid line) and rates one order higher (dashed-dotted line) or lower (dotted line), thus improving the accuracy of determination of the coupling rate. This approach (competition experiment plus antibody), with a well-characterized NRP1 antibody, would allow more accurate determination of the coupling rate. This could also be done with radiolabeled VEGF165 as in Fig. 1B, but the differences between the coupling rates are not predicted to be as pronounced (data not shown).



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  		Fig. 6. Simulation of VEGF isoform competition experiments. Simulation of competition experiments (similar to Fig. 1B) in which increasing concentrations of cold VEGF165 (thin solid line) and VEGF121 (thick solid line) are added to wells in which 125I-VEGF121 binds to COS-1 cells coexpressing VEGFR2 and NRP1 in the absence (left) or presence (right) of 1 µM NRP1 Ab is shown. Curve for theoretical diffusion-limited coupling rate (solid lines) is indicated; decreasing coupling rates are 10-fold (dotted line), 100-fold (dashed line), and 1,000-fold (dashed-double dotted line) lower. Results for coupling rates 10-fold higher than the diffusion-limited rate are also discernible (dashed-dotted line).

 
Similarly, this antibody may be used to find the binding site populations and affinities for multiple receptor types on the same cell where Scatchard plots are difficult to interpret. For a cell that expresses both VEGFR2 and NRP1, the affinity of VEGF121 or PlGF2 for the receptors may not be a good surrogate for the VEGF165 affinity, and a large quantity of VEGF121 or PlGF2 would be required to compete VEGF165 off one of the receptors (as shown in Fig. 1B) to find the affinity of the other. If, instead, we use the NRP1 antibody, the competition becomes easier, and thus we can combine the antibody and receptor-specific growth factors to find the VEGF165 affinity for individual populations.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 REFERENCES
 
NRPs have been shown to act as coreceptors for semaphorin signaling through plexins on neurons. The discovery of NRP1 as an isoform-specific VEGFR on endothelial cells (36) suggested that they may serve a similar function for blood vessels. Here, we present a model of the mechanism of action of a VEGF isoform, VEGF165, in binding to both NRP1 and the signaling receptor VEGFR2 that explains the resultant increase in VEGFR2 binding, phosphorylation, and signaling. Another isoform, VEGF121, is unable to bind NRP1 but does bind VEGFR2. The observed isoform-specific increases in binding to VEGFR2 and NRP1 are recapitulated by the model, as are the increases in total VEGF binding at low added VEGF concentrations in coculture experiments. Receptor tyrosine kinase autophosphorylation is not modeled explicitly, but using the VEGF-VEGFR2 complex formation as a surrogate marker, the results of phosphorylation experiments are well predicted by the model. NRP1 is shown by the model to be responsible for the differential effects of VEGF165 and VEGF121, as observed in the experiment. The parameters used in the model are derived from experimental literature.

Although we have demonstrated that the observed effects of NRP1-VEGFR2 interactions can be explained by the quantitative effects of coupling alone, it remains possible that NRP1 affects the VEGF-VEGFR2 complex phosphorylation in a qualitative way, perhaps through conformational change, although as NRP1 does not interact directly with VEGFR2 that may be unlikely.

The binding kinetics of VEGF to VEGF receptors have been measured in cell-free experimental studies (8, 18) and can be deduced from cell surface binding studies (5, 25). However, the rate of coupling of surface receptor-bound VEGF to a second surface receptor has not been directly measured. Predictions for a diffusion-limited rate of coupling can be made using theory (11) and can be expressed in compact analytic form (10). The use of a VEGF isoform competition experiment is a novel method for estimating the coupling rate. This is the first experimentally derived estimate of the VEGFR2-NRP1 coupling rate on the cell surface, and, to the best of our knowledge, the first measurement of such a receptor-receptor coupling rate for any system of two distinct receptors. Our results are in agreement with the finding that the experimentally measured coupling rate for Fc receptors on human basophils bridged by covalently linked IgE is close to the diffusion-limited rate (9) and also agree well with the absolute value of the coupling rate measured in that study (see APPENDIX). Note that the method used in that homodimerization system to find the coupling rate would not have worked in this case of heterodimerization; the excess-ligand inhibition of signaling necessary was not observed in the VEGFR2-NRP1 system. In addition, our approach is based on measurement of ligand binding, which is a closer measure of receptor coupling than the measurement of cellular response (histamine release from the basophils) used in that study, as the response is the result of signaling downstream from ligand binding and thus may be several steps removed from receptor coupling.

