A multiscale computational model predicts distribution of anti-angiogenic isoform VEGF165b in peripheral arterial disease in human and mouse

Angiogenesis is the growth of new blood vessels from pre-existing microvessels. Peripheral arterial disease (PAD) is caused by atherosclerosis that results in ischemia mostly in the lower extremities. Clinical trials including VEGF-A administration for therapeutic angiogenesis have not been successful. The existence of anti-angiogenic isoform (VEGF165b) in PAD muscle tissues is a potential cause for the failure of therapeutic angiogenesis. Experimental measurements show that in PAD human muscle biopsies the VEGF165b isoform is at least as abundant if not greater than the VEGF165a isoform. We constructed three-compartment models describing VEGF isoforms and receptors, in human and mouse, to make predictions on the secretion rate of VEGF165b and the distribution of various isoforms throughout the body based on the experimental data. The computational results are consistent with the data showing that in PAD calf muscles secrete mostly VEGF165b over total VEGF. In the PAD calf compartment of human and mouse models, most VEGF165a and VEGF165b are bound to the extracellular matrix. VEGF receptors VEGFR1, VEGFR2 and Neuropilin-1 (NRP1) are mostly in ‘Free State’. This study provides a computational model of VEGF165b in PAD supported by experimental measurements of VEGF165b in human and mouse, which gives insight of VEGF165b in therapeutic angiogenesis and VEGF distribution in human and mouse PAD model.

VEGFR2 activation that cannot induce torsional rotation required for autophosphorylation and downstream signaling. Hence, the balance between VEGF 165a and VEGF 165b levels may play a crucial role in promoting angiogenesis especially in ischemic cardiovascular diseases such as peripheral arterial disease (PAD) or coronary artery disease (CAD).
PAD is caused by atherosclerosis, which results in ischemia most frequently in the lower extremities. Clinical trials including exogenous VEGF-A administration to activate VEGFR2 dependent therapeutic angiogenesis were not successful. While suboptimal delivery or dosage might be the contributing factors, induction of VEGF 165b in ischemic muscle could compete with pro-angiogenic VEGF 165a isoform for binding sites on VEGFR2 to decrease VEGFR2 activation. The mechanism of VEGF 165b binding to VEGFR2 suggests the potential reason for the failure of therapeutic angiogenesis in VEGF-A clinical trials. Currently, the balance between VEGF 165b and VEGF 165a isoforms that can modulate VEGFR2 activation and angiogenic signaling in the ischemic skeletal muscle of PAD patients is not fully understood.
We have previously reported experimental evidence that VEGF 165b levels are significantly higher in biopsies of PAD patients 3 . Kikuchi et al. measured the ratios of VEGF 165b versus VEGF 165a in serum (by western blot analysis) and peripheral blood mononuclear cells (PBMCs, by mRNA) in PAD patients, which are 4:1 and 8:1, respectively 4 . Currently there is no study measuring the ratio of VEGF 165b and VEGF 165a in the calf muscles to correlate with VEGFR2 activation in PAD patients. Besides, the understanding of the secretion rates of VEGF 165b in different compartments such as diseased calf muscles, blood and normal tissues (all tissues and organs except the diseased calf) is currently lacking. In this study, we expand the previously developed three-compartment models 5,6 to predict the concentration of VEGF 165b and VEGF 165a in PAD patients. We also report the experimental measurements of the expression level of VEGF 165b and VEGF 164a in experimental PAD non-ischemic and ischemic muscle samples in mice with hindlimb ischemia to support our computational models.

Results
In this study, we use both experimental and computational approaches to predict the secretion rate of VEGF 165b and receptor occupancy of VEGFR1 and VEGFR2 in PAD. In practice, it is not possible to measure the secretion rates of VEGF in different tissues in vivo. These important physiological parameters could be only estimated or calculated from the model. This is the first computational model to investigate and account for the experimental ratios of VEGF 165b and total VEGF 165 in human PAD muscle biopsies. The predominance of VEGF 165b in human muscles provides the potential mechanism why the clinical trials of VEGF therapeutic angiogenesis  have failed. Based on the measurement of ratio of VEGF 165b and total VEGF 165 in muscle biopsies, we use the three-compartment model to predict the secretion rates of VEGF 165b in different tissues. This model enables prediction of receptor occupancy with VEGF 165b and other isoforms in human and mouse.
