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

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.

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.

The miR-7 identified from collagen biomaterial-based three-dimensional cultured cells regulates neural stem cell differentiation

Increasing evidence suggests that three-dimensional (3D) cultures provide more appropriate microenvironments to control stem cell response compared with traditional two-dimensional (2D) cultures. However, the molecular mechanism involved in 3D cultured stem cells is not well known. Several microRNAs whose target genes involved in the regulation of self-renewal and differentiation of stem cells were found to be downregulated in 3D cultured PA-1 cells. Among them, miR-7 was predicted to target Kruppel-like factor 4 (Klf4), a key gene for self-renewal of neural stem cells (NSCs). We showed that the differentiation of NSCs was inhibited in 3D collagen scaffolds compared with 2D cultured cells. The quantitative real-time PCR (qPCR) analysis indicated that the expression of miR-7 and Klf4 changed significantly in 2D cultures, whereas the expression stability of miR-7 and Klf4 was detected in 3D cultures. Using luciferase assay and western blot, Klf4 was identified as a target of miR-7 indicating that miR-7 plays a critical role in maintaining the self-renewal capacity through a Klf4-dependent mechanism in 3D cultured cells. Thus, the collagen scaffold-based 3D cell cultures may provide a platform to reveal the regulatory mechanism of cell regulators, which are difficult to find in traditional 2D cell cultures.

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.

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.

Spatial pattern dynamics of 3D stem cell loss of pluripotency via rules-based computational modeling

Pluripotent embryonic stem cells (ESCs) have the unique ability to differentiate into cells from all germ lineages, making them a potentially robust cell source for regenerative medicine therapies, but difficulties in predicting and controlling ESC differentiation currently limit the development of therapies and applications from such cells. A common approach to induce the differentiation of ESCs in vitro is via the formation of multicellular aggregates known as embryoid bodies (EBs), yet cell fate specification within EBs is generally considered an ill-defined and poorly controlled process. Thus, the objective of this study was to use rules-based cellular modeling to provide insight into which processes influence initial cell fate transitions in 3-dimensional microenvironments. Mouse embryonic stem cells (D3 cell line) were differentiated to examine the temporal and spatial patterns associated with loss of pluripotency as measured through Oct4 expression. Global properties of the multicellular aggregates were accurately recapitulated by a physics-based aggregation simulation when compared to experimentally measured physical parameters of EBs. Oct4 expression patterns were analyzed by confocal microscopy over time and compared to simulated trajectories of EB patterns. The simulations demonstrated that loss of Oct4 can be modeled as a binary process, and that associated patterns can be explained by a set of simple rules that combine baseline stochasticity with intercellular communication. Competing influences between Oct4+ and Oct4- neighbors result in the observed patterns of pluripotency loss within EBs, establishing the utility of rules-based modeling for hypothesis generation of underlying ESC differentiation processes. Importantly, the results indicate that the rules dominate the emergence of patterns independent of EB structure, size, or cell division. In combination with strategies to engineer cellular microenvironments, this type of modeling approach is a powerful tool to predict stem cell behavior under a number of culture conditions that emulate characteristics of 3D stem cell niches.

Three-dimensional modeling of angiogenesis in porous biomaterial scaffolds

Vascularization of biomaterial scaffolds is essential for the successful clinical application of engineered tissues. Experimental studies are often performed to investigate the role of scaffold architecture on vascularized tissue formation. However, experiments are expensive and time-consuming and synthesis protocols often do not allow for independent investigation of specific scaffold properties. Computational models allow for rapid screening of potential material designs with control over scaffold properties that is difficult in laboratory settings. We have developed and tested a three-dimensional agent-based framework for investigating the effect of scaffold pore architecture on angiogenesis. Software agents represent endothelial cells, interacting together and with their micro-environment, leading to the invasion of blood vessels into the scaffold. A rule base, driven by experimental findings, governs the behavior of individual agents. 3D scaffold models with well-defined homogeneous and heterogeneous pore architectures were simulated to investigate the impact of various design parameters. Simulation results indicate that pores of larger size with higher interconnectivity and porosity support rapid and extensive angiogenesis. The developed framework can be used to screen biomaterial scaffold designs for optimal vascularization and investigate complex interactions among invading blood vessels and their micro-environment.

