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Receptor tyrosine kinases (RTKs) are cell membrane proteins that provide cells with the ability to sense proteins in their environments. Many RTKs are essential to development and organ growth. Derangement of RTKs-by mutation or by overexpression-is central to several developmental and adult disorders including cancer, short stature, and vascular pathologies. The mechanism of action of RTKs is complex and is regulated by contextual components, including the existence of multiple competing ligands and receptors in many families, the intracellular location of the RTK, the dynamic and cell-specific coexpression of other RTKs, and the commonality of downstream signaling pathways. This means that both the state of the cell and the microenvironment outside the cell play a role, which makes sense given the pivotal location of RTKs as the nexus linking the extracellular milieu to intracellular signaling and modification of cell behavior. In this review, we describe these different contextual components through the lens of systems biology, in which both computational modeling and experimental "omics" approaches have been used to better understand RTK networks. The complexity of these networks is such that using these systems biology approaches is necessary to get a handle on the mechanisms of pathology and the design of therapeutics targeting RTKs. In particular, we describe in detail three concrete examples (involving ErbB3, VEGFR2, and AXL) that illustrate how systems approaches can reveal key mechanistic and therapeutic insights. This article is categorized under: Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models Translational, Genomic, and Systems Medicine > Therapeutic Methods.

Developing and improving mechanism-oriented computational models to better explain biological phenomena is a dynamic and expanding frontier. As the complexity of targeted phenomena has increased, so too has the diversity in methods and terminologies, often at the expense of clarity, which can make reproduction challenging, even problematic. To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena. We cluster explanations of phenomena into three broad groups. We then expand them into seven workflow-related model types having distinguishable features. We name each type and illustrate with examples drawn from the literature. These model types may contribute to the foundation of an ontology of mechanism-based biomedical simulation research. We show that the different model types manifest and exert their scientific usefulness by enhancing and extending different forms and degrees of explanation. The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions. Those descriptions are transformed into software and used to perform experimental explorations by running and examining simulation output. The credibility of inferences is thus linked to having easy access to the scientific and technical provenance from each workflow stage.

Inducing therapeutic angiogenesis to effectively form hierarchical, non-leaky networks of perfused vessels in tissue engineering applications and ischemic disease remains an unmet challenge, despite extensive research and multiple clinical trials. Here, we use a previously-developed, multi-scale, computational systems pharmacology model of human peripheral artery disease to screen a diverse array of promising pro-angiogenic strategies, including gene therapy, biomaterials, and antibodies. Our previously-validated model explicitly accounts for VEGF immobilization, Neuropilin-1 binding, and weak activation of VEGF receptor 2 (VEGFR2) by the “VEGF(xxxb)” isoforms. First, we examine biomaterial-based delivery of VEGF engineered for increased affinity to the extracellular matrix. We show that these constructs maintain VEGF close to physiological levels and extend the duration of VEGFR2 activation. We demonstrate the importance of sub-saturating VEGF dosing to prevent angioma formation. Second, we examine the potential of ligand- or receptor-based gene therapy to normalize VEGF receptor signaling. Third, we explore the potential for antibody-based pro-angiogenic therapy. Our model supports recent observations that improvement in perfusion following treatment with anti-VEGF(165b) in mice is mediated by VEGF-receptor 1, not VEGFR2. Surprisingly, the model predicts that the approved anti-VEGF cancer drug, bevacizumab, may actually improve signaling of both VEGFR1 and VEGFR2 via a novel ‘antibody swapping’ effect that we demonstrate here. Altogether, this model provides insight into the mechanisms of action of several classes of pro-angiogenic strategies within the context of the complex molecular and physiological processes occurring in vivo. We identify molecular signaling similarities between promising approaches and key differences between promising and ineffective strategies. INSIGHT STATEMENT: Inducing angiogenesis to form hierarchical networks of perfused vessels remains an unmet challenge. We use a computational systems pharmacology model to screen multiple promising pro-angiogenic strategies, highlighting the dependence of therapy action on the complex underlying molecular and physiological processes occurring in vivo. We show that biomaterial-based delivery of VEGF engineered for increased affinity to the extracellular matrix maintains VEGF close to physiological levels and extends the duration of VEGFR2 activation without saturating VEGFR2. We also explore antibody-based pro-angiogenic therapy, demonstrating accurate model prediction of signaling in mice following treatment with anti-VEGF(165b). Intriguingly, the model predicts that an approved anti-VEGF drug, bevacizumab, may improve signaling of both VEGFR1 and VEGFR2 via a novel ‘antibody swapping’ effect that we demonstrate here.

