Predicting the future: Towards symbiotic computational and experimental angiogenesis research

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

Vascular Endothelial Cell Biology: An Update

The vascular endothelium, a monolayer of endothelial cells (EC), constitutes the inner cellular lining of arteries, veins and capillaries and therefore is in direct contact with the components and cells of blood. The endothelium is not only a mere barrier between blood and tissues but also an endocrine organ. It actively controls the degree of vascular relaxation and constriction, and the extravasation of solutes, fluid, macromolecules and hormones, as well as that of platelets and blood cells. Through control of vascular tone, EC regulate the regional blood flow. They also direct inflammatory cells to foreign materials, areas in need of repair or defense against infections. In addition, EC are important in controlling blood fluidity, platelet adhesion and aggregation, leukocyte activation, adhesion, and transmigration. They also tightly keep the balance between coagulation and fibrinolysis and play a major role in the regulation of immune responses, inflammation and angiogenesis. To fulfill these different tasks, EC are heterogeneous and perform distinctly in the various organs and along the vascular tree. Important morphological, physiological and phenotypic differences between EC in the different parts of the arterial tree as well as between arteries and veins optimally support their specified functions in these vascular areas. This review updates the current knowledge about the morphology and function of endothelial cells, particularly their differences in different localizations around the body paying attention specifically to their different responses to physical, biochemical and environmental stimuli considering the different origins of the EC.

Dual Roles of the AMP-Activated Protein Kinase Pathway in Angiogenesis

Angiogenesis plays important roles in development, stress response, wound healing, tumorigenesis and cancer progression, diabetic retinopathy, and age-related macular degeneration. It is a complex event engaging many signaling pathways including vascular endothelial growth factor (VEGF), Notch, transforming growth factor-beta/bone morphogenetic proteins (TGF-β/BMPs), and other cytokines and growth factors. Almost all of them eventually funnel to two crucial molecules, VEGF and hypoxia-inducing factor-1 alpha (HIF-1α) whose expressions could change under both physiological and pathological conditions. Hypoxic conditions stabilize HIF-1α, while it is upregulated by many oncogenic factors under normaxia. HIF-1α is a critical transcription activator for VEGF. Recent studies have shown that intracellular metabolic state participates in regulation of sprouting angiogenesis, which may involve AMP-activated protein kinase (AMPK). Indeed, AMPK has been shown to exert both positive and negative effects on angiogenesis. On the one hand, activation of AMPK mediates stress responses to facilitate autophagy which stabilizes HIF-1α, leading to increased expression of VEGF. On the other hand, AMPK could attenuate angiogenesis induced by tumor-promoting and pro-metastatic factors, such as the phosphoinositide 3-kinase /protein kinase B (Akt)/mammalian target of rapamycin (PI3K/Akt/mTOR), hepatic growth factor (HGF), and TGF-β/BMP signaling pathways. Thus, this review will summarize research progresses on these two opposite effects and discuss the mechanisms behind the discrepant findings.

Vascular architecture in the bacteriogenic light organ of Euprymna tasmanica (Cephalopoda: Sepiolidae)

Symbiosis between southern dumpling squid, Euprymna tasmanica (Cephalopoda: Sepiolidae), and its luminescent symbiont, the bacterium Vibrio fischeri, provides an experimentally tractable system to examine interactions between the eukaryotic host and its bacterial partner. Luminescence emitted by the symbiotic bacteria provides light for the squid in a behavior termed "counter-illumination," which allows the squid to mask its shadow amidst downwelling moonlight. Although this association is beneficial, light generated from the bacteria requires large quantities of oxygen to maintain this energy-consuming reaction. Therefore, we examined the vascular network within the light organ of juveniles of E. tasmanica with and without V. fischeri. Vessel type, diameter, and location of vessels were measured. Although differences between symbiotic and aposymbiotic squid demonstrated that the presence of V. fischeri does not significantly influence the extent of vascular branching at early stages of symbiotic development, these finding do provide an atlas of blood vessel distribution in the organ. Thus, these results provide a framework to understand how beneficial bacteria influence the development of a eukaryotic closed vascular network and provide insight to the evolutionary developmental dynamics that form during mutualistic interactions.