It should be noted that a thermodynamic cycle exists in our reaction system, i.e., in thermodynamic equilibrium, all the equations are not independent and the result is a constraint on the kinetic coefficients (16). This should have the effect of reducing the number of independent kinetic parameters by one. However, our calculations show that adjustment of the kinetic parameters to fulfill this requirement does not affect the outcome of the simulations, because the coupling rates are very fast. We also investigated whether the coupling rate could be approximated with a constant rather than the receptor concentration-dependent function given in the APPENDIX. The coupling rate function varies by a factor of only 3 over the range of 1–106 unbound receptors (Fig. 7A) and, using any constant value for the coupling rate in this range (9 x 1013–3 x 1014 cm2·mol–1·s–1) gives results that are not significantly different from those presented here, in keeping with our observation that the results are not sensitive to a 10-fold variation in the coupling rate.

We also describe a method, using a NRP1 antibody, of the mechanism of action that we have characterized here, to find the coupling rate with greater accuracy and with a broader range of sensitivity, as the rate may in fact be higher than that found here. How can the actual coupling rate be higher than the diffusion-limited rate? First, the theoretical rate is an approximation based on diffusivities for receptor tyrosine kinases (19), but diffusivity has not been measured for VEGFRs specifically. Second, the calculation assumes that the receptors move throughout the entire cell surface with the same diffusivity. However, VEGFR2 has been shown to form clusters in response to VEGF (1). This clustering can have two opposing effects on the transfer rate: the receptors are closer together, decreasing (locally) the mean distance to a free binding partner; and lipid membrane variation can cause decreased protein diffusivity in these clusters, slowing receptor lateral motion. The experiments described here allow better determination of the coupling rate. We also describe experiments that would allow specific determination of VEGF165 affinities for individual receptors on cells coexpressing VEGFR2 and NRP1.

We have not included ligand-independent association of NRP1 and VEGFR2 in our model. Although such complexes were observed in two transformed cell lines (14, 35, 42), they were not observed in the endothelial cells studied (35, 42), and the difference may be due to autocrine growth factor production or an artifact of overexpression. Additionally, the VEGFR2 phosphorylation in response to VEGF is substantially greater than that in the absence of VEGF (14, 35). The extracellular domains have been shown not to interact directly (12), although this does not preclude the possibility of an association caused by a third membrane molecule (e.g., HSPGs) or by intracellular scaffolding. A mutant NRP1 lacking the VEGF binding site was also unable to block VEGF-induced coupling of wild-type NRP1 and VEGFR2 or VEGFR2 phosphorylation by VEGF on endothelial cells (32), suggesting ligand-induced association is the primary pathway for NRP1-VEGFR2 association.

HSPGs have not been included explicitly in this study; their effect was instead folded into the effective binding rates. The rates were estimated from cell surface experiments that did not remove HSPGs. Loss of HSPGs from the cell surface inhibits both VEGF165 and VEGF121 binding (6), even though VEGF121 is not a heparin-binding isoform. This suggests that the HSPGs may be affecting the receptors rather than the ligands. As just noted, it is possible that one HSPG molecule could bind both VEGFR2 and NRP1 simultaneously, thus increasing the stability of the VEGF165-VEGFR2-NRP1 complex; however, this would also allow ligand-independent receptor coupling formation, which is not seen in endothelial cells.