Specificity and sensitivity of VEGF-A and VEGF 165b antibodies. VEGF-A ELISA detected both recombinant VEGF 165a and VEGF 165b with equal sensitivity and specificity. This result indicates that the actual  The results show that VEGF 165a in the disease compartment and VEGF 165b in the blood compartment are more sensitive to VEGFR2 than VEGFR1, whereas VEGF 121 in the disease and blood compartment is sensitive to both VEGFR1 and VEGFR2. VEGF 165a , VEGF 165b , VEGF 121 are not sensitive to NRP1. The sensitivity analysis demonstrates the importance of VEGF 165b -VEGFR2 binding.
Scientific RepoRts | 6:37030 | DOI: 10.1038/srep37030 measurement of pro-angiogenic VEGF-A by VEGF-A antibodies have been overestimated due to its cross reactivity with anti-angiogenic VEGF 165b isoforms. However, VEGF 165b antibody raised against the unique 6 amino acid sequence (SLTRKD) used in ELISA specifically detected only recombinant VEGF 165b but not recombinant VEGF 165a at any concentrations indicating that a ratio of VEGF 165b :total VEGF 165 measurements will be needed to determine the actual amount of pro-angiogenic VEGF-A isoforms in biological samples (Fig. 1).
Three-compartmental models of PAD: motivation, assumptions and simulations. In our western analysis we observed a significant increase in total VEGF 165 levels in ischemic muscle compared to non-ischemic at day 3 and day 7 post hindlimb ischemia (HLI). However, the levels of VEGF 165b were also significantly higher at day 3 and day 7 post HLI. The ratio VEGF 165b :VEGF-A (from the densitometry values of western blot analysis) showed a ~4 fold induction in the fraction of VEGF 165b in total VEGF-A in ischemic muscle at day 7 post HLI compared to non-ischemic (i.e. VEGF 165b isoforms constitute ~80% of total VEGF-A) in experimental PAD muscle compared to control (Fig. 2).
We used the above experimental results in our model to predict the concentrations of VEGF 165b and VEGF 165a in the calf muscles. Kikuchi et al. measured the ratios of VEGF 165b versus VEGF 165a in serum (protein) and peripheral blood mononuclear cells (PBMCs, mRNA) in PAD patients, which were reported as 4:1 and 8:1, respectively 4 . Hoier et al. measured the interstitial total VEGF protein concentration (i.e. including both VEGF 165a and VEGF 165b ) in the thigh skeletal muscle of PAD patients as 69 ± 21 and 190 ± 78 pg/ml in rest and active exercise, respectively. We convert these numbers to molar concentrations as 69 pg/ml · 1000 ml/l · 1 mole/46000 g = 1.5 pM and 190 pg/ml = 4.1 pM, respectively, based on the molecular weight 46 kDa for VEGF homodimers 7 . We have constrained the model so that the predictions of steady-state concentration of VEGF 165b and total VEGF 165 are within an experimentally observed range (e.g. 0-10 pM) in any of the three compartments to be consistent with the experimental data.
However, because of the sparseness of experimental data it is not possible to identify all the unknown parameters from the available data. Thus, we choose an initial set of secretion rates based on our previous analyses and perform the sensitivity analysis to determine a range of secretion rates constrained with available experimental data, both our own and others. Note that future experiments may provide additional data that could allow further constraining the solutions; presently, the analysis is heuristic aiming at stimulating further experiments.
Prediction of secretion rates of VEGF 165b and secretion ratio of VEGF 165b over total VEGF in three compartments. The values of secretion rate of VEGF in normal and blood compartments are adopted from the tumor angiogenesis model 8 . The secretion rate in PAD calf compartment is set up the same as the secretion rate in the normal compartment. The initial set of secretion rates of total VEGF including VEGF 165a , VEGF 165b and VEGF 121 is assumed as 0.02, 0.031 and 0.02 molecules/cell/s, respectively, in all the three compartments (normal, blood and PAD calf). The secretion ratio of VEGF 121 over total VEGF (VEGF 165a + VEGF 165b + VEGF 121 ) is assumed to be 10%, i.e. 0.002, 0.0031 and 0.002 in normal, blood and disease compartments, respectively. We scan the ratio of secretion rate of VEGF 165b over total VEGF 165 (i.e. the sum of VEGF 165a and VEGF 165b ) in the three compartments from 0 and 1 in 0.1 increments. When the ratio of VEGF 165b over total VEGF 165 is 0.5 in all three compartments (i.e. secretion rates of VEGF 165a and VEGF 165b have equal values 0.009, 0.01395 and 0.009 in normal and disease compartments, respectively), the concentration of VEGF 165b in the normal compartment reaches 31 pM. When the ratio of VEGF 165b over total VEGF 165 in all three compartments is 10%, the concentration of VEGF 165b in the normal compartment drops to 6.5 pM, which is within the experimentally observed range (< 10 pM).
