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Several cytokine families have roles in development, maintenance and remodeling of the microcirculation. Of these, the VEGF family is one of the best studied and one of the most complex. Five VEGF ligand genes and five cell surface receptor genes are known in the human, and each of these may be transcribed as multiple splice isoforms to generate an extensive family of proteins, many of which are subject to further proteolytic processing. Using the VEGF family as an example, we describe the current knowledge of growth factor expression, processing and transport in vivo. Experimental studies and computational simulations are being used to measure and predict the activity of these molecules, and we describe avenues of research that seek to fill the remaining gaps in our understanding of VEGF family behavior.
The vascular endothelial growth factor (VEGF) family and its receptors have roles in the development, maintenance and remodeling of the vasculature. This ligand-receptor system is very complex (Figure 1): five ligand genes give rise to at least 17 homodimeric proteins and an unknown number of heterodimeric proteins that each have distinct binding characteristics for the products of the five receptor genes (Figure 2). The receptors themselves heterodimerize , resulting in multiple parallel nonexclusive downstream signaling pathways per ligand (Figure 3). Extracellular processing of ligands and receptors results in a complex picture of VEGF transport in tissue (Figure 4).
For a complex system such as this, a systems biology approach can be very useful. With so many interacting components, experiments focusing on any one or small number of molecules at the expense of the others risk making incomplete or even flawed interpretations of results. Computational models based on current biological knowledge allow us to design and make predictions for future experiments that can fill gaps in our knowledge. The results of computational models can either confirm or conflict with our mechanistic understanding, and in both cases we learn more about the system, generating new testable hypotheses. Additional, possibly counterintuitive results can give us further unique insights. Here we review the computational and experimental systems biology work that has been done in the field of VEGF research, and identify areas in which more work would be vital to the advancement of designed VEGF-based or VEGF-targeting therapeutics.
The computational models described in the text vary widely in scope, and none include all of the processes described in Figure 4. Instead, each model focuses on a subset of the VEGF system, e.g. the regulation of a transcription factor HIF1α that regulates VEGF, or the interstitial transport of VEGF, or the activation of matrix metalloproteinases that degrade the matrix, releasing stored VEGF. In this way, each component of the overall VEGF system is modeled and validated independently. To truly describe the overall systems these modules will be coupled together to create a meta-model that allows simultaneous simulation at multiple scales: inside the nucleus, in the cytoplasm, at the cell surface, throughout the tissue and throughout the body.
Most of the models presented here are molecularly-detailed, meaning that each molecular species in the network being studied is explicitly represented along with their interactions and transport signaling pathways. This approach allows for the computational testing of therapeutic approaches, if the interaction of the drug with the components of the model is known. That is, molecular therapeutics can be tested with a molecularly-detailed model, without resorting to lumped or effective parameters.
The first molecularly-detailed models of VEGF transport were developed to simulate the interactions of exogenous VEGF with receptors expressed on cultured cells in vitro [93, 94]. These models were useful for hypothesis testing, for example, the shifting of ligands from VEGFR1 to VEGFR2 was predicted not to be central to the observed synergy between placental growth factor and VEGF-A ; and the mechanism of action of an antibody to VEGF co-receptor Neuropilin-1 was elucidated from an application of the computational models to experimental data on VEGF receptor activation [94, 112]. The validated model of ligand-receptor interactions was then used to build compartmental models of VEGF transport in vivo in multiple tissues, including human breast cancer  and human vastus lateralis muscle . Three-dimensional anatomically-detailed models of VEGF transport in rat extensor digitorum longus muscle, including predictions of VEGF gradients, have also been generated [66, 90–92].
Molecularly-detailed models of other ligand-receptor systems have been made, including epidermal growth factor (EGF) [78, 104] and platelet-derived growth factor (PDGF) . Transport of a hypothetical generic tumor angiogenic factor (TAF), that reflects some of the VEGF transport processes, is included in models of neovascularization [23, 150]. Elements of VEGF transport are also considered in concert with models that simulate many cells undergoing cellular-level responses (e.g., migration and proliferation) during angiogenesis [11, 115]. The role of the Notch-Dll4 system combined with VEGF transport has been simulated as part of a three-dimensional model of cellular behavior during angiogenic sprouting . The role of Notch-Dll4 and VEGF interactions in filopodial extension and tip cell selection have also been modeled . Stochastic models of VEGF (i.e. that take into account the effects of low concentrations by including each individual molecule in the simulation) have been developed to study both in vitro and in vivo behavior [3, 99].
