Multiscale models of angiogenesis

Modeling oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

An agent-based model of cancer stem cell initiated avascular tumour growth and metastasis: the effect of seeding frequency and location

It is very important to understand the onset and growth pattern of breast primary tumours as well as their metastatic dissemination. In most cases, it is the metastatic disease that ultimately kills the patient. There is increasing evidence that cancer stem cells are closely linked to the progression of the metastatic tumour. Here, we investigate stem cell seeding to an avascular tumour site using an agent-based stochastic model of breast cancer metastatic seeding. The model includes several important cellular features such as stem cell symmetric and asymmetric division, migration, cellular quiescence, senescence, apoptosis and cell division cycles. It also includes external features such as stem cell seeding frequency and location. Using this model, we find that cell seeding rate and location are important features for tumour growth. We also define conditions in which the tumour growth exhibits decremented and exponential growth patterns. Overall, we find that seeding, senescence and division limit affect not only the number of stem cells, but also their spatial and temporal distribution.

Systems biology of the microvasculature

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.

Cell, isoform, and environment factors shape gradients and modulate chemotaxis

Chemokine gradient formation requires multiple processes that include ligand secretion and diffusion, receptor binding and internalization, and immobilization of ligand to surfaces. To understand how these events dynamically shape gradients and influence ensuing cell chemotaxis, we built a multi-scale hybrid agent-based model linking gradient formation, cell responses, and receptor-level information. The CXCL12/CXCR4/CXCR7 signaling axis is highly implicated in metastasis of many cancers. We model CXCL12 gradient formation as it is impacted by CXCR4 and CXCR7, with particular focus on the three most highly expressed isoforms of CXCL12. We trained and validated our model using data from an in vitro microfluidic source-sink device. Our simulations demonstrate how isoform differences on the molecular level affect gradient formation and cell responses. We determine that ligand properties specific to CXCL12 isoforms (binding to the migration surface and to CXCR4) significantly impact migration and explain differences in in vitro chemotaxis data. We extend our model to analyze CXCL12 gradient formation in a tumor environment and find that short distance, steep gradients characteristic of the CXCL12-γ isoform are effective at driving chemotaxis. We highlight the importance of CXCL12-γ in cancer cell migration: its high effective affinity for both extracellular surface sites and CXCR4 strongly promote CXCR4+ cell migration. CXCL12-γ is also more difficult to inhibit, and we predict that co-inhibition of CXCR4 and CXCR7 is necessary to effectively hinder CXCL12-γ-induced migration. These findings support the growing importance of understanding differences in protein isoforms, and in particular their implications for cancer treatment.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

Mesoscopic and continuum modelling of angiogenesis

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.

A coupled model of neovessel growth and matrix mechanics describes and predicts angiogenesis in vitro

During angiogenesis, sprouting microvessels interact with the extracellular matrix (ECM) by degrading and reorganizing the matrix, applying traction forces, and producing deformation. Morphometric features of the resulting microvascular network are affected by the interaction between the matrix and angiogenic microvessels. The objective of this study was to develop a continuous-discrete modeling approach to simulate mechanical interactions between growing neovessels and the deformation of the matrix in vitro. This was accomplished by coupling an existing angiogenesis growth model which uses properties of the ECM to regulate angiogenic growth with the nonlinear finite element software FEBio (www.febio.org). FEBio solves for the deformation and remodeling of the matrix caused by active stress generated by neovessel sprouts, and this deformation was used to update the ECM into the current configuration. After mesh resolution and parameter sensitivity studies, the model was used to accurately predict vascular alignment for various matrix boundary conditions. Alignment primarily arises passively as microvessels convect with the deformation of the matrix, but active alignment along collagen fibrils plays a role as well. Predictions of alignment were most sensitive to the range over which active stresses were applied and the viscoelastic time constant in the material model. The computational framework provides a flexible platform for interpreting in vitro investigations of vessel-matrix interactions, predicting new experiments, and simulating conditions that are outside current experimental capabilities.

