As we have seen, angiogenesis is a tightly regulated, multi-step process required in many physiological conditions. A balance of pro-angiogenic factors (e.g. VEGF, FGF and Ang-1) and anti-angiogenic factors (e.g. thrombospondin-1 and endostatin) is required to maintain homeostasis in normal physiology  (Fig. 2). Although a shift in the relative balance of these factors must occur in response to changes in metabolic demand, for example vascular adaptation in exercise , an imbalance can also lead to pathological conditions. The angiogenic balance governing the extent of vascularization can be exploited in order to treat conditions for which increased vascularization is desired (e.g. coronary and peripheral artery diseases) or diseases characterized by hypervascularization (e.g. cancer and retinopathy).
Administration of exogenous factors or therapeutics can be used to control the angiogenic balance. There are already several examples of anti-angiogenic agents approved for the treatment of various forms of cancer and wet age-related macular degeneration (AMD). For example, bevacizumab (Genentech, South San Francisco, CA, USA), a recombinant humanized monoclonal antibody to VEGF, is approved for the treatment of metastatic colorectal and kidney cancer, glioblastoma and non-small cell lung cancer. Depending on the indication, bevacizumab is a monotherapy or given in combination with other drugs such as chemotherapy agents and interferon. Aflibercept (Regeneron, Tarrytown, NY, USA), a soluble fusion protein, is approved for the treatment of metastatic colorectal cancer. Pegaptanib (Pfizer, New York City, NY, USA), an RNA aptamer that specifically binds the VEGF165 isoform of VEGF-A, ranibizumab (Genentech), a monoclonal antibody for VEGF, and aflibercept are approved therapies to treat AMD patients. Additionally, bevacizumab is prescribed off-label to treat AMD . Tyrosine kinase inhibitors (TKIs) such as pazopanib (GlaxoSmithKline, London, UK) and sunitinib (Pfizer) are approved cancer therapies and target receptors from multiple growth factor families, including receptors for FGF, PDGF and VEGF [138, 139]. Other drugs are in clinical trials, such as the TKI dovitinib (Novartis, Basel, Switzerland) , EZN-2968 (Enzon, Piscataway, NJ, USA), an RNA antagonist that targets HIF-1α , ABT-510 (Abbott, Abbott Park, IL, USA), a peptide mimetic of TSP-1  and AMG386 (Amgen, Thousand Oaks, CA, USA), a peptibody that neutralizes Ang-1 and -2 . In contrast, no pro-angiogenic therapeutic agents have been approved, despite successes in pre-clinical animal models. For example, VEGF , HIF-1  and FGF gene therapy  have failed in clinical trials . However, additional pro-angiogenic therapies are in the pipeline . Endogenous proteins also contribute to the regulation of angiogenesis. Platelets are a rich source of these regulatory proteins  and play a role in tumour angiogenesis and cancer progression [150-152]. In fact, pro- and anti-angiogenic factors are separated into specific α-granules in platelets and may be released under different conditions to promote or reduce angiogenesis [153, 154]. Additionally, it has been shown that platelets sequester bevacizumab, and that the antibody can neutralize platelet VEGF .
The number and complexity of the events that occur during angiogenesis, along with the large number of molecular species involved, suggest that systems biology approaches are vital to the study of the process of angiogenesis. Here, we describe the use of systems biology in the development of pro- and anti-angiogenic therapies, organized according to the stages of angiogenesis presented in the previous section. Computational methods combined with quantitative experimental tools can be used to generate and validate biological hypotheses and may lead to the development of effective therapies targeting angiogenesis by predicting promising drug targets, providing a framework to test hypotheses and identifying patient population that will respond to a particular therapy.
Targeting angiogenic stimuli
We have previously described the signals that promote angiogenesis, which include hypoxic, metabolic or mechanical cues. Given the prominent role of HIF-1 in stimulating angiogenesis and the signalling and metabolic pathways regulated by this molecular species, it is the target of numerous anti-angiogenic therapies [156-158]. For example, inhibitors of HIF-1α mRNA expression  and translation  are currently in clinical trials. Efforts to understand the HIF-1 systems have resulted in the development of several computational models [31, 160-164], which can be used to identify potential therapeutic targets and predict the effects of targeting HIF-1 signalling. For example, the cellular microenvironment can promote hydroxylation of HIF-1α leading to reduced HIF-1α levels . Another model predicts that PHD is able to inactivate HIF-1 and could be targeted in anti-angiogenic therapy . Interestingly, recent modelling of HIF-1α signalling supported by experimental studies predicts that degradation not mediated by PHD can control the HIF-1α response during hypoxia, and asparaginyl hydroxylation provides protection from this degradation . Integration of phosphoproteomics and computational modelling of insulin-like growth factor-1 (IGF-1) signalling in breast cancer was used to predict optimal drug combinations that target IGF-1 and inhibit VEGF expression . One computational methodology identified cell signalling components involved in deviation from homeostasis . The methodology was applied to investigate the genes that regulate the angiogenic switch (a term describing the preponderance of pro-angiogenic ligands over endogenous angiogenesis inhibitors) in pancreatic tissue, and allows for discovery of novel therapeutics that inhibit this process .
