Coupling of cytoplasm and adhesion dynamics determines cell polarization and locomotion

Observations of single epidermal cells on flat adhesive substrates have revealed two distinct morphological and functional states, namely a non-migrating symmetric unpolarized state and a migrating asymmetric polarized state. These states are characterized by different spatial distributions and dynamics of important biochemical cell components: F-actin and myosin-II form the contractile part of the cytoskeleton, and integrin receptors in the plasma membrane connect F-actin filaments to the substratum. In this way, focal adhesion complexes are assembled, which determine cytoskeletal force transduction and subsequent cell locomotion. So far, physical models have reduced this phenomenon either to gradients in regulatory control molecules or to different mechanics of the actin filament system in different regions of the cell. Here we offer an alternative and self-organizational model incorporating polymerization, pushing and sliding of filaments, as well as formation of adhesion sites and their force dependent kinetics. All these phenomena can be combined into a non-linearly coupled system of hyperbolic, parabolic and elliptic differential equations. Aim of this article is to show how relatively simple relations for the small-scale mechanics and kinetics of participating molecules may reproduce the emergent behavior of polarization and migration on the large-scale cell level.Comment: v2 (updates from proof): add TOC, clarify Fig. 4, fix several typo

The capital gains tax: A curse but also a blessing for venture capital investment

This article documents a statistical association between the number and success of venture capital investments and the capital gains tax rate. To do this, we analyze investment data and taxes of 32 countries from 2000 to 2010. In our data, higher capital gains tax rates are associated with fewer firms financed and a lower probability for ventures receiving follow-up funding. However, if the first investment is received when taxes are high, the probability of a firm eventually going public or being acquired increases. We conclude that high tax rates are associated with fewer, but on average more successful companies. --capital gains tax,venture capital,investment

Evidence for Environmental Changes in the Submillimeter Dust Opacity

The submillimeter opacity of dust in the diffuse interstellar medium (ISM) in the Galactic plane has been quantified using a pixel-by-pixel correlation of images of continuum emission with a proxy for column density. We used multi-wavelength continuum data: three Balloon-borne Large Aperture Submillimeter Telescope bands at 250, 350, and 500 μm and one IRAS band at 100 μm. The proxy is the near-infrared color excess, E(J – K_s), obtained from the Two Micron All Sky Survey. Based on observations of stars, we show how well this color excess is correlated with the total hydrogen column density for regions of moderate extinction. The ratio of emission to column density, the emissivity, is then known from the correlations, as a function of frequency. The spectral distribution of this emissivity can be fit by a modified blackbody, whence the characteristic dust temperature T and the desired opacity σ_e(1200) at 1200 GHz or 250 μm can be obtained. We have analyzed 14 regions near the Galactic plane toward the Vela molecular cloud, mostly selected to avoid regions of high column density (N_H > 10^(22) cm^(–2)) and small enough to ensure a uniform dust temperature. We find σ_e(1200) is typically (2-4) × 10^(–25) cm^2 H^(–1) and thus about 2-4 times larger than the average value in the local high Galactic latitude diffuse atomic ISM. This is strong evidence for grain evolution. There is a range in total power per H nucleon absorbed (and re-radiated) by the dust, reflecting changes in the strength of the interstellar radiation field and/or the dust absorption opacity. These changes in emission opacity and power affect the equilibrium T, which is typically 15 K, colder than at high latitudes. Our analysis extends, to higher opacity and lower temperature, the trend of increasing σ_e(1200) with decreasing T that was found at high latitudes. The recognition of changes in the emission opacity raises a cautionary flag because all column densities deduced from dust emission maps, and the masses of compact structures within them, depend inversely on the value adopted

Erfahrungen mit mathematischer Modellierung in der Hochschulausbildung

Auf lange Sicht ist es von größter Bedeutung, Lehrkräfte zukunftsweisend auszubilden. Dazu gehört, dass sie schon an der Hochschule die Problemlösungsfähigkeit der Mathematik erfahren und lernen sollten sie einzusetzen. Während numerische Mathematik an den meisten Fachbereichen gelehrt und auch implementiert wird, gibt es nicht überall Lehrveranstaltungen, in denen Lehramtsstudierende lernen zu modellieren. Solche Veranstaltungen zu entwickeln, mit den numerischen Methoden zu koppeln und schließlich Simulationen zu programmieren, die zur Vorhersage und auch zur Optimierung der simulierten Systeme genutzt werden können, ist eine neue Aufgabe in der Ausbildung von Lehrkräften. Dieser Beitrag stellt exemplarisch verschiedene Veranstaltungen vor, in denen an der TU Kaiserslautern ein Fokus auf die mathematische Modellierung gelegt wird

The Capital Gains Tax: A Curse but Also a Blessing for Venture Capital Investment

Our study analyzes the effect of the capital gains tax on the individual investment decisions of venture capitalists. By doing so, we are able to study the decisions for a sample of 76,852 funding rounds in 32 countries from 2000 to 2012. Our results support the predictions of the theoretical model that higher capital gains tax rates are associated with fewer start-ups financed and a lower probability of receiving follow-up funding. However, the results concerning the effect on the probability of success of start-ups show that a higher tax burden is associated with a higher probability of eventual start-up success

Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein-Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.Comment: v1: 34 pages, 19 figures v2: reformatted 43 pages, 21 figures, 1 table; minor clarifications, extended supplementary materia