Discovery of High-Affinity PDGF-VEGFR Interactions: Redefining RTK Dynamics

Nearly all studies of angiogenesis have focused on uni-family ligand-receptor binding, e.g., VEGFs bind to VEGF receptors, PDGFs bind to PDGF receptors, etc. The discovery of VEGF-PDGFRs binding challenges this paradigm and calls for investigation of other ligand-receptor binding possibilities. We utilized surface plasmon resonance to identify and measure PDGF-to-VEGFR binding rates, establishing cut-offs for binding and non-binding interactions. We quantified the kinetics of the recent VEGF-A:PDGFRβ interaction for the first time with KD = 340 pM. We discovered new PDGF:VEGFR2 interactions with PDGF-AA:R2 KD = 530 nM, PDGF-AB:R2 KD = 110 pM, PDGF-BB:R2 KD = 40 nM, and PDGF-CC:R2 KD = 70 pM. We computationally predict that cross-family PDGF binding could contribute up to 96% of VEGFR2 ligation in healthy conditions and in cancer. Together the identification, quantification, and simulation of these novel cross-family interactions posits new mechanisms for understanding anti-angiogenic drug resistance and presents an expanded role of growth factor signaling with significance in health and disease.


Results
Validation of SPR protocol. We measured the kinetic rate constants between PDGF ligands and VEGF receptors using a surface plasmon resonance (SPR) assay. We injected the ligands at 40, 20 and 10 nM (process summarized in Fig. 2) and fit their association and dissociation curves using a 1:1 Langmuir binding model. To measure the accuracy of our kinetic analyses we applied a χ 2 -to-R max ratio heuristic. For known interactions, a χ 2 -to-R max value < 0.20, represents a well-established filter for high-quality fitting of kinetic parameters obtained via SPR [34][35][36] . The χ 2 -to-R max ratio can be helpful in detecting new 1:1 binding interactions, because this value describes how well the obtained sensogram curves fit a 1:1 Langmuir interaction model. When the fitting noise  Surface plasmon resonance (SPR) workflow. Using a dextran-coated gold (CM5)-type sensor chip, SPR is performed as follows: (I) Carboxymethyl groups on the sensor surface are activated with NHS:EDC, enabling (II) amine-coupling between target (receptor or reference protein, Ang-4) and the dextran matrix semi-permanently. Such binding allows multiple kinetic cycles to be performed without requiring remobilization of the target. In a kinetic study cycle, (III) ligand is injected across the bound target; called the association phase, binding events are sensed and detected in real-time. (IV) Next running buffer (HBS-EP) alone is injected. In this dissociation phase, the instrument detects only the dissociation of ligand from the target. (V) A regeneration solution is injected to clear any remaining bound ligands before another kinetic study is performed.
SCIentIfIC RepoRtS | 7:16439 | DOI: 10.1038/s41598-017-16610-z (χ 2 ) exceeds the maximal response (R max ), the interaction cannot be said to follow the binding model. We therefore introduce a heuristic where a χ 2 -to-R max ratio ≤ 1.0 is attributed to "true" interactions, and those >1.0 are described as non-1:1 Langmuir interactions resulting from non-specific binding.
To validate the χ 2 -to-R max cut-off approach, we examined ligand:receptor pairs known to bind and non-interactions (i.e. pairs known not to bind). The χ 2 -to-R max cut-off approach correctly identified well-established VEGF:VEGFR and PDGF:PDGFR ligand:receptor pairs as real interactions (χ 2 -to-R max < 1.0), and accurately excluded those known to not interact (χ 2 -to-R max > 1.0). Specifically, VEGF-A:VEGFR1 and VEGFR2, PDGF-AA:PDGFRa, PDGF-AB:PDGFRα, PDGF-BB:PDGFRs, and PDGF-CC:PDGFRa were correctly designated as real interactions, with χ 2 -to-R max < 1.0 for each (Supplementary Table S1). The following known non-binding pairs were correctly excluded: VEGF-A:VEGFR3 37 and PDGF-AA:PDGFRβ 38 , with χ 2 -to-R max ratios 6.0-and 8.6-fold larger than the cut-off. The validation of the heuristic across 7 ligand:receptor pairs of the VEGFR and PDGFR families offers strong support for its extension to cross-family interactions within these families ( Fig. 1 and Supplementary Table S1).
