Do endothelial cells dream of eclectic shape?

Mathematical models of developmental vascular remodelling: A review

Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.

Substrate stiffness modulates migration and local intercellular membrane motion in pulmonary endothelial cell monolayers

The pulmonary artery endothelium forms a semipermeable barrier that limits macromolecular flux through intercellular junctions. This barrier is maintained by an intrinsic forward protrusion of the interacting membranes between adjacent cells. However, the dynamic interactions of these membranes have been incompletely quantified. Here, we present a novel technique to quantify the motion of the peripheral membrane of the cells, called paracellular morphological fluctuations (PMFs), and to assess the impact of substrate stiffness on PMFs. Substrate stiffness impacted large-length scale morphological changes such as cell size and motion. Cell size was larger on stiffer substrates, whereas the speed of cell movement was decreased on hydrogels with stiffness either larger or smaller than 1.25 kPa, consistent with cells approaching a jammed state. Pulmonary artery endothelial cells moved fastest on 1.25 kPa hydrogel, a stiffness consistent with a healthy pulmonary artery. Unlike these large-length scale morphological changes, the baseline of PMFs was largely insensitive to the substrate stiffness on which the cells were cultured. Activation of store-operated calcium channels using thapsigargin treatment triggered a transient increase in PMFs beyond the control treatment. However, in hypocalcemic conditions, such an increase in PMFs was absent on 1.25 kPa hydrogel but was present on 30 kPa hydrogel-a stiffness consistent with that of a hypertensive pulmonary artery. These findings indicate that 1) PMFs occur in cultured endothelial cell clusters, irrespective of the substrate stiffness; 2) PMFs increase in response to calcium influx through store-operated calcium entry channels; and 3) stiffer substrate promotes PMFs through a mechanism that does not require calcium influx.

Active perception during angiogenesis: filopodia speed up Notch selection of tip cells in silico and in vivo

How do cells make efficient collective decisions during tissue morphogenesis? Humans and other organisms use feedback between movement and sensing known as 'sensorimotor coordination' or 'active perception' to inform behaviour, but active perception has not before been investigated at a cellular level within organs. Here we provide the first proof of concept in silico/in vivo study demonstrating that filopodia (actin-rich, dynamic, finger-like cell membrane protrusions) play an unexpected role in speeding up collective endothelial decisions during the time-constrained process of 'tip cell' selection during blood vessel formation (angiogenesis). We first validate simulation predictions in vivo with live imaging of zebrafish intersegmental vessel growth. Further simulation studies then indicate the effect is due to the coupled positive feedback between movement and sensing on filopodia conferring a bistable switch-like property to Notch lateral inhibition, ensuring tip selection is a rapid and robust process. We then employ measures from computational neuroscience to assess whether filopodia function as a primitive (basal) form of active perception and find evidence in support. By viewing cell behaviour through the 'basal cognitive lens' we acquire a fresh perspective on the tip cell selection process, revealing a hidden, yet vital time-keeping role for filopodia. Finally, we discuss a myriad of new and exciting research directions stemming from our conceptual approach to interpreting cell behaviour. This article is part of the theme issue 'Basal cognition: multicellularity, neurons and the cognitive lens'.

A multiscale model of complex endothelial cell dynamics in early angiogenesis

We introduce a hybrid two-dimensional multiscale model of angiogenesis, the process by which endothelial cells (ECs) migrate from a pre-existing vascular bed in response to local environmental cues and cell-cell interactions, to create a new vascular network. Recent experimental studies have highlighted a central role of cell rearrangements in the formation of angiogenic networks. Our model accounts for this phenomenon via the heterogeneous response of ECs to their microenvironment. These cell rearrangements, in turn, dynamically remodel the local environment. The model reproduces characteristic features of angiogenic sprouting that include branching, chemotactic sensitivity, the brush border effect, and cell mixing. These properties, rather than being hardwired into the model, emerge naturally from the gene expression patterns of individual cells. After calibrating and validating our model against experimental data, we use it to predict how the structure of the vascular network changes as the baseline gene expression levels of the VEGF-Delta-Notch pathway, and the composition of the extracellular environment, vary. In order to investigate the impact of cell rearrangements on the vascular network structure, we introduce the mixing measure, a scalar metric that quantifies cell mixing as the vascular network grows. We calculate the mixing measure for the simulated vascular networks generated by ECs of different lineages (wild type cells and mutant cells with impaired expression of a specific receptor). Our results show that the time evolution of the mixing measure is directly correlated to the generic features of the vascular branching pattern, thus, supporting the hypothesis that cell rearrangements play an essential role in sprouting angiogenesis. Furthermore, we predict that lower cell rearrangement leads to an imbalance between branching and sprout elongation. Since the computation of this statistic requires only individual cell trajectories, it can be computed for networks generated in biological experiments, making it a potential biomarker for pathological angiogenesis.