In this review we focus on the kinetics of the biochemical reactions between VEGF and its receptors (Figure 2), and the transport processes that involve these species (Figure 4), and will not include the signaling downstream of the VEGF receptors. Several excellent reviews on the multiple signaling pathways induced by VEGF through its receptors are available [113, 136, 173, 178]. We also focus on the transport of VEGF and its receptors in the adult animal rather than in development. There is extensive literature on the behavior of the VEGF system during development, including intriguing results such as the haploinsufficiency of the VEGF-A ligand gene [20, 40] but not of the receptor genes [44, 134]. We will not explore that literature here. Finally, the VEGF system is also critical for the lymphatic network, but we will focus on the vascular system here.
A sampling of the opportunities for further exploration of a complex system.
The study of the vascular endothelial growth factor (VEGF) system using a systems biology approach is made difficult by the complexity of the growth factor and receptor system. Multiple genes are present for both ligands and receptors; each gene encodes multiple splice variant proteins with different properties; these protein products form both homo- and heterodimers; and there are many ligand-receptor pairs that each induces distinct cellular signaling. This complexity – leading to at least 17 distinct ligands, and at least 60 distinct ligand-receptor complexes – should all be included in a comprehensive systems biology study and computational simulations will be important in understanding the behavior of the system.
Five genes of the VEGF family are present in humans: VEGF-A, -B, -C, -D and placental growth factor (PlGF) . These genes encode the ligands of the VEGF system. More is known of the regulation and behavior of VEGF-A than of the other genes. VEGF-A is expressed by many parenchymal and stromal cells , but autocrine expression by endothelial cells [171, 174] also appears to be essential for survival .
Many factors contribute to the regulation of VEGF gene expression . Multiple growth factors can stimulate expression of the genes in various tumor and normal cells , including basic fibroblast growth factor , IL-1  and TGF-β . Mechanical factors, such as muscle contraction [5, 63, 103] and exercise , and environmental factors such as hypoxia  and inflammation , also regulate VEGF expression. Cells transformed by oncogenes (e.g. ras) may express VEGF family members [81, 124]. Each of these regulators acts through transcription factors. Many transcription factors are involved in the upregulation or repression of VEGF gene transcription , including: hypoxia inducible factors (HIF1 and HIF2), Sp1, Ap-1, NF-κB, E2F1, and ZNF24 . How these factors come together to regulate the cell type-, tissue- and context-specific expression of each of the VEGF genes is unclear. Interactions between all of these regulatory elements must be synthesized to fully understand VEGF regulation.
Molecular-level models of HIF-1α regulation have been developed [118, 119] that include the prolyl dehydroxylase enzymes that stabilize HIF; ascorbate, iron and other cofactors; and the Von Hippel-Lindau (VHL) pathway for HIF ubiquitination. These simulations detail how the oxygen-sensing mechanism of the cell regulates HIF-1α RNA stability and therefore transcription of genes containing the hypoxia response promoter element. Both switch-like and gradual responses are predicted to be possible, depending on the cellular environment. How sharp, switch-like responses of the hypoxia response system are brought about has been studied using theoretical models by multiple groups [79, 175]. Other HIF-1α models have been used to explore how to blunt the VEGF response in hypoxia . VEGF expression in tissue experiencing low oxygen tension has also been modeled [66, 91, 92], using simulations of blood flow and oxygen distribution across skeletal muscle tissue, coupled to an experimentally-based [67, 154] VEGF-O2 dependence. However, no gene network-style modeling of the VEGF system has yet been performed, and there is an opportunity for modeling HIF and the numerous other transcription factor pathways and their interactions; the methodology and tools required for simulating gene regulatory networks are now well developed [52, 88].
Systematic Chromatin ImmunoPrecipitation (ChIP) assays  in conjunction with gene expression profiling would be an extremely powerful tool to piece together the regulation of each VEGF gene, especially given the known cell-type-specific behavior of the system. Multiple pathways stimulated in combination would give insight into the crosstalk between the multiple VEGF regulators. Recent work on another pro-angiogenic molecule, PNF1, describes a novel method of using network analysis tools to integrate experimental and bioinformatic datasets in determining the critical signaling and regulation pathways . Advances in proteomic technologies, e.g. mass spectrometry, can enhance the study of transcription factor pathways and networks, with information on multiple pathway elements available in parallel .
Three genes encoding signaling receptors for the VEGF family are known in the human body: VEGFR1, VEGFR2 and VEGFR3 . Two additional genes encode co-receptors for a subset of the VEGF family: Neuropilin-1 and -2 .
The VEGF receptor tyrosine kinases were originally considered to be specific to and characteristic of vascular and lymphatic endothelial cells, but it was noted that VEGFR1 was expressed on monocytes, where it mediates VEGF-dependent chemotaxis  and is now used as a lineage marker . Recently, the expression of these receptors has been observed on non-endothelial cells , including pericytes , smooth muscle cells , skeletal myocytes , neural cells , and some tumor cells . Neuropilins, initially identified on neurons, were found on endothelial and tumor cells  as co-receptors for VEGF.
