F-tests for Hypotheses with Block Matrices and Under Conditions of Orthogonality in the General Multivariate Gauss-Markoff Model

The multivariate general Gauss-Markoff (MGM) model (U, XB, ∑?σ²V) when the matrices V ≥ 0 and ∑ > 0 are known and the scalar σ² > 0 is unknown, is considered. The present paper is a continuation of two earlier works (Oktaba, 1988a, b). If XB = X₁Σ + X₂Δ, then the F-test for verification the hypothesis WΣA = 0 is presented. Moreover, under conditions of orthogonality the decomposition of the matrix S_A (?BCA)′L^?(?BCA) into the sum of s = r(L) matrices is given, where ?BCA is the estimator of the parametric estimable functions ?BCA, Cov (?BCA) = A′ ∑?σ²L = ?C₄?′, B? = (X′T^?X)^?X′T^?U, C₄ = (X′T^?X)^?M, where M = M′ is any arbitrary matrix such that R(X) ? R(T), T=V+XMX′; T^? is any c-inverse. R(A) is the linear space generated by the colums of A. Then under additional assumption on normality of U the statistics F for testing ?BA = 0 is deduced. Under conditions of normality of U and decomposition of S_A, the statistics F₁, …, F_s for the hypotheses jⁱ BA = 0 (i = 1,…, s) are established.     

An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Estimation of Finite Population Variance Using Ratio and Product Methods of Estimation

For estimating finite population variance σ_y² of a character y under our study, estimators using auxiliary information on a character x in the form of ratio, product, ratio-type or product-type estimators have been suggested, and their comparative study with the conventional unbiased estimator s_y² of σ_y² has been made in simple random sampling with replacement. A generalized estimator representing a class of estimators for the finite populations variance, has also been studied.     

Additional Sodium Insertion into Polyanionic Cathodes for Higher‐Energy Na‐Ion Batteries

Na‐ion technology is increasingly studied as a low‐cost solution for grid storage applications. Many positive electrode materials have been reported, mainly among layered oxides and polyanionic compounds. The vanadium oxy/flurophosphate solid solution Na₃V₂(PO₄)₂F_3‐y O_2y (0 ≤ y ≤ 1), in particular, has proven the ability to deliver ≈500 Wh kg^‐1, operating on the V³⁺/V⁴⁺ (y = 0) or V⁴⁺/V⁵⁺ redox couples (y = 1). This paper reports here on a significant increase in specific energy by enabling sodium insertion into Na₃V₂(PO₄)₂FO₂ to reach Na₄V₂(PO₄)₂FO₂ upon discharge. This occurs at ≈1.6 V and increases the theoretical specific energy to 600 Wh kg^?1, rivaling that of several Li‐ion battery cathodes. This improvement is achieved by the judicious modification of the composition either as O for F substitution, or Al for V substitution, both of which disrupt Na‐ion ordering and thereby enable insertion of the 4th Na. This paper furthermore shows from operando X‐Ray Diffraction (XRD) that this energy is obtained in the cycling range Na₄V₂(PO₄)₂FO₂–NaV₂(PO₄)₂FO₂ with a very small overall volume change of 1.7%, which is one of the smallest volume changes for Na‐ion cathodes and which is a crucial requisite for stable long‐term cycling.     

Multisubstrate kinetics of PAH mixture biodegradation: analysis in the double-logarithmic plot

The proposed method of kinetic analysis of aqueous-phase biodegradation of polycyclic aromatic hydrocarbons (PAH) mixture presupposes representation of kinetic curves for each pair of mixture components, S _x and S _y , in double-logarithmic coordinates (ln S _x ; ln S _y ). If PAH mixture conversion corresponds to the multisubstrate model with a common active site, then the graphs in double-logarithmic coordinates are straight lines with the angular coefficients equal to the ratio of respective first-order rate constants k_x^y = \fracV_y K_x K_y V_x k_{x}^{y} = {\frac{{V_{y} K_{x} }}{{K_{y} V_{x} }}} , where K _x and K _y are half-saturation constants, V _x and V _y are the maximum conversion rates for substrates S _x and S _y ; the graph slope does not depend on any concentrations and remains constant during the change of reaction rates as a result of inhibition, induction/inactivation of enzymes or biomass growth. The formulated method has been used to analyze PAH mixture conversion by the culture of Sphingomonas sp. VKM B-2434. It has been shown that this process does not satisfy the multisubstrate model with a single active site. The results suggest that the strain VKM B-2434 contains at least two dioxygenases of different substrate specificity: one enzyme converts phenanthrene and fluoranthene and the other converts acenaphthene and acenaphthylene. The ratios of first-order rate constants have been obtained for these pairs of substrates.     

