Autonomy and Non-autonomy of Angiogenic Cell Movements Revealed by Experiment-Driven Mathematical Modeling

FOXO1 stimulates tip cell-enriched gene expression in endothelial cells

Forkhead box O (FOXO) family proteins are expressed in various cells, and play crucial roles in cellular metabolism, apoptosis, and aging. FOXO1-null mice exhibit embryonic lethality due to impaired endothelial cell (EC) maturation and vascular remodeling. However, FOXO1-mediated genome-wide regulation in ECs remains unclear. Here, we demonstrate that VEGF dynamically regulates FOXO1 cytosol-nucleus translocation. FOXO1 re-localizes to the nucleus via PP2A phosphatase. RNA-seq combined with FOXO1 overexpression/knockdown in ECs demonstrated that FOXO1 governs the VEGF-responsive tip cell-enriched genes, and further inhibits DLL4-NOTCH signaling. Endogenous FOXO1 ChIP-seq revealed that FOXO1 binds to the EC-unique tip-enriched genes with co-enrichment of EC master regulators, and the condensed chromatin region as a pioneer factor. We identified new promoter/enhancer regions of the VEGF-responsive tip cell genes regulated by FOXO1: ESM1 and ANGPT2. This is the first study to identify cell type-specific FOXO1 functions, including VEGF-mediated tip cell definition in primary cultured ECs.

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.

A three-dimensional model with two-body interactions for endothelial cells in angiogenesis

We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contributing to the formation of branching structures. While most mathematical models are two-dimensional, we aim to investigate whether ellipsoids also form branch-like structures and how their shape affects the pattern. In our model, the shape of a vascular endothelial cell is represented as a spheroid, and a discrete dynamical system is constructed based on the simple assumption of two-body interactions. Numerical simulations demonstrate that our model reproduces the patterns of elongation and branching observed in the early stages of angiogenesis. We show that the pattern formation of the cell population is strongly dependent on the cell shape. Finally, we demonstrate that our current mathematical model reproduces the cell behaviours, specifically cell-mixing, observed in sprouts.

Coordinated linear and rotational movements of endothelial cells compartmentalized by VE-cadherin drive angiogenic sprouting

Angiogenesis is a sequential process to extend new blood vessels from preexisting ones by sprouting and branching. During angiogenesis, endothelial cells (ECs) exhibit inhomogeneous multicellular behaviors referred to as "cell mixing," in which ECs repetitively exchange their relative positions, but the underlying mechanism remains elusive. Here we identified the coordinated linear and rotational movements potentiated by cell-cell contact as drivers of sprouting angiogenesis using in vitro and in silico approaches. VE-cadherin confers the coordinated linear motility that facilitated forward sprout elongation, although it is dispensable for rotational movement, which was synchronous without VE-cadherin. Mathematical modeling recapitulated the EC motility in the two-cell state and angiogenic morphogenesis with the effects of VE-cadherin-knockout. Finally, we found that VE-cadherin-dependent EC compartmentalization potentiated branch elongations, and confirmed this by mathematical simulation. Collectively, we propose a way to understand angiogenesis, based on unique EC behavioral properties that are partially dependent on VE-cadherin function.

Pattern formation of elliptic particles by two-body interactions: A model for dynamics of endothelial cells in angiogenesis

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

Cdc42 has important roles in postnatal angiogenesis and vasculature formation

Cdc42, a Rho family low molecular weight G protein, has important roles in various cell functions, including cytoskeletal rearrangement, cell adhesion and cell proliferation and differentiation. To investigate the involvement of Cdc42 in the activities of vascular endothelial cells, we generated Cdc42 conditional knockout mice in which Cdc42 was time -specifically deficient in vascular endothelial cells (Cdc42 ​fl/fl; VE-Cad CreERT: Cdc42 cKO). When the Cdc42 gene was deleted after birth, Cdc42 cKO mice were smaller than the control mice, and died between postnatal day 8 (P8) and P10. Necropsy findings confirmed that these mice had various pathological aberrances in the vessels of most organs, such as blood flow congestion and blood cell invasion. Electron microscopic observations also revealed that capillary endothelial cells were detached from the basement membrane as well as phagocytosis of dead endothelial cells induced by macrophages. Moreover, vascular sprouting from aortic rings induced by VEGF-A was diminished in samples from the Cdc42 cKO mice because of an endothelial cell proliferation defect. These results suggest that Cdc42 in vascular endothelial cells has important roles in blood vessel formation after birth.

Anomalous Angiogenesis in Retina

Age-related macular degeneration (AMD) may cause severe loss of vision or blindness, particularly in elderly people. Exudative AMD is characterized by the angiogenesis of blood vessels growing from underneath the macula, crossing the blood–retina barrier (which comprises Bruch’s membrane (BM) and the retinal pigmentation epithelium (RPE)), leaking blood and fluid into the retina and knocking off photoreceptors. Here, we simulate a computational model of angiogenesis from the choroid blood vessels via a cellular Potts model, as well as BM, RPE cells, drusen deposits and photoreceptors. Our results indicate that improving AMD may require fixing the impaired lateral adhesion between RPE cells and with BM, as well as diminishing Vessel Endothelial Growth Factor (VEGF) and Jagged proteins that affect the Notch signaling pathway. Our numerical simulations suggest that anti-VEGF and anti-Jagged therapies could temporarily halt exudative AMD while addressing impaired cellular adhesion, which could be more effective over a longer time-span.