The regulation of VEGF receptor genes has been less well studied than the ligands. Shear stress has been shown to upregulate VEGFR2 , as well as activating the receptor . VEGFR2 is also increased during the induction of both sprouting and splitting forms of angiogenesis . Exercise training [66, 87, 131, 156], acute exercise [46, 53] and electrical stimulation  affect the expression of each VEGF receptor differently. Indirect downregulation of VEGFR2 and Neuropilin-1 by VEGF has recently been shown to occur through a juxtacrine Dll4-Notch pathway [57, 166] and this has been suggested to be essential for controlled vascular network growth .
Detailed models of the regulation of VEGF receptor expression have not yet been published. As the experimental information on the regulatory elements and transcription factors emerges, this would be an important area to develop.
VEGF receptor expression regulation is clearly an area in need of further study. See the previous section on strategies for examining regulation of VEGF ligand genes.
The RNA transcribed from the VEGF and VEGF receptor genes can undergo several alternative splicing events to produce proteins of differing lengths and properties  (Figure 1). For the ligands, these proteins are generally referred to by numbers corresponding to the number of amino acids comprising the translated protein; e.g. VEGF-A121, VEGF-B167. The placental growth factor splice isoforms of length 131, 152, 203 and 224 are commonly referred to as PlGF1, PlGF2, PlGF3 and PlGF4 respectively [19, 172]. The receptors may be alternatively spliced to form either transmembrane receptors with intracellular kinase and signal transduction domains, or secreted receptors with ligand binding domains only (Figure 1); this has been definitively shown to result in endogenously expressed proteins only for VEGFR1 [74, 75, 137], VEGFR2  and Neuropilin-1  so far but has not been ruled out for the others.
The splice isoforms of VEGF-A are the most studied, and at least 9 have been identified. These are divided into two families: the ‘pro-angiogenic’ isoforms characterized by Exon 8a, and the ‘anti-angiogenic’ isoforms characterized by Exon 8b . Each of the protein products has distinct receptor binding profiles (Figure 2 and Section 2) and other properties. However, the control and regulation of alternative splicing is less well known. Relative abundances of the isoform RNAs across different tissues  appears to correspond to the architecture of the tissue and the requirements placed on the VEGF system [100, 101], but the genetic, molecular and cellular basis for these tissue patterns have not yet been elucidated. In addition, those studies included only the three most studied pro-angiogenic isoforms of VEGF-A and thus the more recently discovered isoforms – which have been found to be as or more abundant in some tissues  – will need to be included in future studies.
Models of the protein products of the VEGF and PlGF mRNA alternative splicing have been created. These models have been used to test hypotheses of the mechanisms of PlGF-VEGF synergy on cells in vitro  and to predict the differential signaling of VEGFR homo- and hetero-dimers in the presence of isoforms of these two genes . These ligand-receptor binding kinetics used in these models are based on independent experimental data. Models of in vivo VEGF transport use available RNA data to give the parameters for relative isoform abundance, but they do not address the heart of regulation of alternative splicing.
The complexity of generating antibodies for all the possible proteins generated by alternative splicing of the ten VEGF and VEGFR genes suggests that RNA expression would be more amenable point to high-throughput study. The study of the effects of the protein products is also complicated by the existence of pro- and anti-angiogenic isoforms of identical length and with only a six amino acid change at the C-terminal end. A comprehensive study of the expression level of all of the isoforms in tissue explants has yet to be conducted and would pave the way for studies involving stimuli and other perturbations. Balance of the pro-angiogenic VEGF165 and anti-angiogenic VEGF165b isoforms is clearly important for homeostasis. For example, diabetic proliferative retinopathy, pre-eclampsia, and the progression of colorectal, prostate and renal cell carcinomas are all accompanied by a shift from the anti-angiogenic to the pro-angiogenic VEGF-A isoforms [9, 10, 83, 116]. How this takes place is not clear.
VEGF proteins secreted into the interstitial space are dimers, covalently linked by two cysteine-cysteine linkages  (Figure 5). If only one isoform of one gene is being spliced by the cell, then homodimers of that VEGF isoform will form. However, multiple VEGF isoform RNAs are found in all tissues  and unless each isoform is produced by a different cell, the VEGF monomers can heterodimerize. To further complicate matters, ligand heterodimers are not only formed by isoforms of the same gene; PlGF-VEGF heterodimers have been noted [25, 33]. Because the receptor-binding domains are formed at the interface of the dimers, it is difficult to predict the properties of the dimer a priori from its component monomers.
VEGF heterodimers have not been dealt with in published mathematical modeling. Given the profile of RNA transcripts in a cell type, predictions of the relative amounts of each heterodimer and homodimer formed and secreted by that cell can be made. These predictions, tested against the secreted protein profile, would reveal the intracellular regulation of heterodimer formation.
