A computational model of intracellular oxygen sensing by hypoxia-inducible factor HIF1 alpha

Hypoxia-dependent sequestration of an oxygen sensor by a widespread structural motif can shape the hypoxic response--a predictive kinetic model

Background

The activity of the heterodimeric transcription factor hypoxia inducible factor (HIF) is regulated by the post-translational, oxygen-dependent hydroxylation of its α-subunit by members of the prolyl hydroxylase domain (PHD or EGLN)-family and by factor inhibiting HIF (FIH). PHD-dependent hydroxylation targets HIFα for rapid proteasomal degradation; FIH-catalysed asparaginyl-hydroxylation of the C-terminal transactivation domain (CAD) of HIFα suppresses the CAD-dependent subset of the extensive transcriptional responses induced by HIF. FIH can also hydroxylate ankyrin-repeat domain (ARD) proteins, a large group of proteins which are functionally unrelated but share common structural features. Competition by ARD proteins for FIH is hypothesised to affect FIH activity towards HIFα; however the extent of this competition and its effect on the HIF-dependent hypoxic response are unknown.

Results

To analyse if and in which way the FIH/ARD protein interaction affects HIF-activity, we created a rate equation model. Our model predicts that an oxygen-regulated sequestration of FIH by ARD proteins significantly shapes the input/output characteristics of the HIF system. The FIH/ARD protein interaction is predicted to create an oxygen threshold for HIFα CAD-hydroxylation and to significantly sharpen the signal/response curves, which not only focuses HIFα CAD-hydroxylation into a defined range of oxygen tensions, but also makes the response ultrasensitive to varying oxygen tensions. Our model further suggests that the hydroxylation status of the ARD protein pool can encode the strength and the duration of a hypoxic episode, which may allow cells to memorise these features for a certain time period after reoxygenation.

Conclusions

The FIH/ARD protein interaction has the potential to contribute to oxygen-range finding, can sensitise the response to changes in oxygen levels, and can provide a memory of the strength and the duration of a hypoxic episode. These emergent properties are predicted to significantly shape the characteristics of HIF activity in animal cells. We argue that the FIH/ARD interaction should be taken into account in studies of the effect of pharmacological inhibition of the HIF-hydroxylases and propose that the interaction of a signalling sensor with a large group of proteins might be a general mechanism for the regulation of signalling pathways.

VEGF and soluble VEGF receptor-1 (sFlt-1) distributions in peripheral arterial disease: an in silico model

Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis, the growth of new capillaries from existing microvasculature. In peripheral arterial disease (PAD), lower extremity muscle ischemia develops downstream of atherosclerotic obstruction. A working hypothesis proposed that the maladaptive overexpression of soluble VEGF receptor 1 (sVEGFR1) in ischemic muscle tissues, and its subsequent antagonism of VEGF bioactivity, may contribute to the deficient angiogenic response in PAD, as well as the limited success of therapeutic angiogenesis strategies where exogenous VEGF genes/proteins are delivered. The objectives of this study were to develop a computational framework for simulating the systemic distributions of VEGF and sVEGFR1 (e.g., intramuscular vs. circulating, free vs. complexed) as observed in human PAD patients and to serve as a platform for the systematic optimization of diagnostic tools and therapeutic strategies. A three-compartment model was constructed, dividing the human body into the ischemic calf muscle, blood, and the rest of the body, connected through macromolecular biotransport processes. Detailed molecular interactions between VEGF, sVEGFR1, endothelial surface receptors (VEGFR1, VEGFR2, NRP1), and interstitial matrix sites were modeled. Our simulation results did not support a simultaneous decrease in plasma sVEGFR1 during PAD-associated elevations in plasma VEGF reported in literature. Furthermore, despite the overexpression in sVEGFR1, our PAD control demonstrated increased proangiogenic signaling complex formation, relative to our previous healthy control, due to sizeable upregulations in VEGFR2 and VEGF expression, thus leaving open the possibility that impaired angiogenesis in PAD may be rooted in signaling pathway disruptions downstream of ligand-receptor binding.

Structural analysis to determine the core of hypoxia response network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network's dynamics. The question that begs for an answer is how to identify the core that is representative of a network's dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.

Ascorbate inhibition of angiogenesis in aortic rings ex vivo and subcutaneous Matrigel plugs in vivo

Background

Angiogenesis is critical to tumor growth and is therefore a potential target for cancer therapy. As many current inhibitors of angiogenesis exhibit host toxicity, natural alternatives are needed. At millimolar concentrations, ascorbate (vitamin C) inhibits migration and tubule formation by mature endothelial cells and endothelial progenitors. In the present study, we examined the effects of ascorbate, at levels relevant during intravenous infusion therapy, on angiogenesis using an ex vivo an in vivo assay.