The purpose of our study was to improve our ability to predict response to therapy by integrating mechanistic kinetic data of protein interactions with patient-specific gene and protein expression data. The genetic heterogeneity of cancer results in patient-to-patient variability that makes it difficult to predict whether the patient will respond to a treatment. Molecular biomarkers such as the expression levels of genes or proteins have proven useful in limited cases, for example ErbB2 and trastuzumab, particularly in the epidermal growth factor (EGF) family, but these kinds of markers are still unable to accurately predict all responsive patients. These biomarkers are typically univariate and linear, whereas multivariate, nonlinear biomarkers are needed to adequately describe the network of molecular interactions targeted by a drug. Here, we present a method for building multivariate biomarkers that incorporate BOTH patient-specific transcriptomic/proteomic data AND detailed mechanistic models of the nonlinear interactions between ligands and receptors. The mechanistic models that we use are computational pharmacodynamic models, with multiple compartments, each with multiple cell types that express the ligands and receptors under investigation. The models incorporate detailed protein-protein interaction networks to simulate the complex dynamics of growth factor families and their receptors. By integrating this molecular detail into whole-body simulations with tumors, we can evaluate many different therapeutic approaches – different drugs, doses, schedules, and routes of administration. Our models make predictions of the dynamics of receptor tyrosine kinase activity and of key blood-borne biomarkers following therapeutic intervention. These predictions can and have been validated against clinical experimental data. We applied the method to the EGFR/ErbB family in breast cancer, using individualized data from The Cancer Genome Atlas (TCGA), and showed that the personalized models were able to capture the observed variability in receptor phosphorylation. Before the addition of drugs, the models behaved in a relatively monotonic fashion, with signaling outputs closely following the expression of the key ligands. However, the response to the addition of drugs was much more complex; the baseline expression of genes/proteins was not as good a predictor of the response. We simulated the addition of three antibody drugs that each target one of EGFR, HER2, and HER3. We applied principal component analysis to characterize the output of our simulations – post-therapy time course response. We derived metrics that accounted for both target-specific and off-target effects. We then used multivariate supervised learning methods to develop predictive biomarkers. We found that biomarkers derived from gene expression data were outperformed by biomarkers derived from simulated baseline tumor behavior (i.e. that combined quantitative mechanistic information with gene expression data). This suggested that linear transformations of transcriptomic and proteomic data may not be adequate for predicting drug response; instead, the nonlinear mechanism-based transformation that is central to the computational model is more predictive. In addition, for each of the antibodies investigated, the incorporation of mechanistic protein interactions resulted in the identification of off-target effects with high inter-individual heterogeneity that have the potential to significantly blunt the response. In conclusion, transforming individualized expression data through a detailed kinetic model of molecular interactions improves predictiveness of treatment response. Citation Format: Robert Joseph Bender, Feilim Mac Gabhann. Population pharmacodynamics: Mechanism-based modeling of receptor tyrosine kinase networks in cancer. [abstract]. In: Proceedings of the AACR Special Conference on Computational and Systems Biology of Cancer; Feb 8-11 2015; San Francisco, CA. Philadelphia (PA): AACR; Cancer Res 2015;75(22 Suppl 2):Abstract nr B1-36.

Making drug development a more efficient and cost-effective process will have a transformative effect on human health. A key, yet underutilized, tool to aid in this transformation is mechanistic computational modeling. By incorporating decades of hard-won prior knowledge of molecular interactions, cellular signaling, and cellular behavior, mechanistic models can achieve a level of predictiveness that is not feasible using solely empirical characterization of drug pharmacodynamics. These models can integrate diverse types of data from cell culture and animal experiments, including high-throughput systems biology experiments, and translate the results into the context of human disease. This provides a framework for identification of new drug targets, measurable biomarkers for drug action in target tissues, and patient populations for which a drug is likely to be effective or ineffective. Additionally, mechanistic models are valuable in virtual screening of new therapeutic strategies, such as gene or cell therapy and tissue regeneration, identifying the key requirements for these approaches to succeed in a heterogeneous patient population. These capabilities, which are distinct from and complementary to those of existing drug development strategies, demonstrate the opportunity to improve success rates in the drug development pipeline through the use of mechanistic computational models.

