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1.  Ultrasensitivity in Phosphorylation-Dephosphorylation Cycles with Little Substrate 
PLoS Computational Biology  2013;9(8):e1003175.
Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with phosphosites, we find an upper bound of the Hill number of , and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.
doi:10.1371/journal.pcbi.1003175
PMCID: PMC3738489  PMID: 23950701
2.  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.
doi:10.1371/journal.pone.0067438
PMCID: PMC3689841  PMID: 23805312
3.  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.
doi:10.1371/journal.pone.0063984
PMCID: PMC3661658  PMID: 23724012
4.  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.
doi:10.1371/journal.pone.0061788
PMCID: PMC3648524  PMID: 23667446
5.  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.
doi:10.3791/50218
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
6.  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.
doi:10.1371/journal.pone.0044375
PMCID: PMC3445540  PMID: 23028531
7.  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.
doi:10.1089/ten.tea.2010.0404
PMCID: PMC3043977  PMID: 20874260
8.  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.
doi:10.1371/journal.pcbi.1002371
PMCID: PMC3276540  PMID: 22346743
9.  Adjusting Phenotypes by Noise Control 
PLoS Computational Biology  2012;8(1):e1002344.
Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.
Author Summary
Stochastic gene expression at the single cell level can lead to significant phenotypic variation at the population level. To obtain a desired phenotype, the noise levels of intracellular protein concentrations may need to be tuned and controlled. Noise levels often decrease in relative amount as the mean values increase. This implies that the noise levels can be passively controlled by changing the mean values. In an engineering perspective, the noise levels can be further controlled while the mean values can be simultaneously adjusted to desired values. Here, systematic schemes for such simultaneous control are described by identifying where and by how much the system needs to be perturbed. The schemes can be applied to the design process of a potential therapeutic HIV-drug that targets a certain set of reactions that are identified by the proposed analysis, to prevent stochastic transition to the lytic state. In some cases, the simultaneous control cannot be performed efficiently, when the noise levels strongly change with the mean values. This problem is shown to be resolved by applying extra noise and feedback.
doi:10.1371/journal.pcbi.1002344
PMCID: PMC3257291  PMID: 22253584
10.  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.
doi:10.1158/0008-5472.CAN-10-1419
PMCID: PMC3058319  PMID: 21118974
angiogenesis; anti-VEGF; bevacizumab; anti-angiogenic therapy; mathematical model
11.  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.
doi:10.1002/wsbm.92
PMCID: PMC2990677  PMID: 20890966
Drug efficacy; Drug transport; Physiome; Protein interaction networks; Systems medicine
12.  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.
doi:10.3389/fphys.2011.00062
PMCID: PMC3185289  PMID: 22007175
angiogenesis; vascular development; computational model; mathematical model; sFlt-1; VEGF; capillary sprouting
13.  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
14.  Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis 
BMC Systems Biology  2011;5:59.
Background
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.
Results
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.
Conclusions
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.
doi:10.1186/1752-0509-5-59
PMCID: PMC3113235  PMID: 21535871
16.  Module-based multiscale simulation of angiogenesis in skeletal muscle 
Background
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.
Results
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.
Conclusions
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.
doi:10.1186/1742-4682-8-6
PMCID: PMC3079676  PMID: 21463529
17.  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.
doi:10.1111/j.1582-4934.2009.00941.x
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
18.  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.
doi:10.1016/S0076-6879(09)67018-X
PMCID: PMC3001233  PMID: 19897104
19.  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.
doi:10.1007/s10439-010-0208-y
PMCID: PMC3033523  PMID: 21132372
Systems biology; Human disease; Protein signaling; Comparative meta-analysis; Sensitivity analysis
20.  Quantifying the Proteolytic Release of Extracellular Matrix-Sequestered VEGF with a Computational Model 
PLoS ONE  2010;5(7):e11860.
Background
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.
Conclusions
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.
doi:10.1371/journal.pone.0011860
PMCID: PMC2912330  PMID: 20686621
21.  Collateral Capillary Arterialization following arteriolar ligation in murine skeletal muscle 
OBJECTIVE
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.
METHODS
Whole-muscle spinotrapezius microvascular networks of mouse strains C57Bl/6, Balb/c and CD1 were imaged using confocal microscopy following ligation of feeding arterioles.
RESULTS
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.
