General expression for probabilistic estimation of multiphase structure invariants in the case of a native protein and multiple derivatives. Application to estimates of the three-phase structure invariants

Concise probabilistic formulae with definite crystallographic implications are obtained from the distribution for eight three-phase structure invariants (3PSIs) in the case of a native protein and a heavy-atom derivative [Hauptman (1982). Acta Cryst. A38, 289-294] and from the distribution for 27 3PSIs in the case of a native and two derivatives [Fortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646-651]. The main results of the probabilistic formulae for the four-phase structure invariants are presented and compared with those for the 3PSIs. The analysis directly leads to a general formula of probabilistic estimation for the n-phase structure invariants in the case of a native and m derivatives. The factors affecting the estimated accuracy of the 3PSIs are examined using the diffraction data from a moderate-sized protein. A method to estimate a set of the large-modulus invariants, each corresponding to one of the eight 3PSIs, that has the largest \Delta\ values and relatively large structure-factor moduli between the native and derivative is suggested, which remarkably improves the accuracy, and thus a phasing procedure making full use of all eight 3PSIs is proposed.

A general treatment for the conductivity of electrolytes in the whole concentration range in aqueous and nonaqueous solutions

Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.

EXPRESSION OF THE HUMAN PLACENTAL LACTOGEN GENES

The placenta is the site of synthesis of various peptide and steroid hormones related to pregnancy. Human placental lactogen (hPL) is the predominant peptide hormone secreted by term placenta and its synthesis is tissue-specific and coupled to placenta development. The objective of this work was to study the structure and expression of the hPL.^ Poly(A('+))RNA from human term placenta was translated in a mouse-derived cell-free system. A major band corresponding to pre-hPL and a minor band comigrating with mature hPL, represent (TURN)15% of the total radioactively labeled proteins. Analysis of the poly(A('+))RNA showed a prominent band at approximately 860 nucleotides. A corresponding band was observed in Northern blots of total RNA, hybridized with {('32)P}-labeled recombinant plasmid containing a portion of hPL cDNA. Similar analyses of nuclear RNA showed at least four additional bands at 990, 1200, 1460 and 1760 nucleotides, respectively, which are likely precursors of hPL mRNA. Poly(A('+))RNA was used to construct a cDNA library, of which approximately 5% of the clones were found to hybridize to hPL DNA sequences. Heteroduplexes constructed between a clone containing a 815 bp hPL cDNA insert and a hPL genomic DNA clone revealed four small intervening sequences which can account for the lengths observed in hnRNA molecules.^ Recombinant plasmid HCS-pBR322 containing a 550 bp insert of a cDNA transcript of human placental lactogen (hPL) mRNA was ('3)H-labeled an hybridized in situ to human chromosome preparations. These experiments allowed assignment of the hPL and growth hormone (hGH) genes, which have over 90% nucleotide homology in their coding sequences, to band q22-24 of chromosome 17. A gene copy number experiment showed that both genes are present in (TURN)3 copies per haploid genome.^ Experiments were designed to determine if all members of the hPL gene cluster, consisting of four non-allelic genes, are transcribed in term placenta. Advantage was taken of differences in restriction endonuclease sites in the coding portions of the different hPL genes, to distinguish the putative cDNAs of the transcriptionally active genes. Two genes were found to be represented in the cDNA library and their cDNA transcripts were isolated and characterized. Three independent methods showed that their corresponding mRNAs are about equally represented in the hPL mRNA population. The two cDNAs code for prehPL proteins which differ at a single amino acid position. However the secreted hPLs have identical amino acid sequences. A tetramer insertion duplication was found in a palindrome area of the 3' untranslated region of one of the hPL mRNAs. ^

Stimulation of mouse mammary tumor virus superantigen expression by an intragenic enhancer.

The mechanisms regulating expression of mouse mammary tumor virus (MMTV)-encoded superantigens from the viral sag gene are largely unknown, due to problems with detection and quantification of these low-abundance proteins. To study the expression and regulation of the MMTV sag gene, we have developed a sensitive and quantitative reporter gene assay based on a recombinant superantigen-human placental alkaline phosphatase fusion protein. High sag-reporter expression in Ba/F3, an early B-lymphoid cell line, depends on enhancers in either of the viral long terminal repeats (LTRs) and is largely independent of promoters in the 5' LTR. The same enhancer region is also required for general expression of MMTV genes from the 5' LTR. The enhancer was mapped to a 548-bp fragment of the MMTV LTR lying within sag and shown to be sufficient to stimulate expression from a heterologous simian virus 40 promoter. No enhancer activity of the MMTV LTR was observed in XC sarcoma cells, which are permissive for MMTV. Our results demonstrate a major role for this enhancer in MMTV gene expression in early B-lymphoid cells.

Mössbauer Lineshape in the Presence of Radio-Frequency Fields

A general expression for the Mössbauer lineshape in the presence of a radio frequency field is derived. As an example the effect of the rf field on Fe57 nuclei is discussed for a situation where the 3/2 sublevel of 14.4 keV state of Fe57 is selectively populated. At resonance, both the diagonal and non-diagonal matrix elements contribute to the correlation function. As a result, in addition to a slight rf induced distortion of the main Mössbauer line. additional transition lines are obtained. Thus the present calculation supports the experimental observations of Heiman et al.

