Synergy of Cell-Cell Repulsion and Vacuolation in a Computational Model of Lumen Formation

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

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 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

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

Computational modeling of angiogenesis: towards a multi-scale understanding of cell-cell and cell-matrix interactions

Combined with in vitro and in vivo experiments, mathematical and com- putational modeling are key to unraveling how mechanical and chemical signaling by endothelial cells coordinates their organization into capillary-like tubes. While in vitro and in vivo experiments can unveil the effects of for example environmental changes or gene knockouts, computational models provide a way to formalize and understand the mechanisms underlying these observations. This chapter reviews re- cent computational approaches to model angiogenesis, and discusses the insights they provide in the mechanisms of angiogenesis. We introduce a new cell-based computational model of an in vitro assay of angio- genic sprouting from endothelial monolayers in fibrin matrices. Endothelial cells are modeled by the Cellular Potts Model, combined with continuum descriptions to model haptotaxis and proteolysis of the extracellular matrix. The computational model demonstrates how a variety of cellular structural properties and behaviors determine the dynamics of tube formation. We aim to extend this model to a multi-scale model in the sense that cells, extracellular matrix and cell-regulation are de- scribed at different levels of detail and feedback on each other. Finally we discuss how computational modeling, combined with in vitro and in vivo modeling steers experiments, and how it generates new experimental hypotheses and insights on the mechanics of angiogenesis

A global sensitivity analysis approach for morphogenesis models

{\bf Background} %if any Morphogenesis is a developmental process in which cells organize into shapes and patterns. Complex, non-linear and multi-factorial models with images as output are commonly used to study morphogenesis. It is difficult to understand the relation between the uncertainty in the input and the output of such `black-box' models, giving rise to the need for sensitivity analysis tools. In this paper, we introduce a workflow for a global sensitivity analysis approach to study the impact of single parameters and the interactions between them on the output of morphogenesis models. {\bf Results} %if any To demonstrate the workflow, we used a published, well-studied model of vascular morphogenesis. The parameters of this cellular Potts model (CPM) represent cell properties and behaviors that drive the mechanisms of angiogenic sprouting. The global sensitivity analysis correctly identified the dominant parameters in the model, consistent with previous studies. Additionally, the analysis provided information on the relative impact of single parameters and of interactions between them. This is very relevant because interactions of parameters impede the experimental verification of the predicted effect of single parameters. The parameter interactions, although of low impact, provided also new insights in the mechanisms of \emph{in silico} sprouting. Finally, the analysis indicated that the model could be reduced by one parameter. {\bf Conclusions} %if any We propose global sensitivity analysis as an alternative approach to study the mechanisms of morphogenesis. Comparison of the ranking of the impact of the model parameters to knowledge derived from experimental data and from manipulation experiments can help to falsify models and to find the operand mechanisms in morphogenesis. The workflow is applicable to all `black-box' models, including high-throughput \emph{in vitro} models in which output measures are affected by a set of experimental perturbations

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

A local uPAR-plasmin-TGFβ1 positive feedback loop in a qualitative computational model of angiogenic sprouting explains the in vitro effect of fibrinogen variants

In experimental assays of angiogenesis in three-dimensional fibrin matrices, a temporary scaffold formed during wound healing, the type and composition of fibrin impacts the level of sprouting. More sprouts form on high molecular weight (HMW) than on low molecular weight (LMW) fibrin. It is unclear what mechanisms regulate the number and the positions of the vascular-like structures in cell cultures. To address this question, we propose a mechanistic simulation model of endothelial cell migration and fibrin proteolysis by the plasmin system. The model is a hybrid, cell-based and continuum, computational model based on the cellular Potts model and sets of partial-differential equations. Based on the model results, we propose that a positive feedback mechanism between uPAR, plasmin and transforming growth factor β1 (TGFβ1) selects cells in the monolayer for matrix invasion. Invading cells releases TGFβ1 from the extracellular matrix through plasmin-mediated fibrin degradation. The activated TGFβ1 further stimulates fibrin degradation and keeps proteolysis active as the sprout invades the fibrin matrix. The binding capacity for TGFβ1 of LMW is reduced relative to that of HMW. This leads to reduced activation of proteolysis and, consequently, reduced cell ingrowth in LMW fibrin compared to HMW fibrin. Thus our model predicts that endothelial cells in LMW fibrin matrices compared to HMW matrices show reduced sprouting due to a lower bio-availability of TGFβ1