CONCLUSIONS
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.
doi:10.1111/j.1549-8719.2010.00034.x
PMCID: PMC2907254  PMID: 20618691
22.  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.
doi:10.1371/journal.pcbi.1000622
PMCID: PMC2790341  PMID: 20041209
23.  Systems Biology of Vascular Endothelial Growth Factors 
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.
doi:10.1080/10739680802095964
PMCID: PMC2722038  PMID: 18608994
angiogenesis; vegf; mathematical modeling; computational modeling; transport
24.  Dimerization of VEGF receptors and implications for signal transduction: a computational study 
Biophysical chemistry  2007;128(2-3):125-139.
Vascular endothelial growth factor (VEGF) is a potent cytokine involved in the induction of neovascularization. Secreted as a cysteine-linked dimer, it has two binding sites at opposite poles through which it may bind VEGF receptors (VEGFRs), receptor tyrosine kinases found on the surface of endothelial and other cells. The binding of a VEGF molecule to two VEGFR molecules induces transphosphorylation of the intracellular domains of the receptors, leading to signal transduction. The dominant mechanism of receptor dimerization is not clear: the receptors may be present in an inactive pre-dimerized form, VEGF binding first to one of the receptors, the second receptor then ideally located for dimerization; or VEGF may bind receptor monomers on the cell surface, which then diffuse and bind to available unligated receptor monomers to complete the activation. Both processes take place and one or other may dominate on different cell types. We demonstrate the impact of dimerization mechanism on the binding of VEGF to the cell surface and on the formation of active signaling receptor complexes. We describe two methods to determine which process dominates, based on binding and phosphorylation assays. The presence of two VEGF receptor populations, VEGFR1 and VEGFR2, can result in receptor heterodimer formation. Our simulations predict that heterodimers will comprise 10–50% of the active, signaling VEGF receptor complexes, and that heterodimers will form at the expense of homodimers of VEGFR1 when VEGFR2 populations are larger. These results have significant implications for VEGF signal transduction and interpretation of experimental studies. These results may be applicable to other ligand-receptor pairs, in particular PDGF.
doi:10.1016/j.bpc.2007.03.010
PMCID: PMC2711879  PMID: 17442480
homodimer; heterodimer; growth factor; receptor tyrosine kinase; mathematical model
25.  A Compartment Model of VEGF Distribution in Humans in the Presence of Soluble VEGF Receptor-1 Acting as a Ligand Trap 
PLoS ONE  2009;4(4):e5108.
Vascular endothelial growth factor (VEGF), through its activation of cell surface receptor tyrosine kinases including VEGFR1 and VEGFR2, is a vital regulator of stimulatory and inhibitory processes that keep angiogenesis – new capillary growth from existing microvasculature – at a dynamic balance in normal physiology. Soluble VEGF receptor-1 (sVEGFR1) – a naturally-occurring truncated version of VEGFR1 lacking the transmembrane and intracellular signaling domains – has been postulated to exert inhibitory effects on angiogenic signaling via two mechanisms: direct sequestration of angiogenic ligands such as VEGF; or dominant-negative heterodimerization with surface VEGFRs. In pre-clinical studies, sVEGFR1 gene and protein therapy have demonstrated efficacy in inhibiting tumor angiogenesis; while in clinical studies, sVEGFR1 has shown utility as a diagnostic or prognostic marker in a widening array of angiogenesis–dependent diseases. Here we developed a novel computational multi-tissue model for recapitulating the dynamic systemic distributions of VEGF and sVEGFR1. Model features included: physiologically-based multi-scale compartmentalization of the human body; inter-compartmental macromolecular biotransport processes (vascular permeability, lymphatic drainage); and molecularly-detailed binding interactions between the ligand isoforms VEGF121 and VEGF165, signaling receptors VEGFR1 and VEGFR2, non-signaling co-receptor neuropilin-1 (NRP1), as well as sVEGFR1. The model was parameterized to represent a healthy human subject, whereupon we investigated the effects of sVEGFR1 on the distribution and activation of VEGF ligands and receptors. We assessed the healthy baseline stability of circulating VEGF and sVEGFR1 levels in plasma, as well as their reliability in indicating tissue-level angiogenic signaling potential. Unexpectedly, simulated results showed that sVEGFR1 – acting as a diffusible VEGF sink alone, i.e., without sVEGFR1-VEGFR heterodimerization – did not significantly lower interstitial VEGF, nor inhibit signaling potential in tissues. Additionally, the sensitivity of plasma VEGF and sVEGFR1 to physiological fluctuations in transport rates may partially account for the heterogeneity in clinical measurements of these circulating angiogenic markers, potentially hindering their diagnostic reliability for diseases.
doi:10.1371/journal.pone.0005108
PMCID: PMC2663039  PMID: 19352513

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