Angiogenesis, the process by which new blood vessels are formed by sprouting from the pre-existing vascular bed, plays a key role in both physiological and pathological processes, including tumour growth. The structure of a growing vascular network is determined by the coordinated behaviour of endothelial cells in response to various signalling cues. Recent experimental studies have highlighted the importance of cell rearrangements as a driver for sprout elongation. However, the functional role of this phenomenon remains unclear. We formulate a new multiscale model of angiogenesis which, by accounting explicitly for the complex dynamics of endothelial cells within growing angiogenic sprouts, is able to reproduce generic features of angiogenic structures (branching, chemotactic sensitivity, cell mixing, etc.) as emergent properties of its dynamics. We validate our model against experimental data and then use it to quantify the phenomenon of cell mixing in vascular networks generated by endothelial cells of different lineages. Our results show that there is a direct correlation between the time evolution of cell mixing in a growing vascular network and its branching structure, thus paving the way for understanding the functional role of cell rearrangements in angiogenesis.

Remodeling of the Microvasculature: May the Blood Flow Be With You

The vasculature ensures optimal delivery of nutrients and oxygen throughout the body, and to achieve this function it must continually adapt to varying tissue demands. Newly formed vascular plexuses during development are immature and require dynamic remodeling to generate well-patterned functional networks. This is achieved by remodeling of the capillaries preserving those which are functional and eliminating other ones. A balanced and dynamically regulated capillary remodeling will therefore ensure optimal distribution of blood and nutrients to the tissues. This is particularly important in pathological contexts in which deficient or excessive vascular remodeling may worsen tissue perfusion and hamper tissue repair. Blood flow is a major determinant of microvascular reshaping since capillaries are pruned when relatively less perfused and they split when exposed to high flow in order to shape the microvascular network for optimal tissue perfusion and oxygenation. The molecular machinery underlying blood flow sensing by endothelial cells is being deciphered, but much less is known about how this translates into endothelial cell responses as alignment, polarization and directed migration to drive capillary remodeling, particularly in vivo. Part of this knowledge is theoretical from computational models since blood flow hemodynamics are not easily recapitulated by in vitro or ex vivo approaches. Moreover, these events are difficult to visualize in vivo due to their infrequency and briefness. Studies had been limited to postnatal mouse retina and vascular beds in zebrafish but new tools as advanced microscopy and image analysis are strengthening our understanding of capillary remodeling. In this review we introduce the concept of remodeling of the microvasculature and its relevance in physiology and pathology. We summarize the current knowledge on the mechanisms contributing to capillary regression and to capillary splitting highlighting the key role of blood flow to orchestrate these processes. Finally, we comment the potential and possibilities that microfluidics offers to this field. Since capillary remodeling mechanisms are often reactivated in prevalent pathologies as cancer and cardiovascular disease, all this knowledge could be eventually used to improve the functionality of capillary networks in diseased tissues and promote their repair.

Report on Workshop: Planning the Future of Agent Simulation

In May 2019, a workshop on principled development of future agent-based simulations was held at Keele University. Participants spanned companies and academia, and a range of domains of interest, as well as participant career stages. This report summarizes the discussions and main outcomes from this workshop.

Integrated Multiparametric High-Content Profiling of Endothelial Cells

Endothelial cells (ECs) are widely heterogeneous at the cell level and serve different functions at the vessel and tissue levels. EC-forming colonies derived from induced pluripotent stem cells (iPSC-ECFCs) alongside models such as primary human umbilical vein ECs (HUVECs) are slowly becoming available for research with future applications in cell therapies, disease modeling, and drug discovery. We and others previously described high-content analysis approaches capturing unbiased morphology-based measurements coupled with immunofluorescence and used these for multidimensional reduction and population analysis. Here, we report a tailored workflow to characterize ECs. We acquire images at high resolution with high-magnification water-immersion objectives with Hoechst, vascular endothelial cadherin (VEC), and activated NOTCH staining. We hypothesize that via these key markers alone we would be able to distinguish and assess different EC populations. We used cell population software analysis to phenotype HUVECs and iPSC-ECFCs in the absence or presence of vascular endothelial growth factor (VEGF). To our knowledge, this study presents the first parallel quantitative high-content multiparametric profiling of EC models. Importantly, it highlights a simple strategy to benchmark ECs in different conditions and develop new approaches for biological research and translational applications for regenerative medicine.