We can also change the secretion ratio of VEGF 165b to total VEGF 165 in each of the three compartments individually. We plot the predictions for steady-state concentrations of VEGF 165b and VEGF 165a in Fig. 3. We first change the secretion ratio of VEGF 165b /total VEGF 165 from 0 to 1 in 0.1 increments in the normal compartment while keeping the total secretion rate of VEGF 165 (VEGF 165a + VEGF 165b ) constant at 0.018 molecules/cell/s in the normal and disease compartments and fixing the secretion ratios in blood and disease compartments at 0.1 (Fig. 3A). We follow the same strategy in Fig. 3B,C, except we vary the secretion ratio of VEGF 165b /total VEGF 165 in the blood compartment for B and the disease compartment for C, while the total secretion rates are fixed and the ratios are fixed at 0.1 in the other compartments. The model predicts that the concentration of VEGF 165b remains at approximately 6.5 pM, when the VEGF 165b /total VEGF 165 secretion ratio is 0.1 in normal and blood, across the full range of secretion ratios in the disease compartment (Fig. 3, left column). Additionally, the steady state concentration of VEGF 165b is consistently predicted to be approximately 30% higher than VEGF 165a in the disease compartment. This result is qualitatively consistent with our experimental data. This prediction gives us an important biological insight that the PAD disease calf muscles comprise mostly VEGF 165b over other total VEGF isoforms. This finding could be further extended for the development of VEGF 165b antibody treatment in PAD.
Sensitivity analysis of VEGF 165a , VEGF 165b and sVEGFR1. We use SimBiology to perform a local sensitivity analysis, which quantifies how changes in a given parameter value influence predicted concentrations of interest.  We calculate the normalized sensitivity coefficient based on the algorithm 9 , where Y is the species VEGF 165a , VEGF 165b and VEGF 121 , and X is the three VEGF receptors VEGFR1, VEGFR2 and NRP1 in the disease compartments; [X] and [Y] denote the molar concentrations. Figure 4 shows that VEGF 165a in the disease compartment and VEGF 165b in the blood compartment are more sensitive to VEGFR2 than VEGFR1, whereas VEGF 121 in the disease and blood compartment is sensitive to both VEGFR1 and VEGFR2. VEGF 165a , VEGF 165b , VEGF 121 are not sensitive to NRP1. The sensitivity analysis in Fig. 4 demonstrates the importance of VEGF 165b -VEGFR2 binding.
Tissue VEGF distribution and VEGFR occupancy in human three compartment model. We show the steady-state distribution of VEGF ligands and their receptors for each tissue in Fig. 5A,B, respectively. The y-axis represents the percentage of each species in x-axis in each VEGF ligand (VEGF 165a , VEGF 165b and VEGF 121 ) in Fig. 5A and each receptor (VEGFR1, VEGFR2, NRP1, and sVEGFR1) in Fig. 5B. In PAD calf, most VEGF 165a is bound to the ECM and parenchymal basement membrane (PBM) (55% and 17%, respectively); most VEGF 165b is also bound to ECM and PBM (62% and 20%, respectively). Here ECM represents the total extracellular matrix minus the endothelial and parenchymal basement membranes. Most VEGF 121 isoform is bound to VEGFR1 and NRP1 as the VEGF 121 :VEGFR1:NRP1 complex in the disease (48%) and normal (51%) compartment. Regarding receptor occupancy, in the normal compartment, the three receptors VEGFR1, VEGFR2 and NRP1 are in the free states, except the VEGF 121 :VEGFR1:NRP1 (33%) and VEGF 165a :VEGFR2:NRP1 (49%). In the PAD calf compartment, most receptors are in the free states, except the complexes VEGF 165a :VEGFR2:NRP1 (20%) and VEGFR1:NRP1 (18%). Most sVEGFR1 are bound to ECM, endothelial basement membrane (EBM) and PBM (62%, 15% and 19%, respectively). Our model in PAD resembles the similar distribution of VEGF and VEGFR occupancy in tumor 10 .

