Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Fluoromycobacteriophages for rapid, specific, and sensitive antibiotic susceptibility testing of Mycobacterium tuberculosis

Rapid antibiotic susceptibility testing of Mycobacterium tuberculosis is of paramount importance as multiple- and extensively- drug resistant strains of M. tuberculosis emerge and spread. We describe here a virus-based assay in which fluoromycobacteriophages are used to deliver a GFP or ZsYellow fluorescent marker gene to M. tuberculosis, which can then be monitored by fluorescent detection approaches including fluorescent microscopy and flow cytometry. Pre-clinical evaluations show that addition of either Rifampicin or Streptomycin at the time of phage addition obliterates fluorescence in susceptible cells but not in isogenic resistant bacteria enabling drug sensitivity determination in less than 24 hours. Detection requires no substrate addition, fewer than 100 cells can be identified, and resistant bacteria can be detected within mixed populations. Fluorescence withstands fixation by paraformaldehyde providing enhanced biosafety for testing MDR-TB and XDR-TB infections. © 2009 Piuri et al

The stellar and sub-stellar IMF of simple and composite populations

The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.Comment: 167 pages, 37 figures, 3 tables, published in Stellar Systems and Galactic Structure, Vol.5, Springer. This revised version is consistent with the published version and includes additional references and minor additions to the text as well as a recomputed Table 1. ISBN 978-90-481-8817-

Shunting Inhibition Controls the Gain Modulation Mediated by Asynchronous Neurotransmitter Release in Early Development

The sensitivity of a neuron to its input can be modulated in several ways. Changes in the slope of the neuronal input-output curve depend on factors such as shunting inhibition, background noise, frequency-dependent synaptic excitation, and balanced excitation and inhibition. However, in early development GABAergic interneurons are excitatory and other mechanisms such as asynchronous transmitter release might contribute to regulating neuronal sensitivity. We modeled both phasic and asynchronous synaptic transmission in early development to study the impact of activity-dependent noise and short-term plasticity on the synaptic gain. Asynchronous release decreased or increased the gain depending on the membrane conductance. In the high shunt regime, excitatory input due to asynchronous release was divisive, whereas in the low shunt regime it had a nearly multiplicative effect on the firing rate. In addition, sensitivity to correlated inputs was influenced by shunting and asynchronous release in opposite ways. Thus, asynchronous release can regulate the information flow at synapses and its impact can be flexibly modulated by the membrane conductance

Enumerating Pathways of Proton Abstraction Based on a Spatial and Electrostatic Analysis of Residues in the Catalytic Site

The pathways of proton abstraction (PA), a key aspect of most catalytic reactions, is often controversial and highly debated. Ultrahigh-resolution diffraction studies, molecular dynamics, quantum mechanics and molecular mechanic simulations are often adopted to gain insights in the PA mechanisms in enzymes. These methods require expertise and effort to setup and can be computationally intensive. We present a push button methodology – Proton abstraction Simulation (PRISM) – to enumerate the possible pathways of PA in a protein with known 3D structure based on the spatial and electrostatic properties of residues in the proximity of a given nucleophilic residue. Proton movements are evaluated in the vicinity of this nucleophilic residue based on distances, potential differences, spatial channels and characteristics of the individual residues (polarity, acidic, basic, etc). Modulating these parameters eliminates their empirical nature and also might reveal pathways that originate from conformational changes. We have validated our method using serine proteases and concurred with the dichotomy in PA in Class A β-lactamases, both of which are hydrolases. The PA mechanism in a transferase has also been corroborated. The source code is made available at www.sanchak.com/prism

Gamma estimator of Jarzynski equality for recovering binding energies from noisy dynamic data sets

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. In practice, the exponentially averaged work value is estimated as the mean of finite samples. Numerical simulations have shown that samples having thousands of measurements are not large enough for the mean to converge when the fluctuation of external work is above 4 kBT, which is easily observable in biomolecular interactions. We report the first example of a statistical gamma work distribution applied to single molecule pulling experiments. The Gibbs free energy of surface adsorption can be accurately evaluated even for a small sample size. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations

Lhx2 Is Required for Patterning and Expansion of a Distinct Progenitor Cell Population Committed to Eye Development

Progenitor cells committed to eye development become specified in the prospective forebrain and develop subsequently into the optic vesicle and the optic cup. The optic vesicle induces formation of the lens placode in surface ectoderm from which the lens develops. Numerous transcription factors are involved in this process, including the eye-field transcription factors. However, many of these transcription factors also regulate the patterning of the anterior neural plate and their specific role in eye development is difficult to discern since eye-committed progenitor cells are poorly defined. By using a specific part of the Lhx2 promoter to regulate Cre recombinase expression in transgenic mice we have been able to define a distinct progenitor cell population in the forebrain solely committed to eye development. Conditional inactivation of Lhx2 in these progenitor cells causes an arrest in eye development at the stage when the optic vesicle induces lens placode formation in the surface ectoderm. The eye-committed progenitor cell population is present in the Lhx2−/− embryonic forebrain suggesting that commitment to eye development is Lhx2-independent. However, re-expression of Lhx2 in Lhx2−/− progenitor cells only promotes development of retinal pigment epithelium cells, indicating that Lhx2 promotes the acquisition of the oligopotent fate of these progenitor cells. This approach also allowed us to identify genes that distinguish Lhx2 function in eye development from that in the forebrain. Thus, we have defined a distinct progenitor cell population in the forebrain committed to eye development and identified genes linked to Lhx2's function in the expansion and patterning of these progenitor cells

The Comprehensive Native Interactome of a Fully Functional Tagged Prion Protein

The enumeration of the interaction partners of the cellular prion protein, PrPC, may help clarifying its elusive molecular function. Here we added a carboxy proximal myc epitope tag to PrPC. When expressed in transgenic mice, PrPmyc carried a GPI anchor, was targeted to lipid rafts, and was glycosylated similarly to PrPC. PrPmyc antagonized the toxicity of truncated PrP, restored prion infectibility of PrPC-deficient mice, and was physically incorporated into PrPSc aggregates, indicating that it possessed all functional characteristics of genuine PrPC. We then immunopurified myc epitope-containing protein complexes from PrPmyc transgenic mouse brains. Gentle differential elution with epitope-mimetic decapeptides, or a scrambled version thereof, yielded 96 specifically released proteins. Quantitative mass spectrometry with isotope-coded tags identified seven proteins which co-eluted equimolarly with PrPC and may represent component of a multiprotein complex. Selected PrPC interactors were validated using independent methods. Several of these proteins appear to exert functions in axomyelinic maintenance