Computational models of sprouting angiogenesis and cell migration: towards multiscale mechanochemical models of angiogenesis

Angiogenesis, the formation of new bloods vessels from the existing vasculature, is a process that is essential during development and regeneration of tissues, and that plays a major role in diseases like cancer. Computational models have been designed to obtain a better understanding of the mechanisms behind angiogenesis. In this paper we review computational models of sprouting angiogenesis. These models can be subdivided into three categories: models that mainly focus on tip cell migration, models that make a distinction between the role of tip cells and stalk cells, and models that consider cell shape dynamics. Many models combine discrete modeling of individual cells with continuous modeling of the extracellular matrix (ECM) and diffusing solutes, in this way resulting in a hybrid model. We discuss their merits in unraveling the role of certain factors for vascular network formation, such as the role of (chemotactic, haptotactic, contact) guidance cues in the dynamics and morphology of vascular network formation, and the role of cell-cell interactions that govern tip cell selection and phenotypic changes in general. At the same time, we identify a need for the inclusion of cell mechanical principles in models of angiogenesis, in particular for the description of cell migration, cell-matrix and cell-cell interaction, as the generation of cellular forces is key to cell migration. To further underline this we review models of single cell migration that incorporate such principles, which could be the starting point for formulating novel models of angiogenesis that respect the fundamental laws of classical mechanics at the cell level. As the generation of cellular forces is strongly mediated by pro-angiogenic signals, such models must couple cell mechanical principles to molecular signaling into multiscale mechanochemical models of angiogenesis. Finally, a tight coupling between models and experiments will be required to facilitate model improvements and the generation of novel insights on the regulation of angiogenesis.status: publishe

Three-dimensional rapid visualisation of matrix deformations around angiogenic sprouts

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Quantification of 3D Matrix Deformations induced by Angiogenic Sprouts in Fibrillar Gels

Cell-matrix mechanical interactions play a key role in a variety of physiological processes. Recently, the quantification of cellular tractions by means of traction force microscopy has been extended to 3D cell cultures. However, typically assumed simplifications during the mechanical characterization of the matrix could affect the retrieved traction magnitudes. On the other hand, cell induced matrix displacements already provide quantitative information on cell-matrix mechanical interaction, avoiding the complexity inherent to traction reconstruction. In this study, we assess the deformations induced by angiogenic cellular sprouts in a fibrillar matrix under chemically defined culture conditions from the full field displacements obtained with and without fluorescent beads acting as fiducial markers. Human umbilical vein endothelial cells (HUVEC) were seeded on top of a collagen gel and induced with pro-angiogenic factors to form multicellular sprouts. The sprouts were grown in endothelial cell growth medium (EGM2) supplemented with or without blebbistatin or cytochalasin D. As control for the calculation of the matrix deformations, 200 nm fluorescent beads were attached to the collagen fibers. Second harmonic generation (SHG) and laser-scanning confocal microscopy were used to acquire Z-stacks of label-free collagen fibers and fluorescent beads, respectively, during the live imaging before and after chemically induced relaxation of cells. The calculation of the matrix deformations was formulated as a B-spline –based 3D non-rigid image registration process that warps the image of the stressed gel to match the image of the gel after relaxation [1]. The calculation of these displacements was independently performed from fiber (without fiducial markers) and bead images. We observed that the recovered displacements (Figure 1) from the label-free fiber images were equivalent to the ones obtained from bead images, showing magnitudes ranging between 1 to 8 µm before the blocking effects of blebbistatin or cytochalasin D on acto-myosin force generation. Our methodology allows mapping cell-induced 3D matrix deformations around multicellular sprouts embedded in fibrillar gels without the need for fluorescent beads, which could alter the matrix mechanical properties. The resulting information is expected to provide a quantitative view of the cell-matrix mechanical interaction of HUVECs in 3D and leads to a better comprehension of cell mechanobiology in sprouting angiogenesis.status: accepte

Spatiotemporal analyses of cellular tractions describe subcellular effect of substrate stiffness and coating