Computational modelling of the VEGF/VEGFR system has investigated the effects of targeting molecular species involved in this signalling pathway [167-171]. A model investigating the efficacy of targeting the VEGF co-receptor neuropilin predicted that inhibiting NRP-VEGFR coupling is a more effective strategy than blocking NRP1 expression or preventing VEGF-NRP binding . Computational models are particularly strong in testing alternate hypotheses in this way. A compartment model of VEGF distribution in the body was used to investigate the mechanisms by which free VEGF in the plasma increases following anti-VEGF treatment, a counterintuitive effect that has been clinically observed [172-174]. The increase in plasma VEGF was an emergent property of the model, and could be attributed to a shuttling mechanism resulting from intercompartment transport of the antibody complexed with VEGF, i.e. movement of the complex between tumour, normal tissue and blood . The model was expanded to include experimental quantification of VEGF receptor density, VEGF degradation and VEGF secretion by tumour cells, and a sensitivity study was performed to determine the model parameters that influence the response to anti-VEGF treatment. The resulting model predicts that upon administration of a VEGF-neutralizing agent, unbound tumour VEGF can vary depending on receptor internalization and expression on tumour cells and the specific rate of secretion of the VEGF isoforms [167, 171]. The model was also applied to investigate the effect of isoform-specific anti-VEGF agents, and predicted that targeting VEGF121 would reduce unbound (free) VEGF in the tumour and would be an effective treatment strategy . Additionally, a model of VEGF distribution in the mouse , validated using experimental data for VEGF Trap pharmacokinetics , provides a framework to explore therapies that target the VEGF pathway and can be directly compared to preclinical studies. A model of tumour growth that includes the contribution of endothelial progenitor cells (EPCs) in tumour growth was used to compare the efficacy of various anti-angiogenic therapies . EPCs are bone marrow-derived cells that can localize in tumour vessels and enhance angiogenesis. The model was applied to predict the local and systemic effects of therapies targeting EC migration, VEGFR2 signalling, or the balance of pro- and anti-angiogenic factors, as well as chemo- and combination therapy. Targeting the ECs and EPCs together via blocking VEGFR2 signalling, restoring the balance of angiogenic factors, or combining chemotherapy and anti-angiogenic treatment, is predicted to induce systemic effects and inhibit tumour growth.
Computational models can also be applied to investigate physiological angiogenesis and pro-angiogenic therapy. A model of wound healing simulates the development of blood vessels in response to macrophage-derived angiogenesis factors . The model recapitulates experimental evidence that oxygen concentration provides a feedback mechanism for vessel growth, whereby low oxygen levels influence vessel density. Oxygenation is predicted to be the dominant mechanism controlling the rate of wound healing. Another model of angiogenesis in wound healing investigates the role of macrophages and oxygen treatment to improve healing . Models of VEGF distribution in skeletal muscle have been used to predict the effect of promoting VEGF signalling: up-regulation of VEGF in muscle tissue via cell-based or gene therapy or exercise training (e.g. increasing VEGFR expression) [56, 58, 178]. The models predict that increasing receptor expression leads to an increase in VEGF gradients and VEGFR activation for longer periods of time than up-regulation of VEGF, as well as targeting VEGFR2 signalling specifically. Thus, these models enable quantitative comparison of pro-angiogenic therapies.
