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1.  Site-Specific Phosphorylation of VEGFR2 Is Mediated by Receptor Trafficking: Insights from a Computational Model 
PLoS Computational Biology  2015;11(6):e1004158.
Matrix-binding isoforms and non-matrix-binding isoforms of vascular endothelial growth factor (VEGF) are both capable of stimulating vascular remodeling, but the resulting blood vessel networks are structurally and functionally different. Here, we develop and validate a computational model of the binding of soluble and immobilized ligands to VEGF receptor 2 (VEGFR2), the endosomal trafficking of VEGFR2, and site-specific VEGFR2 tyrosine phosphorylation to study differences in induced signaling between these VEGF isoforms. In capturing essential features of VEGFR2 signaling and trafficking, our model suggests that VEGFR2 trafficking parameters are largely consistent across multiple endothelial cell lines. Simulations demonstrate distinct localization of VEGFR2 phosphorylated on Y1175 and Y1214. This is the first model to clearly show that differences in site-specific VEGFR2 activation when stimulated with immobilized VEGF compared to soluble VEGF can be accounted for by altered trafficking of VEGFR2 without an intrinsic difference in receptor activation. The model predicts that Neuropilin-1 can induce differences in the surface-to-internal distribution of VEGFR2. Simulations also show that ligated VEGFR2 and phosphorylated VEGFR2 levels diverge over time following stimulation. Using this model, we identify multiple key levers that alter how VEGF binding to VEGFR2 results in different coordinated patterns of multiple downstream signaling pathways. Specifically, simulations predict that VEGF immobilization, interactions with Neuropilin-1, perturbations of VEGFR2 trafficking, and changes in expression or activity of phosphatases acting on VEGFR2 all affect the magnitude, duration, and relative strength of VEGFR2 phosphorylation on tyrosines 1175 and 1214, and they do so predictably within our single consistent model framework.
Author Summary
Vascular endothelial growth factor (VEGF) is an important regulator of blood vessel growth. To date, therapies attempting to harness the VEGF system to promote blood vessel growth (e.g. for wound healing or ischemic disease) have achieved only limited success. To improve VEGF-based therapies, we need to better understand how VEGF promotes development of functional blood vessels. We have developed a computational model of VEGF binding to the receptor VEGFR2, trafficking of VEGFR2 through endosomal compartments in the cell, and activation of VEGFR2 on several tyrosine residues. The pattern of tyrosines activated on VEGFR2 influences cell behavior, promoting cell survival, proliferation, or migration. The combination of these cues influences the diameter of vessels, degree of branching, and leakiness of the resultant vessel network. Our model shows that changes in VEGFR2 trafficking as a result of VEGF immobilization to the extracellular matrix are sufficient to describe observed changes in the pattern of VEGFR2 activation compared to stimulation with purely soluble VEGF. This model can be used to predict how VEGF immobilization, interactions with co-receptors or proteins that deactivate VEGFR2, and changes to VEGFR2 trafficking can be tuned to promote development of functional blood vessel networks for tissue engineering applications.
PMCID: PMC4466579  PMID: 26067165
2.  Multiplexed Component Analysis to Identify Genes Contributing to the Immune Response during Acute SIV Infection 
PLoS ONE  2015;10(5):e0126843.
Immune response genes play an important role during acute HIV and SIV infection. Using an SIV macaque model of AIDS and CNS disease, our overall goal was to assess how the expression of genes associated with immune and inflammatory responses are longitudinally changed in different organs or cells during SIV infection. To compare RNA expression of a panel of 88 immune-related genes across time points and among three tissues – spleen, mesenteric lymph nodes (MLN) and peripheral blood mononuclear cells (PBMC) – we designed a set of Nanostring probes. To identify significant genes during acute SIV infection and to investigate whether these genes are tissue-specific or have global roles, we introduce a novel multiplexed component analysis (MCA) method. This combines multivariate analysis methods with multiple preprocessing methods to create a set of 12 “judges”; each judge emphasizes particular types of change in gene expression to which cells could respond, for example, the absolute or relative size of expression change from baseline. Compared to bivariate analysis methods, our MCA method improved classification rates. This analysis allows us to identify three categories of genes: (a) consensus genes likely to contribute highly to the immune response; (b) genes that would contribute highly to the immune response only if certain assumptions are met – e.g. that the cell responds to relative expression change rather than absolute expression change; and (c) genes whose contribution to immune response appears to be modest. We then compared the results across the three tissues of interest; some genes are consistently highly-contributing in all tissues, while others are specific for certain tissues. Our analysis identified CCL8, CXCL10, CXCL11, MxA, OAS2, and OAS1 as top contributing genes, all of which are stimulated by type I interferon. This suggests that the cytokine storm during acute SIV infection is a systemic innate immune response against viral replication. Furthermore, these genes have approximately equal contributions to all tissues, making them possible candidates to be used as non-invasive biomarkers in studying PBMCs instead of MLN and spleen during acute SIV infection experiments. We identified clusters of genes that co-vary together and studied their correlation with regard to other gene clusters. We also developed novel methods to faithfully visualize multi-gene correlations on two-dimensional polar plots, and to visualize tissue specificity of gene expression responses.