Objective Define a role for perivascular cells during developmental retinal angiogenesis in the context of EC Notch1-DLL4 signaling at the multicellular network level. Methods The retinal vasculature is highly sensitive to growth factor-mediated intercellular signaling. Although EC signaling has been explored in detail, it remains unclear how PC function to modulate these signals that lead to a diverse set of vascular network patterns in health and disease. We have developed an ABM of retinal angiogenesis that incorporates both ECs and PCs to investigate the formation of vascular network patterns as a function of pericyte coverage. We use our model to test the hypothesis that PC modulate Notch1-DLL4 signaling in endothelial cell-endothelial cell interactions. Results Agent-based model (ABM) simulations that include PCs more accurately predict experimentally observed vascular network morphologies than simulations that lack PCs, suggesting that PCs may influence sprouting behaviors through physical blockade of endothelial intercellular connections. Conclusions This study supports a role for PCs as a physical buffer to signal propagation during vascular network formation-a barrier that may be important for generating healthy microvascular network patterns.

Objective CCA, outward remodeling of capillaries that anastomose 2 arteriolar trees with different parent feed arteries, may represent a therapeutic target for patients who lack collaterals. ACCs can reperfuse an ischemic tree, but their functional capacity is unknown. Therefore, we determined whether ACCs mature into resistance vessels that regulate blood flow following arterial occlusion. Methods We ligated the lateral spinotrapezius feed artery in Balb/C mice, which induces CCA. At days 7 and 21 following occlusion, we measured vasodilation of ACCs using intravital microscopy and blood flow in the ischemic tree using LSF. We determined the presence of ACCs and neurovascular alignment with immunofluorescence. Results At day 7, ACCs do not vasodilate following muscle contraction and have reduced responses to endothelial- and smooth muscle-dependent agents. By day 21, ACCs exhibit normal vasodilation, accompanied by normalized increases in relative blood flow to the ischemic zone. Although functioning as resistance vessels by regulating blood flow, ACCs do not appear to be innervated. Conclusions ACCs mature into resistance vessels that regulate blood flow to the downstream tissue. Therefore, induction of mature ACCs may be a target for reducing ischemia in patients who lack collateral networks.

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.

The splice isoforms of vascular endothelial growth A (VEGF) each have different affinities for the extracellular matrix (ECM) and the coreceptor NRP1, which leads to distinct vascular phenotypes in model systems expressing only a single VEGF isoform. ECM-immobilized VEGF can bind to and activate VEGF receptor 2 (VEGFR2) directly, with a different pattern of site-specific phosphorylation than diffusible VEGF. To date, the way in which ECM binding alters the distribution of isoforms of VEGF and of the related placental growth factor (PlGF) in the body and resulting angiogenic signaling is not well-understood. Here, we extend our previous validated cell-level computational model of VEGFR2 ligation, intracellular trafficking, and site-specific phosphorylation, which captured differences in signaling by soluble and immobilized VEGF, to a multi-scale whole-body framework. This computational systems pharmacology model captures the ability of the ECM to regulate isoform-specific growth factor distribution distinctly for VEGF and PlGF, and to buffer free VEGF and PlGF levels in tissue. We show that binding of immobilized growth factor to VEGF receptors, both on endothelial cells and soluble VEGFR1, is likely important to signaling in vivo. Additionally, our model predicts that VEGF isoform-specific properties lead to distinct profiles of VEGFR1 and VEGFR2 binding and VEGFR2 site-specific phosphorylation in vivo, mediated by Neuropilin-1. These predicted signaling changes mirror those observed in murine systems expressing single VEGF isoforms. Simulations predict that, contrary to the ‘ligand-shifting hypothesis,’ VEGF and PlGF do not compete for receptor binding at physiological concentrations, though PlGF is predicted to slightly increase VEGFR2 phosphorylation when over-expressed by 10-fold. These results are critical to design of appropriate therapeutic strategies to control VEGF availability and signaling in regenerative medicine applications., Author summary Angiogenesis, the growth of new blood vessels from the existing vasculature, is critical for maintenance of health and response to injury. In ischemic disease, this process is impaired, but therapies targeting a key family of proteins, the vascular endothelial growth factors (VEGF), have failed to translate clinically. This suggests a need for deeper understanding of the complex regulation underlying angiogenic signaling. Here, we translate a previously developed and validated model of VEGF family signaling into a human, whole-body framework. The different splice isoforms of VEGF and the related PlGF proteins have different affinities for the extracellular matrix (ECM) and the co-receptor Neuropilin-1. Using our model, we examine the effect of these different binding properties on the distribution of each isoform in tissue, and subsequent receptor signaling. The model predicts isoform-specific receptor activation that is consistent with observed vascular phenotypes in mice expressing a single VEGF isoform; non-ECM-binding isoforms lead to signaling that promotes cell proliferation, while strong ECM-binding promotes migratory signaling and increased vessel branching. This understanding is critical for design of biomaterials that manipulate VEGF-ECM binding to control growth factor delivery, and for understanding of splicing-induced changes in VEGF family signaling in different tissues and in disease.