Methods

Two assays were used to evaluate effect of high-doses ascorbic acid on angiogenesis: ex vivo rat aortic ring explant assay in Matrigel matrices and in vivo Matrigel plug assay. In aortic rings, we quantified microvessel growth, branching and vessel regression under different treatment conditions. In murine angiogenesis assay, male C57 mice 6-8 weeks old were treated by high-dose ascorbic acid and the number of microvessels was analyzed by histological method. To characterize the population of cells that formed capillary network and microvessels, the sections were stained by CD34 and CD31 antibodies.

Results

Results show that sprouting of endothelial tubules from aortic rings was reduced in a concentration-dependent fashion by ascorbate: while controls roughly tripled sprout densities during the study, ascorbate (1 mg/mL, 5.5 mM) actually reduced sprout density. In vivo, the ability of mice to vascularize subcutaneously implanted Matrigel plug was diminished if the mice were treated with 430 mg/kg vitamin C: numbers of vessels, and vessel densities, in plugs from treated mice were roughly 30% less than those in plugs from untreated mice.

Conclusions

We conclude that the inhibition of angiogenesis by ascorbate suggested in vitro is confirmed in vivo, and that angiogenesis inhibition may be one mechanism by which intravenous ascorbate therapy shows efficacy in animal experiments and clinical case studies.

Fumarate hydratase deficiency in renal cancer induces glycolytic addiction and hypoxia-inducible transcription factor 1alpha stabilization by glucose-dependent generation of reactive oxygen species

Hereditary leiomyomatosis and renal cell cancer (HLRCC) is an inherited cancer syndrome linked to biallelic inactivation of the gene encoding the tricarboxylic acid cycle enzyme fumarate hydratase (FH). Individuals with HLRCC are at risk to develop cutaneous and uterine leiomyomas and an aggressive form of kidney cancer. Pseudohypoxic drive-the aberrant activation of cellular hypoxia response pathways despite normal oxygen tension-is considered to be a likely mechanism underlying the etiology of this tumor. Pseudohypoxia requires the oxygen-independent stabilization of the alpha subunit of the hypoxia-inducible transcription factor (HIF-1alpha). Under normoxic conditions, proline hydroxylation of HIF-1alpha permits VHL recognition and subsequent targeting for proteasomal degradation. Here, we demonstrate that inactivating mutations of FH in an HLRCC-derived cell line result in glucose-mediated generation of cellular reactive oxygen species (ROS) and ROS-dependent HIF-1alpha stabilization. Additionally, we demonstrate that stable knockdown of FH in immortalized renal epithelial cells results in ROS-dependent HIF-1alpha stabilization. These data reveal that the obligate glycolytic switch present in HLRCC is critical to HIF stabilization via ROS generation.

Gene regulation in response to graded hypoxia: the non-redundant roles of the oxygen sensors PHD and FIH in the HIF pathway

Hypoxia Inducible Factor (HIF), being the master protein involved in adaptation to low pO(2), plays a major role in many physiological and pathological phenomena: development, inflammation, ischemia and cancer. Prolyl hydroxylase (PHD) and factor inhibiting HIF (FIH) are the two oxygen sensors that regulate the HIF pathway. Here we model the regulatory dynamics in an oxygen gradient by a system of differential equations. A part of the work consists in a qualitative analysis, driven independently of the values of the parameters, which explains the non-redundant functional roles of FIH and PHD. In a second part, we use biological experiments to fit the model in a physiologically relevant context and run simulations. Simulation results are confronted with success to independent biological experiments. The combination of biological data and mathematical analysis stresses that FIH is a fine modulator determining whether a given gene should be induced in mildly or in strongly hypoxic areas. Moreover it gives access to other functional predictions that are not directly accessible by pure experiments, for instance the stoichiometry of prolyl-hydroxylation on HIF, and the switch-like properties of the system.

AVAILABILITY

an interactive simulation interface is available at http://sdi.ljad.free.fr/spip.php?article111.

Multiscale models of angiogenesis

Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.

Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting

BACKGROUND

Angiogenesis, the growth of capillaries from preexisting blood vessels, has been extensively studied experimentally over the past thirty years. Molecular insights from these studies have lead to therapies for cancer, macular degeneration and ischemia. In parallel, mathematical models of angiogenesis have helped characterize a broader view of capillary network formation and have suggested new directions for experimental pursuit. We developed a computational model that bridges the gap between these two perspectives, and addresses a remaining question in angiogenic sprouting: how do the processes of endothelial cell elongation, migration and proliferation contribute to vessel formation?