PMCID: PMC4436129  PMID: 25984721
3.  Computational Model of VEGFR2 pathway to ERK activation and modulation through receptor trafficking 
Cellular signalling  2013;25(12):10.1016/j.cellsig.2013.08.015.
Vascular Endothelial Growth Factor (VEGF) signal transduction is central to angiogenesis in development and in pathological conditions such as cancer, retinopathy and ischemic diseases. We constructed and validated a computational model of VEGFR2 trafficking and signaling, to study the role of receptor trafficking kinetics in modulating ERK phosphorylation in VEGF-stimulated endothelial cells. Trafficking parameters were optimized and validated against four previously published in vitro experiments. Based on these parameters, model simulations demonstrated interesting behaviors that may be highly relevant to understanding VEGF signaling in endothelial cells. First, at moderate VEGF doses, VEGFR2 phosphorylation and ERK phosphorylation are related in a log-linear fashion, with a stable duration of ERK activation; but with higher VEGF stimulation, phosphoERK becomes saturated, and its duration increases. Second, a large endosomal fraction of VEGFR2 makes the ERK activation reaction network less sensitive to perturbations in VEGF dosage. Third, extracellular-matrix-bound VEGF binds and activates VEGFR2, but by internalizing at a slower rate, matrix-bound VEGF-induced intracellular ERK phosphorylation is predicted to be greater in magnitude and more sustained, in agreement with experimental evidence. Fourth, different endothelial cell types appear to have different trafficking rates, which result in different levels of endosomal receptor localization and different ERK response profiles.
PMCID: PMC3865527  PMID: 23993967
Angiogenesis; mathematical model; receptor tyrosine kinase; systems biology; endothelial signaling; trafficking
4.  Integration of Experimental and Computational Approaches to Sprouting Angiogenesis 
Current opinion in hematology  2012;19(3):184-191.
Purpose of review
We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches.
Recent findings
Experimental data extends beyond the tip cell vs. stalk cell paradigm, and involves numerous molecular inputs such as VEGF and Notch. This data is being used to generate and validate computational models, which can then be used to predict the results of hypothetical experiments that are difficult to perform in the laboratory, and to generate new hypotheses that account for system-wide interactions. As a result of this integration, descriptions of critical gradients of growth factor-receptor complexes have been generated, and new modulators of cell behavior have been described.
We suggest that the recent emphasis on the different stages of sprouting angiogenesis, and integration of experimental and computational approaches, should provide a way to manage the complexity of this process and help identify new regulatory paradigms and therapeutic targets.
PMCID: PMC4132663  PMID: 22406822
Sprouting angiogenesis; experimental models; computational models; stages of angiogenesis
5.  Computational Model of Gab1/2-Dependent VEGFR2 Pathway to Akt Activation 
PLoS ONE  2013;8(6):e67438.
Vascular endothelial growth factor (VEGF) signal transduction is central to angiogenesis in development and in pathological conditions such as cancer, retinopathy and ischemic diseases. However, no detailed mass-action models of VEGF receptor signaling have been developed. We constructed and validated the first computational model of VEGFR2 trafficking and signaling, to study the opposing roles of Gab1 and Gab2 in regulation of Akt phosphorylation in VEGF-stimulated endothelial cells. Trafficking parameters were optimized against 5 previously published in vitro experiments, and the model was validated against six independent published datasets. The model showed agreement at several key nodes, involving scaffolding proteins Gab1, Gab2 and their complexes with Shp2. VEGFR2 recruitment of Gab1 is greater in magnitude, slower, and more sustained than that of Gab2. As Gab2 binds VEGFR2 complexes more transiently than Gab1, VEGFR2 complexes can recycle and continue to participate in other signaling pathways. Correspondingly, the simulation results show a log-linear relationship between a decrease in Akt phosphorylation and Gab1 knockdown while a linear relationship was observed between an increase in Akt phosphorylation and Gab2 knockdown. Global sensitivity analysis demonstrated the importance of initial-concentration ratios of antagonistic molecular species (Gab1/Gab2 and PI3K/Shp2) in determining Akt phosphorylation profiles. It also showed that kinetic parameters responsible for transient Gab2 binding affect the system at specific nodes. This model can be expanded to study multiple signaling contexts and receptor crosstalk and can form a basis for investigation of therapeutic approaches, such as tyrosine kinase inhibitors (TKIs), overexpression of key signaling proteins or knockdown experiments.