Recently, Sack et al. (2016) presented an interesting, novel data set in Journal of Cellular Physiology examining the effect of substrate stiffness on VEGF processing and signaling. The data represent a clear contribution to the field. However, the authors' conclusion that "extracellular matrix binding is essential for VEGF internalization" conflicts with other knowledge in the field, and is not supported by their data. Instead, their data demonstrate the effect of heparin addition and changing ECM stiffness on both VEGF binding to fibronectin and VEGF binding to endothelial receptors. This is consistent with other work showing that matrix binding reduces VEGF-VEGFR internalization, shifting downstream signaling. J. Cell. Physiol. 232: 36-37, 2017. © 2016 Wiley Periodicals, Inc.

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.Experimental data extends beyond the tip cell vs. stalk cell paradigm, and involves numerous molecular inputs such as vascular endothelial growth factor 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.

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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 S1P(1) and S1P(3) 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 S1P(1) and S1P(3), 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 S1P(1) and S1P(3) receptor-selective agonists (such as FTY720) in promoting microvascular growth for tissue engineering applications.

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.

Vascular endothelial growth factor (VEGF) signal transduction through the cell surface receptors VEGFR1 and VEGFR2 regulates angiogenesis—the growth of new capillaries from preexistent microvasculature. Soluble VEGF receptor-1 (sVEGFR1), a nonsignaling truncated variant of VEGFR1, has been postulated to inhibit angiogenic signaling via direct sequestration of VEGF ligands or dominant-negative heterodimerization with surface VEGFRs. The relative contributions of these two mechanisms to sVEGFR1's purported antiangiogenic effects in vivo are currently unknown. We previously developed a computational model for predicting the compartmental distributions of VEGF and sVEGFR1 throughout the healthy human body by simulating the molecular interaction networks of the VEGF ligand-receptor system as well as intercompartmental macromolecular biotransport processes. In this study, we decipher the dynamic processes that led to our prior prediction that sVEGFR1, through its ligand trapping mechanism alone, does not demonstrate significant steady-state antiangiogenic effects. We show that sVEGFR1-facilitated tissue-to-blood shuttling of VEGF accounts for a counterintuitive and drastic elevation in plasma free VEGF concentrations after both intramuscular and intravascular sVEGFR1 infusion. While increasing intramuscular VEGF production reduces free sVEGFR1 levels through increased VEGF-sVEGFR1 complex formation, we demonstrate a competing and opposite effect in which increased VEGF occupancy of neuropilin-1 (NRP1) and the corresponding reduction in NRP1 availability for internalization of sVEGFR1 unexpectedly increases free sVEGFR1 levels. In conclusion, dynamic intercompartmental transport processes give rise to our surprising prediction that VEGF trapping alone does not account for sVEGFR1's antiangiogenic potential. sVEGFR1's interactions with cell surface receptors such as NRP1 are also expected to affect its molecular interplay with VEGF.

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.

Extensive experimental studies have identified vascular endothelial growth factor (VEGF) concentrations and concentration gradients as major factors in angiogenesis; however, localized in vivo measurements of these parameters have not been possible. We developed a three-dimensional computational model of skeletal muscle fibers, blood vessels, and interstitial space. Here it is applied to rat extensor digitorum longus. VEGF isoforms are secreted by myocytes, diffuse through extracellular matrix and basement membranes, and bind endothelial cell surface receptors on blood vessels. In addition, one isoform, VEGF164, binds to proteoglycans in the interstitial space. VEGF secretion rate is determined from the predicted tissue oxygen level through its effect on the hypoxia inducible factor-1α transcription factor. We estimate VEGF secretion and its concentrations and gradients in resting muscle and for different levels of exercise. The effects of low levels of inspired oxygen are also studied. We predict that the high spatial heterogeneity of muscle fiber VEGF secretion in hypoxic tissue leads to significant gradients of VEGF concentration and VEGF receptor activation. VEGF concentration gradients are predicted to be significant in both resting and exercising muscle (4% and 6–8% change in VEGF over 10 μm, respectively), sufficient for chemotactic guidance of 50-μm-long sprout tip cells. VEGF gradients also result in heterogeneity in VEGF receptor activation—a possible explanation for the stochasticity of sprout location. In the absence of interstitial flow, gradients are 10-fold steeper in the transverse direction (i.e., perpendicular to the muscle fibers) than in the longitudinal direction. This may explain observed perpendicular anastomoses in skeletal muscle.

