Radial Distribution Function for Semiflexible Polymers Confined in Microchannels

An analytic expression is derived for the distribution $G(\vec{R})$ of the end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that $G(\vec{R})$ is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microchannels. This allows an unambiguous determination of persistence length $L_P$ and the dependence of statistical properties such as Odijk's deflection length $\lambda$ on the channel width $D$. It is shown that neglecting the effect of confinement leads to a significant overestimation of bending rigidities for filaments

FGF Signaling Mediates Regeneration of the Differentiating Cerebellum through Repatterning of the Anterior Hindbrain and Reinitiation of Neuronal Migration

To address the regenerative capability of the differentiating hindbrain, we ablated the cerebellum in wild-type and transgenic zebrafish embryos. These larvae showed no obvious locomotive malfunction several days after the ablation. Expression analysis and in vivo time-lapse recording in GFP (green fluorescent protein)-transgenic embryos indicate that cerebellar neuronal cells can regenerate from the remaining anterior hindbrain. The onset of regeneration is accompanied by repatterning within the anterior hindbrain. Inhibition of FGF signaling immediately after cerebellar ablation results in the lack of regenerating cerebellar neuronal cells and the absence of cerebellar structures several days later. Moreover, impaired FGF signaling inhibits the repatterning of the anterior hindbrain and the reexpression of rhombic lip marker genes soon after cerebellar ablation. This demonstrates that the hindbrain is highly plastic in recapitulating early embryonic differentiation mechanisms during regeneration. Moreover, the regenerating system offers a means to uncouple cerebellar differentiation from complex morphogenetic tissue rearrangements

Harmonically confined, semiflexible polymer in a channel: response to a stretching force and spatial distribution of the endpoints

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.Comment: 14 pages including figure

Direct imaging of in vivo neuronal migration in the developing cerebellum

The upper rhombic lip (URL), a germinal zone in the dorsoanterior hindbrain, has long been known to be a source for neurons of the vertebrate cerebellum [1]. It was thought to give rise to dorsally migrating granule cell precursors [2](Figure 1e); however, recent fate mapping studies have questioned the exclusive contributions of the URL to granule cells 3, 4 and 5. By taking advantage of the clarity of the zebrafish embryo during the stages of brain morphogenesis, we have followed the fate of neuronal precursor cells generated within the upper rhombic lip directly. Combining a novel GFP labeling strategy with in vivo time-lapse imaging, we find, contrary to the former view, that most URL-descendants migrate anterior toward the midhindbrain boundary (MHB) and then course ventrally along the MHB (Figure 1f). As the migrating neuronal precursors reach the MHB, they form ventrally extending projections, likely axons, and continue ventral migration to settle outside of the cerebellum, in the region of the ventral brainstem. Thus, we define a new pathway for URL-derived neuronal precursor cells consistent with the recent fate maps. In addition, our results strongly suggest that the MHB plays a crucial role, not only in induction and patterning of the cerebellar anlage, but also in organizing its later morphogenesis by influencing cell migration

Mechanics of individual keratin bundles in living cells

AbstractAlong with microtubules and microfilaments, intermediate filaments are a major component of the eukaryotic cytoskeleton and play a key role in cell mechanics. In cells, keratin intermediate filaments form networks of bundles that are sparser in structure and have lower connectivity than, for example, actin networks. Because of this, bending and buckling play an important role in these networks. Buckling events, which occur due to compressive intracellular forces and cross-talk between the keratin network and other cytoskeletal components, are measured here in situ. By applying a mechanical model for the bundled filaments, we can access the mechanical properties of both the keratin bundles themselves and the surrounding cytosol. Bundling is characterized by a coupling parameter that describes the strength of the linkage between the individual filaments within a bundle. Our findings suggest that coupling between the filaments is mostly complete, although it becomes weaker for thicker bundles, with some relative movement allowed

Spatial and temporal variability in the stomach content of herring and sprat in the Bornholm Basin

Herring and sprat stomachs and zooplankton samples were collected on 8 sites in the Bornholm Basin in May/June 1999 at different times of the day. Sprat showed a distinct increase in stomach content from early morning to the afternoon, whereas the stomach content of herring remained rather constant. Both herring and sprat showed a clear dominance of mesozooplankton in food composition with only small contributions of makrozooplankton and ichthyo-plankton. Both clupeid species showed similar preferences in selection of food items with a dominance of the copepods P. elongatus and T. longicornis. Compared to herring, other copepod species, especially Acartia spp. contributed to a larger extent to the food of sprat. Cladocerans played a less important role as food for both species. Spatial differences in stomach content have been revealed between the sampling sites. These resulted from differences in the distribution of food organisms in the water column as well as a different vertical distribution of the predators at different times of day. The share of juvenile copepods in herring stomachs was bigger than in sprat stomachs. Generally, selective feeding seemed to be stronger developed in sprat than in herring

Helices at Interfaces

Helically coiled filaments are a frequent motif in nature. In situations commonly encountered in experiments coiled helices are squeezed flat onto two dimensional surfaces. Under such 2-D confinement helices form "squeelices" - peculiar squeezed conformations often resembling looped waves, spirals or circles. Using theory and Monte-Carlo simulations we illuminate here the mechanics and the unusual statistical mechanics of confined helices and show that their fluctuations can be understood in terms of moving and interacting discrete particle-like entities - the "twist-kinks". We show that confined filaments can thermally switch between discrete topological twist quantized states, with some of the states exhibiting dramatically enhanced circularization probability while others displaying surprising hyperflexibility

The zebrafish cerebellar rhombic lip is spatially patterned in producing granule cell populations of different functional compartments

AbstractThe upper rhombic lip, a prominent germinal zone of the cerebellum, was recently demonstrated to generate different neuronal cell types over time from spatial subdomains. We have characterized the differentiation of the upper rhombic lip derived granule cell population in stable GFP-transgenic zebrafish in the context of zebrafish cerebellar morphogenesis. Time-lapse analysis followed by individual granule cell tracing demonstrates that the zebrafish upper rhombic lip is spatially patterned along its mediolateral axis producing different granule cell populations simultaneously. Time-lapse recordings of parallel fiber projections and retrograde labeling reveal that spatial patterning within the rhombic lip corresponds to granule cells of two different functional compartments of the mature cerebellum: the eminentia granularis and the corpus cerebelli. These cerebellar compartments in teleosts correspond to the mammalian vestibulocerebellar and non-vestibulocerebellar system serving balance and locomotion control, respectively. Given the high conservation of cerebellar development in vertebrates, spatial partitioning of the mammalian granule cell population and their corresponding earlier-produced deep nuclei by patterning within the rhombic lip may also delineate distinct functional compartments of the cerebellum. Thus, our findings offer an explanation for how specific functional cerebellar circuitries are laid down by spatio-temporal patterning of cerebellar germinal zones during early brain development