PMCID: PMC3689841  PMID: 23805312
6.  APOBEC3G-Augmented Stem Cell Therapy to Modulate HIV Replication: A Computational Study 
PLoS ONE  2013;8(5):e63984.
The interplay between the innate immune system restriction factor APOBEC3G and the HIV protein Vif is a key host-retrovirus interaction. APOBEC3G can counteract HIV infection in at least two ways: by inducing lethal mutations on the viral cDNA; and by blocking steps in reverse transcription and viral integration into the host genome. HIV-Vif blocks these antiviral functions of APOBEC3G by impeding its encapsulation. Nonetheless, it has been shown that overexpression of APOBEC3G, or interfering with APOBEC3G-Vif binding, can efficiently block in vitro HIV replication. Some clinical studies have also suggested that high levels of APOBEC3G expression in HIV patients are correlated with increased CD4+ T cell count and low levels of viral load; however, other studies have reported contradictory results and challenged this observation. Stem cell therapy to replace a patient’s immune cells with cells that are more HIV-resistant is a promising approach. Pre-implantation gene transfection of these stem cells can augment the HIV-resistance of progeny CD4+ T cells. As a protein, APOBEC3G has the advantage that it can be genetically encoded, while small molecules cannot. We have developed a mathematical model to quantitatively study the effects on in vivo HIV replication of therapeutic delivery of CD34+ stem cells transfected to overexpress APOBEC3G. Our model suggests that stem cell therapy resulting in a high fraction of APOBEC3G-overexpressing CD4+ T cells can effectively inhibit in vivo HIV replication. We extended our model to simulate the combination of APOBEC3G therapy with other biological activities, to estimate the likelihood of improved outcomes.
PMCID: PMC3661658  PMID: 23724012
7.  Expression of VEGF and Semaphorin Genes Define Subgroups of Triple Negative Breast Cancer 
PLoS ONE  2013;8(5):e61788.
Triple negative breast cancers (TNBC) are difficult to treat due to a lack of targets and heterogeneity. Inhibition of angiogenesis is a promising therapeutic strategy, but has had limited effectiveness so far in breast cancer. To quantify heterogeneity in angiogenesis-related gene expression in breast cancer, we focused on two families – VEGFs and semaphorins – that compete for neuropilin co-receptors on endothelial cells. We compiled microarray data for over 2,600 patient tumor samples and analyzed the expression of VEGF- and semaphorin-related ligands and receptors. We used principal component analysis to identify patterns of gene expression, and clustering to group samples according to these patterns. We used available survival data to determine whether these clusters had prognostic as well as therapeutic relevance. TNBC was highly associated with dysregulation of VEGF- and semaphorin-related genes; in particular, it appeared that expression of both VEGF and semaphorin genes were altered in a pro-angiogenesis direction. A pattern of high VEGFA expression with low expression of secreted semaphorins was associated with 60% of triple-negative breast tumors. While all TNBC groups demonstrated poor prognosis, this signature also correlated with lower 5-year survival rates in non-TNBC samples. A second TNBC pattern, including high VEGFC expression, was also identified. These pro-angiogenesis signatures may identify cancers that are more susceptible to VEGF inhibition.
PMCID: PMC3648524  PMID: 23667446
8.  Murine Spinotrapezius Model to Assess the Impact of Arteriolar Ligation on Microvascular Function and Remodeling 
The murine spinotrapezius is a thin, superficial skeletal support muscle that extends from T3 to L4, and is easily accessible via dorsal skin incision. Its unique anatomy makes the spinotrapezius useful for investigation of ischemic injury and subsequent microvascular remodeling. Here, we demonstrate an arteriolar ligation model in the murine spinotrapezius muscle that was developed by our research team and previously published1-3. For certain vulnerable mouse strains, such as the Balb/c mouse, this ligation surgery reliably creates skeletal muscle ischemia and serves as a platform for investigating therapies that stimulate revascularization. Methods of assessment are also demonstrated, including the use of intravital and confocal microscopy. The spinotrapezius is well suited to such imaging studies due to its accessibility (superficial dorsal anatomy) and relative thinness (60-200 μm). The spinotrapezius muscle can be mounted en face, facilitating imaging of whole-muscle microvascular networks without histological sectioning. We describe the use of intravital microscopy to acquire metrics following a functional vasodilation procedure; specifically, the increase in arterilar diameter as a result of muscle contraction. We also demonstrate the procedures for harvesting and fixing the tissues, a necessary precursor to immunostaining studies and the use of confocal microscopy.
