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

Dynamics of Endothelial Cell Diversity and Plasticity in Health and Disease

Endothelial cells (ECs) are vital structural units of the cardiovascular system possessing two principal distinctive properties: heterogeneity and plasticity. Endothelial heterogeneity is defined by differences in tissue-specific endothelial phenotypes and their high predisposition to modification along the length of the vascular bed. This aspect of heterogeneity is closely associated with plasticity, the ability of ECs to adapt to environmental cues through the mobilization of genetic, molecular, and structural alterations. The specific endothelial cytoarchitectonics facilitate a quick structural cell reorganization and, furthermore, easy adaptation to the extrinsic and intrinsic environmental stimuli, known as the epigenetic landscape. ECs, as universally distributed and ubiquitous cells of the human body, play a role that extends far beyond their structural function in the cardiovascular system. They play a crucial role in terms of barrier function, cell-to-cell communication, and a myriad of physiological and pathologic processes. These include development, ontogenesis, disease initiation, and progression, as well as growth, regeneration, and repair. Despite substantial progress in the understanding of endothelial cell biology, the role of ECs in healthy conditions and pathologies remains a fascinating area of exploration. This review aims to summarize knowledge and concepts in endothelial biology. It focuses on the development and functional characteristics of endothelial cells in health and pathological conditions, with a particular emphasis on endothelial phenotypic and functional heterogeneity.

Analysis of Expression of the ANG1, CaSR and FAK Proteins in Uterine Fibroids

Understanding the molecular factors involved in the development of uterine myomas may result in the use of pharmacological drugs instead of aggressive surgical treatment. ANG1, CaSR, and FAK were examined in myoma and peripheral tissue samples taken from women after myoma surgery and in normal uterine muscle tissue samples taken from the control group. Tests were performed using tissue microarray immunohistochemistry. No statistically significant differences in ANG1 expression between the tissue of the myoma, the periphery, and the normal uterine muscle tissue of the control group were recorded. The CaSR value was reduced in the myoma and peripheral tissue and normal in the group of women without myomas. FAK expression was also lower in the myoma and periphery compared to the healthy uterine myometrium. Calcium supplementation could have an effect on stopping the growth of myomas.

Toward a predictive understanding of epithelial cell death

Epithelial cell death is highly prevalent during development and tissue homeostasis. While we have a rather good understanding of the molecular regulators of programmed cell death, especially for apoptosis, we still fail to predict when, where, how many and which specific cells will die in a tissue. This likely relies on the much more complex picture of apoptosis regulation in a tissular and epithelial context, which entails cell autonomous but also non-cell autonomous factors, diverse feedback and multiple layers of regulation of the commitment to apoptosis. In this review, we illustrate this complexity of epithelial apoptosis regulation by describing these different layers of control, all demonstrating that local cell death probability is a complex emerging feature. We first focus on non-cell autonomous factors that can locally modulate the rate of cell death, including cell competition, mechanical input and geometry as well as systemic effects. We then describe the multiple feedback mechanisms generated by cell death itself. We also outline the multiple layers of regulation of epithelial cell death, including the coordination of extrusion and regulation occurring downstream of effector caspases. Eventually, we propose a roadmap to reach a more predictive understanding of cell death regulation in an epithelial context.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

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.

Soliton approximation in continuum models of leader-follower behavior

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

On the role of mechanical signals on sprouting angiogenesis through computer modeling approaches

Sprouting angiogenesis, the formation of new vessels from preexisting vasculature, is an essential process in the regeneration of new tissues as well as in the development of some diseases like cancer. Although early studies identified chemical signaling as the main driver of this process, many recent studies have shown a strong role of mechanical signals in the formation of new capillaries. Different types of mechanical signals (e.g., external forces, cell traction forces, and blood flow-induced shear forces) have been shown to play distinct roles in the process; however, their interplay remains still largely unknown. During the last decades, mathematical and computational modeling approaches have been developed to investigate and better understand the mechanisms behind mechanically driven angiogenesis. In this manuscript, we review computational models of angiogenesis with a focus on models investigating the role of mechanics on the process. Our aim is not to provide a detailed review on model methodology but to describe what we have learnt from these models. We classify models according to the mechanical signals being investigated and describe how models have looked into their role on the angiogenic process. We show that a better understanding of the mechanobiology of the angiogenic process will require the development of computer models that incorporate the interactions between the multiple mechanical signals and their effect on cellular responses, since they all seem to play a key in sprout patterning. In the end, we describe some of the remaining challenges of computational modeling of angiogenesis and discuss potential avenues for future research.