Cells interplay with their environment through mechanical and chemical interactions. To characterize this interplay, endothelial cells were cultured on polyacrylamide hydrogels of varying stiffness, coated with either fibronectin or collagen. We developed a novel analysis technique, complementary to traction force microscopy, to characterize the spatiotemporal evolution of cellular tractions: We identified subpopulations of tractions, termed traction foci, and tracked their magnitude and lifetime. Each focus consists of tractions associated with a local single peak of maximal traction. Individual foci were spread over a larger area in cells cultured on collagen relative to those on fibronectin and exerted higher tractions on stiffer hydrogels. We found that the trends with which forces increased with increasing hydrogel stiffness were different for foci and whole-cell measurements. These differences were explained by the number of foci and their average strength. While on fibronectin multiple short-lived weak foci contributed up to 30% to the total traction on hydrogels with intermediate stiffness, short-lived foci in such a number were not observed on collagen despite the higher tractions. Our approach allows for the use of existing traction force microscopy data to gain insight at the subcellular scale without molecular probes or spatial constraining of cellular tractions.status: publishe

Mapping traction-induced matrix displacements of in vitro angiogenic sprouts

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Quantifying extracellular matrix deformations and cellular forces around angiogenic sprouts

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Fast quantitative time lapse displacement imaging of endothelial cell invasion.

In order to unravel rapid mechano-chemical feedback mechanisms in sprouting angiogenesis, we combine selective plane illumination microscopy (SPIM) and tailored image registration algorithms - further referred to as SPIM-based displacement microscopy - with an in vitro model of angiogenesis. SPIM successfully tackles the problem of imaging large volumes while upholding the spatial resolution required for the analysis of matrix displacements at a subcellular level. Applied to in vitro angiogenic sprouts, this unique methodological combination relates subcellular activity - minute to second time scale growing and retracting of protrusions - of a multicellular systems to the surrounding matrix deformations with an exceptional temporal resolution of 1 minute for a stack with multiple sprouts simultaneously or every 4 seconds for a single sprout, which is 20 times faster than with a conventional confocal setup. Our study reveals collective but non-synchronised, non-continuous activity of adjacent sprouting cells along with correlations between matrix deformations and protrusion dynamics.status: Published onlin

3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10 μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling.publisher: Elsevier articletitle: 3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation journaltitle: Biomaterials articlelink: http://dx.doi.org/10.1016/j.biomaterials.2017.05.015 content_type: article copyright: © 2017 Elsevier Ltd. All rights reserved.status: publishe

Image processing-based automatic 3D quantification of sprouting angiogenesis in spheroid assays

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Matrix deformations around angiogenic sprouts correlate to sprout dynamics and suggest pulling activity

Angiogenesis is the formation of new blood vessels from the pre-existing vasculature. It is essential for normal tissue growth and regeneration, but also plays a key role in many diseases. Cytoskeletal components have been shown to be important for angiogenic sprout initiation and maintenance as well as endothelial cell shape control during invasion. The exact nature of cytoskeleton-mediated forces for sprout initiation and progression, however, remains poorly understood. Questions on the importance of tip cell pulling versus stalk cell pushing are to a large extent unanswered, which among others has to do with the difficulty of quantifying and resolving those forces in time and space. We developed methods based on time lapse confocal microscopy and image processing – further termed 4D displacement microscopy - to acquire detailed, spatially and temporally resolved extracellular matrix (ECM) deformations, indicative of cell-ECM mechanical interactions around invading sprouts. We demonstrate that matrix deformations dependent on actin-mediated force generation are spatio-temporally correlated with sprout morphological dynamics. Furthermore, sprout tips were found to exert radially pulling forces on the extracellular matrix, which were quantified by means of a computational model of collagen ECM mechanics. Protrusions from extending sprouts mostly increase their pulling forces, while retracting protrusions mainly reduce their pulling forces. Displacement microscopy analysis further unveiled a characteristic dipole-like deformation pattern along the sprout direction that was consistent among seemingly very different sprout shapes - with oppositely oriented displacements at sprout tip versus sprout base and a transition zone of negligible displacements in between. These results demonstrate that sprout-ECM interactions are dominated by pulling forces and underline the key role of tip cell pulling for sprouting angiogenesis.status: Published onlin