Computational systems biology approaches to anti-angiogenic cancer therapeutics

Angiogenesis is an exquisitely regulated process that is required for physiological processes and is also important in numerous diseases. Tumors utilize angiogenesis to generate the vascular network needed to supply the cancer cells with nutrients and oxygen, and many cancer drugs aim to inhibit tumor angiogenesis. Anti-angiogenic therapy involves inhibiting multiple cell types, molecular targets, and intracellular signaling pathways. Computational tools are useful in guiding treatment strategies, predicting the response to treatment, and identifying new targets of interest. Here, we describe progress that has been made in applying mathematical modeling and bioinformatics approaches to study anti-angiogenic therapeutics in cancer.

Integrative analysis of cancer imaging readouts by networks

Cancer is a multifactorial and heterogeneous disease. The corresponding complexity appears at multiple levels: from the molecular and the cellular constitution to the macroscopic phenotype, and at the diagnostic and therapeutic management stages. The overall complexity can be approximated to a certain extent, e.g. characterized by a set of quantitative phenotypic observables recorded in time‐space resolved dimensions by using multimodal imaging approaches. The transition from measures to data can be made effective through various computational inference methods, including networks, which are inherently capable of mapping variables and data to node‐ and/or edge‐valued topological properties, dynamic modularity configurations, and functional motifs. We illustrate how networks can integrate imaging data to explain cancer complexity, and assess potential pre‐clinical and clinical impact.

Computational Multiplexing Imaging merges imaging and networks.

Networks show signatures of tumor heterogeneity and phenotypic profiles observed in‐vivo.

A profile ensemble establishes a tumor fingerprint, and this constitutes a novel type of marker.

Personalized treatment is embedded in a systems medicine approach.

Do endothelial cells dream of eclectic shape?

Endothelial cells (ECs) exhibit dramatic plasticity of form at the single- and collective-cell level during new vessel growth, adult vascular homeostasis, and pathology. Understanding how, when, and why individual ECs coordinate decisions to change shape, in relation to the myriad of dynamic environmental signals, is key to understanding normal and pathological blood vessel behavior. However, this is a complex spatial and temporal problem. In this review we show that the multidisciplinary field of Adaptive Systems offers a refreshing perspective, common biological language, and straightforward toolkit that cell biologists can use to untangle the complexity of dynamic, morphogenetic systems.

Multiscale and multi-modality visualization of angiogenesis in a human breast cancer model

Angiogenesis in breast cancer helps fulfill the metabolic demands of the progressing tumor and plays a critical role in tumor metastasis. Therefore, various imaging modalities have been used to characterize tumor angiogenesis. While micro-CT (μCT) is a powerful tool for analyzing the tumor microvascular architecture at micron-scale resolution, magnetic resonance imaging (MRI) with its sub-millimeter resolution is useful for obtaining in vivo vascular data (e.g. tumor blood volume and vessel size index). However, integration of these microscopic and macroscopic angiogenesis data across spatial resolutions remains challenging. Here we demonstrate the feasibility of 'multiscale' angiogenesis imaging in a human breast cancer model, wherein we bridge the resolution gap between ex vivo μCT and in vivo MRI using intermediate resolution ex vivo MR microscopy (μMRI). To achieve this integration, we developed suitable vessel segmentation techniques for the ex vivo imaging data and co-registered the vascular data from all three imaging modalities. We showcase two applications of this multiscale, multi-modality imaging approach: (1) creation of co-registered maps of vascular volume from three independent imaging modalities, and (2) visualization of differences in tumor vasculature between viable and necrotic tumor regions by integrating μCT vascular data with tumor cellularity data obtained using diffusion-weighted MRI. Collectively, these results demonstrate the utility of 'mesoscopic' resolution μMRI for integrating macroscopic in vivo MRI data and microscopic μCT data. Although focused on the breast tumor xenograft vasculature, our imaging platform could be extended to include additional data types for a detailed characterization of the tumor microenvironment and computational systems biology applications.

