Spiraling of approximations and spherical averages of Siegel transforms

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We consider the question of how approximations satisfying Dirichlet’s theorem spiral around vectors in Rd. We give pointwise almost everywhere results (using only the Birkhoff ergodic theorem on the space of lattices). In addition, we show that for every unimodular lattice, on average, the directions of approximates spiral in a uniformly distributed fashion on the d − 1 dimensional unit sphere. For this second result, we adapt a very recent proof of Marklof and Strombergsson [19] to show a spherical average result for Siegel transforms on SLd+1(R)/ SLd+1(Z). Our techniques are elementary. Results like this date back to the work of Eskin-Margulis-Mozes [9] and KleinbockMargulis [14] and have wide-ranging applications. We also explicitly construct examples in which the directions are not uniformly distributedJ.S.A. partially supported by NSF grant DMS 1069153, and NSF grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). A.G. partially supported by the Royal Society. J.T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 291147

The Demand Side: Uses of Research in Child and Adolescent Mental Health Services

This special issue on child and adolescent mental health contains a thoughtful set of papers that address many of the challenges in bridging research and practice. These articles, however, focus predominantly on the supply side of producing research for use by a range of audiences, including practitioners, administrators and policy makers. This commentary emphasizes the importance of attending to, and better understanding, the demand side with regard to how research evidence is evaluated, understood, and utilized. Drawing from work underway at the William T. Grant Foundation, the authors argue for the need to understand three broad topics: user settings and perspectives, political, economic and social contexts, and the various uses of research. Furthermore, understanding the use of research evidence, or the demand side, is itself a topic for empirical investigation. The authors conclude that, when it comes to supplying evidence, don’t forget the demand side

Effects of deletion of the Streptococcus pneumoniae lipoprotein diacylglyceryl transferase gene lgt on ABC transporter function and on growth in vivo

Lipoproteins are an important class of surface associated proteins that have diverse roles and frequently are involved in the virulence of bacterial pathogens. As prolipoproteins are attached to the cell membrane by a single enzyme, prolipoprotein diacylglyceryl transferase (Lgt), deletion of the corresponding gene potentially allows the characterisation of the overall importance of lipoproteins for specific bacterial functions. We have used a Δlgt mutant strain of Streptococcus pneumoniae to investigate the effects of loss of lipoprotein attachment on cation acquisition, growth in media containing specific carbon sources, and virulence in different infection models. Immunoblots of triton X-114 extracts, flow cytometry and immuno-fluorescence microscopy confirmed the Δlgt mutant had markedly reduced lipoprotein expression on the cell surface. The Δlgt mutant had reduced growth in cation depleted medium, increased sensitivity to oxidative stress, reduced zinc uptake, and reduced intracellular levels of several cations. Doubling time of the Δlgt mutant was also increased slightly when grown in medium with glucose, raffinose and maltotriose as sole carbon sources. These multiple defects in cation and sugar ABC transporter function for the Δlgt mutant were associated with only slightly delayed growth in complete medium. However the Δlgt mutant had significantly reduced growth in blood or bronchoalveolar lavage fluid and a marked impairment in virulence in mouse models of nasopharyngeal colonisation, sepsis and pneumonia. These data suggest that for S. pneumoniae loss of surface localisation of lipoproteins has widespread effects on ABC transporter functions that collectively prevent the Δlgt mutant from establishing invasive infection

Crown Lengthening Revisited

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141178/1/cap0233.pd

Resolving the Role of Actoymyosin Contractility in Cell Microrheology

Einstein's original description of Brownian motion established a direct relationship between thermally-excited random forces and the transport properties of a submicron particle in a viscous liquid. Recent work based on reconstituted actin filament networks suggests that nonthermal forces driven by the motor protein myosin II can induce large non-equilibrium fluctuations that dominate the motion of particles in cytoskeletal networks. Here, using high-resolution particle tracking, we find that thermal forces, not myosin-induced fluctuating forces, drive the motion of submicron particles embedded in the cytoskeleton of living cells. These results resolve the roles of myosin II and contractile actomyosin structures in the motion of nanoparticles lodged in the cytoplasm, reveal the biphasic mechanical architecture of adherent cells—stiff contractile stress fibers interdigitating in a network at the cell cortex and a soft actin meshwork in the body of the cell, validate the method of particle tracking-microrheology, and reconcile seemingly disparate atomic force microscopy (AFM) and particle-tracking microrheology measurements of living cells

Assessment of heterologous butyrate and butanol pathway activity by measurement of intracellular pathway intermediates in recombinant Escherichia coli

In clostridia, n-butanol production from carbohydrates at yields of up to 76% of the theoretical maximum and at titers of up to 13 g/L has been reported. However, in Escherichia coli, several groups have reported butyric acid or butanol production from recombinant expression of clostridial genes, at much lower titers and yields. To pinpoint deficient steps in the recombinant pathway, we developed an analytical procedure for the determination of intracellular pools of key pathway intermediates and applied the technique to the analysis of three sets of E. coli strains expressing various combinations of butyrate biosynthesis genes. Low expression levels of the hbd-encoded S-3-hydroxybutyryl-CoA dehydrogenase were insufficient to convert acetyl-CoA to 3-hydroxybutyryl-CoA, indicating that hbd was a rate-limiting step in the production of butyryl-CoA. Increasing hbd expression alleviated this bottleneck, but in resulting strains, our pool size measurements and thermodynamic analysis showed that the reaction step catalyzed by the bcd-encoded butyryl-CoA dehydrogenase was rate-limiting. E. coli strains expressing both hbd and ptb-buk produced crotonic acid as a byproduct, but this byproduct was not observed with expression of related genes from non-clostridial organisms. Our thermodynamic interpretation of pool size measurements is applicable to the analysis of other metabolic pathways

The distinct roles of the nucleus and nucleus-cytoskeleton connections in three-dimensional cell migration

Cells often migrate in vivo in an extracellular matrix that is intrinsically three-dimensional (3D) and the role of actin filament architecture in 3D cell migration is less well understood. Here we show that, while recently identified linkers of nucleoskeleton to cytoskeleton (LINC) complexes play a minimal role in conventional 2D migration, they play a critical role in regulating the organization of a subset of actin filament bundles – the perinuclear actin cap - connected to the nucleus through Nesprin2giant and Nesprin3 in cells in 3D collagen I matrix. Actin cap fibers prolong the nucleus and mediate the formation of pseudopodial protrusions, which drive matrix traction and 3D cell migration. Disruption of LINC complexes disorganizes the actin cap, which impairs 3D cell migration. A simple mechanical model explains why LINC complexes and the perinuclear actin cap are essential in 3D migration by providing mechanical support to the formation of pseudopodial protrusions