We have not included VEGFR1 in this study and restricted our simulations to experiments on cells that express little or no VEGFR1. This receptor interacts directly with NRP1, also affecting VEGF165 binding (12). Fewer cell-based studies are available on this interaction, but the interaction must be studied further to build a complete model of VEGF isoform interactions with endothelial cells. For cells with a VEGFR1 concentration significantly less than that of NRP1, e.g., HUVECs, our simulations (data not shown) suggest that the qualitative conclusions of this study remain valid. The sink effect of VEGFR1 would be mitigated by binding to NRP1 and subsequent coupling to VEGFR2. The model can be further expanded by the inclusion of other NRP1, VEGFR1, and VEGFR2 binding partners, including the full-length PlGF2, both isoforms of VEGF-B, and heparin (27–29). Some information is also available on the effect of NRP2 on VEGF binding.

This is the first computational model to include the interactions of VEGF, VEGFR2, and NRP1 explicitly and in biophysical detail. We used the model to find a first estimate for the coupling rate of these two receptors on the cell surface. We have validated this rate and the model against several independent sets of in vitro experiments. Therefore, it provides a quantitative interpretation of these experiments. We also proposed further experiments that, the model suggests, will better elucidate the coupling rate and the affinities of VEGF for its receptors on cells expressing multiple binding site populations. This model will be expanded to include additional ligands and receptors of the VEGF and VEGFR families.

This model simulates in vitro experiments; it has not been shown whether NRP1 uses the same mechanism to increase VEGF binding in vivo, although it is clear from knockout experiments that NRP1 is essential to VEGF signaling. The in vivo situation, where instead of a large initial VEGF concentration, there is a constant secretion and uptake of extracellular ligands by endothelial and parenchymal cells as well as ligand binding to low-affinity receptors on the extracellular matrix, is a logical next step for this analysis. A detailed biophysical model of the growth factor-receptor interactions in vivo would allow us to investigate how a dose of a drug, e.g., an antiangiogenic agent, or perturbation in endogenous secretion or in the microenvironment can result in observed effects.

This model has applications for both proangiogenic and antiangiogenic therapies. The induction of angiogenesis has the potential to ameliorate peripheral vascular disease and coronary ischemia and to improve wound healing. It is also important in tissue engineering to be able to induce blood vessels to vascularize tissue implants. Inhibition of angiogenesis is central to the treatment of cancers as well as other diseases of excessive vascularization, e.g., diabetic retinopathy. Use of models such as the one presented here can lead to increased understanding of the molecular mechanisms of these diseases and therapies as well as aiding clinical translation of this information by determination of effective or therapeutic concentrations of drugs.


   APPENDIX
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
REFERENCES
 
Detailed Methods: Computational Model

Model equations. To simulate the interactions of VEGF family ligands with endothelial cell surface receptors, we constructed a model that reflects the geometry of the in vitro situation where endothelial cells are plated as confluent monolayers in cell culture chambers and bathed in growth factor-containing cell culture medium. Thus, while growth factors diffuse in solution in three dimensions, they bind to receptors restricted to the surface of the cells. We assume that the concentrations of VEGF and its receptors are uniform on and parallel to the surface of the cells, and thus we model in one space dimension only, z, perpendicular to the cell surface. The model explicitly includes the kinetics of all ligand-receptor interactions, which allows us to examine both short-term and long-term behavior of the system. This model builds on our previous simulations of VEGF-VEGFR interactions (26) by adding NRP1 and receptor coupling. The parameters for the model are obtained from experimental literature.

The concentration of cell surface receptors VEGFR2 and NRP1 and the growth factor-receptor complexes they form are governed by the following equations:

(1)

(2)

(3)

(4)

(5)

(6)
The variables and parameters are defined in Table 1. The concentration of growth factor in solution is governed by a reaction-diffusion equation:

(7)

(8)
At the cell surface, the boundary condition is a balance of secretion and binding:

(9)

(10)
At the free surface of the cell culture medium, a reflective (no-flux) boundary condition is applied.


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  		Table 1. Variables used in the model

 
Model solution. The equations were nondimensionalized, discretized according to a fully implicit, centered-space finite difference scheme, and simulated on a personal computer using FORTRAN. The iterations were carried out until a 10–10 fractional accuracy was achieved. An adaptive time step allowed speed up of the computation while maintaining accuracy at early time points.