Understanding the regulation of formation of VEGF heterodimers requires a match of the RNA transcripts and the proteins produced. A synthetic biology approach to determine which combinations of heterodimers can form would be particularly informative in this situation, and mass spectrometry could be used to determine those isoforms that are actually made and secreted, avoiding the need for extensive antibody generation and validation.
Following secretion of the VEGF dimers, they may be sequestered by the extracellular matrix or soluble receptors; be proteolytically processed to smaller proteins; and bind to the receptors. The transport and processing of the ligands results in distinct receptor signaling profiles (Figure 2, ,44).
The longer VEGF isoforms include a basic heparin-binding domain [38, 76, 83], that confers binding to certain glycosaminoglycan chains and other components of the extracellular matrix and basement membranes [47, 129, 165]. This sequestration gives the tissue a large, non-diffusing reservoir of VEGF that can be released on demand by certain proteases.
Proteases such as MMP2, MMP3 and MMP9 serve dual purposes in angiogenesis: they can degrade the structural proteins of the extracellular matrix and thus provide a pathway for a migrating cell (e.g. the tip cell of a sprout); and by cleaving the matrix proteins or VEGF directly, they can release VEGF in a more diffusible form [76, 86]. This has two effects: first, there is a large store of VEGF available to amplify the signal at appropriate times; second, the proteolytic degradation may allow the formation of chemotactic VEGF gradients that would not be formed simply by releasing from the cell surface [42, 59].
An important open question is whether the cell surface receptors can bind and sense the matrix-bound VEGF ligands. Addition of heparan sulfate generally increases the binding of VEGF to its receptors in vitro , and heparinases decrease this binding ; the matrix-binding site on VEGF is distant from the receptor binding site (Figure 5), and the existence of receptor-ligand-matrix complexes is supported by observations that the VEGF-binding domain of fibronectin potentiates binding to cell-surface receptors . Although much of the matrix-bound VEGF is beyond the reach of the receptors on the cell surface, the density of the endothelial basement membrane and the extension of filopodia allow the receptors to come into contact with matrix-bound VEGF. In addition to increasing the effective concentration of VEGF that the cell would sense, this would also allow a mechanical interaction between the matrix and the cell, a combination of chemotaxis and haptotaxis. It is notable that an ‘uncleavable’ form of VEGF, which cannot be proteolytically freed from the matrix, can still support angiogenesis, though without the formation of enlarged vessels that characterizes the more diffusible isoforms . Modified forms of VEGF, conjugated to a synthetic matrix, but with different release characteristics, are observed to promote endothelial cell proliferation and differentiation, and may be a useful substrate for therapeutic angiogenesis .
Proteolytic cleavage of in-situ cell membrane VEGF receptors (‘shedding’) may provide an alternate pathway for the release of soluble VEGF receptors . Soluble receptors in the interstitial space bind and sequester the VEGF ligands, but additionally may heterodimerize with cell surface receptors to form unactivatable ‘dummy’ receptors . This sequestration of VEGF ligand has been shown to be important in maintaining avascularity of the cornea , and overproduction of soluble VEGFR1 is implicated in preeclampsia [1, 107]. The regulation of membrane and soluble forms of VEGFR1 appears to be altered in diabetic models of peripheral arterial disease .
Models of VEGF transport in both rat and human skeletal muscle that includes both VEGF-receptor binding and VEGF-ECM sequestration have predicted that much more VEGF is bound to the matrix than is freely diffusing [90, 97]. Those predictions are based on extracellular matrix binding sites for basic fibroblast growth factor [36, 41]; although VEGF binding sites in the matrix have not been quantified, VEGF and FGF bind to many of the same matrix components with similar affinities [47, 165]. MMP regulation includes a complex interplay of extracellular autocalytic and inhibitory pathways, and this has been modeled for MMP2, MMP3 and MMP9 [72, 159]. Optimal conditions for matrix processing were predicted  that were later verified experimentally . Membrane-bound proteases were predicted to be more important for vessel sprout growth than diffusible proteases . The addition to these models of the processing of matrix-bound VEGF to release diffusible isoforms will allow modeling of an important feedback loop in sprouting, as VEGF signaling can increase MMP production [48, 161].
The binding of sequestered VEGF to cell surface receptors, and the cleavage of VEGF by proteases, further increase the complexity of the VEGF ligandome (the set of all VEGF ligands). These sequestered and cleaved forms should be included in any study of the effects of various isoforms of VEGF, e.g. studies using proteomic arrays. Care must be taken to avoid confusing or conflating proteolytic products and their parent proteins.