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.

In vitro formation and characterization of a perfusable three-dimensional tubular capillary network in microfluidic devices

This paper describes the in vitro formation and characterization of perfusable capillary networks made of human umbilical vein endothelial cells (HUVECs) in microfluidic devices (MFDs). Using this platform, an array of three-dimensional (3D) tubular capillaries of various dimensions (50-150 μm in diameter and 100-1600 μm in length) can be formed reproducibly. To generate connected blood vessels, MFDs were completely filled with fibrin gel and subsequently processed to selectively leave behind gel structures inside the bridge channels. Following gel solidification, HUVECs were coated along the gel walls, on opposite ends of the patterned 3D fibrin gel. After 3-4 days, HUVECs migrating into the fibrin gel from opposite ends fused with each other, spontaneously forming a connected vessel that expressed tight junction proteins (e.g., ZO-1), which are characteristic of post-capillary venules. With ready access to a perfusable capillary network, we demonstrated perfusion of the vessels and imaged red blood cells (RBCs) and beads flowing through them. The results were reproducible (∼50% successful perfusable capillaries), consistent, and could be performed in a parallel manner (9 devices per well plate). Additionally, compatibility with high resolution live-cell microscopy and the possibility of incorporating other cell types makes this a unique experimental platform for investigating basic and applied aspects of angiogenesis, anastomosis, and vascular biology.

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.

A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.

Multiscale models of cell signaling

Computational models of signal transduction face challenges of scale below the resolution of a single cell. Here, we organize these challenges around three key interfaces for multiscale models of cell signaling: molecules to pathways, pathways to networks, and networks to outcomes. Each interface requires its own set of computational approaches and systems-level data, and no single approach or dataset can effectively bridge all three interfaces. This suggests that realistic "whole-cell" models of signaling will need to agglomerate different model types that span critical intracellular scales. Future multiscale models will be valuable for understanding the impact of signaling mutations or population variants that lead to cellular diseases such as cancer.

An agent-based model for the investigation of neovascularization within porous scaffolds

The ability to control blood vessel assembly in polymer scaffolds is important for clinical success in tissue engineering. A mathematical and computational representation of the relationship between scaffold properties and neovascularization may provide a better understanding of the fundamental process itself and help guide the design of new therapeutic approaches. This article proposes a multilayered, multiagent framework to model sprouting angiogenesis in porous scaffolds and examines the impact of pore structure on vessel invasion and network structure. We have defined the speed of vessel sprouting in the agent-based model based on in vivo results in the absence of a polymer scaffold. A number of cases were run to investigate the effect of scaffold pore size on angiogenesis. The simulation results indicate that the rate of scaffold vascularization increases with pore size. Pores of larger size (160-270 μm) support rapid and extensive angiogenesis throughout the scaffold. Model predictions were compared to experimental results of vascularization in porous poly(ethylene glycol) hydrogels to validate the results. This model can be used to provide insight into optimal scaffold properties that support vascularization of engineered tissues.

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.

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.

Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling

We introduce an agent-based model of epithelial cell morphogenesis to explore the complex interplay between apoptosis, proliferation, and polarization. By varying the activity levels of these mechanisms we derived phenotypic transition maps of normal and aberrant morphogenesis. These maps identify homeostatic ranges and morphologic stability conditions. The agent-based model was parameterized and validated using novel high-content image analysis of mammary acini morphogenesis in vitro with focus on time-dependent cell densities, proliferation and death rates, as well as acini morphologies. Model simulations reveal apoptosis being necessary and sufficient for initiating lumen formation, but cell polarization being the pivotal mechanism for maintaining physiological epithelium morphology and acini sphericity. Furthermore, simulations highlight that acinus growth arrest in normal acini can be achieved by controlling the fraction of proliferating cells. Interestingly, our simulations reveal a synergism between polarization and apoptosis in enhancing growth arrest. After validating the model with experimental data from a normal human breast line (MCF10A), the system was challenged to predict the growth of MCF10A where AKT-1 was overexpressed, leading to reduced apoptosis. As previously reported, this led to non growth-arrested acini, with very large sizes and partially filled lumen. However, surprisingly, image analysis revealed a much lower nuclear density than observed for normal acini. The growth kinetics indicates that these acini grew faster than the cells comprising it. The in silico model could not replicate this behavior, contradicting the classic paradigm that ductal carcinoma in situ is only the result of high proliferation and low apoptosis. Our simulations suggest that overexpression of AKT-1 must also perturb cell-cell and cell-ECM communication, reminding us that extracellular context can dictate cellular behavior.