RESULTS

We present a multiscale systems model that closely simulates the mechanisms underlying sprouting at the onset of angiogenesis. Designed by agent-based programming, the model uses logical rules to guide the behavior of individual endothelial cells and segments of cells. The activation, proliferation, and movement of these cells lead to capillary growth in three dimensions. By this means, a novel capillary network emerges out of combinatorially complex interactions of single cells. Rules and parameter ranges are based on literature data on endothelial cell behavior in vitro. The model is designed generally, and will subsequently be applied to represent species-specific, tissue-specific in vitro and in vivo conditions. Initial results predict tip cell activation, stalk cell development and sprout formation as a function of local vascular endothelial growth factor concentrations and the Delta-like 4 Notch ligand, as it might occur in a three-dimensional in vitro setting. Results demonstrate the differential effects of ligand concentrations, cell movement and proliferation on sprouting and directional persistence.

CONCLUSION

This systems biology model offers a paradigm closely related to biological phenomena and highlights previously unexplored interactions of cell elongation, migration and proliferation as a function of ligand concentration, giving insight into key cellular mechanisms driving angiogenesis.

Iron behaving badly: inappropriate iron chelation as a major contributor to the aetiology of vascular and other progressive inflammatory and degenerative diseases

BACKGROUND

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular 'reactive oxygen species' (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation.

REVIEW

We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation).The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible.This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, since in some circumstances (especially the presence of poorly liganded iron) molecules that are nominally antioxidants can actually act as pro-oxidants. The reduction of redox stress thus requires suitable levels of both antioxidants and effective iron chelators. Some polyphenolic antioxidants may serve both roles.Understanding the exact speciation and liganding of iron in all its states is thus crucial to separating its various pro- and anti-inflammatory activities. Redox stress, innate immunity and pro- (and some anti-)inflammatory cytokines are linked in particular via signalling pathways involving NF-kappaB and p38, with the oxidative roles of iron here seemingly involved upstream of the IkappaB kinase (IKK) reaction. In a number of cases it is possible to identify mechanisms by which ROSs and poorly liganded iron act synergistically and autocatalytically, leading to 'runaway' reactions that are hard to control unless one tackles multiple sites of action simultaneously. Some molecules such as statins and erythropoietin, not traditionally associated with anti-inflammatory activity, do indeed have 'pleiotropic' anti-inflammatory effects that may be of benefit here.

CONCLUSION

Overall we argue, by synthesising a widely dispersed literature, that the role of poorly liganded iron has been rather underappreciated in the past, and that in combination with peroxide and superoxide its activity underpins the behaviour of a great many physiological processes that degrade over time. Understanding these requires an integrative, systems-level approach that may lead to novel therapeutic targets.

Modeling of growth factor-receptor systems from molecular-level protein interaction networks to whole-body compartment models

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 multiscale nature (intratissue vs. intertissue transport and local vs. systemic effects within an organism) involved in modeling growth factor system interactions and effects. This chapter 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; mesoscale single-tissue 3D models can simulate the effects of multicellular 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 intertissue 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.

Integration of angiogenesis modules at multiple scales: from molecular to tissue

Multiscale modeling has emerged as a powerful approach to interpret and capitalize on the biological complexity underlying blood vessel growth. We present a multiscale model of angiogenesis that heralds the start of a large scale initiative to integrate related biological models. The goal of the integrative project is to better understand underlying biological mechanisms from the molecular level up through the organ systems level, and test new therapeutic strategies. Model methodology includes ordinary and partial differential equations, stochastic models, complex logical rules, and agent-based architectures. Current modules represent blood flow, oxygen transport, growth factor distribution and signaling, cell sensing, cell movement and cell proliferation. Challenges of integration lie in connecting modules that are diversely designed, seamlessly coordinating feedback, and representing spatial and time scales from ligand-receptor interactions and intracellular signaling, to cell-level movement and cell-matrix interactions, to vessel branching and capillary network formation, to tissue level characteristics, to organ system response. We briefly introduce the individual modules, discuss our approach to integration, present initial results from the coordination of modules, and propose solutions to some critical issues facing angiogenesis multiscale modeling and integration.

HIF-1: an age-dependent regulator of lens cell proliferation

PURPOSE

The lens grows throughout life, and lens size is a major risk factor for nuclear and cortical cataracts. A previous study showed that the hypoxic environment around the lens suppressed lens growth in older rats. The present study was conducted to investigate the mechanism responsible for the age-dependent decline in lens cell proliferation.