Endothelial cells migrate into the ECM in response to pro-angiogenic stimuli. Computational models have been used to simulate the early stages of vessel sprouting and provide insight into the complex interactions of ECs [77, 78, 103, 179, 180]. Artel et al. combine agent-based modelling of sprouting angiogenesis in a polymer scaffold and experimental studies to investigate the relationship between neovascularization and scaffold properties . Specifically, the authors vary the pore size and predict that larger pores promote faster vascularization. This study is relevant for tissue engineering applications. Another agent-based model predicts how patterns of EC behaviour such as migration, proliferation, branching and elongation lead to unique capillary sprouting in response to VEGF and brain-derived neurotrophic factor . The model provides insight into how migration, proliferation, branching and elongation influence capillary structure and can aid in the development of strategies that promote vascularization in neurovascular disease. A model of blood flow in capillary networks was used to investigate the efficiency of chemotherapeutics  and was later extended to account for vessel pruning as a result of anti-vascular and anti-angiogenic drugs . A model combining blood flow and vessel growth in tumours, termed dynamic adaptive tumour-induced angiogenesis (DATIA, described earlier), examines the effects of physical and biological parameters on the capillary network and identifies several vascular properties that are potential therapeutic targets . Tip and stalk cell selection, mediated by the Notch ligand Dll-4 have been modelled [78, 95, 103] and complement experimental data showing that targeting Dll-4 is a promising anti-angiogenic therapy [183, 184], although studies on the effects of targeting Notch/Dll-4 indicate that toxicity may prevent long-term inhibition of this pathway [185-187].
A bioinformatics approach was used to identify anti-angiogenic peptide sequences involved in inhibiting cell proliferation and migration . A systematic computational analysis compared the sequences of endogenous anti-angiogenic peptides to known proteins in order to identify the common motifs and classify the peptides. Based on the analyses, several protein families were identified, including collagen type IV, CXC chemokines, somatotropins, serpins and TSP1-domain containing proteins. The ability of the peptides to inhibit proliferation and migration was validated using in vitro assays [188, 189] and in vivo tumour xenografts models [190-195]. This systems biology approach revealed more than a hundred anti-angiogenic peptides that can be further studied to investigate their therapeutic potential. Additionally, Rivera et al. used the human interactome, which catalogues physical interactions between proteins, DNA and RNA, to identify proteins that mediate cross-talk between the families of anti-angiogenic peptides  and novel and missing angiogenesis annotations [197, 198]. In both cases, the predictions generated through bioinformatic approaches were validated by analysis of time series gene expression data. This study illustrates that bioinformatics and related systems biology techniques have great potential utility in identifying novel targets.
Targeting elongation and branching
Proteases are released by the sprout, both as it initiates and as it migrates, to degrade the ECM, linking the sprouting and elongation phases of angiogenesis. MMPs are a particularly well-studied family of proteases involved in angiogenesis, as described above, and they have been targeted in anti-tumour therapies. Clinical trials involving MMP inhibitors showed little therapeutic effect, in part because the inhibitors have low selectivity for specific MMPs that promote angiogenesis and tumour growth . Systems biology tools can aid in the development of anti-angiogenic therapies that selectively target MMP and their substrates. For example, proteomic analysis has been shown to be a useful systems-level tool to understand the substrates of MMPs and identify potential therapeutic targets . Recently, Miller et al. developed Proteolytic Activity Matrix Analysis (PrAMA), a novel HTP method to quantify metalloproteinase activity by combining experimental measurements and mathematical analysis [201, 202]. In the first step of PrAMA, experimental fluorimetric data are obtained for several metalloproteinases against a panel of FRET-based protease substrates. The data are then fit to a kinetic model in order to determine the catalytic activity of each individual enzyme. The enzymes are clustered according to their similarity, and this serves as a ‘cleavage signature’ that can be used to infer the activity of particular enzymes in a complex biological sample. This quantitative biological information is needed to generate predictive computational models of MMP kinetics [64-66, 68, 203-205]. For example, a model of MMP inhibition in a multi-scale model of tumour growth  predicted that as cancer cells become less sensitive to anti-growth signals, the efficacy of MMP inhibition is impaired. These results may provide an explanation for the unsatisfactory results of MMP inhibitors in clinical trials, particularly since the drugs were tested in cancer patients with advanced disease. Of particular interest is a recent application of systems biology tools to predict and validate the effects of an MMP-9 inhibitor. Dufour et al. used in silico docking to identify compounds that selectively target MMP-9 and evaluated the drug candidates in biological assays and an in vivo breast tumour xenograft model . The docking analysis revealed compounds that specifically target the haemopexin domain, a less-conserved, non-catalytic site of the MMPs, resulting in highly selective drug candidates. Based on the docking study, they identified and validated a compound that inhibits cell migration, tumour growth and metastasis induced by MMP-9. Additionally, the role of the anti-angiogenic molecule angiostatin as a protease inhibitor has been explored using mathematical models [206-208].