PMCID: PMC3622090  PMID: 23486360
Biomedical Engineering; Issue 73; Medicine; Anatomy; Physiology; Surgery; Immunology; Hematology; Microvessels; Capillaries; Arterioles; Venules; Vascular Diseases; Ischemia; spinotrapezius; peripheral vascular disease; functional vasodilation; arteriolar ligation; vessels; circulation; confocal microscopy; animal model
9.  Computational models of VEGF-associated angiogenic processes in cancer 
Tumour angiogenesis allows a growing mass of cancer cells to overcome oxygen diffusion limitation and to increase cell survival. The growth of capillaries from pre-existing blood vessels is the result of numerous signalling cascades involving different molecules and of cellular events involving multiple cell and tissue types. Computational models offer insight into the mechanisms governing angiogenesis and provide quantitative information on parameters difficult to assess by experiments alone. In this article, we summarize results from computational models of tumour angiogenic processes with a focus on the molecular-detailed vascular endothelial growth factor-associated models that have been developed in our laboratory, spanning multiple scales from the molecular to whole body.
PMCID: PMC4104688  PMID: 21266494
computational biology; systems biology; angiogenesis
10.  Effects of Fiber Type and Size on the Heterogeneity of Oxygen Distribution in Exercising Skeletal Muscle 
PLoS ONE  2012;7(9):e44375.
The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.
PMCID: PMC3445540  PMID: 23028531
11.  Selective Activation of Sphingosine 1-Phosphate Receptors 1 and 3 Promotes Local Microvascular Network Growth 
Tissue Engineering. Part A  2010;17(5-6):617-629.
Proper spatial and temporal regulation of microvascular remodeling is critical to the formation of functional vascular networks, spanning the various arterial, venous, capillary, and collateral vessel systems. Recently, our group has demonstrated that sustained release of sphingosine 1-phosphate (S1P) from biodegradable polymers promotes microvascular network growth and arteriolar expansion. In this study, we employed S1P receptor-specific compounds to activate and antagonize different combinations of S1P receptors to elucidate those receptors most critical for promotion of pharmacologically induced microvascular network growth. We show that S1P1 and S1P3 receptors act synergistically to enhance functional network formation via increased functional length density, arteriolar diameter expansion, and increased vascular branching in the dorsal skinfold window chamber model. FTY720, a potent activator of S1P1 and S1P3, promoted a 107% and 153% increase in length density 3 and 7 days after implantation, respectively. It also increased arteriolar diameters by 60% and 85% 3 and 7 days after implantation. FTY720-stimulated branching in venules significantly more than unloaded poly(D, L-lactic-co-glycolic acid). When implanted on the mouse spinotrapezius muscle, FTY720 stimulated an arteriogenic response characterized by increased tortuosity and collateralization of branching microvascular networks. Our results demonstrate the effectiveness of S1P1 and S1P3 receptor-selective agonists (such as FTY720) in promoting microvascular growth for tissue engineering applications.
PMCID: PMC3043977  PMID: 20874260
12.  Multi-Scale Modeling of HIV Infection in vitro and APOBEC3G-Based Anti-Retroviral Therapy 
PLoS Computational Biology  2012;8(2):e1002371.
The human APOBEC3G is an innate restriction factor that, in the absence of Vif, restricts HIV-1 replication by inducing excessive deamination of cytidine residues in nascent reverse transcripts and inhibiting reverse transcription and integration. To shed light on impact of A3G-Vif interactions on HIV replication, we developed a multi-scale computational system consisting of intracellular (single-cell), cellular and extracellular (multicellular) events by using ordinary differential equations. The single-cell model describes molecular-level events within individual cells (such as production and degradation of host and viral proteins, and assembly and release of new virions), whereas the multicellular model describes the viral dynamics and multiple cycles of infection within a population of cells. We estimated the model parameters either directly from previously published experimental data or by running simulations to find the optimum values. We validated our integrated model by reproducing the results of in vitro T cell culture experiments. Crucially, both downstream effects of A3G (hypermutation and reduction of viral burst size) were necessary to replicate the experimental results in silico. We also used the model to study anti-HIV capability of several possible therapeutic strategies including: an antibody to Vif; upregulation of A3G; and mutated forms of A3G. According to our simulations, A3G with a mutated Vif binding site is predicted to be significantly more effective than other molecules at the same dose. Ultimately, we performed sensitivity analysis to identify important model parameters. The results showed that the timing of particle formation and virus release had the highest impacts on HIV replication. The model also predicted that the degradation of A3G by Vif is not a crucial step in HIV pathogenesis.