Electroacupuncture improves recovery after hemorrhagic brain injury by inducing the expression of angiopoietin-1 and -2 in rats

Background

Angiopoietin (Ang) is one of the major effectors of angiogenesis, playing a critical role in neurovascular remodeling after stroke. Acupuncture has been widely used for treating stroke in China for a long time. Recently, we have demonstrated that electroacupuncture (EA) can accelerate intracerebral hemorrhage (ICH)-induced angiogenesis in rats. In the present study, we investigated the effect of EA on the expression of Ang-1 and Ang-2 in the brain after ICH.

Methods

ICH was induced by stereotactic injection of collagenase type VII into the right globus pallidus. Adult male Sprague–Dawley rats were randomized into the following four groups: sham-operation (SHAM), stroke-no electroacupuncture (SNE), stroke-EA at the Zusanli acupoint (SEZ), and stroke-EA at a nonacupoint (SEN). EA was applied to the bilateral Zusanli (ST36) acupoint in the SEZ group and a nonacupoint in the SEN group. The expression of Ang-1 and Ang-2 was evaluated by immunohistochemistry and quantitative real-time reverse transcription-polymerase chain reaction (RT-PCR).

Results

Some Ang-1 and Ang-2 immunoreactive microvessels with a dilated outline were detected in the perihematomal tissues after ICH, and the vessels extended into the clot from the surrounding area since day 7. The expression of Ang-1 increased notably as long as 2 weeks after ICH, while Ang-2 immunoreactivity declined at about 7 days following a striking upregulation at 3 days. EA at the Zusanli (ST36) acupoint upregulated the expression of Ang-1 and Ang-2 at both the protein and mRNA levels. However, EA at a nonacupoint had little effect on the expression of Ang-1 and Ang-2.

Conclusions

Our data suggest that EA at the Zusanli (ST36) acupoint exerts neuroprotective effects on hemorrhagic stroke by upregulation of Ang-1 and Ang-2.

Extracellular regulation of VEGF: isoforms, proteolysis, and vascular patterning

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.

A systems biology view of blood vessel growth and remodelling

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.

Systems approaches for synthetic biology: a pathway toward mammalian design

We review methods of understanding cellular interactions through computation in order to guide the synthetic design of mammalian cells for translational applications, such as regenerative medicine and cancer therapies. In doing so, we argue that the challenges of engineering mammalian cells provide a prime opportunity to leverage advances in computational systems biology. We support this claim systematically, by addressing each of the principal challenges to existing synthetic bioengineering approaches—stochasticity, complexity, and scale—with specific methods and paradigms in systems biology. Moreover, we characterize a key set of diverse computational techniques, including agent-based modeling, Bayesian network analysis, graph theory, and Gillespie simulations, with specific utility toward synthetic biology. Lastly, we examine the mammalian applications of synthetic biology for medicine and health, and how computational systems biology can aid in the continued development of these applications.

Compartment model predicts VEGF secretion and investigates the effects of VEGF trap in tumor-bearing mice

Angiogenesis, the formation of new blood vessels from existing vasculature, is important in tumor growth and metastasis. A key regulator of angiogenesis is vascular endothelial growth factor (VEGF), which has been targeted in numerous anti-angiogenic therapies aimed at inhibiting tumor angiogenesis. Systems biology approaches, including computational modeling, are useful for understanding this complex biological process and can aid in the development of novel and effective therapeutics that target the VEGF family of proteins and receptors. We have developed a computational model of VEGF transport and kinetics in the tumor-bearing mouse, which includes three-compartments: normal tissue, blood, and tumor. The model simulates human tumor xenografts and includes human (VEGF121 and VEGF165) and mouse (VEGF120 and VEGF164) isoforms. The model incorporates molecular interactions between these VEGF isoforms and receptors (VEGFR1 and VEGFR2), as well as co-receptors (NRP1 and NRP2). We also include important soluble factors: soluble VEGFR1 (sFlt-1) and α-2-macroglobulin. The model accounts for transport via macromolecular transendothelial permeability, lymphatic flow, and plasma clearance. We have fit the model to available in vivo experimental data on the plasma concentration of free VEGF Trap and VEGF Trap bound to mouse and human VEGF in order to estimate the rates at which parenchymal cells (myocytes and tumor cells) and endothelial cells secrete VEGF. Interestingly, the predicted tumor VEGF secretion rates are significantly lower (0.007-0.023 molecules/cell/s, depending on the tumor microenvironment) than most reported in vitro measurements (0.03-2.65 molecules/cell/s). The optimized model is used to investigate the interstitial and plasma VEGF concentrations and the effect of the VEGF-neutralizing agent, VEGF Trap (aflibercept). This work complements experimental studies performed in mice and provides a framework with which to examine the effects of anti-VEGF agents, aiding in the optimization of such anti-angiogenic therapeutics as well as analysis of clinical data. The model predictions also have implications for biomarker discovery with anti-angiogenic therapies.