Value Units Resources
Human PAD geometric parameters  VEGF distribution and VEGFR occupancy in murine three compartment model. Constructing a computational model of mouse VEGF distribution is necessary to make use of the experimental measurements in hindlimb ischemia (HLI) models in mice where numerous studies have been conducted 3,11,12 . In the mouse, VEGF isoforms are shorter by one amino acid, e.g., VEGF 164a , and VEGF 120 , but VEGF 165b . Construction of the three-compartment model in mouse can help identify the relative concentration of VEGF 164a and VEGF 165b in the different compartments, and predict VEGF receptor occupancy. We replace the geometric parameters in the three-compartment model from human to mouse. These geometric parameters of mouse are described in the tumor xenograft model 6 as well as in the mouse two-compartment model 13 . The results of VEGF distribution and VEGFR occupancy are shown in Fig. 6(A,B), respectively. Figures 5(A) and 6(A) show that VEGF 165b (human and mouse) mostly bind to the ECM and rarely exist as free ligands in both human and mouse. VEGF 164a and VEGF 165b bind to PBM with higher percentage in mouse than the corresponding isoforms in human. The VEGF receptor occupancies in Figs 5(B) and 6(B) show the similar trend between mouse and human. However, there is lower percentage of free VEGFR1 and VEGFR2 in human (Fig. 5B) than in mouse (Fig. 6B). This result is due to the higher percentage of VEGF 121 :VEGFR1:NRP1 and VEGF 165a :VEGFR2:NRP1 in human than the corresponding complexes in mouse.

Discussion
We previously developed the three-compartment models of VEGF in tumor 6,8,10 and in PAD 14 . The anti-angiogenic form of VEGF 165b has not been included in any of the previous computational models; this is the first study to include VEGF 165b in our human PAD model. This is also the first study that compares human PAD and mouse hindlimb ischemia (HLI) models. By changing the geometric parameters in human PAD calf muscles and adding the kinetics equations of VEGF 165b , we predict the VEGF 165b level in the PAD calf, blood and normal tissue compartments. We summarize the predictions in Table 1. Our computational model shows that the ratio of VEGF 165b /VEGF 165a in PAD is higher than 1 (1.70, 2.10 and 1.41 in disease, blood and normal compartments, respectively). This prediction is consistent with the experimental measurements of VEGF 165b as the predominant isoform of VEGF in PAD 4 . The ratio of VEGF 165b /total VEGF 165 in the disease compartment of our model is   slightly lower than the experiment in human biopsies; however, it should be noted that our predictions are for VEGF concentration in the interstitial fluid in the normal and diseased tissues, whereas the measurements represent the bulk tissue including intracellular components. We do not include intrinsic heterogeneity that arises from the stochastic nature of biochemical reactions because we consider relatively large concentrations (pM). It may be more relevant to consider extrinsic heterogeneity (i.e., due to variations in protein concentrations) 15 . Others have included heterogeneity in the receptor distributions 16 and found that variability in receptor expression can influence the response to anti-VEGF cancer treatment. The focus of the present work is to investigate and quantify how VEGF 165b molecular interactions influence overall VEGF distribution in human and mouse. This is the first model to incorporate the VEGF 165b isoform  and we focus on the issues related to the expression of this isoform. Future work can incorporate variability in protein levels. This study is also important for computational modeling of pharmacokinetics and pharmacodynamics (PK/ PD) of administering VEGF 165b -antibody as a potential pro-angiogenic therapeutic. Current VEGF antibodies including bevacizumab bind both total VEGF (VEGF 165a , VEGF 165b and VEGF 121 ). We propose to introduce an antibody to VEGF 165b as a PAD therapeutic to stimulate angiogenesis. This strategy will be explored in upcoming computational and experimental studies.

Conclusions
We applied the three-compartment model of VEGF distribution to predict the concentration of VEGF isoforms, including VEGF 165b , in the body in peripheral arterial disease. The experimental data show that the expression level of VEGF 165b is higher than VEGF 165a in the human biopsies and the computational model results are consistent with these measurements. The secretion ratio of VEGF 165b to total VEGF 165 is estimated as 1 in the disease compartment, and 0.1 in the blood and normal compartments. Our predictions support the importance of the VEGF 165b in PAD, and provide a foundation for therapeutic inhibition of VEGF 165b in PAD in the future. This multiscale model can also provide a basis for simulating the pharmacokinetics of VEGF 165b antibody in PAD in human and mouse models.

ELISA to measure VEGF 165b antibody sensitivity. VEGF-A and VEGF 165b (R&D) Dual sandwich
ELISAs were used to determine the sensitivity and specificity of VEGF-A and VEGF 165b antibodies in differentiating recombinant pro-angiogenic VEGF-A (VEGF 165a ) and anti-angiogenic VEGF-A (VEGF 165b ) isoforms. Recombinant VEGF 165a and VEGF 165b isoforms were serially diluted at 1000, 500, 250, 125 pg/ml concentrations and standard VEGF-A and VEGF 165b ELISA were performed according to manufacturer instructions on all the samples to determine the sensitivity and specificity of VEGF-A and VEGF 165b Mice.