Author Summary
According to UNAIDS (The Joint UN Programme on HIV/AIDS) and WHO, HIV/AIDS has killed more than 25 million people worldwide since its recognition in 1981. Recently, APOBEC3G, a member of the APOBEC family, has been shown to be a potent inhibitor of HIV infection. In contrast, a viral protein, called Vif, is known to protect the virus by binding to APOBEC3G and causing the degradation of this enzyme. We have developed a computational model to simulate in vitro experiments that include A3G-Vif interactions at the intracellular level and T cell-HIV dynamics at the multicellular level. Experimental data were used to establish system parameters and also to validate predictions of our models. We studied various drugs targeting APOBEC3G and Vif pathways to find the optimum therapeutic approach against HIV replication. Our model predicted that a mutated form of APOBEC3G that does not bind to Vif performs significantly better at suppressing HIV replication compared to other drugs. We also found that the drug should be administered shortly after infection and it must be available to all cells in order to be effective.
PMCID: PMC3276540  PMID: 22346743
13.  Increase of plasma VEGF after intravenous administration of bevacizumab is predicted by a pharmacokinetic model 
Cancer research  2010;70(23):9886-9894.
Vascular endothelial growth factor (VEGF) is one of the most potent cytokines targeted in anti-angiogenic therapies. Bevacizumab, a recombinant humanized monoclonal antibody to VEGF, is being used clinically in combination with chemotherapy for colorectal, non-small cell lung and breast cancers, and as a single agent for glioblastoma, and is being tested for other types of cancer in numerous clinical trials. It has been reported that the intravenous injection of bevacizumab leads to an increase of plasma VEGF concentration in cancer patients. The mechanism responsible for this counterintuitive increase has not been elucidated, although several hypotheses have been proposed. We use a multiscale systems biology approach to address this problem. We have constructed a whole-body pharmacokinetic model comprising three compartments: blood, normal tissue and tumor tissue. Molecular interactions between VEGF-A family members, their major receptors, the extracellular matrix, and an anti-VEGF ligand are considered for each compartment. Diffusible molecules extravasate, intravasate, are removed from the healthy tissue through the lymphatics, and are cleared from the blood. Our model reproduces the experimentally-observed increase of plasma VEGF following intravenous administration of bevacizumab, and predicts this increase to be a consequence of inter-compartmental exchange of VEGF, the anti-VEGF agent and the VEGF/anti-VEGF complex. Our results suggest that a fraction of the anti-VEGF drug extravasates, allowing the agent to bind the interstitial VEGF. When the complex intravasates (via a combination of lymphatic drainage and microvascular transport of macromolecules) and dissociates in the blood, VEGF is released and the VEGF concentration increases in the plasma. These results provide a new hypothesis on the kinetics of VEGF and on the VEGF distribution in the body caused by anti-angiogenic therapies, as well as their mechanisms of action and could help in designing anti-angiogenic therapies.
PMCID: PMC3058319  PMID: 21118974
angiogenesis; anti-VEGF; bevacizumab; anti-angiogenic therapy; mathematical model
14.  Systems biology of pro-angiogenic therapies targeting the VEGF system 
Vascular endothelial growth factor (VEGF) is a family of cytokines for which the dysregulation of expression is involved in many diseases; for some excess VEGF causes pathological hypervascularization, while for others VEGF-induced vascular remodeling may alleviate ischemia and/or hypoxia. Anti-angiogenic therapies attacking the VEGF pathway have begun to live up to their promise for treatment of certain cancers and of age-related macular degeneration. However, the corollary is not yet true: in coronary artery disease and peripheral artery disease, clinical trials of pro-angiogenic VEGF delivery have not, so far, proven successful. The VEGF and VEGF-receptor system is complex, with at least five ligand genes, some encoding multiple protein isoforms and five receptor genes. A systems biology approach to designing pro-angiogenic therapies, using a combination of quantitative experimental approaches and detailed computational models, is essential to deal with this complexity and to understand the effects of drugs targeting the system. This approach allows us to learn from unsuccessful clinical trials and to design and test novel single therapeutics or combinations of therapeutics. Among the parameters that can be varied in order to determine optimal strategy are dosage, timing of multiple doses, route of administration, and the molecular target.
PMCID: PMC2990677  PMID: 20890966
Drug efficacy; Drug transport; Physiome; Protein interaction networks; Systems medicine
15.  Computational Modeling of Interacting VEGF and Soluble VEGF Receptor Concentration Gradients 
Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.