Model parameters. The diffusivity in aqueous medium of VEGF121 and VEGF165 at 23°C were estimated as 1.05 and 0.94 x 10–6 cm2/s based on their size using a molecular weight correlation (3). Diffusivities are then calculated for each experimental temperature using the Stokes-Einstein equation, e.g., for the typical in vitro experimental conditions (4°C), the aqueous diffusivities of the isoforms are found to be 5.8 and 5.2 x 10–7 cm2/s, respectively, and at 37°C, 1.4 and 1.3 x 10–6 cm2/s.

The number of receptors on the cells and the affinity of VEGF isoforms for these receptors is key to this analysis. VEGF121 is assumed to have zero affinity for NRP1 in all cases and to have the same affinity as VEGF165 for VEGFR2; in individual cases, VEGF121 and VEGF165 have been shown to have binding affinities differing by a factor of two, but not in a consistent direction (21, 42); thus we assume that on average their VEGFR2 affinities are the same.

COS-1 cells express a small number of VEGFRs (42). COS-1 cells transfected with VEGFR2 were reported to express ~13,700 receptors with an affinity for VEGF of 340 pM; cells transfected with NRP1 demonstrate 152,000 receptors with a 2.1 nM affinity (42). We assume that the cells transfected with both receptors have both populations.

PAE cells do not express receptors for VEGF (40). The number of VEGFR2 receptors expressed by PAE cells transfected with this receptor alone shows high variability, possibly due to culture conditions or transfection efficiencies, with published reports of 39,000 and 150,000 receptors/cell (38, 40). The PAE cells used in the experiments modeled in this paper had fewer VEGFR2 per cell than the cells in those reports; it was possible to calculate the number from experiments quantifying VEGF binding to PAE cells transfected to express NRP1 alone (PAENRP1) or VEGFR2 (PAEVEGFR2) alone (35). Approximately 10-fold more VEGF165 bound to PAENRP1 cells than PAEVEGFR2 cells for VEGF in the range of 25–250 pM. With affinities of 320 pM for the 45,000 NRP1 receptors and 760 pM for VEGFR2 (35, 36, 40), the number of VEGFR2 receptors would be 9,000 to give a 10-fold binding increase.

HUVECs are also difficult to characterize; several published reports have estimated the number of receptors from 500–5,840 for the higher affinity population and 5,850–100,000 for the lower affinity, with variation by passage number and other cell effectors (5, 25, 30, 40). For the cells modeled here, 49,500 total VEGF receptors were observed, with an average affinity of 169 pM (42). We discuss the relative numbers of VEGFR2 and NRP1 in RESULTS.

The total number of VEGFRs on BRE cells was reported to be 154,000 (39); of these, the number of NRP1 was shown to be 68,000 after VEGF stimulation (31). The number of VEGFR2 is thus taken to be 86,000 as VEGFR1 were not observed (39).

The surface area of endothelial cells is taken to be 1,000 µm2 (26). The height of the cell culture medium above the cells varies for each experiment but is typically in the range of 1–2.5 mm. For the experiments modeled here, the height was taken to be 2.5 mm.

The off rate for VEGFRs is taken as 10–3 s–1, which appears to be consistent when the rate is estimated from experiments of VEGF binding to cell surface VEGFRs (5, 25) (data not shown); this is a 2- to 10-fold faster rate than that observed for the receptors in cell-free binding assays (8, 18). The experimental estimate for the rate is assumed to be an effective rate including the impact of the presence of HSPGs on the cell surface. For this reason, HSPGs are not included explicitly in the model. As noted in the Introduction, loss of HSPGs from the cell surface inhibits both VEGF165 and VEGF121 binding (6), suggesting that HSPGs may be affecting the receptors rather than the ligands, another argument for these effective binding rates.

The rate of internalization of receptors and complexes at 4°C is taken to be zero. To simulate coculture experiments of cells of two different types (35), internalization is assumed to be nonzero, and a balancing production term maintains the level of VEGF receptors on the cell surface.

