Ramanujan sums analysis of long-period sequences and 1/f noise

Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to some arithmetical functions appearing in the context of number theory. In this paper, we provide an application of Ramanujan sum expansions to periodic, quasiperiodic and complex time series, as a vital alternative to the Fourier transform. The Ramanujan-Fourier spectrum of the Dow Jones index over 13 years and of the coronal index of solar activity over 69 years are taken as illustrative examples. Distinct long periods may be discriminated in place of the 1/f^{\alpha} spectra of the Fourier transform.Comment: 10 page

Modeling transitional plane Couette flow

The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar flow displays striking similarities with experimental findings.Comment: 33 pages, 10 figure

Laminar-turbulent boundary in plane Couette flow

We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to relaminarize tend towards a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, as for the lower branch solution in in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that choice of initial state is not critical, and that essentially arbitrary initial conditions can be used to find the edge state.Comment: 4 pages, 4 figure

MicroRNA regulation of the paired-box transcription factor Pax3 confers robustness to developmental timing of myogenesis

Commitment of progenitors in the dermomyotome to myoblast fate is the first step in establishing the body musculature. Pax3 is a crucial transcription factor, important for skeletal muscle development and expressed in myogenic progenitors in the dermomyotome of developing somites and in migratory muscle progenitors that populate the limb buds. Down-regulation of Pax3 is essential to ignite the myogenic program, including up-regulation of myogenic regulators, Myf-5 and MyoD. MicroRNAs (miRNAs) confer robustness to developmental timing by posttranscriptional repression of genetic programs that are related to previous developmental stages or to alternative cell fates. Here we demonstrate that the muscle-specific miRNAs miR-1 and miR-206 directly target Pax3. Antagomir-mediated inhibition of miR-1/miR-206 led to delayed myogenic differentiation in developing somites, as shown by transient loss of myogenin expression. This correlated with increased Pax3 and was phenocopied using Pax3-specific target protectors. Loss of myogenin after antagomir injection was rescued by Pax3 knockdown using a splice morpholino, suggesting that miR-1/miR-206 control somite myogenesis primarily through interactions with Pax3. Our studies reveal an important role for miR-1/miR-206 in providing precision to the timing of somite myogenesis. We propose that posttranscriptional control of Pax3 downstream of miR-1/miR-206 is required to stabilize myoblast commitment and subsequent differentiation. Given that mutually exclusive expression of miRNAs and their targets is a prevailing theme in development, our findings suggest that miRNA may provide a general mechanism for the unequivocal commitment underlying stem cell differentiation

Deletion of the gabra2 gene results in hypersensitivity to the acute effects of ethanol but does not alter ethanol self administration

Human genetic studies have suggested that polymorphisms of the GABRA2 gene encoding the GABA(A) α2-subunit are associated with ethanol dependence. Variations in this gene also convey sensitivity to the subjective effects of ethanol, indicating a role in mediating ethanol-related behaviours. We therefore investigated the consequences of deleting the α2-subunit on the ataxic and rewarding properties of ethanol in mice. Ataxic and sedative effects of ethanol were explored in GABA(A) α2-subunit wildtype (WT) and knockout (KO) mice using a Rotarod apparatus, wire hang and the duration of loss of righting reflex. Following training, KO mice showed shorter latencies to fall than WT littermates under ethanol (2 g/kg i.p.) in both Rotarod and wire hang tests. After administration of ethanol (3.5 g/kg i.p.), KO mice took longer to regain the righting reflex than WT mice. To ensure the acute effects are not due to the gabra2 deletion affecting pharmacokinetics, blood ethanol concentrations were measured at 20 minute intervals after acute administration (2 g/kg i.p.), and did not differ between genotypes. To investigate ethanol's rewarding properties, WT and KO mice were trained to lever press to receive increasing concentrations of ethanol on an FR4 schedule of reinforcement. Both WT and KO mice self-administered ethanol at similar rates, with no differences in the numbers of reinforcers earned. These data indicate a protective role for α2-subunits, against the acute sedative and ataxic effects of ethanol. However, no change was observed in ethanol self administration, suggesting the rewarding effects of ethanol remain unchange

Transcriptome analyses based on genetic screens for Pax3 myogenic targets in the mouse embryo

<p>Abstract</p> <p>Background</p> <p>Pax3 is a key upstream regulator of the onset of myogenesis, controlling progenitor cell survival and behaviour as well as entry into the myogenic programme. It functions in the dermomyotome of the somite from which skeletal muscle derives and in progenitor cell populations that migrate from the somite such as those of the limbs. Few Pax3 target genes have been identified. Identifying genes that lie genetically downstream of <it>Pax3 </it>is therefore an important endeavour in elucidating the myogenic gene regulatory network.</p> <p>Results</p> <p>We have undertaken a screen in the mouse embryo which employs a <it>Pax3^GFP</it>allele that permits isolation of Pax3 expressing cells by flow cytometry and a <it>Pax3^PAX3-FKHR</it>allele that encodes PAX3-FKHR in which the DNA binding domain of Pax3 is fused to the strong transcriptional activation domain of FKHR. This constitutes a gain of function allele that rescues the <it>Pax3 </it>mutant phenotype. Microarray comparisons were carried out between <it>Pax3^GFP/+</it>and <it>Pax3^{GFP/PAX3-FKHR}</it>preparations from the hypaxial dermomyotome of somites at E9.5 and forelimb buds at E10.5. A further transcriptome comparison between Pax3-GFP positive and negative cells identified sequences specific to myogenic progenitors in the forelimb buds. Potential Pax3 targets, based on changes in transcript levels on the gain of function genetic background, were validated by analysis on loss or partial loss of function <it>Pax3 </it>mutant backgrounds. Sequences that are up- or down-regulated in the presence of PAX3-FKHR are classified as somite only, somite and limb or limb only. The latter should not contain sequences from Pax3 positive neural crest cells which do not invade the limbs. Verification by whole mount <it>in situ </it>hybridisation distinguishes myogenic markers. Presentation of potential Pax3 target genes focuses on signalling pathways and on transcriptional regulation.</p> <p>Conclusions</p> <p>Pax3 orchestrates many of the signalling pathways implicated in the activation or repression of myogenesis by regulating effectors and also, notably, inhibitors of these pathways. Important transcriptional regulators of myogenesis are candidate Pax3 targets. Myogenic determination genes, such as <it>Myf5 </it>are controlled positively, whereas the effect of <it>Pax3 </it>on genes encoding inhibitors of myogenesis provides a potential brake on differentiation. In the progenitor cell population, <it>Pax7 </it>and also <it>Hdac5 </it>which is a potential repressor of <it>Foxc2</it>, are subject to positive control by <it>Pax3</it>.</p