A hybrid model of the role of VEGF binding in endothelial cell migration and capillary formation

Vascular endothelial growth factor (VEGF) is the most studied family of soluble, secreted mediators of endothelial cell migration, survival, and proliferation. VEGF exerts its function by binding to specific tyrosine kinase receptors on the cell surface and transducing the effect through downstream signaling. In order to study the influence of VEGF binding on endothelial cell motion, we develop a hybrid model of VEGF-induced angiogenesis, based on the theory of reinforced random walks. The model includes the chemotactic response of endothelial cells to angiogenic factors bound to cell-surface receptors, rather than approximating this as a function of extracellular chemical concentrations. This allows us to capture biologically observed phenomena such as activation and polarization of endothelial cells in response to VEGF gradients across their lengths, as opposed to extracellular gradients throughout the tissue. We also propose a novel and more biologically reasonable functional form for the chemotactic sensitivity of endothelial cells, which is also governed by activated cell-surface receptors. This model is able to predict the threshold level of VEGF required to activate a cell to move in a directed fashion as well as an optimal VEGF concentration for motion. Model validation is achieved by comparison of simulation results directly with experimental data.

Systems-based approaches toward wound healing

Wound healing in the pediatric patient is of utmost clinical and social importance because hypertrophic scarring can have aesthetic and psychological sequelae, from early childhood to late adolescence. Wound healing is a well-orchestrated reparative response affecting the damaged tissue at the cellular, tissue, organ, and system scales. Although tremendous progress has been made toward understanding wound healing at the individual temporal and spatial scales, its effects across the scales remain severely understudied and poorly understood. Here, we discuss the critical need for systems-based computational modeling of wound healing across the scales, from short-term to long-term and from small to large. We illustrate the state of the art in systems modeling by means of three key signaling mechanisms: oxygen tension-regulating angiogenesis and revascularization; transforming growth factor-β (TGF-β) kinetics controlling collagen deposition; and mechanical stretch stimulating cellular mitosis and extracellular matrix (ECM) remodeling. The complex network of biochemical and biomechanical signaling mechanisms and the multiscale character of the healing process make systems modeling an integral tool in exploring personalized strategies for wound repair. A better mechanistic understanding of wound healing in the pediatric patient could open new avenues in treating children with skin disorders such as birth defects, skin cancer, wounds, and burn injuries.

Manipulating the microvasculature and its microenvironment

The microvasculature is a dynamic cellular system necessary for tissue health and function. Therapeutic strategies that target the microvasculature are expanding and evolving, including those promoting angiogenesis and microvascular expansion. When considering how to manipulate angiogenesis, either as part of a tissue construction approach or a therapy to improve tissue blood flow, it is important to know the microenvironmental factors that regulate and direct neovessel sprouting and growth. Much is known concerning both diffusible and matrix-bound angiogenic factors, which stimulate and guide angiogenic activity. How the other aspects of the extravascular microenvironment, including tissue biomechanics and structure, influence new vessel formation is less well known. Recent research, however, is providing new insights into these mechanisms and demonstrating that the extent and character of angiogenesis (and the resulting new microcirculation) is significantly affected. These observations and the resulting implications with respect to tissue construction and microvascular therapy are addressed.