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.

Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

During angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Angiogenesis is the process by which new blood vessels grow from existing ones. This process plays a crucial role in organ development, in wound healing and in numerous pathological processes such as cancer growth or in diabetes. Angiogenesis is a complex, multi-step and well regulated process where biochemistry and physics are intertwined. The process entails signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell movement, deformation and proliferation. Mathematical models have the ability to bring together these mechanisms in order to explore their relative relevance in vessel growth. Here, we present a mathematical model of early stage angiogenesis that is able to explore the role of biochemical signaling and tissue mechanics. We use this model to unravel the regulating role of Jagged, Notch and Delta dynamics in vascular cells. These membrane proteins have an important part in determining the leading cell in each neo-vascular sprout. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Cohesive and anisotropic vascular endothelial cell motility driving angiogenic morphogenesis

Vascular endothelial cells (ECs) in angiogenesis exhibit inhomogeneous collective migration called “cell mixing”, in which cells change their relative positions by overtaking each other. However, how such complex EC dynamics lead to the formation of highly ordered branching structures remains largely unknown. To uncover hidden laws of integration driving angiogenic morphogenesis, we analyzed EC behaviors in an in vitro angiogenic sprouting assay using mouse aortic explants in combination with mathematical modeling. Time-lapse imaging of sprouts extended from EC sheets around tissue explants showed directional cohesive EC movements with frequent U-turns, which often coupled with tip cell overtaking. Imaging of isolated branches deprived of basal cell sheets revealed a requirement of a constant supply of immigrating cells for ECs to branch forward. Anisotropic attractive forces between neighboring cells passing each other were likely to underlie these EC motility patterns, as evidenced by an experimentally validated mathematical model. These results suggest that cohesive movements with anisotropic cell-to-cell interactions characterize the EC motility, which may drive branch elongation depending on a constant cell supply. The present findings provide novel insights into a cell motility-based understanding of angiogenic morphogenesis.

Brain-derived neurotrophic factor induces angiogenin secretion and nuclear translocation in human umbilical vein endothelial cells

Brain-derived neurotrophic factor (BDNF) is a well-known humoral protein that induces growth of neurons. Recent studies have suggested that BDNF could act as an angiogenesis inducer similar to vascular endothelial growth factor (VEGF). Angiogenin is a strong mediator of angiogenesis. It has particular characteristics both as a secreted protein and a transcription factor. After being incorporated into the cytoplasm, angiogenin is immediately transferred to the nucleus and then mediates the angiogenic effects of angiogenesis inducers, including VEGF. The aim of this study is to determine the association between BDNF and angiogenin. At first, we determined the secretion of angiogenin from human umbilical vein endothelial cells (HUVEC) induced by BDNF with enzyme-linked immunosorbent assay. Next, we determined BDNF-induced nuclear translocation of angiogenin by immunofluorescent staining. In addition, we examined the mRNA expression of angiogenin in HUVEC before and after BDNF stimulation by quantitative reverse transcriptase-polymerase chain reaction. As a result, we noted that BDNF induced angiogenin secretion and nuclear translocation without an increase in the mRNA expression in HUVEC. Furthermore, we demonstrated that BDNF-induced HUVEC proliferation was significantly suppressed when neomycin, a specific inhibitor of nuclear translocation of angiogenin, was administered. These findings indicate that nuclear translocation of angiogenin is critically involved in BDNF-induced proliferation of HUVEC. In conclusion, angiogenin contributes to angiogenesis induced by BDNF.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

Excess centrosomes perturb dynamic endothelial cell repolarization during blood vessel formation

Excess centrosomes preclude proper interphase MTOC reorientation during sprouting morphogenesis. Normal centrosome numbers are required for dynamic repolarization and migration of sprouting ECs, which contribute to blood vessel formation.

Blood vessel formation requires dynamic movements of endothelial cells (ECs) within sprouts. The cytoskeleton regulates migratory polarity, and centrosomes organize the microtubule cytoskeleton. However, it is not well understood how excess centrosomes, commonly found in tumor stromal cells, affect microtubule dynamics and interphase cell polarity. Here we find that ECs dynamically repolarize during sprouting angiogenesis, and excess centrosomes block repolarization and reduce migration and sprouting. ECs with excess centrosomes initially had more centrosome-derived microtubules but, paradoxically, fewer steady-state microtubules. ECs with excess centrosomes had elevated Rac1 activity, and repolarization was rescued by blockade of Rac1 or actomyosin blockers, consistent with Rac1 activity promoting cortical retrograde actin flow and actomyosin contractility, which precludes cortical microtubule engagement necessary for dynamic repolarization. Thus normal centrosome numbers are required for dynamic repolarization and migration of sprouting ECs that contribute to blood vessel formation.