The temporal basis of angiogenesis

The process of new blood vessel growth (angiogenesis) is highly dynamic, involving complex coordination of multiple cell types. Though the process must carefully unfold over time to generate functional, well-adapted branching networks, we seldom hear about the time-based properties of angiogenesis, despite timing being central to other areas of biology. Here, we present a novel, time-based formulation of endothelial cell behaviour during angiogenesis and discuss a flurry of our recent, integrated in silico/in vivo studies, put in context to the wider literature, which demonstrate that tissue conditions can locally adapt the timing of collective cell behaviours/decisions to grow different vascular network architectures. A growing array of seemingly unrelated ‘temporal regulators’ have recently been uncovered, including tissue derived factors (e.g. semaphorins or the high levels of VEGF found in cancer) and cellular processes (e.g. asymmetric cell division or filopodia extension) that act to alter the speed of cellular decisions to migrate. We will argue that ‘temporal adaptation’ provides a novel account of organ/disease-specific vascular morphology and reveals ‘timing’ as a new target for therapeutics. We therefore propose and explain a conceptual shift towards a ‘temporal adaptation’ perspective in vascular biology, and indeed other areas of biology where timing remains elusive.

This article is part of the themed issue ‘Systems morphodynamics: understanding the development of tissue hardware’.

Glycolytic regulation of cell rearrangement in angiogenesis

During vessel sprouting, endothelial cells (ECs) dynamically rearrange positions in the sprout to compete for the tip position. We recently identified a key role for the glycolytic activator PFKFB3 in vessel sprouting by regulating cytoskeleton remodelling, migration and tip cell competitiveness. It is, however, unknown how glycolysis regulates EC rearrangement during vessel sprouting. Here we report that computational simulations, validated by experimentation, predict that glycolytic production of ATP drives EC rearrangement by promoting filopodia formation and reducing intercellular adhesion. Notably, the simulations correctly predicted that blocking PFKFB3 normalizes the disturbed EC rearrangement in high VEGF conditions, as occurs during pathological angiogenesis. This interdisciplinary study integrates EC metabolism in vessel sprouting, yielding mechanistic insight in the control of vessel sprouting by glycolysis, and suggesting anti-glycolytic therapy for vessel normalization in cancer and non-malignant diseases.

Glycolytic regulator PFKFB3 is a key player in vessel sprouting. Here the authors develop a computational model predicting that PFKFB3 drives endothelial cell rearrangement during vessel sprouting by promoting filopodia formation and reducing intercellular adhesion, and empirically validate this prediction.

Angiogenesis Revisited: An Overlooked Role of Endothelial Cell Metabolism in Vessel Sprouting

During vessel sprouting, endothelial "tip" cells migrate at the forefront, while the endothelial "stalk" cells elongate the sprout; endothelial "phalanx" cells line quiescent vessels. Tip and stalk cells can dynamically switch phenotypes under the control of VEGF and Notch signaling. Novel findings now show that in addition to signaling cascades, metabolism coregulates the formation of the new vasculature. Recent studies demonstrated that ECs rely primarily on glycolysis for ATP production, that glycolysis is further enhanced in angiogenic ECs, and that the key glycolytic regulator PFKFB3 codetermines angiogenesis by controlling the balance of tip versus stalk cells and promoting a migratory tip cell phenotype. On the other hand, FAO regulates endothelial stalk cell proliferation by providing carbon sources for biosynthetic processes, more particularly for de novo nucleotide synthesis for DNA replication. Here, we overview the current understanding of the various metabolic pathways in ECs and their impact on vessel formation in health and disease.

Agent-based modeling of porous scaffold degradation and vascularization: Optimal scaffold design based on architecture and degradation dynamics

A multi-layer agent-based model (ABM) of biomaterial scaffold vascularization is extended to consider the effects of scaffold degradation kinetics on blood vessel formation. A degradation model describing the bulk disintegration of porous hydrogels is incorporated into the ABM. The combined degradation-angiogenesis model is used to investigate growing blood vessel networks in the presence of a degradable scaffold structure. Simulation results indicate that higher porosity, larger mean pore size, and rapid degradation allow faster vascularization when not considering the structural support of the scaffold. However, premature loss of structural support results in failure for the material. A strategy using multi-layer scaffold with different degradation rates in each layer was investigated as a way to address this issue. Vascularization was improved with the multi-layered scaffold model compared to the single-layer model. The ABM developed provides insight into the characteristics that influence the selection of optimal geometric parameters and degradation behavior of scaffolds, and enables easy refinement of the model as new knowledge about the underlying biological phenomena becomes available.