We further validated our experimental approach by reproducing previously measured binding affinities. The VEGF-A:VEGFR1 and VEGF-A:VEGFR2 binding affinities (Fig. 3A and Supplementary Table S2) were both within an order of magnitude of previous SPR measurements, K D = 1 pM (Fig. 3A) versus a previous measured K D = 7.5 pM 39 , and K D = 9.8 pM (Fig. 3B.) versus 52 pM 40 , respectively.
Establishing kinetic and affinity constants for canonical PDGF:PDGFR interactions. We confirmed that the canonical understanding of PDGF:PDGFR holds (Fig. 1). More specifically, PDGF-AA binds only to PDGFRα (Fig. 4A,B) 41 ; both PDGFRs bind PDGF-AB (Fig. 4C,D) 42 , -BB (Fig. 4E,F) 43 , and -CC (Fig. 4G,H) 44 ; and PDGF-DD binds only to PDGFRβ (Fig. 4I,J) 42 . We then compared the obtained affinities, when possible, to previously reported affinities. Currently only PDGF-AA and -BB:PDGFR interactions have been reported via a study that did not use a reference protein cell (Supplementary Table S3). As described in the Materials and Methods, we used to reference protein to measure and account for non-specific binding effects that would affect our kinetics. All binding affinities values are listed exactly in Supplementary Table S2. We measured a PDGF-AA:PDGFRα affinity of the same order of magnitude as previously reported (measured K D = 660 nM versus prior 134 nM 45 ). We determined that PDGF-BB binds both PDGFRα and PDGFRβ with similar affinities K D = 420 nM and 830 nM, respectively. While these measured affinities were lower than a previous report (K D = 150 nM and 1.6 nM for PDGFRα and PDGFRβ, respectively) these previous studies did not use a reference protein 45 . We believe that this difference is critical: without a reference protein, these prior studies measure a weaker binding affinity due to an inflated non-specific binding reference measurement. Furthermore, the relative strength of binding -BB:Rα > -BB:Rβ, is observed in both our study and the work of others.
We also characterized the binding rates and affinities for the canonical PDGF:PDGFR interactions lacking kinetic data (-AB, -CC, -DD:Rα and -AB, -CC, -DD:Rβ). We observed that PDGF-AB:PDGFRα binding affinity was ~2.6x stronger than PDGF-AB:PDGFRβ, with affinity constants of K D = 840 nM versus K d = 2,200 nM, respectively (Fig. 5A).We measured strong affinities between PDGF-CC:PDGFRα and PDGF-CC:PDGFRβ with K D = 3.4 nM and 1.9 nM, (Fig. 5A) Finally, we observed that PDGF-DD binds PDGFRβ with moderate affinity, K D = 67 nM (Fig. 5A). PDGF-DD:PDGFRβ has a 50-fold larger peak association response than its binding to PDGFRα, but its kinetic fitting for this interaction produced a χ 2 -to-R max of 2.2 (Supplementary Table S1). But since it is >1.0, it displays high noise to signal, which we interpret as not true 1:1 Langmuir interactions.
Novel cross-family PDGF:VEGFR2 interactions. We identified novel interactions between PDGF-AA, -AB, -BB, and -CC with VEGFR2 ( Fig. 6A-D, respectively). These interactions all exhibited classic signal responses, characterized by a steady signal increase upon ligand injection, association-phase, followed by a steady signal decrease during buffer injection, dissociation-phase (Fig. 6). We show examples of this in PDGF:PDGFR binding (Fig. 5), and all were all found to have χ 2 -to-R max < 1.0, indicating true 1:1 Langmuir interactions (Supplementary Table S1.) There was no evidence of PDGF interactions with VEGFR1 or VEGFR3 ( Supplementary Fig. S1). A summary of the novel interactions identified can be found in Fig. 7. When we quantified kinetic binding rates (k a and k d ) and affinity constants (K D = k d /k a ), we observed that PDGF-CC:VEGFR2 had an affinity constant of the same order of magnitude as native VEGF-A:VEGFR2 binding with K D (-CC:R2) 70 pM versus (VEGF-A:R2) ~10 pM. The other PDGFs presented VEGFR2 binding affinities with decreasing strength as follows: PDGF-AB > -BB > -AA. Another notable finding was that PDGF-CC bound VEGFR2 at an affinity greater than or equal its binding to either PDGFR (Fig. 5A). PDGF-AA:VEGFR2 was a higher affinity, but similar order of magnitude as PDGF-AA:PDGFRα binding, K D (-AA:R2) = 100 nM, vs. (-AA:Rα) = 660 nM. PDGF-AB:VEGFR2 binding was higher affinity than its binding to PDGF-AB:PDGFRs with K D (-AB:R2) = 110 pM vs. (AB:PDGFRs) >800 nM. Additionally, PDGF-BB:VEGFR2 binding was higher affinity than its binding to PDGFRs, K D (-BB:R2) = 37 nM vs. (-BB:PDGFRs) >400 nM (Fig. 5A). The exact values obtained for binding affinities can be found listed in Supplementary Table S2.