Agent-based computational model of retinal angiogenesis simulates microvascular network morphology as a function of pericyte coverage

OBJECTIVE

Define a role for perivascular cells during developmental retinal angiogenesis in the context of EC Notch1-DLL4 signaling at the multicellular network level.

METHODS

The retinal vasculature is highly sensitive to growth factor-mediated intercellular signaling. Although EC signaling has been explored in detail, it remains unclear how PC function to modulate these signals that lead to a diverse set of vascular network patterns in health and disease. We have developed an ABM of retinal angiogenesis that incorporates both ECs and PCs to investigate the formation of vascular network patterns as a function of pericyte coverage. We use our model to test the hypothesis that PC modulate Notch1-DLL4 signaling in endothelial cell-endothelial cell interactions.

RESULTS

Agent-based model (ABM) simulations that include PCs more accurately predict experimentally observed vascular network morphologies than simulations that lack PCs, suggesting that PCs may influence sprouting behaviors through physical blockade of endothelial intercellular connections.

CONCLUSIONS

This study supports a role for PCs as a physical buffer to signal propagation during vascular network formation-a barrier that may be important for generating healthy microvascular network patterns.

Defective endothelial cell migration in the absence of Cdc42 leads to capillary-venous malformations

Formation and homeostasis of the vascular system requires several coordinated cellular functions, but their precise interplay during development and their relative importance for vascular pathologies remain poorly understood. Here, we investigated the endothelial functions regulated by Cdc42 and their in vivo relevance during angiogenic sprouting and vascular morphogenesis in the postnatal mouse retina. We found that Cdc42 is required for endothelial tip cell selection, directed cell migration and filopodia formation, but dispensable for cell proliferation or apoptosis. Although the loss of Cdc42 seems generally compatible with apical-basal polarization and lumen formation in retinal blood vessels, it leads to defective endothelial axial polarization and to the formation of severe vascular malformations in capillaries and veins. Tracking of Cdc42-depleted endothelial cells in mosaic retinas suggests that these capillary-venous malformations arise as a consequence of defective cell migration, when endothelial cells that proliferate at normal rates are unable to re-distribute within the vascular network.

Multi-physics interactions drive VEGFR2 relocation on endothelial cells

Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM). We develop a mathematical model in order to simulate the relocation of VEGFR2 on the cell membrane during the mechanical adhesion of cells onto a ligand-enriched substrate. Co-designing the in vitro experiments with the simulations allows identifying three phases of the receptor dynamics, which are controlled respectively by the high chemical reaction rate, by the mechanical deformation rate, and by the diffusion of free receptors on the membrane. The identification of the laws that regulate receptor polarization opens new perspectives toward developing innovative anti-angiogenic strategies through the modulation of EC activation.

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’.

Cell-Cell Contact Area Affects Notch Signaling and Notch-Dependent Patterning

During development, cells undergo dramatic changes in their morphology. By affecting contact geometry, these morphological changes could influence cellular communication. However, it has remained unclear whether and how signaling depends on contact geometry. This question is particularly relevant for Notch signaling, which coordinates neighboring cell fates through direct cell-cell signaling. Using micropatterning with a receptor trans-endocytosis assay, we show that signaling between pairs of cells correlates with their contact area. This relationship extends across contact diameters ranging from microns to tens of microns. Mathematical modeling predicts that dependence of signaling on contact area can bias cellular differentiation in Notch-mediated lateral inhibition processes, such that smaller cells are more likely to differentiate into signal-producing cells. Consistent with this prediction, analysis of developing chick inner ear revealed that ligand-producing hair cell precursors have smaller apical footprints than non-hair cells. Together, these results highlight the influence of cell morphology on fate determination processes.