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.

Notch signaling in the vasculature

Notch signaling is an evolutionarily conserved, intercellular signaling mechanism that plays myriad roles during vascular development and physiology in vertebrates. These roles include the regulation of arteriovenous specification and differentiation in both endothelial cells and vascular smooth muscle cells, regulation of blood vessel sprouting and branching during normal and pathological angiogenesis, and the physiological responses of vascular smooth muscle cells. Defects in Notch signaling also cause inherited vascular diseases, such as the degenerative vascular disorder cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy. This review summarizes recent studies that highlight the multiple roles the Notch signaling pathway plays during vascular development and physiology.

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

Harnessing systems biology approaches to engineer functional microvascular networks

Microvascular remodeling is a complex process that includes many cell types and molecular signals. Despite a continued growth in the understanding of signaling pathways involved in the formation and maturation of new blood vessels, approximately half of all compounds entering clinical trials will fail, resulting in the loss of much time, money, and resources. Most pro-angiogenic clinical trials to date have focused on increasing neovascularization via the delivery of a single growth factor or gene. Alternatively, a focus on the concerted regulation of whole networks of genes may lead to greater insight into the underlying physiology since the coordinated response is greater than the sum of its parts. Systems biology offers a comprehensive network view of the processes of angiogenesis and arteriogenesis that might enable the prediction of drug targets and whether or not activation of the targets elicits the desired outcome. Systems biology integrates complex biological data from a variety of experimental sources (-omics) and analyzes how the interactions of the system components can give rise to the function and behavior of that system. This review focuses on how systems biology approaches have been applied to microvascular growth and remodeling, and how network analysis tools can be utilized to aid novel pro-angiogenic drug discovery.

A hybrid continuum-discrete modelling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology

Angiogenesis is crucial during many physiological processes and is influenced by various biochemical and biomechanical factors. Models have proved useful in understanding the mechanisms of angiogenesis and also the characteristics of the capillaries formed as part of the process. We have developed a three-dimensional hybrid, agent-field model where individual cells are modelled as sprout-forming agents in a matrix field. Cell independence, cell-cell communication and stochastic cell response are integral parts of the model. The model simulations incorporate probabilities of an individual cell to transition into one of four stages--quiescence, proliferation, migration and apoptosis. We demonstrate that several features, such as continuous sprouts, cell clustering and branching, that are observed in microfluidic experiments conducted under controlled conditions using few angiogenic factors can be reproduced by this model. We also identify the transition probabilities that result in specific sprout characteristics such as long continuous sprouts and specific branching patterns. Thus, this model can be used to cluster sprout morphology as a function of various influencing factors.

Endothelial beta1 integrins regulate sprouting and network formation during vascular development