Association and dissociation rate constants reveal affinity trends. The affinity of the PDGF:VEGFR2 is best understood by examining the association and dissociation rate constants. Here we observe that the high-VEGF:VEGFR2 affinity is attributed to fast association, ~10 6 M −1 s −1 (Fig. 5B), and slow dissociation, ~1 day −1 (Fig. 5C.) Only the PDGF-CC:PDGFRβ association nears these VEGF-A:VEGFR2 association    dynamics, which supports its high-affinity binding to PDGFRβ (Fig. 5A). All other association dynamics are <~10 5 M −1 s −1 . The slow VEGF:VEGFR2 dissociation rate constant is exceeded by PDGF-AB:VEGFR2, ~1/7 days (i.e. dissociating on average once per week), explaining its ~100 pM binding affinity (Fig. 5A). All other dissociation rate constants are "faster"-i.e. higher values-in the range 1/minutes and 1/hours (i.e. one molecule dissociates on average per minute and per hour, approximately). (The exact values obtained for association and dissociation rate constants can be found listed in Supplementary Table S2.)

Model construction and validation.
To predict the significance of PDGF-VEGFR2 cross-family binding, we derived the ordinary differential equations describing these ligand-receptor interactions based on the law of mass action. Klipp et al. and Linderman & Lauffenburger offer comprehensive explanation of this approach for representing protein-protein interactions [46][47][48][49][50] . Towards this goal, we simulated two sets of models governing VEGFR ligation: one describing the canonical, uni-family VEGF-A:VEGFR binding and one describing cross-family binding that includes both the canonical uni-family VEGF:VEGFR and our newly derived cross-family PDGF:VEGFR2 binding (PDGF-AA, -AB, & -BB with VEGFR2) (see model schematic Fig. 8). We do not include PDGF-CC in the model because PDGF-CC has not been found to be expressed in humans under healthy or cancer conditions, but is instead observed following a an ischemic event like a stroke or myocardial infarction 51 . We recapitulated the benchmark, uni-family VEGF-A:VEGFR model by Mac Gabhann 52 , showing consistent VEGFR1 and VEGFR2 fractional occupancies (Fig. 9A) and maximal responses (Fig. 9B).
We analyzed these two models for ligand concentrations found in healthy physiology, breast cancer, and anti-VEGF-A therapy in breast cancer. Bevacizumab is used as the basis of the anti-VEGF-A treatment, implemented as a binding interaction between bevacizumab and non-receptor-bound VEGF-A. Model equations and parameters are listed in full in Supplementary Files 1 and Supplementary Table S4, respectively.
Localized PDGF cross-family binding enhances VEGFR2 activation in health and cancer. We predict increased VEGFR2 complex formation in every case where PDGF:VEGFR2 cross-family interactions are considered. First, the cross-family model in comparison to the uni-family model predicts a 14-fold increase in VEGFR2 ligation under healthy physiology (Fig. 10A). Similarly, the cross-family model predicts a 15-fold increase in VEGFR2 ligation in breast cancer xenograft-derived endothelial cells over the canonical, uni-family framework (Fig. 10A). Also, we observe that an anti-VEGF drug, like bevacizumab, would only contribute a ~5% decrease in VEGFR2 ligation when cross-family binding is considered in breast cancer xenograft-derived endothelial cells (Fig. 10A). Therefore, we predict that cross-family interactions may allow VEGFR2 complex formation to remain relatively unchanged when bevacizumab is administered, despite the fact that PDGFs bind VEGFR2 with affinities ~2 orders of magnitude weaker than VEGF-A (Fig. 10A).