Background The vascular endothelial growth factor (VEGF) family is central to cancer angiogenesis. However, targeting VEGF as an anti-cancer therapeutic approach has shown success for some tumor types but not others. Here we examine the expression of the expanded VEGF family in prostate cancer, including the Semaphorin (Sema) family members that compete with VEGFs for Neuropilin binding and can themselves have pro- or anti-angiogenic activity. Results First, we used multivariate statistical methods, including partial least squares and clustering, to examine VEGF/Sema gene expression variability in previously published prostate cancer microarray datasets. We show that unlike some cancers, such as kidney cancer, primary prostate cancer is characterized by both a down-regulation of the pro-angiogenic members of the VEGF family and a down-regulation of anti-angiogenic members of the Sema family. We found pro-lymphangiogenic signatures, including the genes encoding VEGFC and VEGFD, associated with primary tumors that ultimately became aggressive. In contrast to primary prostate tumors, prostate cancer metastases showed increased expression of key pro-angiogenic VEGF family members and further repression of anti-angiogenic class III Sema family members. Given the lack of success of VEGF-targeting molecules so far in prostate cancer, this suggests that the reduction in anti-angiogenic Sema signaling may potentiate VEGF signaling and even promote resistance to VEGF-targeting therapies. Inhibition of the VEGF ‘accelerator’ may need to be accompanied by promotion of the Sema ‘brake’ to block cancer angiogenesis. To leverage our mechanistic understanding, and to link multigene expression changes to outcomes, we performed individualized computational simulations of competitive VEGF and Sema receptor binding across many tumor samples. The simulations suggest that loss of Sema expression promotes angiogenesis by lowering plexin signaling, not by potentiating VEGF signaling via relaxation of competition. Conclusions The combined analysis of bioinformatic data with computational modeling of ligand-receptor interactions demonstrated that enhancement of angiogenesis in prostate cancer metastases may occur through two different routes: elevation of VEGFA and reduction of class 3 Semaphorins. Therapeutic inhibition of angiogenesis in metastatic prostate cancer should account for both of these routes. Electronic supplementary material The online version of this article (doi:10.1186/s12918-015-0201-z) contains supplementary material, which is available to authorized users.

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell–cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

Our objective is to build an integrated model of ligand-receptor interactions, receptor trafficking, and site-specific phosphorylation of vascular endothelial growth factor (VEGF) receptors; the mo...

Supplemental Methods, Figures and Tables for bioinformatic analysis. Table S1. Datasets used in this study. Table S2. Gene expression-based prognostic markers. Table S3. Primary tumor characteristics. Table S4. Plasma concentrations of VEGF family members. Table S5. Angiogenesis inhibitor clinical trial results in prostate cancer. Table S6. Significant genes in the 478-gene angiome. Table S7. Significant genes in the 1233-gene extended angiome. Figure S1. Flowchart of the methods in this study. Figure S2. Differential expression of VEGF/Sema3 ligands and receptors in prostate cancer. Figure S3. Differential expression of Sema4/5/6/7 ligands and receptors in prostate cancer. Figure S4. Differential expression of VEGF/Sema3 ligands and receptors in renal cell carcinoma. Figure S5. Differential expression of Sema4/5/6/7 ligands and receptors in renal cell carcinoma. Figure S6. ROC curves for LOOCV of PLS-DA models of VEGF/Sema expression in aggressive and indolent tumors in the TCGA and GSE21034 datasets. Figure S7. Biomarker performance in TCGA and GSE21034 datasets. Figure S8. Cox proportional hazards modeling of the association between PLS-DA biomarkers and biochemical recurrence (BCR). Figure S9. PLS-DA models. Figure S10. Consensus K-means clustering. Figure S11. Isoform ratios of genes with alternative splicing. Figure S12. Tumor cell receptor binding profiles. (DOCX 6623 kb)

Computational model development, parameters and supplemental figures. Table S8. Geometric parameters. Table S9. Rate constants of ligand-receptor binding reactions. Table S10. Rate constants of receptor coupling reactions. Table S11. Target free ligand concentrations. Table S12. Model parameters. Figure S13. Reactions in the VEGF/Sema model. Figure S14. Receptor fractional occupancies at steady-state. Figure S15. Effect of ligand secretion rates on receptor binding. (DOCX 5884 kb)

The vascular endothelial growth factor (VEGF) family binds multiple endothelial cell surface receptors. Our goal is to build comprehensive models of these interactions for the purpose of simulating angiogenesis. In view of low concentrations of growth factors in vivo and in vitro, stochastic modeling of molecular interactions may be necessary. Here, we compare Monte Carlo simulations of the stochastic binding of VEGF and two of its major receptors on cells in vitro to equivalent deterministic simulations. In the range of typical VEGF concentrations, the stochastic and deterministic models are in agreement. However, we observe significant variability in receptor binding, which may be linked to biological stochastic events, e.g., blood vessel sprout initiation. We study patches of cell surface of varying sizes to investigate spatial integration of the signal by the cell, which impacts directly the variability of binding, and find significant variability up to the single-cell level. Dimerization of VEGF receptors does not significantly alter the variability in ligand binding. A ‘sliding window’ approach demonstrated no reduction in the variability of binding by temporal integration. The variability is expected to be more prominent in in vivo situations where the number of ligand molecules available for binding is less.