The aged niche disrupts muscle stem cell quiescence

SUMMARY The niche is a conserved regulator of stem cell quiescence and function. During aging, stem cell function declines. To what extent and by which means age-related changes within the niche contribute to this phenomenon are unknown. We demonstrate that the aged muscle stem cell niche, the muscle fiber, expresses FGF2 under homeostatic conditions, driving a subset of satellite cells to break quiescence and lose self-renewing capacity. We show that relatively dormant aged satellite cells robustly express Sprouty1 (spry1), an inhibitor of FGF signalling. Increasing FGF signalling in aged satellite cells under homeostatic conditions by removing spry1, results in the loss of quiescence, satellite cell depletion and diminished regenerative capacity. Conversely, reducing niche-derived FGF activity through inhibition of FGFR1 signalling or overexpression of spry1 in satellite cells prevents their depletion. These experiments identify an age-dependent change in the stem cell niche that directly influences stem cell quiescence and function

The myogenic transcriptional network

Myogenesis has been a leading model for elucidating the molecular mechanisms that underlie tissue differentiation and development since the discovery of MyoD. During myogenesis, the fate of myogenic precursor cells is first determined by Pax3/Pax7. This is followed by regulation of the myogenic differentiation program by muscle regulatory factors (Myf5, MyoD, Myog, and Mrf4) to form muscle tissues. Recent studies have uncovered a detailed myogenic program that involves the RP58 (Zfp238)-dependent regulatory network, which is critical for repressing the expression of inhibitor of DNA binding (Id) proteins. These novel findings contribute to a comprehensive understanding of the muscle differentiation transcriptional program

Integrated Functions of Pax3 and Pax7 in the Regulation of Proliferation, Cell Size and Myogenic Differentiation

Pax3 and Pax7 are paired-box transcription factors with roles in developmental and adult regenerative myogenesis. Pax3 and Pax7 are expressed by postnatal satellite cells or their progeny but are down regulated during myogenic differentiation. We now show that constitutive expression of Pax3 or Pax7 in either satellite cells or C2C12 myoblasts results in an increased proliferative rate and decreased cell size. Conversely, expression of dominant-negative constructs leads to slowing of cell division, a dramatic increase in cell size and altered morphology. Similarly to the effects of Pax7, retroviral expression of Pax3 increases levels of Myf5 mRNA and MyoD protein, but does not result in sustained inhibition of myogenic differentiation. However, expression of Pax3 or Pax7 dominant-negative constructs inhibits expression of Myf5, MyoD and myogenin, and prevents differentiation from proceeding. In fibroblasts, expression of Pax3 or Pax7, or dominant-negative inhibition of these factors, reproduce the effects on cell size, morphology and proliferation seen in myoblasts. Our results show that in muscle progenitor cells, Pax3 and Pax7 function to maintain expression of myogenic regulatory factors, and promote population expansion, but are also required for myogenic differentiation to proceed

Duplication and Diversification of the Hypoxia-Inducible IGFBP-1 Gene in Zebrafish

Gene duplication is the primary force of new gene evolution. Deciphering whether a pair of duplicated genes has evolved divergent functions is often challenging. The zebrafish is uniquely positioned to provide insight into the process of functional gene evolution due to its amenability to genetic and experimental manipulation and because it possess a large number of duplicated genes.We report the identification and characterization of two hypoxia-inducible genes in zebrafish that are co-ortholgs of human IGF binding protein-1 (IGFBP-1). IGFBP-1 is a secreted protein that binds to IGF and modulates IGF actions in somatic growth, development, and aging. Like their human and mouse counterparts, in adult zebrafish igfbp-1a and igfbp-1b are exclusively expressed in the liver. During embryogenesis, the two genes are expressed in overlapping spatial domains but with distinct temporal patterns. While zebrafish IGFBP-1a mRNA was easily detected throughout embryogenesis, IGFBP-1b mRNA was detectable only in advanced stages. Hypoxia induces igfbp-1a expression in early embryogenesis, but induces the igfbp-1b expression later in embryogenesis. Both IGFBP-1a and -b are capable of IGF binding, but IGFBP-1b has much lower affinities for IGF-I and -II because of greater dissociation rates. Overexpression of IGFBP-1a and -1b in zebrafish embryos caused significant decreases in growth and developmental rates. When tested in cultured zebrafish embryonic cells, IGFBP-1a and -1b both inhibited IGF-1-induced cell proliferation but the activity of IGFBP-1b was significantly weaker.These results indicate subfunction partitioning of the duplicated IGFBP-1 genes at the levels of gene expression, physiological regulation, protein structure, and biological actions. The duplicated IGFBP-1 may provide additional flexibility in fine-tuning IGF signaling activities under hypoxia and other catabolic conditions