Secretion of VEGF from these cells is taken to be zero, as any secretion would be outweighed by the addition of a large quantity of exogenous VEGF. The VEGF concentration in the cell culture medium is assumed to be uniform at the beginning of each simulation (time = 0), but the fluid is not mixed after this, and gradients can develop.

The coupling rate, kc, is the rate at which VEGF-VEGFR2 or VEGF-NRP1 complexes bind unligated NRP1 or VEGFR2 to form the ternary complex VEGF-VEGFR2-NRP1. This rate is not known for VEGFR or other cell surface receptor tyrosine kinases. A theoretical diffusion-limited estimate for the rate is described in Theorectical estimate of VEGFR2-NRP1 coupling rate and shown in Fig. 7. We used this estimate as a reference and examined a range of coupling rates. We estimated the actual coupling rate using experimental data (see RESULTS) and used this to explain the binding and phosphorylation of VEGFR2 by VEGF in the presence of NRP1.

Theoretical estimate of VEGFR2-NRP1 coupling rate. Whereas the binding affinities and kinetic rates of VEGF interactions with receptors are well understood, the rate at which VEGF-VEGFR2 or VEGF-NRP1 complexes interact with free (unbound) receptors on the cell surface to form the ternary complex VEGF-VEGFR2-NRP1 is not known. The diffusion-limited rate for these lateral interactions has been calculated (10, 11). This theoretically predicted rate depends on the lateral diffusivity of the ligand-receptor complex on the cell surface (D), the rate of VEGF-receptor complex dissociation (koff), and the concentration of free receptors available for binding. The predicted coupling rate is shown in Fig. 7A for a D of 2 x 10–10 cm2/s, which is within the range of measured diffusivities for other receptor tyrosine kinases (19). We assume that this diffusivity is the same for both receptors, making the coupling rate symmetrical for VEGF-VEGFR2 and VEGF-NRP1. Although NRP1 is smaller than VEGFR2, other factors including interaction with other membrane molecules will affect the diffusivity of receptors. The result is not sensitive to the kinetic rate of the complex dissociation for values of koff of 10–2, 10–3 and 10–4 s–1 (solid lines). Fitting a power law function of the form kc = a[R]b, where R is the concentration of unbound receptors available for binding (mol/cm2), we find that the coupling rate is well represented by a = 8.1 x 1015 cm2(1+b)·mol–(1+b)·s–1, where b = 0.109 (Fig. 7A, dashed line). This diffusion-limited rate is used as a reference in finding the coupling rate from experimental competition data (see RESULTS). Varying the coupling rate is done by increasing or decreasing the function by a factor of 10 (although this coupling rate is a theoretical upper bound, the true coupling rate may be higher; see DISCUSSION). The power law relation is shown to be a good fit by plotting the coupling rate times the unbound receptor concentration (Fig. 7B). The coupling rate is multiplied by this unbound concentration in Eqs. 1–6. Note that use of a constant value, rather than the power law expression above, for the coupling rate (Fig. 7, dotted lines) results in a significant deviation from the concentration-dependent rate at low free receptor levels.

The predicted coupling rate is less than that predicted by the collision coupling method (33), which, when converted to equivalent units, would be 9.6 x 1014 cm2·mol–1·s–1. The coupling rate has been experimentally measured for the binding of covalently linked IgE dimers to two Fc receptors on human basophils: 3 x 1014 cm2·mol–1·s–1 in equivalent units (9). This is entirely consistent with the predictions here for diffusion-limited coupling.


   ACKNOWLEDGMENTS
 
The authors thank Drs. Patricia A. D'Amore, Michael Klagsbrun, Shay Soker, Hitoshi Takagi, Alex L. Kolodkin, and David D. Ginty for helpful discussions on VEGF and neuropilins and specific in vitro experiments. We also thank Dr. Kameran Lashkari, who suggested the simulation in Fig. 6.


   FOOTNOTES
 

Address for reprint requests and other correspondence: F. Mac Gabhann, Dept. of Biomedical Engineering, Johns Hopkins Univ. School of Medicine, 720 Rutland Ave., #611 Traylor, Baltimore, MD 21205 (E-mail: feilim{at}jhu.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


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