Recently, Sack et al. (2016) presented an interesting, novel data set in Journal of Cellular Physiology examining the effect of substrate stiffness on VEGF processing and signaling. The data represent a clear contribution to the field. However, the authors' conclusion that "extracellular matrix binding is essential for VEGF internalization" conflicts with other knowledge in the field, and is not supported by their data. Instead, their data demonstrate the effect of heparin addition and changing ECM stiffness on both VEGF binding to fibronectin and VEGF binding to endothelial receptors. This is consistent with other work showing that matrix binding reduces VEGF-VEGFR internalization, shifting downstream signaling. J. Cell. Physiol. 232: 36-37, 2017. © 2016 Wiley Periodicals, Inc.

In this issue of the Biophysical Journal, Biedermann et al. (1) describe a new computational package that implements a split GPU-CPU algorithm for speeding up the calculations of particle dynamics and reaction kinetics in heterogeneous biomolecular mixtures. The movement and interactions of proteins and other biomolecules are central to understanding drug action and improving drug design. Computational models of these molecular movements and reactions are indispensable, and many different simulation scales are available (Fig. 1 A), from atom-level resolution using molecular-dynamics packages such as CHARMM (www.charmm.org) (2) to continuum reaction-diffusion models at the tissue level (3) and compartmental models at the whole-body level (4). Figure 1 Simulation of heterogeneous molecular mixtures. (A) As the level of particle detail and particle discrimination increases (to the right), the computational time increases, while the ability to simulate large volumes and long times decreases. (B) Simplified ... If we focus on cell-level and subcellular-level simulations, then low-protein-copy number, spatial crowding, compartmentalization, and heterogeneity can make stochasticity a key consideration. At this scale, discriminating between the individual molecules becomes more important, and continuum approaches cannot do this. Methods that can explicitly simulate individual molecules are computationally costly; one approach to reduce the cost is to couple different model types. For example, molecular-dynamics simulations over short times can be used to estimate binding and unbinding energies; these can then be used in continuum models to estimate the longer-term behavior of a population of molecules in response to a perturbation. However, in many cases, to understand the system we will want to track each of the molecules individually; for these purposes the appropriate simulation scale is not atomistic, but instead that of individual molecular particles, each trackable over time as it moves and becomes involved in intermolecular reactions. Several packages have been developed to facilitate this level of simulation of individual particle movement and reaction, including MCell by groups at Salk Institute for Biological Studies (La Jolla, CA) and the University of Pittsburgh (Pittsburgh, PA; mcell.org) (5); Smoldyn by the Andrews group at the Fred Hutchinson Cancer Research Center (Seattle, WA; www.smoldyn.org) (6); and ReaDDy by the Noe group at the Free University of Berlin (Berlin, Germany; www.readdy-project.org) (7). Several of these modules have been or are being integrated into the larger simulation environments that model cell signaling, e.g., Spatiocyte in E-Cell (www.e-cell.org) and Smoldyn in VCell (University of Connecticut Health Center, Farmington, CT; www.nrcam.uchc.edu). Packages that use a lattice-based movement system and do not discriminate between all particles are also available, such as the following: MesoRD by the Elf lab at Uppsala University (Uppsala, Sweden; http://mesord.sourceforge.net/); StochSim by the Bray group at The University of Cambridge (Cambridge, United Kingdom; http://sourceforge.net/projects/stochsim/). Spatiocyte by the Tomita group at the Institute for Advanced Biosciences, Keio University (Fujisawa, Japan; spatiocyte.org) (8) uses a lattice, but individual molecules are still represented. The key problem with this level of simulation—tracking individual particles—is the computational cost; the time required to simulate all proteins within a single cell can be prohibitive. This cost increases with particle density, with simulation volume, and with the complexity and heterogeneity of the spatial domain. For the most part, this computational cost is not due to the calculation of the reactions that the proteins undergo with each other, but instead to the particle dynamics. Methods to speed up the calculation of particle dynamics could greatly enhance the ability to simulate subcellular processes such as signaling. Biedermann et al. (1), in this issue, report a new implementation of the ReaDDy package, ReaDDyMM, that leverages OpenMM and splits the calculations—the particle dynamics (movement, e.g., Brownian dynamics) to be calculated by the GPU and the reactions to be calculated by the CPU (Fig. 1 B). Three conditions must be met for this to obtain the reported two-orders of magnitude speedup, as follows. 1. There must be considerable separation in timescales between the particle dynamics and the reaction kinetics. ReaDDyMM takes advantage of the separation in timescales by running many smaller timesteps of particle dynamics for each larger timestep of reaction kinetics (Fig. 1 C). If this were not the case, then communication between the processors would make the algorithm inefficient. Greater timescale separation—faster diffusion, slower reactions—allows increased n (the number of GPU dynamics steps per CPU kinetics step; Fig. 1 B). 2. The level of speedup increases with particle density. At lower densities, both the overall computational time and the speedup are lower. This methodology thus appears particularly suited to understanding highly crowded biological environments. 3. Both the diffusion timestep (τ) and the reaction timestep (nτ) must be less than their corresponding characteristic timescales; otherwise, accuracy can be severely affected. ReaDDyMM split CPU-GPU calculation is distinct from Smoldyn’s GPU implementation, in which both diffusion and reactions are calculated on the GPU (9), and thus may provide an improvement for complex reaction networks. Benchmarking for both accuracy and computation time in various scenarios may indicate application-specific benefits to one approach over the other. Are two orders of magnitude of speedup sufficient to make this form of molecular simulation feasible? The answer depends on the application. The volumes simulated in the presented examples (1) are small—an attoLiter, or one-thousandth of an Escherichia coli cell. Mammalian cells are larger still. The protein densities used are similar to the total protein densities in E. coli. Thus, simulating a whole cell using this method would take one or more weeks, but this may have the potential to be further improved through parallelization. The benefit is the level of detail and accuracy possible, and for subcellular components this method will be both quick and highly detailed. ReaDDyMM is a useful advance and increases the tools and feature sets available for simulation of heterogeneous multimolecular simulations. This is an opportune time for such simulation packages, as superresolution microscopy and other advances make possible the experimental tracking of individual molecules within a complex cellular context.