A Morphomolecular Approach to Alveolar Capillary Dysplasia

Alveolar capillary dysplasia (ACD) is a rare lung developmental disorder leading to persistent pulmonary arterial hypertension and fatal outcomes in newborns. The current study analyzed the microvascular morphology and the underlying molecular background of ACD. One ACD group (n = 7), one pulmonary arterial hypertension group (n = 20), and one healthy con1trol group (n = 16) were generated. Samples of histologically confirmed ACD were examined by exome sequencing and array-based comparative genomic hybridization. Vascular morphology was analyzed using scanning electron microscopy of microvascular corrosion casts. Gene expression and biological pathways were analyzed using two panels on inflammation/kinase-specific genes and a comparison analysis tool. Compartment-specific protein expression was analyzed using immunostaining. In ACD, there was an altered capillary network, a high prevalence of intussusceptive angiogenesis, and increased activity of C-X-C motif chemokine receptor 4 (CXCR4), hypoxia-inducible factor 1α (HIF1A), and angiopoietin signaling pathways compared with pulmonary arterial hypertension/healthy controls. Histologically, there was a markedly increased prevalence of endothelial tyrosine kinase receptor (TEK/TIE2)⁺ macrophages in ACD, compared with the other groups, whereas the CXCR4 ligand CXCL12 and HIF1A showed high expression in all groups. ACD is characterized by dysfunctional capillaries and a high prevalence of intussusceptive angiogenesis. The results indicate that endothelial CXCR4, HIF1A, and angiopoietin signaling as well as TIE2⁺ macrophages are crucial for the induction of intussusceptive angiogenesis and vascular remodeling. Future studies should address the use of anti-angiogenic agents in ACD, where TIE2 appears as a promising target.

Engineered patterns of Notch ligands Jag1 and Dll4 elicit differential spatial control of endothelial sprouting

Spatial regulation of angiogenesis is important for the generation of functional engineered vasculature in regenerative medicine. The Notch ligands Jag1 and Dll4 show distinct expression patterns in endothelial cells and, respectively, promote and inhibit endothelial sprouting. Therefore, patterns of Notch ligands may be utilized to spatially control sprouting, but their potential and the underlying mechanisms of action are unclear. Here, we coupled in vitro and in silico models to analyze the ability of micropatterned Jag1 and Dll4 ligands to spatially control endothelial sprouting. Dll4 patterns, but not Jag1 patterns, elicited spatial control. Computational simulations of the underlying signaling dynamics suggest that different timing of Notch activation by Jag1 and Dll4 underlie their distinct ability to spatially control sprouting. Hence, Dll4 patterns efficiently direct the sprouts, whereas longer exposure to Jag1 patterns is required to achieve spatial control. These insights in sprouting regulation offer therapeutic handles for spatial regulation of angiogenesis.

Computational model of brain endothelial cell signaling pathways predicts therapeutic targets for cerebral pathologies

Brain endothelial cells serve many critical homeostatic functions. In addition to sensing and regulating blood flow, they maintain blood-brain barrier function, including precise control of nutrient exchange and efflux of xenobiotics. Many signaling pathways in brain endothelial cells have been implicated in both health and disease; however, our understanding of how these signaling pathways functionally integrate is limited. A model capable of integrating these signaling pathways could both advance our understanding of brain endothelial cell signaling networks and potentially identify promising molecular targets for endothelial cell-based drug or gene therapies. To this end, we developed a large-scale computational model, wherein brain endothelial cell signaling pathways were reconstructed from the literature and converted into a network of logic-based differential equations. The model integrates 63 nodes (including proteins, mRNA, small molecules, and cell phenotypes) and 82 reactions connecting these nodes. Specifically, our model combines signaling pathways relating to VEGF-A, BDNF, NGF, and Wnt signaling, in addition to incorporating pathways relating to focused ultrasound as a therapeutic delivery tool. To validate the model, independently established relationships between selected inputs and outputs were simulated, with the model yielding correct predictions 73% of the time. We identified influential and sensitive nodes under different physiological or pathological contexts, including altered brain endothelial cell conditions during glioma, Alzheimer's disease, and ischemic stroke. Nodes with the greatest influence over combinations of desired model outputs were identified as potential druggable targets for these disease conditions. For example, the model predicts therapeutic benefits from inhibiting AKT, Hif-1α, or cathepsin D in the context of glioma - each of which are currently being studied in clinical or pre-clinical trials. Notably, the model also permits testing multiple combinations of node alterations for their effects on the network and the desired outputs (such as inhibiting AKT and overexpressing the P75 neurotrophin receptor simultaneously in the context of glioma), allowing for the prediction of optimal combination therapies. In all, our approach integrates results from over 100 past studies into a coherent and powerful model, capable of both revealing network interactions unapparent from studying any one pathway in isolation and predicting therapeutic targets for treating devastating brain pathologies.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Mechanistic characterization of endothelial sprouting mediated by pro-angiogenic signaling

Objective

We aim to quantitatively characterize the crosstalk between VEGF‐ and FGF‐mediated angiogenic signaling and endothelial sprouting, to gain mechanistic insights and identify novel therapeutic strategies.

Methods

We constructed an experimentally validated hybrid agent‐based mathematical model that characterizes endothelial sprouting driven by FGF‐ and VEGF‐mediated signaling. We predicted the total sprout length, number of sprouts, and average length by the mono‐ and co‐stimulation of FGF and VEGF.