beta1 integrins are important regulators of vascular differentiation and development, as their endothelial-specific deletion results in embryonic lethality. In the present study, we investigated the molecular mechanisms underlying the prominent vascular abnormalities that occur in the absence of beta1 integrins. Because of the early embryonic lethality of knockout mice, we studied endothelial cell and vessel development in beta1-integrin-deficient murine embryonic stem cells to gain novel insights into the role of beta1 integrins in vasculo-angiogenesis. We found that vessel development was strongly defective in the mutant embryoid bodies (EBs), as only primitive and short sprouts developed from clusters of vascular precursors in beta1 integrin(-/-) EBs, whereas complex network formation of endothelial tubes was observed in wild-type EBs. The vascular defect was due to deficient beta1 integrin expression in endothelial cells, as its endothelial-specific re-expression rescued the phenotype entirely. The mechanism responsible for defective vessel formation was found to be reduced endothelial cell maturation, migration and elongation. Moreover, the lower number of endothelial cells in beta1 integrin(-/-) EBs was due to an increased apoptosis versus proliferation rate. The enhanced apoptosis and proliferation of beta1 integrin(-/-) endothelial cells was related to the elevation of peNOS and pAKT signaling molecules, respectively. Our data demonstrate that endothelial beta1 integrins are determinants of vessel formation and that this effect is mediated via different signaling pathways.

Microarray analysis of retinal endothelial tip cells identifies CXCR4 as a mediator of tip cell morphology and branching

The development of the vertebrate vascular system is mediated by both genetic patterning of vessels and by angiogenic sprouting in response to hypoxia. Both of these processes depend on the detection of environmental guidance cues by endothelial cells. A specialized subtype of endothelial cell known as the tip cell is thought to be involved in the detection and response to these cues, but the molecular signaling pathways used by tip cells to mediate tissue vascularization remain largely uncharacterized. To identify genes critical to tip cell function, we have developed a method to isolate them using laser capture microdissection, permitting comparison of RNA extracted from endothelial tip cells with that of endothelial stalk cells using microarray analysis. Genes enriched in tip cells include ESM-1, angiopoietin-2, and SLP-76. CXCR4, a receptor for the chemokine stromal-cell derived factor-1, was also identified as a tip cell-enriched gene, and we provide evidence for a novel role for this receptor in mediating tip cell morphology and vascular patterning in the neonatal retina.

A cell-based model of endothelial cell migration, proliferation and maturation during corneal angiogenesis

The motivation of this work stems from two critical experimental observations associated with corneal angiogenesis: (1) angiogenesis will not succeed without endothelial cell proliferation, and (2) proliferation mainly occurs at the leading edge of developing sprouts (Sholley et al., Lab. Invest. 51:624-634, 1984). To discover the underlying mechanisms of these phenomena, we develop a cell-based mathematical model that integrates a mechanical model of elongation with a biochemical model of cell phenotype variation regulated by angiopoietins within a developing sprout. This model allows for a detailed study of the relative roles of endothelial cell migration, proliferation, and maturation. The model is validated by quantitatively comparing its predictions with data derived from corneal angiogenesis experiments. We conclude that cell elasticity and cell-to-cell adhesion allow only limited sprout extension in the absence of proliferation, and the maturation process combined with bioavailability of VEGF can explain the localization of proliferation to the leading edge. We also use this model to investigate the effects of X-ray irradiation, Ang-2 inhibition, and extracellular matrix anisotropy on sprout morphology and extension.

Cancer systems biology: a network modeling perspective

Cancer is now appreciated as not only a highly heterogenous pathology with respect to cell type and tissue origin but also as a disease involving dysregulation of multiple pathways governing fundamental cell processes such as death, proliferation, differentiation and migration. Thus, the activities of molecular networks that execute metabolic or cytoskeletal processes, or regulate these by signal transduction, are altered in a complex manner by diverse genetic mutations in concert with the environmental context. A major challenge therefore is how to develop actionable understanding of this multivariate dysregulation, with respect both to how it arises from diverse genetic mutations and to how it may be ameliorated by prospective treatments. While high-throughput experimental platform technologies ranging from genomic sequencing to transcriptomic, proteomic and metabolomic profiling are now commonly used for molecular-level characterization of tumor cells and surrounding tissues, the resulting data sets defy straightforward intuitive interpretation with respect to potential therapeutic targets or the effects of perturbation. In this review article, we will discuss how significant advances can be obtained by applying computational modeling approaches to elucidate the pathways most critically involved in tumor formation and progression, impact of particular mutations on pathway operation, consequences of altered cell behavior in tissue environments and effects of molecular therapeutics.

Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, 'stabilised' tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.