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

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

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics

Biological Sciences; Cell Biology; Biophysics; In Silico Biology; Biomaterials; Structural Biology; Biochemistry; Biocomputational MethodMany cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions

Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.Comment: 25 pages, 6 figures, accepted for publication in PLoS Computational Biolog

Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro

During the embryonic development of multicellular organisms, millions of cells cooperatively build structured tissues, organs and whole organisms, a process called morphogenesis. How the behavior of so many cells is coordinated to produce complex structures is still incompletely understood. Most biomedical research focuses on the molecular signals that cells exchange with one another. It has now become clear that cells also communicate biomechanically during morphogenesis. In cell cultures, endothelial cells—the building blocks of blood vessels—can organize into structures resembling networks of capillaries. Experimental work has shown that the endothelial cells pull onto the protein gel that they live in, called the extracellular matrix. On sufficiently compliant matrices, the strains resulting from these cellular pulling forces slow down and reorient adjacent cells. Here we propose a new computational model to show that this simple form of mechanical cell-cell communication suffices for reproducing the formation of blood vessel-like structures in cell cultures. These findings advance our understanding of biomechanical signaling during morphogenesis, and introduce a new set of computational tools for modeling mechanical interactions between cells and the extracellular matrix

Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in the absence of proliferation. In this work, we propose a simple, experimentally plausible mechanism that can drive branching morphogenesis in the absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive from in vitro observations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGFβ1 inhibits the formation of cell protrusions, leading to curvature-dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry-dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in the absence and also in the presence of cell proliferation. This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.</p

Scientific report training workshop interdisciplinary life sciences

This preprint is the outcome of the “Training Workshop Interdisciplinary Life Sciences”, held in October 2013 in the Lorentz Center, Leiden, The Netherlands. The motivation to organize this event stems from the following considerations: The enormous progress in laboratory techniques and facilities leads to the availability of huge amounts of data at all levels of complexity (molecules, cells, tissues, organs, organisms, populations, ecosystems). Especially data at the cellular level reveal details of life processes we were unconscious of until recently. However, it becomes clear that huge amounts of data alone do not automatically lead to understanding. The data explosion in Life Sciences teaches one lesson: life processes are of a highly intricate and integrative nature. To really understand the dynamic processes in living organisms one must integrate experimental data sets in quantitative and predictive models. Only then one may hope to grasp the functioning of these complex systems and be able to convert information in understanding. In the field of physics, for instance, this strong interaction between experiment and theory is already common practice since centuries, culminating in the 20th century being called the ’Century of Physics’. In contrast to physics, the complex nature of the Life Sciences forces us to work in an interdisciplinary fashion. The necessary expertise is available, but scattered over many scientific disciplines. Only the combined efforts of biologists, chemists, mathematicians, physicists, engineers, and informaticians will lead to progress in tackling the huge challenge of understanding the complexity of life. Researchers in the Life Sciences often focus their research on a rather narrow research field. However, the majority of the upcoming generation of researchers in the Life Sciences should be trained to expand their skills, becoming able to tackle complex, multi-dimensional systems. The knowledge they have to incorporate in their research will stem from a diverse range of disciplines, So, they should be trained to integrate a broad range of modelling approaches in order to deduce quantitative, predictive and often multi-scale models from highly diverse data sets. Present curricula in the Life Sciences hardly offer this kind of training yet. This workshop intends to start filling this gap. Three teams worked on the following open problems: 1) Modeling the influence of temperature on the Regulation of flowering time in Arabidopsis thaliana; 2) Validation of computational models of angiogenesis to experimental data; 3) Reconstructing the gene network that regulates branching in Tomato. This preprint bundles the reports of the three teams