The regulation of vascular endothelial growth factor A (VEGF) is critical to neovascularization in numerous tissues under physiological and pathological conditions. VEGF has multiple isoforms, created by alternative splicing or proteolytic cleavage, and characterized by different receptor-binding and matrix-binding properties. These isoforms are known to give rise to a spectrum of angiogenesis patterns marked by differences in branching, which has functional implications for tissues. In this review, we detail the extensive extracellular regulation of VEGF and the ability of VEGF to dictate the vascular phenotype. We explore the role of VEGF-releasing proteases and soluble carrier molecules on VEGF activity. While proteases such as MMP9 can 'release' matrix-bound VEGF and promote angiogenesis, for example as a key step in carcinogenesis, proteases can also suppress VEGF's angiogenic effects. We explore what dictates pro- or anti-angiogenic behavior. We also seek to understand the phenomenon of VEGF gradient formation. Strong VEGF gradients are thought to be due to decreased rates of diffusion from reversible matrix binding, however theoretical studies show that this scenario cannot give rise to lasting VEGF gradients in vivo. We propose that gradients are formed through degradation of sequestered VEGF. Finally, we review how different aspects of the VEGF signal, such as its concentration, gradient, matrix-binding, and NRP1-binding can differentially affect angiogenesis. We explore how this allows VEGF to regulate the formation of vascular networks across a spectrum of high to low branching densities, and from normal to pathological angiogenesis. A better understanding of the control of angiogenesis is necessary to improve upon limitations of current angiogenic therapies.

The vascular endothelial growth factor (VEGF) family of cytokines promotes vascularization, tumorigenesis and metastasis in many cancers. Our goal is to develop computational models that combine mechanistic topological data on the VEGF protein interaction network with gene expression datasets for a large population of prostate cancers. We have assembled databases of prostate cancer gene expression data, and analyzed the data using bioinformatic techniques, identifying key VEGF-based subgroups of prostate cancer plus biomarkers that identify these groups. This year, we have submitted and revised a manuscript based on this analysis, we expect it to be accepted soon. We have also created new computational models to simulate prostate cancer, based on the individualized gene expression data. We have used these models to simulate therapies that target the VEGF pathway, including anti-ligands such as bevacizumab and anti-receptors. Among are predictions are estimates of the high degree of variability in response to drugs that is predicted by the model, which is reflected in the results of clinical trials targeting VEGF in prostate cancer. This progress will continue into Year 3, where we will expand the VEGF family members included in our models, and extract key biomarkers indicative of likely success of VEGF- or VEGFR-targeting therapies.