MOSAIC: a multiscale model of osteogenesis and sprouting angiogenesis with lateral inhibition of endothelial cells

The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Expression of VEGF receptors on endothelial cells in mouse skeletal muscle

VEGFR surface localization plays a critical role in converting extracellular VEGF signaling towards angiogenic outcomes, and the quantitative characterization of these parameters is critical for advancing computational models; however the levels of these receptors on blood vessels is currently unknown. Therefore our aim is to quantitatively determine the VEGFR localization on endothelial cells from mouse hindlimb skeletal muscles. We contextualize this VEGFR quantification through comparison to VEGFR-levels on cells in vitro. Using quantitative fluorescence we measure and compare the levels of VEGFR1 and VEGFR2 on endothelial cells isolated from C57BL/6 and BALB/c gastrocnemius and tibialis anterior hindlimb muscles. Fluorescence measurements are calibrated using beads with known numbers of phycoerythrin molecules. The data show a 2-fold higher VEGFR1 surface localization relative to VEGFR2 with 2,000-3,700 VEGFR1/endothelial cell and 1,300-2,000 VEGFR2/endothelial cell. We determine that endothelial cells from the highly glycolytic muscle, tibialis anterior, contain 30% higher number of VEGFR1 surface receptors than gastrocnemius; BALB/c mice display ~17% higher number of VEGFR1 than C57BL/6. When we compare these results to mouse fibroblasts in vitro, we observe high levels of VEGFR1 (35,800/cell) and very low levels of VEGFR2 (700/cell), while in human endothelial cells in vitro, we observe that the balance of VEGFRs is inverted, with higher levels VEGFR2 (5,800/cell) and lower levels of VEGFR1 (1,800/cell). Our studies also reveal significant cell-to-cell heterogeneity in receptor expression, and the quantification of these dissimilarities ex vivo for the first time provides insight into the balance of anti-angiogenic or modulatory (VEGFR1) and pro-angiogenic (VEGFR2) signaling.

Angiogenic microRNA-210 is present in cells surrounding osteonecrosis

A role of microRNAs (miRNAs), which are ≈ 22-nucleotide non-coding RNAs, has recently been recognized in human diseases. The objective of this study was to identify the expression pattern of miRNA (miR)-210, known to be associated with angiogenesis, in bone from patients with osteonecrosis (ON) of the femoral head. The expression of miR-210 in bone from 10 patients with osteoarthritis (OA) of the hip and ten with ON was analyzed by quantitative reverse transcription-polymerase chain reaction (RT-PCR) and by in situ hybridization. In addition, immunohistochemical staining for von Willebrand factor (vWF) and vascular endothelial growth factor (VEGF) was performed to identify the miR-210 expressing cells. We found that in ON samples, the expression of mature, primary miR-210, VEGF, matrix metalloproteinase (MMP)-2, and MMP-7 was significantly higher than that of OA samples. Section in situ hybridization of mature miR-210 revealed that mature miR-210 is expressed around the necrotic area. vWF and VEGF were also strongly expressed in the miR-210 expressing cells. This study shows that miR-210 is intensely expressed in ON, and might play a role in ON pathogenesis. The present study provides a solid basis for further functional analyses of miRNAs in ON.

Multiscale imaging and computational modeling of blood flow in the tumor vasculature

The evolution in our understanding of tumor angiogenesis has been the result of pioneering imaging and computational modeling studies spanning the endothelial cell, microvasculature and tissue levels. Many of these primary data on the tumor vasculature are in the form of images from pre-clinical tumor models that provide a wealth of qualitative and quantitative information in many dimensions and across different spatial scales. However, until recently, the visualization of changes in the tumor vasculature across spatial scales remained a challenge due to a lack of techniques for integrating micro- and macroscopic imaging data. Furthermore, the paucity of three-dimensional (3-D) tumor vascular data in conjunction with the challenges in obtaining such data from patients presents a serious hurdle for the development and validation of predictive, multiscale computational models of tumor angiogenesis. In this review, we discuss the development of multiscale models of tumor angiogenesis, new imaging techniques capable of reproducing the 3-D tumor vascular architecture with high fidelity, and the emergence of "image-based models" of tumor blood flow and molecular transport. Collectively, these developments are helping us gain a fundamental understanding of the cellular and molecular regulation of tumor angiogenesis that will benefit the development of new cancer therapies. Eventually, we expect this exciting integration of multiscale imaging and mathematical modeling to have widespread application beyond the tumor vasculature to other diseases involving a pathological vasculature, such as stroke and spinal cord injury.