METHODS

Transgenic mice expressing Cre recombinase in the lens were bred to mice containing floxed Hif1a alleles. Transgenic mice expressing oxygen insensitive forms of HIF-1alpha in lens epithelial cells were exposed to room air or 60% oxygen. Proliferation was measured by BrdU labeling and cell death by using the TUNEL assay. Morphology was assessed in histologic sections. HIF-1alpha and p27(KIP1) levels were determined by Western blot. The expression of HIF-regulated genes was assessed on microarrays.

RESULTS

Lenses lacking Hif1a degenerated, precluding study in older animals. Breathing 60% oxygen reduced HIF-1alpha levels and HIF-1-regulated transcripts in lens epithelial cells from young and older lenses. Overexpression of oxygen-insensitive HIF-1alpha had no effect on lens size, but suppressed increased proliferation in response to oxygen. Systemic injection of the iron chelator, 1,10-phenanthroline prevented the degradation of HIF-1alpha and reduced oxygen-induced proliferation. Increasing oxygen decreased levels of p27(KIP1) in the epithelial cells of older mice, which was prevented by expressing oxygen-insensitive forms of HIF-1alpha.

CONCLUSIONS

HIF-1alpha is present and HIF-1 is transcriptionally active throughout life, but suppresses growth only in older lenses. Maintaining elevated levels of p27(KIP1) in older lenses requires HIF-1. p27(KIP1) and other growth regulators may selectively suppress the proliferation of older lens epithelial cells.

Systems biology of vascular endothelial growth factors

Several cytokine families have roles in the development, maintenance, and remodeling of the microcirculation. Of these, the vascular endothelial growth factor (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.

Reactive oxygen species regulate hypoxia-inducible factor 1alpha differentially in cancer and ischemia

In exercise, as well as cancer and ischemia, hypoxia-inducible factor 1 (HIF1) transcriptionally activates hundreds of genes vital for cell homeostasis and angiogenesis. While potentially beneficial in ischemia, upregulation of the HIF1 transcription factor has been linked to inflammation, poor prognosis in many cancers, and decreased susceptibility of tumors to radiotherapy and chemotherapy. Considering HIF1's function, HIF1alpha protein and its hydroxylation cofactors look increasingly attractive as therapeutic targets. Independently, antioxidants have shown promise in lowering the risk of some cancers and improving neurological and cardiac function following ischemia. The mechanism of how different antioxidants and reactive oxygen species influence HIF1alpha expression has drawn interest and intense debate. Here we present an experimentally based computational model of HIF1alpha protein degradation that represents how reactive oxygen species and antioxidants likely affect the HIF1 pathway differentially in cancer and ischemia. We use the model to demonstrate effects on HIF1alpha expression from combined doses of five potential therapeutically targeted compounds (iron, ascorbate, hydrogen peroxide, 2-oxoglutarate, and succinate) influenced by cellular oxidation-reduction and involved in HIF1alpha hydroxylation. Results justify the hypothesis that reactive oxygen species work by two opposite ways on the HIF1 system. We also show how tumor cells and cells under ischemic conditions would differentially respond to reactive oxygen species via changes to HIF1alpha expression over the course of hours to days, dependent on extracellular hydrogen peroxide levels and largely independent of initial intracellular levels, during hypoxia.

Age decreases endothelial progenitor cell recruitment through decreases in hypoxia-inducible factor 1alpha stabilization during ischemia

BACKGROUND

Advanced age is known to impair neovascularization. Because endothelial progenitor cells (EPCs) participate in this process, we examined the effects of aging on EPC recruitment and vascular incorporation.

METHODS AND RESULTS

Murine neovascularization was examined by use of an ischemic flap model, which demonstrated aged mice (19 to 24 months) had decreased EPC mobilization (percent mobilized 1.4+/-0.2% versus 0.4+/-0.1%, P<0.005) that resulted in impaired gross tissue survival compared with young mice (2 to 6 months). This decrease correlated with diminished tissue perfusion (P<0.005) and decreased CD31+ vascular density (P<0.005). Gender-mismatched bone marrow transplantation demonstrated significantly fewer chimeric vessels in aged mice (P<0.05), which confirmed a deficit in bone marrow-mediated vasculogenesis. Age had no effect on total EPC number in mice or humans. Reciprocal bone marrow transplantations confirmed that impaired neovascularization resulted from defects in the response of aged tissue to hypoxia and not from intrinsic defects in EPC function. We demonstrate that aging decreased hypoxia-inducible factor 1alpha stabilization in ischemic tissues because of increased prolyl hydroxylase-mediated hydroxylation (P<0.05) and proteasomal degradation. This resulted in a diminished hypoxia response, including decreased stromal cell-derived factor 1 (P<0.005) and vascular endothelial growth factor (P<0.0004). This effect can be reversed with the iron chelator deferoxamine, which results in hypoxia-inducible factor 1alpha stabilization and increased tissue survival.