The increased VEGFR2 ligation that we predict under a cross-family paradigm is attributed to the 10-100-fold higher PDGF to VEGF concentrations in serum under healthy physiological conditions. Indeed, we have included a meta-analysis comparing serum concentrations of VEGF-A and PDGFs across healthy and pathological conditions to contextualize these differences (Fig. 11). Such high PDGF concentrations may subsequently enable PDGFs to account for up to ~96% of VEGFR2 ligation under healthy conditions (Fig. 10B). Similarly, breast cancer patient serum is measured to have 25-to-40-fold higher PDGF levels than VEGF (Fig. 10A), so when considering VEGF-A and PDGFs, we predict up to 90% steady state ligation by PDGFs in breast cancer and nearly 100% ligation by PDGFs under conditions of anti-VEGF therapy (Fig. 10B). Our model suggests that this buffering of angiogenic signaling during anti-VEGF therapy may be mediated as follows: PDGF-AB >PDGF-AA >PDGF-BB >VEGF-A (Fig. 10B).
As previously described, we do not include PDGF-CC in the model given its limited expression pattern (e.g., ischemic event) 51 . However, we expect that PDGF-CC:VEGFR2 will dominate VEGFR2 ligation following ischemic damage for two reasons: (1) after ischemic injury PDGF-CC has a 150-300 fold greater serum concentration than VEGF-A (Fig. 11), and (2) PDGF-CC has similar, high-affinity (~100 pM) VEGFR2 binding as canonical VEGF-A:VEGFR2. Furthermore, we predict that PDGF-CC:VEGFR2 ligation would dominate whenever PDGF-CC serum concentrations are 2-fold greater than VEGF-A. We can extend a similar analysis to the other PDGF ligands. Our meta-analysis of PDGF and VEGF serum concentrations would also suggest that in every case where any PDGF serum concentration is at least 25-fold greater than VEGF, then PDGF:VEGFR2 ligation should significantly modulate VEGFR2 signaling. This would include in cancer, post-stroke, and during exercise (Fig. 11).

Discussion
In this study, we established a χ 2 -to-R max cut-off (where values are < 1.0) for distinguishing non-binding and binding interactions, which we used in the discovery of new PDGF-VEGFR interactions: (1) PDGF-AA to VEGFR2, (2) PDGF-AB to VEGFR2, (3) PDGF-BB to VEGFR2, and (4) PDGF-CC to VEGFR2 (summarized in Fig. 7). We measured both the kinetics of these new interactions; and for the first time, we measured the kinetics for VEGF-A:PDGFRβ 27 binding. In a cross-family signaling system, where several ligands compete to bind with the same receptor, the ligand concentrations and ligand-receptor binding kinetics determine which ligand(s) dominate signaling. Therefore, our computational analysis provided quantitative evidence that PDGF:VEGFR2, cross-family binding should significantly participate in VEGFR2 ligation under conditions of health physiology, breast cancer, and pathologies where PDGFs significantly outnumber VEGFs. Furthermore, our modeling offers predictions on how PDGF:VEGFR2 interactions may sustain VEGFR2 ligation when VEGF-A is inhibited (e.g., bevacizumab, ziv-aflibercept). Together these findings offer new insight into several fields of research, including anti-angiogenic drug development and cancer, which we contextualize herein.

Cross-family interactions may shed new light on anti-angiogenic drug development.
Our discovery of cross-family interactions can advance anti-angiogenic drug development, which is currently guided by a uni-family view 53,54 . Anti-VEGF success has been limited, due to both intrinsic resistance and acquired resistance (relapse) 55 . Several mechanisms have been proposed to explain anti-VEGF resistance, a few include: (1) Increased mural cells: some tumors resist anti-angiogenic drug treatment via increased pericyte coverage of tumor vessels 55,56 , providing a permeability barrier to anti-VEGF therapy. (2) Increased tumor invasiveness: tumor undergoes enhanced metastasis into healthy tissue as a means of co-opting existing vasculature 57 ; thereby seeking to avoid hypoxia or nutrient deprivation and bypassing anti-VEGF therapy. (3) Ancillary growth factors: some tumors secrete additional growth factors, such as PDGFs and fibroblast growth factors 55 , which enable ancillary angiogenic signaling axes to bypass anti-VEGF therapy. The latter mechanism may be supported by our findings if PDGF:VEGFR2 complexes lead to VEGFR2 activation and angiogenic signaling. Therefore, future work should determine how PDGF:VEGFR2 ligation regulates native VEGFR2 signaling.