Murine Model of Hindlimb Ischemia. Hindlimb ischemia (HLI) induced by femoral artery ligation and
resection was used as an experimental model of human PAD. All animal experiments were approved by the University of Virginia Animal Care and Use Committee and conformed to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health. HLI was performed on 8-to 12-week-old age and sex matched C57Bl/6 mice as described previously 11,12 . Briefly, mice were anesthetized by a combination of ketamine and Xylazine (ketamine 90 mg/kg and xylazine 10 mg/kg) and femoral artery was ligated and resected from just above the inguinal ligament to its bifurcation at the origin of saphenous and popliteal arteries. The inferior epigastric, lateral circumflex, and superficial epigastric artery branches were also ligated.  Western blotting, Densitometry and Statistics. Mice were sacrificed with an overdose of anesthesia and non-ischemic and ischemic gastrocnemius muscle samples were collected at day 3 and day 7 post HLI. Tissue was homogenized in RIPA with protease inhibitor cocktail. Equal amounts of protein were resolved by Sodium Dodecyl Sulphate-Poly Acrylamide Gel Electrophoresis, transferred onto nitro cell cellulose membranes and western blotted against VEGF 165b , VEGF-A and Actin by chemiluminescent method. Bands on the film were scanned and quantified by densitometric analysis of the band intensity by NIH image-J (1.6) software. Densitometric values were plotted on Graph PAD Prism 6 or 7 and analyzed for statistical significance. One-way ANOVA with Dunnetts post-test was used to check statistical significance. p < 0.05 considered statistically significant.
Three-compartment models for human and mouse. The model is comprised of three components: normal tissue (representing all tissues and organs except the diseased calf and blood), blood, and diseased calf of PAD (Fig. 7). For clarity, we use the notation VEGF 165a to denote the pro-angiogenic isoform; we refer to the combination of VEGF 165a and VEGF 165b as total VEGF 165 . VEGF 165a , VEGF 165b and VEGF 121 are secreted by myocytes and possibly stromal cells in the normal tissues and by calf muscles in PAD, respectively, and also by endothelial cells in all compartments. VEGF receptors (VEGFR1 and VEGFR2) and co-receptor neuropilin-1 (NRP1) are localized on the surfaces of endothelial and parenchymal cells. We include soluble VEGFR1 and glycosaminoglycan (GAG) chains in the interstitial space of normal and calf compartments, and alpha-2-macroglobulin (α 2M) in the blood. These soluble factors bind VEGF and can be present in high concentrations; therefore, it is important to include them in the model. Geometric parameters are used to characterize the compartment and enable conversion of the concentrations from units used in the model (moles/cm 3 tissue) to more standard units (molarity). The geometric parameters in the normal and blood human compartments are described in ref. 17 where applications to cancer are considered. The geometric parameters in the diseased calf compartment are described in ref. 14. The geometric parameters for mouse compartments are described in refs 6 and 13. We list the details of geometric parameters used in our model in Table 2.
Binding of VEGF 165a , VEGF 165b and VEGF 121 to VEGFR1 and VEGFR2. The molecular interactions between VEGF isoforms and their receptors are illustrated in Fig. 8. VEGFR1 and VEGFR2 are the transmembrane receptors that bind to VEGF 165a , VEGF 165b and VEGF 121 . VEGF 165b has the equivalent binding to VEGFR2 as VEGF 165a 18 , and functions as a competitive inhibitor of the major downstream effects of VEGF 165a . VEGF 165a and VEGF 165b are the two glycoproteins with heparin binding domain that can bind the extracellular matrix. VEGF 121 is a freely diffusible protein lacking a heparin-binding domain. VEGF 165b could bind to VEGFR1 and VEGFR2 but cannot bind the co-receptor NRP1 because it lacks exon 8a 19 . The densities of cell receptors VEGFR1, VEGFR2 and NRP1 are listed in Table 3 based on available in vivo and in vitro experimental data. The kinetic parameters are listed in Table 4. The model is described in terms of 80 ordinary differential equations (ODE) and is presented in the Supplementary File.
We assume that the total secretion rate of VEGF isoforms to be 0.02 molecules/cells/s in the disease and normal compartment, and 0.031 in the blood compartment (see Results for the details). The model equations were implemented in MATLAB R2014b (MathWorks, Natick, MA) using the SimBiology toolbox and were solved with the Sundials solver. Transport parameters. Molecular species are transported between compartments via microvascular permeability (k p ) and lymphatic drainage (k L ) as shown in Fig. 7. All isoforms of unbound VEGF and soluble VEGFR1 (sVEGFR1) in the tissue compartments are subject to proteolytic degradation (k deg ) and are removed from the blood via plasma clearance (c v ). We list the transport parameters in Table 5. , which determines how changes in parameter X influences the output Y by taking the partial derivatives.