Each VEGF isoform has a distinct profile of which receptor tyrosine kinases it binds (Figure 2). In addition, some of the ligands bind to the co-receptors, Neuropilin-1 and -2 [102, 141]. Because the binding sites appear to be non-overlapping [38, 158], some isoforms can bridge the non-interacting receptors VEGFR2 and Neuropilin-1 (Figure 2, Figure 5), while others cannot, resulting in a Neuropilin-dependent enhancement in the binding and activation of VEGFR2 by ligands that bind Neuropilin [140, 162]. VEGF isoform-specific receptor complexes result in each isoform being responsible for different physiological outcomes, as observed in mice engineered to express only one VEGF isoform [22, 144].
Heparin and heparan sulfates appear to play a significant role in VEGF ligand binding by the receptors [24, 51]. A recent crystal structure study of the Neuropilin co-receptor suggest that heparin chains function to extend the ligand-receptor binding surface; specificity is still provided through direct ligand-receptor interactions .
In vitro studies have demonstrated that the presence of Neuropilin on cells results in increased signaling by VEGF165 (which binds it) compared to VEGF121 (which does not) [140, 162]. However, by applying a kinetic model of the VEGF isoform-Neuropilin-VEGFR interaction network (validated against in vitro data ) to simulations of in vivo VEGF transport in human skeletal muscle tissue, it was predicted that the ligand-receptor system behaves differently in vivo . For the same secretion rate of VEGF, Neuropilin expression is predicted to decrease the interstitial VEGF concentration in vivo, rather than increasing VEGFR2 binding. This is because at steady state the flux of VEGF through the tissue is the same – in other words, what is secreted (created) must be internalized or degraded (destroyed). Increased expression of Neuropilin transiently increases VEGF binding and this increases the internalization of VEGF, depleting it from the interstitial space until a new steady state is reached. By contrast, in vitro there is instead a large reservoir of ligand that is close to constant during an experiment. This demonstrates the importance of using computational models to simulate complex interaction networks in vivo, to identify which in vitro results may hold in vivo and which may not.
The ligand-receptor binding story is not straightforward: co-receptors, glycosaminoglycan-assisted binding, and receptor clustering can all have an impact on the binding and activation of receptors. Because the current binding data is based on a small number of cell types, and all in vitro, it should be a priority to obtain independent confirmation of the cell-type specific kinetics of ligand-receptor interactions in vivo. Fluorescence correlation spectroscopy (FCS) holds some promise as a technique to measure the kinetics locally to specific cell types . FCS is an excellent example of the synergy possible by combining experimental methods with computational models. The results of FCS imaging must be processed through a computational model in order to reveal the parameters that are being measured, e.g., diffusion rates and kinetics.
As receptor tyrosine kinases, the activation of VEGFR1, 2 and 3 results from ligand-induced dimerization and autophosphorylation of the intracellular kinase domains . As previously noted the ligands are secreted as dimers, with two receptor binding sites to facilitate receptor dimerization . Multiple tyrosines on each receptor can be phosphorylated on activation, each one capable of initiating different signal transduction pathways . Each ligand activates a different subset of these tyrosine sites, affecting cell decision making . Heterodimerization of VEGF receptors increases the complexity of signaling, as the profile of phosphorylation of the multiple tyrosine sites on each receptor depends on the other receptor in the dimer . That is, VEGFR1 activated in a dimer by another VEGFR1 has a different phosphorylation profile (and thus different signaling pathways) than a VEGFR1 activated in a dimer by VEGFR2. In fact, from a single ligand, the three VEGF receptor tyrosine kinases can initiate nine separate receptor phosphorylation profiles (Figure 3). Thus, the expression level of each receptor and the binding profile of each ligand combine to govern receptor signaling. Unique signaling by heterodimers has been observed [2, 62], and this means that we not yet know, for example, whether the differential phosphorylation of VEGFR1 by PlGF and VEGF  is due to conformational changes recognizing the specific ligand, or by the formation of a different balance of heterodimers and homodimers, or both.
The dimerization of VEGF receptors by bivalent VEGF ligands on cells in vitro has been simulated . The effects on signaling of both ligand-dependent and ligand-independent receptor dimerization were considered. For a single receptor type, the signaling was shown to be almost independent of dimerization mechanism for physiological ranges of VEGF concentration. However, when two or more receptors are present, the formation of receptor heterodimers (e.g. VEGFR1–VEGFR2) was predicted to be particularly significant, whereas homodimers of the less-expressed receptors were predicted to be less prevalent. The initiation of multiple signaling pathways by each ligand binding multiple receptors – or of competing pathways by alternate ligands binding a single receptor – gives a significant opportunity for comprehensive intracellular signaling network modeling.
The kineome (the set of all phosphorylation states of the receptors) may be extremely complex given the existence of multiple homo- and hetero-dimeric ligands and receptors. Each of the phosphorylation sites may behave independently, or cooperativity may be present . A full profile of the kineome during angiogenesis has yet to be obtained; the many phospho-specific antibodies that would be required suggest mass spectrometry as a high-throughput alternative.