PMCID: PMC3185289  PMID: 22007175
angiogenesis; vascular development; computational model; mathematical model; sFlt-1; VEGF; capillary sprouting
16.  Gene Therapy from the perspective of Systems Biology 
Gene therapy research has expanded from its original concept of replacing absent or defective DNA with functional DNA for transcription. Genetic material may be delivered via multiple vectors, including naked plasmid DNA, viruses and even cells with the goal of increasing gene expression; and the targeting of specific tissues or cell types is aimed at decreasing risks of systemic or side effects. As with the development of any drug, there is an amount of empiricism in the choice of gene target, route of administration, dosing and in particular the scaling-up from pre-clinical models to clinical trials. Systems Biology, whose arsenal includes high-throughput experimental and computational studies that account for the complexities of host-disease-therapy interactions, holds significant promise in aiding the development and optimization of gene therapies, including personalized therapies and the identification of biomarkers for success of these strategies. In this review we describe some of the obstacles and successes in gene therapy, using the specific example of growth factor gene delivery to promote angiogenesis and blood vessel remodeling in ischemic diseases; we also make references to anti-angiogenic gene therapy in cancer. The opportunities for Systems Biology and in silico modeling to improve on current outcomes are highlighted.
PMCID: PMC3021921  PMID: 20886389
Mathematical model; computational model; bioinformatics; angiogenesis; gene delivery; coronary artery disease; peripheral artery disease
17.  Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis 
BMC Systems Biology  2011;5:59.
The spatial distribution of vascular endothelial growth factor A (VEGF) is an important mediator of vascular patterning. Previous experimental studies in the mouse hindbrain and retina have suggested that VEGF alternative splicing, which controls the ability of VEGF to bind to heparan sulfate proteoglycans (HSPGs) in the extracellular matrix (ECM), plays a key role in controlling VEGF diffusion and gradients in tissues. Conversely, proteolysis notably by matrix metalloproteinases (MMPs), plays a critical role in pathological situations by releasing matrix-sequestered VEGF and modulating angiogenesis. However, computational models have predicted that HSPG binding alone does not affect VEGF localization or gradients at steady state.
Using a 3D molecular-detailed reaction-diffusion model of VEGF ligand-receptor kinetics and transport, we test alternate models of VEGF transport in the extracellular environment surrounding an endothelial sprout. We show that differences in localization between VEGF isoforms, as observed experimentally in the mouse hindbrain, as well as the ability of proteases to redistribute VEGF in pathological situations, are consistent with a model where VEGF is endogenously cleared or degraded in an isoform-specific manner. We use our predictions of the VEGF distribution to quantify a tip cell's receptor binding and gradient sensing capacity. A novel prediction is that neuropilin-1, despite functioning as a coreceptor to VEGF165-VEGFR2 binding, reduces the ability of a cell to gauge the relative steepness of the VEGF distribution. Comparing our model to available in vivo vascular patterning data suggests that vascular phenotypes are most consistently predicted at short range by the soluble fraction of the VEGF distributions, or at longer range by matrix-bound VEGF detected in a filopodia-dependent manner.
Isoform-specific VEGF degradation provides a possible explanation for numerous examples of isoform specificity in VEGF patterning and examples of proteases relocation of VEGF upon release.
PMCID: PMC3113235  PMID: 21535871
19.  Module-based multiscale simulation of angiogenesis in skeletal muscle 
Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.
We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.
This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.
PMCID: PMC3079676  PMID: 21463529
20.  A systems biology perspective on sVEGFR1: its biological function, pathogenic role & therapeutic use 
Angiogenesis is the growth of new capillaries from pre-existent microvasculature. A wide range of pathological conditions, from atherosclerosis to cancer, can be attributed to either excessive or deficient angiogenesis. Central to the physiological regulation of angiogenesis is the vascular endothelial growth factor (VEGF) system – its ligands and receptors (VEGFRs) are thus prime molecular targets of pro-angiogenic and anti-angiogenic therapies. Of growing interest as a prognostic marker and therapeutic target in angiogenesis-dependent diseases is soluble VEGF receptor-1 (sVEGFR1, also known as sFlt-1) – a truncated version of the cell membrane-spanning VEGFR1. For instance, it is known that sVEGFR1 is involved in the endothelial dysfunction characterizing the pregnancy disorder of pre-eclampsia, and sVEGFR1’s therapeutic potential as an anti-angiogenic agent is being evaluated in pre-clinical models of cancer. This mini-review begins with an examination of the protein domain structure and biomolecular interactions of sVEGFR1 in relation to the full-length VEGFR1. A synopsis of known and inferred physiological and pathological roles of sVEGFR1 is then given, with emphasis on the utility of computational systems biology models in deciphering the molecular mechanisms by which sVEGFR1’s purported biological functions occur. Finally, we present the need for a systems biology perspective in interpreting circulating VEGF and sVEGFR1 concentrations as surrogate markers of angiogenic status in angiogenesis-dependent diseases.
PMCID: PMC3039304  PMID: 19840194
angiogenesis; neovascularization; vascular endothelial growth factor (VEGF); soluble fms-like tyrosine kinase 1 (sFlt-1); molecular systems biology; systems pharmacology; computational modeling; multi-scale modeling
21.  Modeling of growth factor-receptor systems: from molecular-level protein interaction networks to whole-body compartment models 
Methods in enzymology  2009;467:461-497.