Cross-family signaling may also aid our understanding of multi-target small molecule inhibitors, like sorafenib and sunitinib. Sorafenib inhibits VEGFR2, VEGFR3 and PDGFRβ 33 , while sunitinib inhibits PDGFRβ and all VEGFRs 58 . When viewed through the uni-family signaling lens, these small molecules would only inhibit uni-family interactions, i.e. blocking PDGFR autophosphorylation would render PDGF ligands as non-functional. This perspective does not explain why patients also relapse on these cross-family anti-angiogenic drugs. Under a cross-family paradigm, blocking VEGFR and PDGFR would shift VEGF and PDGF binding to receptors of other signaling families. Some possibilities could be other, structurally similar tyrosine kinase receptors with angiogenic function, such as: nerve, fibroblast, and transforming growth factor receptors 59-61 . Our work suggests that drug resistance to multi-target therapeutics can be better informed and overcome by identifying the extent of cross-family binding.

The tip of the iceberg? Structural analysis can guide further cross-family discovery. Our results
open the possibility that that other cross-family interactions exist, but remain undiscovered. Experimentally screening for interactions between every known cytokine with every known receptor would be cost-and time-prohibitive. Instead, structural analysis of shared ligand and receptor structural motifs can guide further discovery. For example, VEGFRs and PDGFRs are tyrosine kinase receptors: PDGFRs have 5 extracellular immunoglobulin-like (IgG-like) domains 62   Domains 2-3 are highly-conserved within PDGFRs, where they play an identical role of housing the PDGF binding site. The common ligand-binding domains suggests that PDGFs could utilize these sites to bind VEGFRs. Moreover, VEGF and PDGF are similar in quaternary structure: VEGF and PDGF have only a 1.93 Å root mean square difference between overlapping structures 66 (Fig. 1B). VEGFs and PDGFs also share structural motifs in their receptor-binding regions 63 . In fact, PDGF ligands have been superimposed within the VEGF-A:VEGFR2 binding domains, illuminating the possible confirmations for the interactions we report 29 . Additionally, VEGFRs and PDGFRs have a similar intracellular structure: having an intracellular split tyrosine-kinase domain 67,68 . Such a feature may lend the possibility of agonist or partial agonist action via cross-family binding.
Cysteine knot ligands 66,69 with some of these VEGF-PDGF structural properties should also be investigated; these include: nerve growth factors, fibroblast growth factors, transforming growth factors, and even glycoprotein hormones, due to their structural similarity to PDGF 66 . Examining other receptors that exhibit multi-ligand binding would offer a good template for understanding the possibilities in cross-family binding. For example, early work by Pennock et al. explored whether VEGF-A served as a cross-family agonist or antagonist for the PDGF receptors, finding the ligand acted antagonistically 70 . Outside the VEGFs and PDGFs, the nicotinic acetylcholine receptor is well known for having several possibilities for receptor assembly, and several molecules, other than nicotine that can bind with agonist-partial agonist-antagonist affect (e.g., epibatidine, choline, etc.) 71 . The transforming growth factor-β superfamily also offers a good template to examine multi-binding interactions, where extensive cross-family ligand:receptor binding between the subgroups, transforming growth factor-βs, bone morphogenetic proteins (BMPs), growth and differentiation factors (GDFs) and the activin/inhibins 72 are responsible for maintaining a complicated regulatory network 73 . Structural analysis, therefore, can enable a focused screening of likely cross-family binding partners.

Computational modeling will drive conceptual understanding of cross-family signaling.
Computational modeling has provided new insight into the uni-family activation of several growth factor-receptor families, including EGF 74 , FGF 75 , PDGF 76 , and VEGF 3,50,77-81 . Here, our PDGF-VEGFR2 modeling and analysis predicted conditions where PDGF-VEGFR2 binding prevails, which included normal physiological conditions. While we do find the high-affinity of these cross-family interactions surprising, we do not find the modeling results to be surprising. It follows that when incorporating a new population of ligands-at concentrations higher than VEGF-A, and which bind the same receptor at affinities either slightly lower or similar to VEGF-A-the receptor would be substantially ligated by these new ligands. We expect that these patterns of ligated-receptor dominance could change when different healthy biological conditions are considered, such as when receptor trafficking rates are altered by changes in blood flowrate-induced sheer stresses 82 . As we continue exploring this new paradigm, additional models will need to determine how cross-family receptor occupancy translates to various receptor activation landscapes. An elegant computational framework for examining the possible receptor landscapes is the recent work on how bone morphogenetic proteins (BMP) and their receptors achieve multiple activation profiles 83 . We expect that further computational modeling of cross-family signaling will enable a similar understanding of receptor activation landscapes (full-agonist, partial-agonist, partial antagonist, and full-antagonist), receptor activation dynamics (fast/burst, slow/sustained, etc.), and effector efficiencies.
