Models for angiogenesis on micro-structured surfaces

Endothelial cell (EC) migration is an essential process in angiogenesis as ECs sprout from preexisting vessels, following chemotactic gradients. However, most of the data obtained about EC migration has been acquired in artificial two dimensional (2D) cell culture environments. Recent reports showed that migration in fibrillary environments can be mimicked by spatial confinement, achieved by micro patterning techniques (Doyle et al. 2009). In the first part of this work it was investigated whether a model system based on linearly structured surfaces allows to draw conclusions about the migration of ECs in fibrillary 3D collagen matrices. In order to estimate the cellular behavior of ECs on linearly structured surfaces, a comprehensive cell biological analysis was performed. ECs on narrow 3 µm wide tracks (also termed 1D in the following) migrated less efficient in comparison to ECs on broader tracks in regard to mean velocity, persistence, and run velocity. Additionally, ECs in 1D displayed a distinct actin cytoskeleton architecture, compressed nuclei, and different orientation of the centrosome in comparison to ECs on wider tracks. The frequent directional changes of ECs on narrow tracks were accompanied by pronounced membrane blebbing, while migrating and elongated cells displayed a lamellipodium as cellular protrusion. This behavior was contractility-dependent as both modes were provoked by using Blebbistatin or Calyculin A, respectively. The comparison between 1D and 3D migrating cells revealed a striking similarity in actin cytoskeleton architecture and in switching between two morphological modes. Cells migrating in 3D moved slower but more persistent after Blebbistatin treatment, which was likewise the case for cells migrating in 1D. In contrast to this, cells in the 2D system migrated faster but less persistent after Blebbistatin treatment. A Rac1 inhibitor used in this study showed the tendency to influence the migratory potential similarly in 1D and 3D, in contrast to 2D. However, a microtubule disrupting agent displayed different effects in 1D and 3D. These experiments demonstrated that the 1D system allows to draw conclusions about certain aspects of 3D migration. Thus, using this 1D migration system, important aspects of 3D migration can be mimicked in a highly controlled setting. In the second part of this work, a system for artificial tip cell formation was investigated. For the analysis of tip and stalk cells specifically structured surfaces were designed. These structures provided areas allowing only a restricted number of cell-cell contacts and areas allowing a high number of cell-cell contacts. ECs with a low number of cell-cell contacts displayed increased VEGFR2 expression levels in comparison to cells with a high number of cell-cell contacts, a phenomenon which was inhibited by using a Notch signaling inhibitor. This system will be a useful tool in the future to decipher tip and stalk cell competition within a defined cellular population and a defined microscopic fram

Comparing efficient computation methods for massless QCD tree amplitudes: Closed Analytic Formulae versus Berends-Giele Recursion

Recent advances in our understanding of tree-level QCD amplitudes in the massless limit exploiting an effective (maximal) supersymmetry have led to the complete analytic construction of tree-amplitudes with up to four external quark-anti-quark pairs. In this work we compare the numerical efficiency of evaluating these closed analytic formulae to a numerically efficient implementation of the Berends-Giele recursion. We compare calculation times for tree-amplitudes with parton numbers ranging from 4 to 25 with no, one, two and three external quark lines. We find that the exact results are generally faster in the case of MHV and NMHV amplitudes. Starting with the NNMHV amplitudes the Berends-Giele recursion becomes more efficient. In addition to the runtime we also compared the numerical accuracy. The analytic formulae are on average more accurate than the off-shell recursion relations though both are well suited for complicated phenomenological applications. In both cases we observe a reduction in the average accuracy when phase space configurations close to singular regions are evaluated. We believe that the above findings provide valuable information to select the right method for phenomenological applications.Comment: 22 pages, 9 figures, Mathematica package GGT.m and example notebook is included in submissio

Models for angiogenesis on micro-structured surfaces

Endothelial cell (EC) migration is an essential process in angiogenesis as ECs sprout from preexisting vessels, following chemotactic gradients. However, most of the data obtained about EC migration has been acquired in artificial two dimensional (2D) cell culture environments. Recent reports showed that migration in fibrillary environments can be mimicked by spatial confinement, achieved by micro patterning techniques (Doyle et al. 2009). In the first part of this work it was investigated whether a model system based on linearly structured surfaces allows to draw conclusions about the migration of ECs in fibrillary 3D collagen matrices. In order to estimate the cellular behavior of ECs on linearly structured surfaces, a comprehensive cell biological analysis was performed. ECs on narrow 3 µm wide tracks (also termed 1D in the following) migrated less efficient in comparison to ECs on broader tracks in regard to mean velocity, persistence, and run velocity. Additionally, ECs in 1D displayed a distinct actin cytoskeleton architecture, compressed nuclei, and different orientation of the centrosome in comparison to ECs on wider tracks. The frequent directional changes of ECs on narrow tracks were accompanied by pronounced membrane blebbing, while migrating and elongated cells displayed a lamellipodium as cellular protrusion. This behavior was contractility-dependent as both modes were provoked by using Blebbistatin or Calyculin A, respectively. The comparison between 1D and 3D migrating cells revealed a striking similarity in actin cytoskeleton architecture and in switching between two morphological modes. Cells migrating in 3D moved slower but more persistent after Blebbistatin treatment, which was likewise the case for cells migrating in 1D. In contrast to this, cells in the 2D system migrated faster but less persistent after Blebbistatin treatment. A Rac1 inhibitor used in this study showed the tendency to influence the migratory potential similarly in 1D and 3D, in contrast to 2D. However, a microtubule disrupting agent displayed different effects in 1D and 3D. These experiments demonstrated that the 1D system allows to draw conclusions about certain aspects of 3D migration. Thus, using this 1D migration system, important aspects of 3D migration can be mimicked in a highly controlled setting. In the second part of this work, a system for artificial tip cell formation was investigated. For the analysis of tip and stalk cells specifically structured surfaces were designed. These structures provided areas allowing only a restricted number of cell-cell contacts and areas allowing a high number of cell-cell contacts. ECs with a low number of cell-cell contacts displayed increased VEGFR2 expression levels in comparison to cells with a high number of cell-cell contacts, a phenomenon which was inhibited by using a Notch signaling inhibitor. This system will be a useful tool in the future to decipher tip and stalk cell competition within a defined cellular population and a defined microscopic fram