Most physiological processes are subjected to molecular regulation by growth factors, which are secreted proteins that activate chemical signal transduction pathways through binding of specific cell-surface receptors. One particular growth factor system involved in the in vivo regulation of blood vessel growth is called the vascular endothelial growth factor (VEGF) system. Computational and numerical techniques are well-suited to handle the molecular complexity (the number of binding partners involved, including ligands, receptors, and inert binding sites) and multi-scale nature (intra-tissue vs. inter-tissue transport and local vs. systemic effects within an organism) involved in modeling growth factor system interactions and effects. This paper introduces a variety of in silico models that seek to recapitulate different aspects of VEGF system biology at various spatial and temporal scales: molecular-level kinetic models focus on VEGF ligand-receptor interactions at and near the endothelial cell surface; meso-scale single-tissue 3D models can simulate the effects of multi-cellular tissue architecture on the spatial variation in VEGF ligand production and receptor activation; compartmental modeling allows efficient prediction of average interstitial VEGF concentrations and cell-surface VEGF signaling intensities across multiple large tissue volumes, permitting the investigation of whole-body inter-tissue transport (e.g., vascular permeability and lymphatic drainage). The given examples will demonstrate the utility of computational models in aiding both basic science and clinical research on VEGF systems biology.
PMCID: PMC3001233  PMID: 19897104
22.  Systems Analysis of Small Signaling Modules Relevant to Eight Human Diseases 
Annals of Biomedical Engineering  2010;39(2):621-635.
Using eight newly generated models relevant to addiction, Alzheimer’s disease, cancer, diabetes, HIV, heart disease, malaria, and tuberculosis, we show that systems analysis of small (4–25 species), bounded protein signaling modules rapidly generates new quantitative knowledge from published experimental research. For example, our models show that tumor sclerosis complex (TSC) inhibitors may be more effective than the rapamycin (mTOR) inhibitors currently used to treat cancer, that HIV infection could be more effectively blocked by increasing production of the human innate immune response protein APOBEC3G, rather than targeting HIV’s viral infectivity factor (Vif), and how peroxisome proliferator-activated receptor alpha (PPARα) agonists used to treat dyslipidemia would most effectively stimulate PPARα signaling if drug design were to increase agonist nucleoplasmic concentration, as opposed to increasing agonist binding affinity for PPARα. Comparative analysis of system-level properties for all eight modules showed that a significantly higher proportion of concentration parameters fall in the top 15th percentile sensitivity ranking than binding affinity parameters. In infectious disease modules, host networks were significantly more sensitive to virulence factor concentration parameters compared to all other concentration parameters. This work supports the future use of this approach for informing the next generation of experimental roadmaps for known diseases.
Electronic supplementary material
The online version of this article (doi:10.1007/s10439-010-0208-y) contains supplementary material, which is available to authorized users.
PMCID: PMC3033523  PMID: 21132372
Systems biology; Human disease; Protein signaling; Comparative meta-analysis; Sensitivity analysis
23.  Quantifying the Proteolytic Release of Extracellular Matrix-Sequestered VEGF with a Computational Model 
PLoS ONE  2010;5(7):e11860.
VEGF proteolysis by plasmin or matrix metalloproteinases (MMPs) is believed to play an important role in regulating vascular patterning in vivo by releasing VEGF from the extracellular matrix (ECM). However, a quantitative understanding of the kinetics of VEGF cleavage and the efficiency of cell-mediated VEGF release is currently lacking. To address these uncertainties, we develop a molecular-detailed quantitative model of VEGF proteolysis, used here in the context of an endothelial sprout.
Methodology and Findings
To study a cell's ability to cleave VEGF, the model captures MMP secretion, VEGF-ECM binding, VEGF proteolysis from VEGF165 to VEGF114 (the expected MMP cleavage product of VEGF165) and VEGF receptor-mediated recapture. Using experimental data, we estimated the effective bimolecular rate constant of VEGF165 cleavage by plasmin to be 328 M−1s−1 at 25°C, which is relatively slow compared to typical MMP-ECM proteolysis reactions. While previous studies have implicated cellular proteolysis in growth factor processing, we show that single cells do not individually have the capacity to cleave VEGF to any appreciable extent (less than 0.1% conversion). In addition, we find that a tip cell's receptor system will not efficiently recapture the cleaved VEGF due to an inability of cleaved VEGF to associate with Neuropilin-1.
