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

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

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