CONCLUSIONS

Aging impairs EPC trafficking to sites of ischemia through a failure of aged tissues to normally activate the hypoxia-inducible factor 1alpha-mediated hypoxia response.

Three autocrine feedback loops determine HIF1 alpha expression in chronic hypoxia

Hypoxia occurs in cancer, prolonged exercise, and long-term ischemia with durations of several hours or more, and the hypoxia-inducible factor 1 (HIF1) pathway response to these conditions differs from responses to transient hypoxia. We used computational modeling, validated by experiments, to gain a quantitative, temporal understanding of the mechanisms driving HIF1 response. To test the hypothesis that HIF1 alpha protein levels during chronic hypoxia are tightly regulated by a series of molecular feedbacks, we took into account protein synthesis and product inhibition, and analyzed HIF1 system changes in response to hypoxic exposures beyond 3 to 4 h. We show how three autocrine feedback loops together regulate HIF 1 alpha hydroxylation in different microenvironments. Results demonstrate that prolyl hydroxylase, succinate and HIF1 alpha feedback determine intracellular HIF1 alpha levels over the course of hours to days. The model provides quantitative insight critical for characterizing molecular mechanisms underlying a cell's response to long-term hypoxia.

Skeletal muscle VEGF gradients in peripheral arterial disease: simulations of rest and exercise

VEGF is a key promoter of angiogenesis and a major target of proangiogenic therapy for peripheral arterial disease (PAD). Greater understanding of VEGF angiogenic signaling and guidance by gradients for new capillaries will aid in developing new proangiogenic therapies and improving existing treatments. However, in vivo measurements of VEGF concentration gradients at the cell scale are currently impossible. We have developed a computational model to quantify VEGF distribution in extensor digitorum longus skeletal muscle using measurements of VEGF, VEGF receptor (VEGFR), and neuropilin-1 (NRP1) expression in an experimental model of rat PAD. VEGF is secreted by myocytes, diffuses through and interacts with extracellular matrix and basement membranes, and binds VEGFRs and NRP1 on endothelial cell surfaces of blood vessels. We simulate the effects of increased NRP1 expression and of therapeutic exercise training on VEGF gradients, receptor signaling, and angiogenesis. Our study predicts that angiogenic therapy for PAD may be achieved not only through VEGF upregulation but also through modulation of VEGFRs and NRP1. We predict that expression of 10(4) NRP1/cell can increase VEGF binding to receptors by 1.7-fold (vs. no NRP1); in nonexercise-trained muscle with PAD, angiogenesis is hindered due to limited VEGF upregulation, signaling, and gradients; in exercise-trained muscle, VEGF signaling is enhanced by upregulation of VEGFRs and NRP1, and VEGF signaling is strongest within the first week of exercise therapy; and hypoxia-induced VEGF release is important to direct angiogenesis towards unperfused tissue.

Computational systems biology in cancer: modeling methods and applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

Multi-scale Computational Models of Pro-angiogenic Treatments in Peripheral Arterial Disease

The induction of angiogenesis is a promising therapeutic strategy for the amelioration of peripheral arterial disease (PAD). This occlusive disease results in muscle ischemia, and neovascularization is a route to increasing the perfusion in the tissue. The vascular endothelial growth factor (VEGF) family of potent pro-angiogenic cytokines is a potential therapeutic agent, increasing VEGF-receptor signaling on tissue vasculature. To investigate the effects of possible therapies on the VEGF concentrations and gradients within the tissue, we consider three such strategies: VEGF gene therapy (e.g. by adeno-associated virus); VEGF cell-based therapy (injected myoblasts that overexpress VEGF); and chronic exercise (which upregulates VEGF receptor expression). The multi-scale computational model used to investigate these strategies is an integration of several components: an anatomical description of the muscle geometry and cell types; microvascular blood flow; tissue oxygen distribution; VEGF secretion from muscle fibers; VEGF transport through interstitial space; and VEGF-receptor binding on microvascular endothelial cells. Exercise training, which results in increased VEGF secretion in hypoxic tissue and increased VEGF receptor expression, exhibits increases in both VEGF concentration and VEGF gradients, and is predicted to be more effective than the other, VEGF-only treatments.