Adhesion failures determine the pattern of choroidal neovascularization in the eye: a computer simulation study

Choroidal neovascularization (CNV) of the macular area of the retina is the major cause of severe vision loss in adults. In CNV, after choriocapillaries initially penetrate Bruch's membrane (BrM), invading vessels may regress or expand (CNV initiation). Next, during Early and Late CNV, the expanding vasculature usually spreads in one of three distinct patterns: in a layer between BrM and the retinal pigment epithelium (sub-RPE or Type 1 CNV), in a layer between the RPE and the photoreceptors (sub-retinal or Type 2 CNV) or in both loci simultaneously (combined pattern or Type 3 CNV). While most studies hypothesize that CNV primarily results from growth-factor effects or holes in BrM, our three-dimensional simulations of multi-cell model of the normal and pathological maculae recapitulate the three growth patterns, under the hypothesis that CNV results from combinations of impairment of: 1) RPE-RPE epithelial junctional adhesion, 2) Adhesion of the RPE basement membrane complex to BrM (RPE-BrM adhesion), and 3) Adhesion of the RPE to the photoreceptor outer segments (RPE-POS adhesion). Our key findings are that when an endothelial tip cell penetrates BrM: 1) RPE with normal epithelial junctions, basal attachment to BrM and apical attachment to POS resists CNV. 2) Small holes in BrM do not, by themselves, initiate CNV. 3) RPE with normal epithelial junctions and normal apical RPE-POS adhesion, but weak adhesion to BrM (e.g. due to lipid accumulation in BrM) results in Early sub-RPE CNV. 4) Normal adhesion of RBaM to BrM, but reduced apical RPE-POS or epithelial RPE-RPE adhesion (e.g. due to inflammation) results in Early sub-retinal CNV. 5) Simultaneous reduction in RPE-RPE epithelial binding and RPE-BrM adhesion results in either sub-RPE or sub-retinal CNV which often progresses to combined pattern CNV. These findings suggest that defects in adhesion dominate CNV initiation and progression.

Integration of experimental and computational approaches to sprouting angiogenesis

PURPOSE OF REVIEW

We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches.

RECENT FINDINGS

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

SUMMARY

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.

Computational approaches for translational clinical research in disease progression

Today, there is an ever-increasing amount of biological and clinical data available that could be used to enhance a systems-based understanding of disease progression through innovative computational analysis. In this article, we review a selection of published research regarding computational methods, primarily from systems biology, which support translational research from the molecular level to the bedside, with a focus on applications in trauma and critical care. Trauma is the leading cause of mortality in Americans younger than 45 years, and its rapid progression offers both opportunities and challenges for computational analysis of trends in molecular patterns associated with outcomes and therapeutic interventions.This review presents methods and domain-specific examples that may inspire the development of new algorithms and computational methods that use both molecular and clinical data for diagnosis, prognosis, and therapy in disease progression.

Pharmacokinetics and pharmacodynamics of VEGF-neutralizing antibodies

Background

Vascular endothelial growth factor (VEGF) is a potent regulator of angiogenesis, and its role in cancer biology has been widely studied. Many cancer therapies target angiogenesis, with a focus being on VEGF-mediated signaling such as antibodies to VEGF. However, it is difficult to predict the effects of VEGF-neutralizing agents. We have developed a whole-body model of VEGF kinetics and transport under pathological conditions (in the presence of breast tumor). The model includes two major VEGF isoforms VEGF₁₂₁ and VEGF₁₆₅, receptors VEGFR1, VEGFR2 and co-receptors Neuropilin-1 and Neuropilin-2. We have added receptors on parenchymal cells (muscle fibers and tumor cells), and incorporated experimental data for the cell surface density of receptors on the endothelial cells, myocytes, and tumor cells. The model is applied to investigate the action of VEGF-neutralizing agents (called "anti-VEGF") in the treatment of cancer.