Overall, VEGF165 cleavage in vivo is likely to be mediated by the combined effect of numerous cells, instead of behaving in a single-cell-directed, autocrine manner. We show that heparan sulfate proteoglycans (HSPGs) potentiate VEGF cleavage by increasing the VEGF clearance time in tissues. In addition, we find that the VEGF-HSPG complex is more sensitive to proteases than is soluble VEGF, which may imply its potential relevance in receptor signaling. Finally, according to our calculations, experimentally measured soluble protease levels are approximately two orders of magnitude lower than that needed to reconcile levels of VEGF cleavage seen in pathological situations.
PMCID: PMC2912330  PMID: 20686621
24.  Collateral Capillary Arterialization following arteriolar ligation in murine skeletal muscle 
Chronic and acute ischemic diseases – peripheral artery disease, coronary artery disease, stroke – result in tissue damage unless blood flow is maintained or restored in a timely manner. Mice of different strains recover from arteriolar ligation (by increasing collateral blood flow) at different speeds. We quantify the spatio-termporal patterns of microvascular network remodeling following arteriolar ligation in different mouse strains to better understand interindividual variability.
Whole-muscle spinotrapezius microvascular networks of mouse strains C57Bl/6, Balb/c and CD1 were imaged using confocal microscopy following ligation of feeding arterioles.
Baseline arteriolar structures of C57Bl/6 and Balb/c mice feature heavily ramified arcades and unconnected dendritic trees, respectively. This network angioarchitecture identifies ischemia-protected and ischemia-vulnerable tissues: unlike C57Bl/6, downstream capillary perfusion in Balb/c spinotrapezius is lost following ligation. Perfusion recovery requires arterialization (expansion and investment of mural cells) of a subset of capillaries forming a new low-resistance collateral pathway between arteriolar trees. Outbred CD1 exhibit either Balb/c-like or C57Bl/6-like spinotrapezius angioarchitecture, predictive of response to arteriolar ligation.
This collateral capillary arterialization process may explain the reported longer time required for blood flow recovery in Balb/c hindlimb ischemia, as low-resistance blood flow pathways along capillary conduits must be formed (‘arterialization’) before reperfusion.
PMCID: PMC2907254  PMID: 20618691
25.  The Presence of VEGF Receptors on the Luminal Surface of Endothelial Cells Affects VEGF Distribution and VEGF Signaling 
PLoS Computational Biology  2009;5(12):e1000622.
Vascular endothelial growth factor (VEGF) is a potent cytokine that binds to specific receptors on the endothelial cells lining blood vessels. The signaling cascade triggered eventually leads to the formation of new capillaries, a process called angiogenesis. Distributions of VEGF receptors and VEGF ligands are therefore crucial determinants of angiogenic events and, to our knowledge, no quantification of abluminal vs. luminal receptors has been performed. We formulate a molecular-based compartment model to investigate the VEGF distribution in blood and tissue in humans and show that such quantification would lead to new insights on angiogenesis and VEGF-dependent diseases. Our multiscale model includes two major isoforms of VEGF (VEGF121 and VEGF165), as well as their receptors (VEGFR1 and VEGFR2) and the non-signaling co-receptor neuropilin-1 (NRP1). VEGF can be transported between tissue and blood via transendothelial permeability and the lymphatics. VEGF receptors are located on both the luminal and abluminal sides of the endothelial cells. In this study, we analyze the effects of the VEGF receptor localization on the endothelial cells as well as of the lymphatic transport. We show that the VEGF distribution is affected by the luminal receptor density. We predict that the receptor signaling occurs mostly on the abluminal endothelial surface, assuming that VEGF is secreted by parenchymal cells. However, for a low abluminal but high luminal receptor density, VEGF binds predominantly to VEGFR1 on the abluminal surface and VEGFR2 on the luminal surface. Such findings would be pertinent to pathological conditions and therapies related to VEGF receptor imbalance and overexpression on the endothelial cells and will hopefully encourage experimental receptor quantification for both luminal and abluminal surfaces on endothelial cells.
Author Summary
Angiogenesis is the growth of new blood vessels from pre-existing vasculature that occurs in physiological (e.g., exercise) and pathological contexts (e.g., cancer). This process is often triggered by a signaling cascade that occurs upon ligand-receptor binding between vascular endothelial growth factor (VEGF) and its receptors (VEGFR1/Flt-1, VEGFR2/KDR). These receptors are expressed by endothelial cells that line the blood vessels. Little is known about the quantitative proportion of abluminal receptors (facing the tissue) as compared to those on the luminal surface (facing the blood). We have built a compartment model with molecular details from human tissues to investigate why such experimental data would be of importance. We conclude that the receptor distribution on the endothelial cells can significantly alter the VEGF distribution and the VEGF signaling (through its binding to the receptors) and that quantification of luminal vs. abluminal VEGF receptors would shed light on VEGF signaling and VEGF-dependent mechanisms of angiogenesis.
PMCID: PMC2790341  PMID: 20041209

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