Tip cell overtaking occurs as a side effect of sprouting in computational models of angiogenesis

During angiogenesis, endothelial cells compete for the tip position during angiogenesis: a phenomenon named tip cell overtaking. It is still unclear to what extent tip cell overtaking is a side effect of sprouting or to what extent a biological function. To address this question, we studied tip cell overtaking in two existing cellular Potts models of angiogenic sprouting. In these models angiogenic sprouting-like behavior emerges from a small set of plausible cell behaviors and the endothelial cells spontaneously migrate forwards and backwards within sprouts, suggesting that tip cell overtaking might occur as a side effect of sprouting. In accordance with experimental observations, in our simulations the cells' tendency to occupy the tip position can be regulated when two cell lines with different levels of Vegfr2 expression are contributing to sprouting (mosaic sprouting assay), where cell behavior is regulated by a simple VEGF-Dll4-Notch signaling network. Our modeling results suggest that tip cell overtaking occurs spontaneously due to the stochastic motion of cells during sprouting. Thus, tip cell overtaking and sprouting dynamics may be interdependent and should be studied and interpreted in combination. VEGF-Dll4-Notch can regulate the ability of cells to occupy the tip cell position, but only when cells in the simulation strongly differ in their levels of Vegfr2. We propose that VEGF-Dll4-Notch signaling might not regulate which cell ends up at the tip, but assures that the cell that randomly ends up at the tip position acquires the tip cell phenotype.Comment: 20 pages, 6 figures, 4 supplementary figure

Computational modelling 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 modelling has contributed to unravelling 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 towards 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 modelling 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 modelling components such models should include in order to investigate its functional role.Comment: 26 pages, 9 figures, 1 table. Submitted for publication to WIREs Mechanisms of Diseas

Computational modeling of angiogenesis : from matrix invasion to lumen formation

In this thesis computational modeling is used to help unravel the mechanisms of key steps in angiogenesis, the formation of new capillaries from existing blood vessels. The first step in angiogenesis is the invasion of new branches into the surrounding tissue by degradation of extracellular matrix proteins, e.g. fibrin. A first model describes how invading sprouts use the so called plasminogen system, which dissolves fibrin matrices. A next model asks how endothelial cells can dynamically switch position during angiogenesis. Based on experimental observations, several authors suggest that dynamic cell shuffling is under strict, genetic control. Our simulations show, however, that shuffling can emerge as a side effect of sprouting. Once a sprout is formed, it needs to hollow to allow blood flow. The mechanisms responsible for this hollowing, or lumen formation, are debated: vacuoles may punch a hole through the cell, or cells might repulse one another. In our simulations, both these hypotheses can work synergistically in lumen formation, suggesting that both hypotheses might work together. In a final chapter, we introduce a workflow to simultaneously test the impact of changes in the value of multiple parameters on the outcome of the type of models used in this thesis.UBL - phd migration 201

Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis

Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its usability for modeling complex developmental phenomena by examining four fundamental examples of tissue morphogenesis: (i) cell sorting, (ii) cyst formation, (iii) tube morphogenesis in kidney development, and (iv) blood vessel formation. The review provides an introduction for biologists for starting simulation analysis using the CPM framework

Modelling the Growth of Blood Vessels in Health and Disease

Throughout our lives our blood vessels form new capillaries whose insufficient or excessive growth is a key factor in disease. During wound healing, insufficient growth of capillaries limits the supply of oxygen and nutrients to the new tissue. Tumours often attract capillaries, giving them their own blood supply and a route for further spread over the body. With the help of biological and medical colleagues our team develops mathematical models that recapitulate how cells can construct new blood vessels. These models are helping us to develop new ideas about how to stimulate or stop the growth of new blood vessels.Analysis and StochasticsAnimal science

eLife

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.DP1 NS092473/NS/NINDS NIH HHS/United StatesR01NS064583/NS/NINDS NIH HHS/United StatesDP1 NS092473/DP/NCCDPHP CDC HHS/United StatesR01 NS064583/NS/NINDS NIH HHS/United StatesT32 NS007484/NS/NINDS NIH HHS/United States26910011PMC481176