Results

Through a sensitivity study, we examine how model parameters influence the level of free VEGF in the tumor, a measure of the response to VEGF-neutralizing drugs. We investigate the effects of systemic properties such as microvascular permeability and lymphatic flow, and of drug characteristics such as the clearance rate and binding affinity. We predict that increasing microvascular permeability in the tumor above 10^-5 cm/s elicits the undesired effect of increasing tumor interstitial VEGF concentration beyond even the baseline level. We also examine the impact of the tumor microenvironment, including receptor expression and internalization, as well as VEGF secretion. We find that following anti-VEGF treatment, the concentration of free VEGF in the tumor can vary between 7 and 233 pM, with a dependence on both the density of VEGF receptors and co-receptors and the rate of neuropilin internalization on tumor cells. Finally, we predict that free VEGF in the tumor is reduced following anti-VEGF treatment when VEGF₁₂₁ comprises at least 25% of the VEGF secreted by tumor cells.

Conclusions

This study explores the optimal drug characteristics required for an anti-VEGF agent to have a therapeutic effect and the tumor-specific properties that influence the response to therapy. Our model provides a framework for investigating the use of VEGF-neutralizing drugs for personalized medicine treatment strategies.

Evaluation of angiogenesis and osteogenesis

Bone regeneration has long been a major focus for tissue engineers and the importance of vascularization to the bone regeneration process has been well documented. Over the past decade, technological advances in the areas of stem cell biology, scaffold fabrication, and protein engineering have significantly enhanced our understanding of the interplay between vascularization and bone growth. This review, therefore, describes the commonly used models for investigating the complex interactions between osteoblastic cells and endothelial cells, evaluates the different tools utilized to investigate the relationship between vascularization and bone growth in vivo, and finally, summarizes possible areas of research related to therapeutic development.

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.

Computational approaches for translational clinical research in disease progression

Today, there is an ever-increasing amount of biological and clinical data available that could be used to enhance a systems-based understanding of disease progression through innovative computational analysis. In this article, we review a selection of published research regarding computational methods, primarily from systems biology, which support translational research from the molecular level to the bedside, with a focus on applications in trauma and critical care. Trauma is the leading cause of mortality in Americans younger than 45 years, and its rapid progression offers both opportunities and challenges for computational analysis of trends in molecular patterns associated with outcomes and therapeutic interventions.This review presents methods and domain-specific examples that may inspire the development of new algorithms and computational methods that use both molecular and clinical data for diagnosis, prognosis, and therapy in disease progression.

Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis

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.

A framework for the study of multiple realizations: the importance of levels of analysis

The brain may undergo functional reorganizations. Selective loss of sensory input or training within a restricted part of a modality cause "shifts" within for instance somatotopic or tonotopic maps. Cross-modal plasticity occurs when input within a modality is absent - e.g., in the congenitally blind. Reorganizations are also found in functional recovery after brain injury. Focusing on such reorganizations, it may be studied whether a cognitive or conscious process can exclusively be mediated by one neural substrate - or may be associated with multiple neural representations. This is typically known as the problem of multiple realization - an essentially empirical issue with wide theoretical implications. This issue may appear to have a simple solution. When, for instance, the symptoms associated with brain injury disappear and the recovery is associated with increased activities within spared regions of the brain, it is tempting to conclude that the processes originally associated with the injured part of the brain are now mediated by an alternative neural substrate. Such a conclusion is, however, not a simple matter. Without a more thorough analysis, it cannot be concluded that a functional recovery of for instance language or attention is necessarily associated with a novel representation of the processes lost to injury. Alternatively, for instance, the recovery may reflect that apparently similar surface phenomena are obtained via dissimilar cognitive mechanisms. In this paper we propose a theoretical framework, which we believe can guide the design and interpretations of studies of post-traumatic recovery. It is essential to distinguish between a number of levels of analysis - including a differentiation between the surface phenomena and the underlying information processing - when addressing, for instance, whether a pre-traumatic and post-traumatically recovered cognitive or conscious process are actually the same. We propose a (somewhat preliminary) system of levels of analysis, which can be applied to such studies.