Results

The experimentally fitted and validated model predicts that FGF induces stronger angiogenic responses in the long‐term compared with VEGF stimulation. Also, FGF plays a dominant role in the combination effects in endothelial sprouting. Moreover, the model suggests that ERK and Akt pathways and cellular responses contribute differently to the sprouting process. Last, the model predicts that the strategies to modulate endothelial sprouting are context‐dependent, and our model can identify potential effective pro‐ and anti‐angiogenic targets under different conditions and study their efficacy.

Conclusions

The model provides detailed mechanistic insight into VEGF and FGF interactions in sprouting angiogenesis. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to endothelial sprouting and to study the effects of pro‐ and anti‐angiogenic therapies.

Mechano-regulated cell-cell signaling in the context of cardiovascular tissue engineering

Cardiovascular tissue engineering (CVTE) aims to create living tissues, with the ability to grow and remodel, as replacements for diseased blood vessels and heart valves. Despite promising results, the (long-term) functionality of these engineered tissues still needs improvement to reach broad clinical application. The functionality of native tissues is ensured by their specific mechanical properties directly arising from tissue organization. We therefore hypothesize that establishing a native-like tissue organization is vital to overcome the limitations of current CVTE approaches. To achieve this aim, a better understanding of the growth and remodeling (G&R) mechanisms of cardiovascular tissues is necessary. Cells are the main mediators of tissue G&R, and their behavior is strongly influenced by both mechanical stimuli and cell-cell signaling. An increasing number of signaling pathways has also been identified as mechanosensitive. As such, they may have a key underlying role in regulating the G&R of tissues in response to mechanical stimuli. A more detailed understanding of mechano-regulated cell-cell signaling may thus be crucial to advance CVTE, as it could inspire new methods to control tissue G&R and improve the organization and functionality of engineered tissues, thereby accelerating clinical translation. In this review, we discuss the organization and biomechanics of native cardiovascular tissues; recent CVTE studies emphasizing the obtained engineered tissue organization; and the interplay between mechanical stimuli, cell behavior, and cell-cell signaling. In addition, we review past contributions of computational models in understanding and predicting mechano-regulated tissue G&R and cell-cell signaling to highlight their potential role in future CVTE strategies.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Progress in understanding of the stalk and tip cells formation involvement in angiogenesis mechanisms

Vascular sprouting is a key process of angiogenesis and mainly related to the formation of stalk and tip cells. Many studies have found that angiogenesis has a great clinical significance in promoting the functional repair of impaired tissues and anti-angiogenesis is a key to treatment of many tumors. Therefore, how the pathways regulate angiogenesis by regulating the formation of stalk and tip cells is an urgent problem for researchers. This review mainly summarizes the research progress of pathways affecting the formation of stalk and tip cells during angiogenesis in recent years, including the main signaling pathways (such as VEGF-VEGFR-Dll4-Notch signaling pathway, ALK-Smad signaling pathway,CCN1-YAP/YAZ signaling pathway and other signaling pathways) and cellular actions (such as cellular metabolisms, intercellular tension and other actions), aiming to further give the readers an insight into the mechanism of regulating the formation of stalk and tip cells during angiogenesis and provide more targets for anti-angiogenic drugs.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

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.

Tracking collective cell motion by topological data analysis

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

Role of biomechanics in vascularization of tissue-engineered bones

Biomaterial based reconstruction is still the most commonly employed method of small bone defect reconstruction. Bone tissue-engineered techniques are improving, and adjuncts such as vascularization technologies allow re-evaluation of traditional reconstructive methods for healingofcritical-sized bone defect. Slow infiltration rate of vasculogenesis after cell-seeded scaffold implantation limits the use of clinically relevant large-sized scaffolds. Hence, in vitro vascularization within the tissue-engineered bone before implantation is required to overcome the serious challenge of low cell survival rate after implantation which affects bone tissue regeneration and osseointegration. Mechanobiological interactions between cells and microvascular mechanics regulate biological processes regarding cell behavior. In addition, load-bearing scaffolds demand mechanical stability properties after vascularization to have adequate strength while implanted. With the advent of bioreactors, vascularization has been greatly improved by biomechanical regulation of stem cell differentiation through fluid-induced shear stress and synergizing osteogenic and angiogenic differentiation in multispecies coculture cells. The benefits of vascularization are clear: avoidance of mass transfer limitation and oxygen deprivation, a significant decrease in cell necrosis, and consequently bone development, regeneration and remodeling. Here, we discuss specific techniques to avoid pitfalls and optimize vascularization results of tissue-engineered bone. Cell source, scaffold modifications and bioreactor design, and technique specifics all play a critical role in this new, and rapidly growing method for bone defect reconstruction. Given the crucial importance of long-term survival of vascular network in physiological function of 3D engineered-bone constructs, greater knowledge of vascularization approaches may lead to the development of new strategies towards stabilization of formed vascular structure.