As with many cell-surface molecules, VEGF receptors are internalized by a clathrin-dependent pathway . Activated VEGF receptors are internalized at a higher rate than non-activated receptors , although other cell-surface molecules such as VE-Cadherin can slow the internalization rate . The internalization of VEGF along with its receptor removes it from the interstitial space and can lead to its intracellular destruction; switching off the signal as VEGF depletes from the extracellular space. However, evidence for nuclear translocation of VEGF receptors [15, 16, 39] suggests that the story does not end there. Signaling by VEGF receptors after internalization may shift from those pathways mediated by molecules that are cell membrane-associated (e.g., PI3K) to those that are distributed throughout the cytoplasm (e.g. PLCγ, p44/p42 MAP kinases) . In this case, blocking the internalization of VEGF receptors may actually block therapeutic signaling rather than prolonging it . This is bolstered by evidence of post-internalization signaling in other receptor tyrosine kinases [18, 31].
The internalization, recycling and destruction of VEGF receptors and their ligand cargo have not been modeled, though this has been done for other ligand-receptor systems . Combined computational-experimental studies to find the trafficking parameters of VEGF receptors would be necessary.
Studies of trafficking, including accurate subcellular localization of the signaling components, would greatly aid the understanding of the role of internalized receptors. Live cell imaging in vitro is an important first step. There is also, as yet, no direct evidence that internalized receptors signal in cells in vivo.
As an autocrine and paracrine system, VEGF is produced by a subset of cell types and internalized by a partly overlapping subset. This leads to the formation of gradients of VEGF concentration within the tissue. These gradients may be required for maintenance and/or activation of the endothelium, or may be more involved with chemotaxis and the guidance of vascular sprouts. Measurement of these gradients has proved difficult, though a gradient of VEGF near a secretion source in the hindbrain midline has been visualized . In the absence of direct measurements in vivo, computational models have been created to predict the size and effect on signaling of these gradients.
The creation of gradients that act in a protease-mediated autocrine manner to allow cells to undergo chemotaxis in response to low interstitial flows has been simulated [42, 59]. In the simulation, the cytokine is released by a cell (e.g. the leading cell of a vascular sprout), and then binds to the extracellular matrix. A protease also released by the cell cleaves and releases the active cytokine. An increasing gradient of the cytokine is then predicted to exist downstream of the cell.
Gradients in a multicellular tissue have been simulated in models of the rat extensor digitorum longus (EDL) muscle [66, 90–92]. By including the detailed three-dimensional microanatomy of the tissue, including a microvascular network and the skeletal myocyte fibers, along with the ligand-receptor kinetics of VEGF, the gradients of VEGF concentration are predicted to be on the order of 3% change in VEGF over 10 µm, a typical cellular scale . Gradients perpendicular to muscle fibers and capillaries are predicted to be ~10-fold higher than those along the fibers . The gradient rises significantly as receptor expression is increased, for example by gene delivery or during exercise. Exercise results in a combination of VEGF and VEGF receptor upregulation [87, 131, 156] and this is predicted to be superior to VEGF upregulation alone in terms of increasing absolute signaling and signaling gradients  (Figure 8).
Along with the ability to determine binding kinetics as noted above, fluorescence correlation spectroscopy (FCS) may be useful in quantifying diffusion and gradient formation by the VEGF isoforms . Applying this technique in tissues in vivo, however, may be quite difficult.
The tissues in the body do not exist in isolation, and not all secreted VEGF remains in the local tissue. Some may be lost through lymphatic drainage, and depending on the permeability of the microvessels, VEGF may also be lost directly to the circulation, and then delivered to a distant tissue (Figure 6). In this way, VEGF ligands may serve a global communication function, and elevated VEGF and soluble VEGFR levels in the blood or urine are being investigated as potential markers of disease progression .
Organs with fenestrated microvessels are assumed to present little barrier to VEGF loss into or gain from the bloodstream. Those with tight vascular barriers (brain, retina) may use only locally-secreted VEGF. For other organs, the transport may be more finely regulated by modifying vascular permeability. VEGF was first discovered as a vascular permeability factor (VPF) , and thus may be responsible for regulating its own global transport. In skeletal muscle and normal breast tissue, the interstitial free VEGF concentrations measured by microdialysis [27, 28, 61] are similar to the plasma levels , suggesting that in these tissues, at least, permeability is sufficiently high to allow equilibrium between plasma and interstitial fluid. However, in cancer, the blood VEGF levels are elevated , presumably due to additional VEGF secretion by the tumor cells, and to the leakiness of tumor vessels .