STATEMENT OF SIGNIFICANCE

This paper proposes a multi-layer agent-based model (ABM) of biomaterial scaffold vascularization integrated with a structural-kinetic model describing bulk degradation of porous hydrogels to consider the effects of scaffold degradation kinetics on blood vessel formation. This enables the assessment of scaffold characteristics and in particular the disintegration characteristics of the scaffold on angiogenesis. Simulation results indicate that higher porosity, larger mean pore size, and rapid degradation allow faster vascularization when not considering the structural support of the scaffold. However, premature loss of structural support by scaffold disintegration results in failure of the material and disruption of angiogenesis. A strategy using multi-layer scaffold with different degradation rates in each layer was investigated as away to address this issue. Vascularization was improved with the multi-layered scaffold model compared to the single-layer model. The ABM developed provides insight into the characteristics that influence the selection of optimal geometric and degradation characteristics of tissue engineering scaffolds.

Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis

There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In this paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.

Making microvascular networks work: angiogenesis, remodeling, and pruning

The adequate and efficient functioning of the microcirculation requires not only numerous vessels providing a large surface area for transport but also a structure that provides short diffusion distances from capillaries to tissue and efficient distribution of convective blood flow. Theoretical models show how a combination of angiogenesis, remodeling, and pruning in response to hemodynamic and metabolic stimuli, termed "angioadaptation," generates well organized, functional networks.

Jagged mediates differences in normal and tumor angiogenesis by affecting tip-stalk fate decision

Angiogenesis is critical during development, wound repair, and cancer progression. During angiogenesis, some endothelial cells adopt a tip phenotype to lead the formation of new branching vessels; the trailing stalk cells proliferate to develop the vessel. Notch and VEGF signaling mediate the selection of these tip endothelial cells. However, how Jagged, a Notch ligand that is overexpressed in cancer, affects angiogenesis remains elusive. Here, by developing a theoretical framework for Notch-Delta-Jagged-VEGF signaling, we found that higher production levels of Jagged destabilizes the tip and stalk cell fates and can give rise to a hybrid tip/stalk phenotype that leads to poorly perfused and chaotic angiogenesis, which is a hallmark of cancer. Consistently, the signaling interactions that restrict Notch-Jagged signaling, such as Fringe, cis-inhibition, and increased production of Delta, stabilize tip and stalk fates and limit the existence of hybrid tip/stalk phenotype. Our results underline how overexpression of Jagged can transform physiological angiogenesis into pathological one.

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.

Effect of treatment on the global dynamics of delayed pathological angiogenesis models

For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.

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.

Synergy of cell-cell repulsion and vacuolation in a computational model of lumen formation

A key step in blood vessel development (angiogenesis) is lumen formation: the hollowing of vessels for blood perfusion. Two alternative lumen formation mechanisms are suggested to function in different types of blood vessels. The vacuolation mechanism is suggested for lumen formation in small vessels by coalescence of intracellular vacuoles, a view that was extended to extracellular lumen formation by exocytosis of vacuoles. The cell–cell repulsion mechanism is suggested to initiate extracellular lumen formation in large vessels by active repulsion of adjacent cells, and active cell shape changes extend the lumen. We used an agent-based computer model, based on the cellular Potts model, to compare and study both mechanisms separately and combined. An extensive sensitivity analysis shows that each of the mechanisms on its own can produce lumens in a narrow region of parameter space. However, combining both mechanisms makes lumen formation much more robust to the values of the parameters, suggesting that the mechanisms may work synergistically and operate in parallel, rather than in different vessel types.

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.

Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution

Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype. What phenotypes can make a cell "successful" in an environment of healthy and cancerous cells, and how? A widely used tool for getting more insight into that question is cell-based modeling. Cell-based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM), a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation, or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell and tissue biophysics, make the CPM the method of choice for modeling cellular processes in tumor development.