Another computational approach that should be enlisted for understanding maximal canonical signaling is the recent "meta-model" from our laboratory, which modeled receptor activation across eight, canonical ligand-receptor pairs 84 . This meta-model offered ranked predictions of receptor signaling, based on the integrated receptor activation response: PDGFRβ >IGFR1 >EGFR >PDGFRα >VEGFR1 >VEGFR2 >Tie2 >FGFR1. Because these receptors activate similar second messengers, this ranking of canonical (uni-axis) signaling provided the first guide for manipulating signaling in cells carrying combinations of these receptors. We envision that a multi-family model that incorporates the foundational model we present here, signaling landscapes 83 , and growth factor receptor hierarchy 84 will offer novel predictions for maximally tuning signaling. Furthermore, we will test more conditions than are accessible by experiment to understand the multiple cross-family signaling permutations.
Future studies: Filtering novel interactions via the χ 2 -to-R max heuristic. Once structural analysis predicts additional cross-family partners, validation can use a similar SPR approach, as we established here. Towards such goals, researchers may apply the χ 2 -to-R max ratio that we discuss to designate "true" interactions from non-specific, non-1:1 Langmuir interactions. Indeed, SPR can often produce large response curves that suggest binding, even where no interaction exists. Such curves are primarily due to two types of non-specific binding: (1) sensor-ligand interactions 85 and (2) receptor-ligand interactions 86 . The former can be corrected by coating a flow cell with a non-binding reference protein. Without the use of a reference protein, non-specific effects would artificially inflate the observed binding affinity strength (lower K D ). For this study we used angiopoietin-4 as a reference (see Materials and Methods); thus minimizing non-specific interactions between ligand and chip. However, previous SPR measurements of PDGF:PDGFR interactions, did not use a reference protein 45 . We believe this critical difference explains our different affinities, with prior studies measuring a weaker binding affinity. Non-specific ligand-receptor interactions can also be accounted for when you consider that such interactions would not likely follow a 1:1 Langmuir binding model. This is due to the fact that many non-specific interactions are mediated by transient electrostatic attractions between amino acid residues on the ligand and receptor. These transiently-interacting residues can be distributed throughout both proteins-are therefore not site-specific-and should not follow a 1:1 interaction pattern [86][87][88] indicated by the χ 2 -to-R max ratio. Future measurements of cross-family binding should apply our finding that χ 2 -to-R max ratio >1.0 is attributed to non-specific binding.

Conclusion
These studies offer new interpretations of tyrosine kinase receptor signaling: a cross-family paradigm. We provide standards for kinetic analyses of novel interactions with broad implications for tyrosine kinase receptor signaling. Through computational modeling, we further predict that cross-family interactions may significantly alter signaling. From these results, we propose a new mechanism for anti-angiogenic drug resistance, which may aid drug development.
In addition to the applications of this work for tumor angiogenesis, PDGF-VEGF cross-family signaling should affect our understanding of cardiovascular-dependent diseases, governed by angiogenic signaling, including: wound healing 13 , exercise 89 , and other cardiovascular pathologies 6,90 . Moreover, it should enable improved vascularization in the areas of tissue engineering and regenerative medicine 89,[91][92][93] .
Finally, our work suggests that structural similarities in signaling ligands and receptors could indicate cross-family binding patterns and that this phenomenon could be common across cell signaling (e.g., agonist/ partial agonist paradigm). These and any new interactions can and should be illuminated through structural analysis and computational modeling.