Mossbauer lineshape in the presence of NMR transitions

The general expression for the Mössbauer lineshape in the presence of radio frequency perturbation derived earlier has been further extended. This involves the calculation of the off-diagonal matrix elements of the correlation function. The results show that there are additional transition lines owing to the nuclear magnetic resonance induced transition in the resonance region. These lines do not show any broadening or splitting. As an example the effect of the rf field on 57Fe nuclei is discussed.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Direct stability evaluation of power systems with detailed generator models using structure-preserving energy functions

Energy-based direct methods for transient stability analysis are potentially useful both as offline tools for planning purposes as well as for online security assessment. In this paper, a novel structure-preserving energy function (SPEF) is developed using the philosophy of structure-preserving model for the system and detailed generator model including flux decay, transient saliency, automatic voltage regulator (AVR), exciter and damper winding. A simpler and yet general expression for the SPEF is also derived which can simplify the computation of the energy function. The system equations and the energy function are derived using the centre-of-inertia (COI) formulation and the system loads are modelled as arbitrary functions of the respective bus voltages. Application of the proposed SPEF to transient stability evaluation of power systems is illustrated with numerical examples.

Solubility of sulfur dioxide at low partial pressures in dilute sulfuric acid solutions

Equilibrium of dissolution of sulfur dioxide at ppm levels in aqueous solutions of dilute sulfuric acid is analyzed, and a general expression is derived relating the total concentration of sulfur dioxide in the liquid phase to the partial pressure of SO2 in the gas and to the concentration of sulfuric acid in the solution. The equation is simplified for zero and high concentrations of the acid. Experiments at high concentrations of sulfuric acid have enabled the direct determination of Henry’s constant and its dependency on temperature. Heat of dissolution is -31.47 kJ/mol. Experiments in the absence of sulfuric acid and the related simplified expression have led to the determination of the equilibrium constant of the hydrolysis of aqueous sulfur dioxide and its temperature dependency.The heat of hydrolysis is 15.69 kJ/mol. The model equation with these parameters predicts the experimental data of the present work as well as the reported data very well.

End-bearing capacity of driven piles in sand using the stress characteristics method: analysis and implementation

The method of stress characteristics has been employed to compute the end-bearing capacity of driven piles. The dependency of the soil internal friction angle on the stress level has been incorporated to achieve more realistic predictions for the end-bearing capacity of piles. The validity of the assumption of the superposition principle while using the bearing capacity equation based on soil plasticity concepts, when applied to deep foundations, has been examined. Fourteen pile case histories were compiled with cone penetration tests (CPT) performed in the vicinity of different pile locations. The end-bearing capacity of the piles was computed using different methods, namely, static analysis, effective stress approach, direct CPT, and the proposed approach. The comparison between predictions made by different methods and measured records shows that the stress-level-based method of stress characteristics compares better with experimental data. Finally, the end-bearing capacity of driven piles in sand was expressed in terms of a general expression with the addition of a new factor that accounts for different factors contributing to the bearing capacity. The influence of the soil nonassociative flow rule has also been included to achieve more realistic results.

Expanding universe: thermodynamical aspects from different models

The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: w(z)=w (0)+w (1)ln(1+z) & . The time scale of instability for this two models is discussed. In the paper we then generalize our result and arrive at general expression for energy density irrespective of the model. The thermodynamical stability for both of the model and the general case is discussed from this viewpoint. We also arrive at a condition on the limiting behavior of thermodynamic parameter to validate the third law of thermodynamics and interpret the general mathematical expression of integration constant U (0) (what we get while integrating energy conservation equation) physically relating it to number of micro states. The constraint on the allowed values of the parameters of the models is discussed which ascertains stability of universe. The validity of thermodynamical laws within apparent and event horizon is discussed.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

Aharonov-Bohm oscillation and chirality effect in optical activity of single-wall carbon nanotubes

We study the Aharonov-Bohm effect in the optical phenomena of single-wall carbon nanotubes (SWCN) and also their chirality dependence. Especially, we consider the natural optical activity as a proper observable and derive its general expression based on a comprehensive symmetry analysis, which reveals the interplay between the enclosed magnetic flux and the tubule chirality for arbitrary chiral SWCN. A quantitative result for this optical property is given by a gauge invariant tight-binding approximation calculation to stimulate experimental measurements.

Nitrogen vacancy scattering in GaN grown by metal-organic vapor phase epitaxy

Electron mobility limited by nitrogen vacancy scattering was taken into account to evaluate the quality of n-type GaN grown by metal-organic vapor phase epitaxy. Two assumptions were made for this potential for the nitrogen vacancy (1) it acts in a short range, and (2) does not diverge at the vacancy core. According to the above assumptions, a general expression to describe the scattering potential U(r) = - U-0 exp[- (r/beta)(n)], (n = 1, 2,...,infinity) was constructed, where beta is the potential well width. The mobilities for n = 1, 2, and infinity were calculated based on this equation, corresponding to the simple exponential, Gaussian and square well scattering potentials, respectively. In the limiting case of kbeta << 1 (where k is the wave vector), all of the mobilities calculated for n = 1, 2, and infinity showed a same result but different prefactor. Such difference was discussed in terms of the potential tail and was found that all of the calculated mobilities have T-1/2 temperature and beta(-6) well width dependences. A mobility taking account of a spatially complicate scattering potential was studied and the same temperature dependence was also found. A best fit between the calculated results and experimental data was obtained by taking account of the nitrogen vacancy scattering. (C) 2002 Elsevier Science Ltd. All rights reserved.