Targeting tubulogenesis and anastomosis
Various steps in the angiogenesis process, including lumen formation, have been examined via high content screening (HCS), which uses HTP and cellular imaging techniques to obtain quantitative data on biological processes . Evensen et al. employ HCS to visualize lumens and monitor the effects of angiogenic inhibitors . ECs and vSMCs were co-cultured and treated with various anti-angiogenic and vascular disrupting agents. The total tube length, measured using live cell HTP imaging, was used to quantify the effect of the drugs. This method screens anti-angiogenic compounds in a HTP manner, enabling the identification of novel angiogenic compounds and visualization of their mode of action.
Anastomosis has been included in several models of angiogenesis [34, 39, 77, 85, 95, 103, 210, 211]. Here, we highlight three models of particular interest. An innovative model by McDougall et al. combines blood flow and capillary growth and incorporates anastomosis . In the model, perfusion and blood transport directly influence the formation of vascular networks, and anastomosis leads to radial adaptation and vessel remodelling. The simulated networks are examined in order to determine what parameters influence efficient transport and perfusion. The model predicts that dilated anastomoses located near a parent vessel prevent effective perfusion. Thus, targeting anastomosis and promoting the tumour vascular network to include dilated loops is a means of inhibiting the supply of blood and nutrients to the tumour . As noted above, Bauer et al. developed the first cell-based model of tumour angiogenesis and included vessel branching and anastomosis . The CPM included interactions between ECs and between an EC and its environment, including the ECM, tumour cells and interstitial fluid. Branching and anastomosis emerge based solely on cellular and molecular dynamics, as the model does not include specific rules for these morphological changes. The model predicts that branching and anastomosis are energetically favourable events that occur even in the absence of blood flow and are influenced by the composition of the stroma and ECM .
Models of intussusceptive angiogenesis take into account haemodynamics and biomechanical properties such as shear stress involved in vessel splitting and pillar formation [21, 113, 114, 212]. These models are very instructive, as intussusception is a relatively new area of study compared to sprouting angiogenesis and much more research is required to gain a deeper understanding of this process . Szczerba et al. developed a model that simulates vascular remodelling in response to haemodynamics, chemical agents and vascular wall stiffness . The inclusion of secreted chemical factors (e.g. signalling molecules) is a novel feature of the model, which enables the prediction of the effects of modulators of intussusception under pathological conditions. Although it has not been investigated computationally, it has been shown that tumours switch from sprouting to intussusceptive angiogenesis after the administration of angiogenesis inhibitors .
Pericyte recruitment and coverage promote vessel maturation and stabilization. PDGF and Ang1 are key promoters of pericyte recruitment and are prime targets for anti-angiogenic therapies. Mitchell et al. have developed a HTP method of quantifying pericyte coverage by measuring expression of regulator of G-protein signalling 5 (RGS5), a pericyte-specific gene . Their method provides quantitative data that can be combined with efforts to model vessel maturation. A model of tumour growth and dynamics, including vessel maturation, was used to simulate anti-angiogenesis and anti-maturation therapy targeting VEGF and Ang1, respectively . The model predicted that anti-VEGF therapy is more effective when the number of immature vessels is large compared to mature vessels, while anti-Ang1 treatment is not affected by this vascular property. Applying the two therapeutic agents together results in prolonged inhibition of tumour growth, as compared to single-agent therapy. The model predictions qualitatively agree with an in vivo model of metastatic ovarian cancer, where VEGF and PDGF are targeted with bevacizumab and a PDGF-aptamer, respectively . Additionally, the development and application of sunitinib, an anti-angiogenic agent that inhibits a number of tyrosine kinases including VEGF and PDGF receptors, demonstrate the clinical relevance of combined therapies that target ECs and pericytes . Similarly, a recent model of angiogenesis that simulates vessel initiation, extension and maturation, shows that inhibiting both VEGF and PDGF-B receptor β is more effective than anti-VEGF treatment alone . Additionally, the model shows that vessel maturation promoted by angiopoietins and pericytes contributes to resistance to anti-VEGF therapy. Other models of tumour angiogenesis include vessel maturation and regression [216, 217] and enable investigation of therapies that target this step of angiogenesis [218, 219].
All of the steps involved in angiogenesis described here lead to an intricate network of vessels uniquely patterned to deliver blood and nutrients to the surrounding tissue. A model of vascular patterning predicts how the capillary network is tailored in response to parameters such as expression of angiogenic factors (both soluble and matrix-bound), MMP activity and EC proliferation rate . This multi-scale phase-field model employs continuum physics, while tracking individual cells, and predicts the characteristics of the morphological features of vascular networks. Travasso et al. find that the diffusion properties and expression levels of the pro-angiogenic factor and the migration and proliferation rate of ECs are the primary factors that govern vascular patterning and reproduces experimental data.