Time to Decide? Dynamical Analysis Predicts Partial Tip/Stalk Patterning States Arise during Angiogenesis

Angiogenesis is a highly dynamic morphogenesis process; however, surprisingly little is known about the timing of the different molecular processes involved. Although the role of the VEGF-notch-DLL4 signaling pathway has been established as essential for tip/stalk cell competition during sprouting, the speed and dynamic properties of the underlying process at the individual cell level has not been fully elucidated. In this study, using mathematical modeling we investigate how specific, biologically meaningful, local conditions around and within an individual cell can influence their unique tip/stalk phenotype switching kinetics. To this end we constructed an ordinary differential equation model of VEGF-notch-DLL4 signaling in a system of two, coupled endothelial cells (EC). Our studies reveal that at any given point in an angiogenic vessel the time it takes a cell to decide to take on a tip or stalk phenotype may be drastically different, and this asynchrony of tip/stalk cell decisions along vessels itself acts to speed up later competitions. We unexpectedly uncover intermediate "partial" yet stable states lying between the tip and stalk cell fates, and identify that internal cellular factors, such as NAD-dependent deacetylase sirtuin-1 (Sirt1) and Lunatic fringe 1 (Lfng1), can specifically determine the length of time a cell spends in these newly identified partial tip/stalk states. Importantly, the model predicts that these partial EC states can arise during normal angiogenesis, in particular during cell rearrangement in sprouts, providing a novel two-stage mechanism for rapid adaptive behavior to the cells highly dynamic environment. Overall, this study demonstrates that different factors (both internal and external to EC) can be used to modulate the speed of tip/stalk decisions, opening up new opportunities and challenges for future biological experiments and therapeutic targeting to manipulate vascular network topology, and our basic understanding of developmental/pathological angiogenesis.

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.

Synchronization of endothelial Dll4-Notch dynamics switch blood vessels from branching to expansion

Formation of a regularly branched blood vessel network is crucial in development and physiology. Here we show that the expression of the Notch ligand Dll4 fluctuates in individual endothelial cells within sprouting vessels in the mouse retina in vivo and in correlation with dynamic cell movement in mouse embryonic stem cell-derived sprouting assays. We also find that sprout elongation and branching associates with a highly differential phase pattern of Dll4 between endothelial cells. Stimulation with pathologically high levels of Vegf, or overexpression of Dll4, leads to Notch dependent synchronization of Dll4 fluctuations within clusters, both in vitro and in vivo. Our results demonstrate that the Vegf-Dll4/Notch feedback system normally operates to generate heterogeneity between endothelial cells driving branching, whilst synchronization drives vessel expansion. We propose that this sensitive phase transition in the behaviour of the Vegf-Dll4/Notch feedback loop underlies the morphogen function of Vegfa in vascular patterning.

Temporal modulation of collective cell behavior controls vascular network topology

Vascular network density determines the amount of oxygen and nutrients delivered to host tissues, but how the vast diversity of densities is generated is unknown. Reiterations of endothelial-tip-cell selection, sprout extension and anastomosis are the basis for vascular network generation, a process governed by the VEGF/Notch feedback loop. Here, we find that temporal regulation of this feedback loop, a previously unexplored dimension, is the key mechanism to determine vascular density. Iterating between computational modeling and in vivo live imaging, we demonstrate that the rate of tip-cell selection determines the length of linear sprout extension at the expense of branching, dictating network density. We provide the first example of a host tissue-derived signal (Semaphorin3E-Plexin-D1) that accelerates tip cell selection rate, yielding a dense network. We propose that temporal regulation of this critical, iterative aspect of network formation could be a general mechanism, and additional temporal regulators may exist to sculpt vascular topology.

DOI:http://dx.doi.org/10.7554/eLife.13212.001

Many animals have a network of blood vessels that supplies oxygen and nutrients to every part of the body. Each organ contains a unique pattern of blood vessels; some have lots of densely packed vessels, while others have fewer vessels that are more widely spaced.

New blood vessels typically form by sprouting from the side of pre-existing vessels. This involves the endothelial cells that line the inner wall of blood vessels moving outwards to create a sprout that is made up of ‘tip cells’ and ‘stalk cells’. Tip cells are found at the front of the growing vessels and encourage the formation of new sprouts, while the stalk cells trail behind and elongate the sprout.