To model the transport of VEGF throughout the body, an integration of pharmacokinetic and molecularly-detailed models is required. The permeability of the blood-interstitium interface, and the production and consumption rates for VEGF, are different in each tissue.
Parallel measurements of VEGF concentration in multiple tissues and in the blood are required to determine the dynamics of global VEGF transport. Some tissues may serve as reservoirs to be called upon and released into the blood, others may act as ‘buffers’ preventing VEGF in other tissues rising or falling catastrophically.
Endothelial cells are polarized, with apical (lumenal) and basolateral (ablumenal) surfaces. The concept of VEGF as a chemoattractant and guidance cue for migrating endothelial cells in vivo is predicated on receptors being expressed on the ablumenal side. However, it is possible that the cell is activated through receptors on the lumenal side, and then, as the activated cell changes its polarity to that of a sprouting tip cell (front: no cell-cell contact, numerous filopodia; back: cell-cell contact to the mother vessel or stalk cells) , the receptors are expressed on the new leading edge of the cell. The localization of the receptors on the endothelial cell in vivo is important for the design of human therapeutics.
VEGF receptors have been shown to cluster, possibly in lipid rafts, rather than be continuously distributed on the membrane . They co-cluster with VE-Cadherin [21, 135] in cell-cell contacts – possibly as a shear stress sensor, Caveolin-1  in pre-caveolae, and certain integrins  in focal adhesion sites.
Along with the previously described subcellullar localization of VEGF receptor signaling (cell-membrane vs. nuclear), future models of VEGF signaling must account for the context of the activated receptors. Lumenal and ablumenal receptors may initiate different signaling pathways, and so too the receptors clustered in focal adhesions and cell-cell contacts.
VEGF can initiate different signaling pathways from similar receptors in disparate microenvironments (even on the same cell). As angiogenesis is a multi-step process, temporal information on the signaling of each subset of receptors during neovascularization is important. Quantifying this subcellular signaling experimentally is a major challenge; even measuring signaling at the whole-cell level is difficult in vivo.
As noted above most of the interstitial VEGF is predicted to be bound to the extracellular matrix or bound to the cell-surface receptors, rather than free and diffusing . However, not all of the VEGF in the body is present in the interstitial space: intracellular VEGF (pre-release and post-internalization) and VEGF in the blood are included when a ‘whole-tissue’ VEGF concentration level is measured. This makes VEGF concentration measurements difficult to compare. Interstitial concentration of freely diffusing VEGF has been measured using microdialysis as 0.5–1.5 pM depending on the tissue [27, 28, 61]. This is very close to the plasma concentration of VEGF measured in healthy subjects . However, on adding this measured interstitial free VEGF, the VEGF in the microvessel (both plasma and platelets), the predicted matrix-bound and receptor-bound VEGF, it amounts to less than 1% of the total VEGF measured by tissue digestion . This suggests that either most VEGF is present intracellularly, or that current measurements of VEGF receptor or ECM binding site density are not accurate.
The low level of free VEGF concentration in the plasma and interstitial space, coupled with the small volumes of interstitial space between cells, leads us to conclude that the absolute number of VEGF molecules present in the interstitial space is small. 1 pM VEGF concentration translates to approximately one molecule per 1000 µm3; for an endothelial cell, with a typical surface area of 1000 µm2, this means one free VEGF molecule within 1 µm of the cell surface. It has been shown that low levels of VEGF concentration can lead to high variability in receptor activation; in vitro this is not a significant issue . In vivo, this low level of VEGF concentration may be partly responsible for the stochastic nature of angiogenic events. However, if the cell surface receptors can sense the matrix-bound VEGF, then the local effective concentration is significantly higher than the free VEGF concentration.
Whole-tissue models of VEGF transport (incorporating all of the processes shown in Figure 4) are necessary to synthesize and reconcile the measurements of VEGF that are made in many different parts of the tissue, and of the tissue as whole.
The diverse measurements currently made of VEGF concentration or distribution within tissues are not sufficient to confidently build a complete picture of VEGF transport. Quantification of the many pools of VEGF (Figure 4) within a single tissue obtained in a consistent, high throughput fashion would facilitate understanding of changes in VEGF trafficking in health and disease.
Along with the concentration of VEGF in the blood plasma mentioned above, there are molecules and formed elements that sequester VEGF. Fibrinogen  and soluble VEGFR1  are two examples of proteins in the blood that can bind a significant amount of VEGF. This may function to inhibit VEGF signaling, or to protect VEGF from degradation and create a reserve to be used at an appropriate later time. Platelets and leukocytes can also sequester VEGF [49, 127], although the mechanism by which this occurs is not known. Recently, alpha granules in platelets were shown to segregate pro- and anti-angiogenic molecules . The purpose of this sequestration is not known but the release of the VEGF-storing alpha granules upon activation of platelets suggests a role in the coagulation cascade and wound healing.