A framework for the study of multiple realizations: the importance of levels of analysis

The brain may undergo functional reorganizations. Selective loss of sensory input or training within a restricted part of a modality cause "shifts" within for instance somatotopic or tonotopic maps. Cross-modal plasticity occurs when input within a modality is absent - e.g., in the congenitally blind. Reorganizations are also found in functional recovery after brain injury. Focusing on such reorganizations, it may be studied whether a cognitive or conscious process can exclusively be mediated by one neural substrate - or may be associated with multiple neural representations. This is typically known as the problem of multiple realization - an essentially empirical issue with wide theoretical implications. This issue may appear to have a simple solution. When, for instance, the symptoms associated with brain injury disappear and the recovery is associated with increased activities within spared regions of the brain, it is tempting to conclude that the processes originally associated with the injured part of the brain are now mediated by an alternative neural substrate. Such a conclusion is, however, not a simple matter. Without a more thorough analysis, it cannot be concluded that a functional recovery of for instance language or attention is necessarily associated with a novel representation of the processes lost to injury. Alternatively, for instance, the recovery may reflect that apparently similar surface phenomena are obtained via dissimilar cognitive mechanisms. In this paper we propose a theoretical framework, which we believe can guide the design and interpretations of studies of post-traumatic recovery. It is essential to distinguish between a number of levels of analysis - including a differentiation between the surface phenomena and the underlying information processing - when addressing, for instance, whether a pre-traumatic and post-traumatically recovered cognitive or conscious process are actually the same. We propose a (somewhat preliminary) system of levels of analysis, which can be applied to such studies.

Module-based multiscale simulation of angiogenesis in skeletal muscle

Background

Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.

Results

We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.

Conclusions

This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.

Computational models of VEGF-associated angiogenic processes in cancer

Tumour angiogenesis allows a growing mass of cancer cells to overcome oxygen diffusion limitation and to increase cell survival. The growth of capillaries from pre-existing blood vessels is the result of numerous signalling cascades involving different molecules and of cellular events involving multiple cell and tissue types. Computational models offer insight into the mechanisms governing angiogenesis and provide quantitative information on parameters difficult to assess by experiments alone. In this article, we summarize results from computational models of tumour angiogenic processes with a focus on the molecular-detailed vascular endothelial growth factor-associated models that have been developed in our laboratory, spanning multiple scales from the molecular to whole body.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Systems biology of pro-angiogenic therapies targeting the VEGF system

Vascular endothelial growth factor (VEGF) is a family of cytokines for which the dysregulation of expression is involved in many diseases; for some, excess VEGF causes pathological hypervascularization, while for others VEGF-induced vascular remodeling may alleviate ischemia and/or hypoxia. Anti-angiogenic therapies attacking the VEGF pathway have begun to live up to their promise for treatment of certain cancers and of age-related macular degeneration. However, the corollary is not yet true: in coronary artery disease and peripheral artery disease, clinical trials of pro-angiogenic VEGF delivery have not, so far, proven successful. The VEGF and VEGF-receptor system is complex, with at least five ligand genes, some encoding multiple protein isoforms and five receptor genes. A systems biology approach 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.

Gene therapy from the perspective of systems biology

Gene therapy research has expanded from its original concept of replacing absent or defective DNA with functional DNA to include the manipulation (increase or decrease) of gene expression by the delivery of modified genes, siRNA or other genetic material via multiple vectors, including naked plasmid DNA, viruses and even cells. Specific tissues or cell types are targeted in order to decrease the risks of systemic or side effects. As with the development of any drug, there is an amount of empiricism in the choice of gene target, route of administration, dosing and, in particular, the scaling-up from preclinical models to clinical trials. High-throughput experimental and computational systems biology studies that account for the complexities of host-disease-therapy interactions hold significant promise in assisting in the development and optimization of gene therapies, including personalized therapies and the identification of biomarkers to evaluate the success of such strategies. This review describes some of the obstacles and successes in gene therapy, using the specific example of growth factor gene delivery to promote angiogenesis and blood vessel remodeling in ischemic diseases; anti-angiogenic gene therapy in cancer is also discussed. In addition, the opportunities for systems biology and in silico modeling to improve on current outcomes are highlighted.