Cellular dynamics models of angiogenesis

Mención Internacional en el título de doctorCancer kills 26.4% of Spanish people. It is the second cause of death, just behind diseases of the circulatory system, 28.3% [1]. The growth of new blood vessels from the existing vasculature in response to chemical signals from a tumor is called tumorinduced angiogenesis and it is closely related to cancer and metastasis. The growth rate of a tumor is considerably increased in its vascular stage compared to its avascular and solid stage, therefore treating cancer turns excessively difficult and the survival rates rapidly decrease [2]. Among diseases that cause disability but not substantial mortality, age-related macular degeneration may cause severe loss of vision or blindness in many people, particularly the elderly. It is projected that 196 million people will be affected by age-related macular degeneration in 2020, increasing to 288 million by 2040 [3], which is likely an underestimation [4]. With age, Bruch’s membrane gets thicker and some damaged cells in the retina become inflamed. The secretion of chemical signals from those cells due to their inflammation induces angiogenesis, but the new blood vessels are disorganized and leaky causing the loss of vision. John Hunter was the pioneer in describing the vessel formation process in 1787 [5], but the first person who coined the word “angiogenesis” was Arthur T. Hertig in 1935 [6]. He was studying the formation of new blood vessel in the primary placenta of the macaque monkey when this word was used for the first time. Years later, in 1971, Judah Folkman hypothesized that tumors emit Tumor Angiogenic Factors (TAF) to attract blood vessels to them [7]. This investigation triggered the research field of angiogenesis in cancer and in 1989 one of the most important angiogenic factors was discovered: the Vascular Endothelial Growth Factor (VEGF). Since then, drugs with antiangiogenic effects have been investigated for cancer, age-related macular degeneration and other diseases, as it is involved in more than seventy different diseases. However, angiogenesis also occurs in normal and vital processes such as wound healing or the growth of a fetus. The difference between physiological and pathological angiogenic processes is a matter of balance. In a healthy process, angiogenesis develops to its proper extent and then stops, while in pathological processes angiogenesis does not stop or it does not develop sufficiently. Angiogenesis keeps the number of blood vessels needed in balance: few blood vessels cause tissue death, while uncontrolled vascular proliferation can lead to cancer, macular degeneration and other diseases. Angiogenesis is a complex, multistep 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. In a later stage of angiogenesis, vessel cells rearrange to form lumen and allow the perfusion of the blood inside the sprout. Depending on what induces the angiogenesis, different environments and cells should be considered, for instance in the retina. A detailed review of the processes involved in angiogenesis from the biological point of view is given in section 1.1. Beyond experimental investigations, mathematical models of angiogenesis try to help in understanding the process and how the relevant mechanisms of angiogenesis interact. The approach of some models focus on a single scale or a single process of those involved to deepen the knowledge about it. Others span multiple scales or the whole process to give an idea about how to prevent or favor angiogenesis. In section 1.2, we briefly review the mathematical models of angiogenesis that have been used to date as well as those when angiogenesis occurs in the retina and models of lumen formation, the late stage of angiogenesis. A crucial question about modeling is how to integrate the multiple scales and mechanisms present in angiogenesis in a mathematical model. A model is expected to be useful to explore methods for promoting and inhibiting angiogenesis. However, answering this question with this expectation is not a simple task. Assembling all the processes involved with their different time and length scales requires to develop a cellular dynamics model combined with models for the continuum fields. We achieved this objective by developing a hybrid cellular Potts model of early stage angiogenesis, given in chapter 2. In contrast to recent models, this mathematical and computational model is able to explore the role of biochemical signaling and tissue mechanics. A exhaustive description of the results of the numerical simulations complete the chapter 2. The advantages of discovering the reasons why angiogenesis starts in the retina or inhibitory mechanisms are innumerable. Unraveling the causes of neovascularization in the retina and giving possible solutions for age-related macular degeneration are our motivation to adapt the angiogenesis model of chapter 2 to the retina. In chapter 3, we present the model and the numerical results. If mathematical models of angiogenesis that incorporate multiple scales and cellular signaling processes are not that common, those that also include lumen formation are almost nonexistent. In chapter 4, we describe two models of lumen formation and their results. The lumen formation in the first model takes place in a already developed sprout. Although some restrictions in the model make its applications and possibilities limited, its study is convenient to establish the basis of the second proposed model. In this second model, the lumenization occurs while the sprout is developing and the pressure of the blood is involved, following recent experiments of lumen formation during angiogenesis. This model is work in progress, but we believe that showing the preliminary results in chapter 4 may be interesting. A critical step in the development of a mathematical and computational model is to analyze the viability of its simulations. The simulations of the model in chapter 2 have been carried out thanks to the parallel computing on Graphics Processing Units (GPUs), as well as simulations of chapters 3 and 4. The large amount of square elements of the grid, nodes, cells and sprouts make this type of computation suitable for these models. The way they have been implemented is explained in chapter 5. Finally, conclusions of this thesis and future work are drawn in the last chapter 6. This chapter highlights and summarizes the research that has been carried out and proposes future extensions and applications of this work.La investigación de esta tesis ha sido financiada por los proyectos de investigación del Ministerio de Economía y Competitividad (ahora FEDER/Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación) No. MTM2014-56948-C2-2-P y No. MTM2017-84446-C2-2-R.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Ana María Carpio Rodríguez.- Secretario: Filippo Terragni.- Vocal: Stephen W. Teitswort

Tip Cells in Angiogenesis

In angiogenesis, the process in which blood vessel sprouts grow out from a pre-existing vascular network, the so-called endothelial tip cells play an essential role. Tip cells are the leading cells of the sprouts; they guide following endothelial cells and sense their environment for guidance cues. Because of this essential role, the tip cells are a potential therapeutic target for anti-angiogenic therapies, which need to be developed for diseases such as cancer and major eye diseases. The potential of anti-tip cell therapies is now widely recognised, and the surge in research this has caused has led to improved insights in the function and regulation of tip cells, as well as the development of novel in vitro and in silico models. These new models in particular will help understand essential mechanisms in tip cell biology and may eventually lead to new or improved therapies to prevent blindness or cancer spread