The sequestration of VEGF by proteins and formed elements in the blood has not yet been simulated; such a model may provide insight into the mechanism of platelet uptake and release of VEGF.
The measurement of VEGF in the blood is now routinely performed for diagnostic and prognostic purposes, for example in cancer patients . A greater understanding of the dynamics of VEGF in the blood would improve the interpretation of these measured numbers, which have large variability.
The concept of angiogenic balance, or the angiogenic switch [55, 173] describes an equilibrium between angiogenesis activators and inhibitors for the maintenance of homeostasis. In exercise, for example, both pro- and anti-angiogenic proteins are expressed , presumably to tightly control any neovascularization. Deviations can result in hyper- or hypo-vascularization, and equilibrium can be restored either by increasing agonists of the desired outcome, or by blocking its antagonists. This gives a useful framework for the selection of therapeutics for diseases of hypervascularization (e.g. cancer and age-related macular degeneration) or those that may be ameliorated by increased vascularity (e.g. coronary artery disease, peripheral arterial disease). Both approved and potential therapies targeting the VEGF pathway are summarized in Figure 7. Examples of the use of computational models to predict the outcomes of therapeutic interventions in peripheral arterial disease and in cancer are given in Figure 8.
Initially, delivery of VEGF by protein, gene or cell therapy was expected to increase functional vascularization in tissues experiencing ischemia and hypoxia. However, numerous clinical trials of VEGF monotherapy in peripheral arterial disease (PAD) have been largely unsuccessful [12, 105, 121, 122, 138]; reviewed in [69, 173]. Clinical trials of VEGF treatment in coronary artery disease have had mixed results [60, 148]; reviewed in [139, 173].
New trials are being designed for delivery of engineered transcription factors that are intended to amplify the body’s response to hypoxia and ischemia, rather than gene delivery of a single isoform of VEGF: VEGF-ZFP increases expression of endogenously expressed VEGF isoforms ; a hypoxia inducible factor–herpes virus VP16 hybrid fusion protein stabilizes HIF1α, increasing VEGF production.
A comparison of cell, gene and exercise therapies in a rat extensor digitorum longus simulation representative of the ischemic hindlimb model of PAD showed that VEGF delivery or upregulation increases mean VEGF receptor signaling, but not the gradients of VEGF within the tissue . In contrast, exercise, the current therapy for PAD, which upregulates both VEGF and VEGF receptors in rat ischemic muscle, results in increased mean VEGF and increased VEGF gradients, the latter even during periods of rest between exercise sessions . The models thus suggest that combinations of VEGF and VEGF receptor upregulation could be more effective than VEGF monotherapy .
The development of high-throughput in vitro or in vivo therapeutic screens that efficiently identify effective pro-angiogenesis therapies would be a major step forward in candidate identification. The assays that currently exist are not always predictive of in vivo success, and so identification of in vitro characteristics that are good indicators of in vivo behavior would be beneficial. In addition, the transition from candidate to clinical trial will be greatly helped by the identification of suitable human biomarkers that are early indicators of success or failure.
Many drugs are in clinical trials, and several approved, for the inhibition of pathological neovascularization by targeting the VEGF-VEGF receptor system (Figure 7). Approved drugs are typically VEGF sequestering molecules or receptor tyrosine kinase inhibitors. There are also possibilities in targeting VEGF secretion or receptor expression, or downstream signaling.
Neuropilin-1 is a VEGF165-specific co-receptor that enhances binding to VEGFR2. Using computational models of human breast cancer, we have shown that Neuropilin expressed on tumor vasculature can be an efficient target for inhibiting VEGFR2 signaling . However, the mode of inhibition is extremely important. Inhibition of Neuropilin expression (e.g. by siRNA) and blocking of VEGF165-Neuropilin binding (e.g. by a competing ligand) are predicted to be effective only in tumors within certain ranges of VEGF receptor expression. Blocking of the Neuropilin-VEGFR2 coupling by a Neuropilin antibody [80, 94], on the other hand, is predicted effective for all tumors expressing Neuropilin . The ability to predict this influence of microenvironmental conditions on the predicted efficacy of therapeutic compounds is a benefit of detailed molecular-level mathematical models.
As noted above, high-throughput screens and in vivo biomarkers would greatly aid drug development.
The authors gratefully acknowledge constructive discussions with Brian Annex, David Bates, Margaret Brown, Patricia D’Amore, David Ginty, Olga Hudlicka, Alex Kolodkin, Christopher Kontos, Gera Neufeld, Shay Soker and Hiroshi Takagi. The authors’ work on the VEGF family supported by NIH grants HL079653 and HL087351. FMG is supported by NIH training grant T32 HL7284 through the Robert M. Berne Cardiovascular Center.