Materials and Methods
Surface plasmon resonance (SPR). All SPR studies were performed with the BIAcore 3000 instrument  Table S6), as follows: 20 µg/mL receptor + 10 mM acetate buffers ranging from pH 3.5 to 0.5-1.0 below the protein isoelectric point (Supplementary Table S6) were prepared. Known receptor-ligand was introduced at 5 µL/min (association), followed by 5-µL injection of ethanolamine-HCL (GE Healthcare AB, Uppsala, Sweden) to clear the surface. We selected the optimal acetate buffer pH for each protein based on (1) the maximum level of protein immobilization reached and (2) the rate of immobilization observed in the pre-concentration study sensograms. Ligand-receptor association and dissociation kinetics. Fresh ligand solutions were prepared at 40, 20 and 10 nM in HBS-EP running buffer each experimental day, including: human recombinant VEGFA (R&D Systems, Cat. #293-VE-010), PDGF-AA (Cat. #221-AA-050), -AB (Cat. #222-AB-050), -BB (Cat. #220-BB-050), -CC (Cat. #1687-CC-025) and -DD (Cat. #1159-SB-025) (Note: All ligands were obtained from R&D Systems, and were human recombinant proteins). 120 μL of each ligand solution was injected into flow cells containing immobilized receptor and Ang-4-a reference for non-specific binding-at 30 μL/min (association). This was followed by a 10 min running-buffer injection (dissociation). Between each sample, we injected, in series, 5 μL of 5 mM HCl and 5 μL of 10 mM NaOH at 5 μL/min to remove any remaining bound ligand. We repeated this cycle for each concentration tested (40,20, and 10 nM, summarized in Fig. 2). Each concentration series were performed in triplicate.
Kinetic analysis. The raw ligand:receptor sensograms were aligned and the background, non-specific binding was subtracted using the sensogram trace from the ligand:Ang-4 flow cell (Supplementary Figure S3). Both the raw ligand:receptor and ligand:Ang-4 sensogram curves were obtained within the BIAcore 3000's detection window (10-70,000 R.U.) for all interactions 94 to ensure detected interactions did not represent system noise. Post-subtraction sensograms with a negative-sloped association phase were excluded from global kinetic fitting and not considered interactions. BIAevaluation removes momentary signal spikes resulting from transient air bubbles.
Global analysis is considered to produce more accurate results than fitting of a single response curve, so global fitting was performed with BIAevaluation software (Version 4.1.1, GE Healthcare), which follows 1:1 Langmuir adsorption isotherm (Equation 1) 95 . The software applies nonlinear least squares analysis to determine association (k a ) and dissociation (k d ) rates fitting best to multiple response curves simultaneously. Additionally, the software provides the goodness-of-fit parameter χ 2 and the peak magnitude of the signal response, R max .
SCIentIfIC RepoRtS | 7:16439 | DOI:10.1038/s41598-017-16610-z Classifying binding. Both the instrument manufacturer (BIAcore) and previous researchers have suggested that when fitting kinetic rate constants using global analysis, a χ 2 -to-R max value (a measure of noise-to-signal) < 0.2 is ideal for confidence in the kinetic parameters obtained when studying known interactions 35,36,96 . A low noise-to-signal indicates that the sensogram signal includes minimal contributions from the following three noise-factors: (1) overall instrument noise, (2) heterogeneities in immobilized receptor or ligand, and (3) non-specific interactions. Using ligand:receptor pairs with known interactions and pairs known not to interact, we established a cut-off value of χ 2 -to-R max < 1.0 that differentiates real, 1:1 Langmuir interactions, from predominantly non-specific interactions, where χ 2 -to-R max > 1.0. We arrived at this via experimentally fitting known interactions and non-interactions (Supplementary Table S1). We then applied the χ 2 -to-R max < 1.0 heuristic to classifying the interactions observed in PDGF:VEGFR binding.
Single-cell model of membrane receptor activation. We recapitulated the uni-family (VEGF:VEGFR)  Table S5). (6) Benchmark kinetic and concentration parameters are used only to recapitulate the benchmark. (7) The cross-family model applied updated kinetic parameters via SPR studies herein, (Supplementary Table S2) and updated VEGFR concentrations, which were based on recent quantitative flow (qFlow) cytometry measurements [99][100][101][102] . All model parameters, their descriptions, and their values are provided in Supplementary Table S4. We modeled anti-angiogenic drug treatment by incorporating the anti-VEGF-A antibody, bevacizumab. In the model, bevacizumab reversibly binds free VEGF-A, with kinetic constants previously-determined via SPR 103 . Drug treatment was modeled as a single, initial bevacizumab dose. The dose concentration used was adopted from an earlier VEGF computational model that based the dosage on patient plasma concentrations following the administration of bevacizumab in advanced cancer treatment 104,105 . Thus, this value correlates with the systemic level of bevacizumab. We excluded bevacizumab clearance and 'secretion' (the movement of bevacizumab from plasma into the area around endothelial cells), to examine the concentrations individual endothelial cells would experience.
Data availability Statement. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.