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.

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 published(1-3). 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.

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.

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.

Adipose-derived stromal/stem cells (ASCs) are a promising cell source for vascular-based approaches to clinical therapeutics, as they have been shown to give rise to both endothelial and perivascular cells. While it is well known that ASCs can present a heterogeneous phenotypic profile, spontaneous interactions among these subpopulations that result in the formation of complex tissue structures have not been rigorously demonstrated. Our study reports the novel finding that ASCs grown in monolayers in the presence of angiogenic cues are capable of self-assembling into complex, three-dimensional vascular structures. This phenomenon is only apparent when the ASCs are seeded at a high density (20,000 cells/cm(2)) and occur through orchestrated interactions among three distinct subpopulations: CD31-positive cells (CD31+), α-smooth muscle actin-positive cells (αSMA+), and cells that are unstained for both these markers (CD31-/αSMA-). Investigations into the kinetics of the process revealed that endothelial vessel-like structures initially arose from individual CD31+ cells through proliferation and their interactions with CD31-/αSMA- cells. During this period, αSMA+ cells proliferated and appeared to migrate toward the vessel structures, eventually engaging in cell-cell contact with them after 1 week. By 2 weeks, the lumen-containing CD31+ vessels grew greater than a millimeter in length, were lined with vascular basement membrane proteins, and were encased within a dense, three-dimensional cluster of αSMA+ and CD31-/αSMA- cells. The recruitment of αSMA+ cells was largely due to platelet-derived growth factor (PDGF) signaling, as the inhibition of PDGF receptors substantially reduced αSMA+ cell growth and vessel coverage. Additionally, we found that while hypoxia increased endothelial gene expression and vessel width, it also inhibited the growth of the αSMA+ population. Together, these findings underscore the potential use of ASCs in forming mature vessels in vitro as well as the need for a further understanding of the heterotypic interactions among ASC subpopulations.

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.

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.

In recent years, Judah Folkman’s vision of anticancer therapeutics based on inhibiting angiogenesis pathways has begun to be realized. In particular, antibodies sequestering VEGF, and small molecule tyrosine kinase inhibitors targeting VEGF receptors, are now approved for various cancers, alone or in combination with other therapies. More are in the development pipeline, with similar or distinct mechanisms of action. The VEGF system is complex, involving multiple ligands and receptors, along with transport throughout the body via the bloodstream. Predicting outcomes of perturbing this system, either by a single agent or combinations, can be aided by in silico models. Here we discuss the ways in which the above drugs target the VEGF pathway in cancer, and describe the development and implementation of multiscale mathematical models to simulate the action of these drugs in order to predict and compare their likely efficacy for various types of tumors.

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.

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.

We have created an experimentally-based computational model describing spatial transport of vascular endothelial growth factor (VEGF) and its receptors to quantitatively understand how guidance cues may modulate blood vessel sprout growth. VEGF binds to endothelial cells and initiates angiogenesis. Both VEGF concentration and VEGF gradients may control sprout formation. Soluble VEGF receptor 1 (sFlt1) can bind and sequester VEGF. Based on observations in developing vasculature, we hypothesize that a local reduction in sFlt1 expression can increase locally available VEGF and thus control angiogenesis. However, the complex VEGF interaction network makes it difficult to isolate how individual proteins contribute to the spatial distribution of the growth factor using experiments alone. Our computational model represents the local environment of a single blood vessel and nearby tissue and directly incorporates the network of VEGF interactions. In the model, parenchymal cells secrete VEGF, which diffuses through interstitial space and binds extracellular matrix (ECM) and sFlt1. VEGF binds endothelial cells via membrane-bound receptors Flt1 and Flk1, and endothelial cells secrete sFlt1. Additionally, the model accounts for degradation of VEGF and sFlt1 as well as internalization of receptor-bound ligands. Using partial differential equations, we simulate this system, which is constrained by experimentally-derived parameters. Our simulations show that when a sprout-leading tip cell secretes less sFlt1 than neighboring cells, there is decreased local sFlt1 sequestration of VEGF, thus resulting in augmented VEGF-Flk1 levels on the surface of the low-sFlt1 secreting tip cell. This could lead to sprout generation. We also show how variations in sFlt1 secretion and tip cell configuration may affect the gradients of guidance cues and directionality of sprout growth.

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.

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.

Microcirculation (2010) 17, 333–347. doi: 10.1111/j.1549-8719.2010.00034.x Abstract 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-temporal patterns of microvascular network remodeling following arteriolar ligation in different mouse strains to better understand inter-individual 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.

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.

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 for 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.