Two signaling pathways that involve two proteins called VEGF and Notch interact with each other to control which cells become tip cells and which become stalk cells. Cells with higher levels of VEGF signaling will become tip cells. These cells also activate Notch signaling, which in turn blocks VEGF signaling in their neighboring cells. This feedback mechanism enables a new sprout to form by forcing cells present around a newly formed tip cell to become stalk cells. However, it was still not understood how the different organs develop blood vessel networks with different densities.

In 2011, researchers revealed that two other proteins, Semaphorin3E and its receptor Plexin-D1, are expressed in tip cells in the back of the eye in mice and control the VEGF/Notch signaling pathway. Now Kur et al. – including some of the researchers involved in the 2011 work – have used a combination of predictive computer simulations and experimental approaches to understand this interaction in more detail.

The analysis showed that Semaphorin3E and Plexin-D1 speed up VEGF/Notch signaling, which causes new tip cells to form at a faster rate, and results in a more densely packed network of blood vessels. For example, in mice that lack Semaphorin3E and Plexin-D1, VEGF/Notch signaling was slower and new tip cells formed more slowly, which resulted in the blood vessel network at the back of the mice’s eyes being less dense.

Kur et al. propose that different organs have different ‘molecular metronomes’ that control the pace of VEGF/Notch signaling. A fast acting metronome would yield a dense network, while a slower one would form a less dense network. This helps to explain how diverse densities of blood vessel networks are formed in different organs. This work may aid efforts to develop therapeutic approaches for controlling the development of new blood vessels in cancers and other diseases.

DOI:http://dx.doi.org/10.7554/eLife.13212.002

VEGF, Notch and TGFβ/BMPs in regulation of sprouting angiogenesis and vascular patterning

The blood vasculature is constantly adapting to meet the demand from tissue. In so doing, branches may form, reorganize or regress. These complex processes employ integration of multiple signalling cascades, some of them being restricted to endothelial and mural cells and, hence, suitable for targeting of the vasculature. Both genetic and drug targeting experiments have demonstrated the requirement for the vascular endothelial growth factor (VEGF) system, the Delta-like-Notch system and the transforming growth factor β (TGFβ)/bone morphogenetic protein (BMP) cascades in vascular development. Although several of these signalling cascades in part converge into common downstream components, they differ in temporal and spatial regulation and expression. For example, the pro-angiogenic VEGFA is secreted by cells in need of oxygen, presented to the basal side of the endothelium, whereas BMP9 and BMP10 are supplied via the bloodstream in constant interaction with the apical side to suppress angiogenesis. Delta-like 4 (DLL4), on the other hand, is provided as an endothelial membrane bound ligand. In the present article, we discuss recent data on the integration of these pathways in the process of sprouting angiogenesis and vascular patterning and malformation.

Applications of computational models to better understand microvascular remodelling: a focus on biomechanical integration across scales

Microvascular network remodelling is a common denominator for multiple pathologies and involves both angiogenesis, defined as the sprouting of new capillaries, and network patterning associated with the organization and connectivity of existing vessels. Much of what we know about microvascular remodelling at the network, cellular and molecular scales has been derived from reductionist biological experiments, yet what happens when the experiments provide incomplete (or only qualitative) information? This review will emphasize the value of applying computational approaches to advance our understanding of the underlying mechanisms and effects of microvascular remodelling. Examples of individual computational models applied to each of the scales will highlight the potential of answering specific questions that cannot be answered using typical biological experimentation alone. Looking into the future, we will also identify the needs and challenges associated with integrating computational models across scales.

Endothelial mechanosensors: the gatekeepers of vascular homeostasis and adaptation under mechanical stress

Endothelial cells (ECs) not only serve as a barrier between blood and extravascular space to modulate the exchange of fluid, macromolecules and cells, but also play a critical role in regulation of vascular homeostasis and adaptation under mechanical stimulus via intrinsic mechanotransduction. Recently, with the dissection of microdomains responsible for cellular responsiveness to mechanical stimulus, a lot of mechanosensing molecules (mechanosensors) and pathways have been identified in ECs. In addition, there is growing evidence that endothelial mechanosensors not only serve as key vascular gatekeepers, but also contribute to the pathogenesis of various vascular disorders. This review focuses on recent findings in endothelial mechanosensors in subcellular microdomains and their roles in regulation of physiological and pathological functions under mechanical stress.