High Capacity and High‐Rate NASICON‐Na3.75V1.25Mn0.75(PO4)3 Cathode for Na‐Ion Batteries via Modulating Electronic and Crystal Structures

Sodium superionic conductor (NASICON) cathodes are attractive for Na‐ion battery applications as they exhibit both high structural stability and high sodium ion mobility. Herein, a comprehensive study is presented on the structural and electrochemical properties of the NASICON‐Na_3+yV_2?yMn_y(PO₄)₃ (0 ≤ y ≤ 1) series. A phase miscibility gap is observed at y = 0.5, defining two solid solution domains with low and high Mn contents. Although, members of each of these domains Na_3.25V_1.75Mn_0.25(PO₄)₃ and Na_3.75V_1.25Mn_0.75(PO₄)₃ reversibly exchange sodium ions with high structural integrity, the activity of the Mn³⁺/Mn²⁺ redox couple is found to be absent and present in the former and latter candidate, respectively. Galvanostatic cycling and rate studies reveal higher capacity and rate capability for the Na_3.75V_1.25Mn_0.75(PO₄)₃ cathode (100 and 89 mA h g^?1 at 1C and 5C rate, respectively) in the Na_3+yV_2?yMn_y(PO₄)₃ series. Such a remarkable performance is attributed to optimum bottleneck size (≈5 Ų) and modulated V‐ and Mn‐redox centers as deduced from Rietveld analysis and DFT calculations, respectively. This study shows how important it is to manipulate electronic and crystal structures to achieve high‐performance NASICON cathodes.     

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y- of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y-, the ratio estimator y-_R = y-X-/x-, Sisodia and Dwivedi (1981) estimator y-_s = y-(X- + C_x)/(x- + C_x) and Singh and Kakran (1993) estimator y-_k = y[X- + β₂(x)]/[x- + β₂(x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.     

Contributions of the σW, σM and σX regulons to the lantibiotic resistome of Bacillus subtilis

In Bacillus subtilis, the extracytoplasmic function (ECF) σ factors σ^M, σ^W and σ^X all contribute to resistance against lantibiotics. Nisin, a model lantibiotic, has a dual mode of action: it inhibits cell wall synthesis by binding lipid II, and this complex also forms pores in the cytoplasmic membrane. These activities can be separated in a nisin hinge‐region variant (N20P M21P) that binds lipid II, but no longer permeabilizes membranes. The major contribution of σ^M to nisin resistance is expression of ltaSa, encoding a stress‐activated lipoteichoic acid synthase, and σ^X functions primarily by activation of the dlt operon controlling d ‐alanylation of teichoic acids. Together, σ^M and σ^X regulate cell envelope structure to decrease access of nisin to its lipid II target. In contrast, σ^W is principally involved in protection against membrane permeabilization as it provides little protection against the nisin hinge region variant. σ^W contributes to nisin resistance by regulation of a signal peptide peptidase (SppA), phage shock proteins (PspA and YvlC, a PspC homologue) and tellurite resistance related proteins (YceGHI). These defensive mechanisms are also effective against other lantibiotics such as mersacidin, gallidermin and subtilin and comprise an important subset of the intrinsic antibiotic resistome of B. subtilis.     

Multiple Comparisons of Polynomial Distributions

Asymptotically correct 90 and 95 percentage points are given for multiple comparisons with control and for all pair comparisons of several independent samples of equal size from polynomial distributions. Test statistics are the maxima of the X²-statistics for single comparisons. For only two categories the asymptotic distributions of these test statistics result from DUNNETT'S many-one tests and TUKEY'S range test (cf. MILLER, 1981). The percentage points for comparisons with control are computed from the limit distribution of the test statistic under the overall hypothesis H₀. To some extent the applicability of these bounds is investigated by simulation. The bounds can also be used to improve Holm's sequentially rejective Bonferroni test procedure (cf. HOLM, 1979). The percentage points for all pair comparisons are obtained by large simulations. Especially for 3×3-tables the limit distribution of the test statistic under H₀ is derived also for samples of unequal size. Also these bounds can improve the corresponding Bonferroni-Holm procedure. Finally from SKIDÁK's probability inequality for normal random vectors (cf. SKIDÁK, 1967) a similar inequality is derived for dependent X²-variables applicable to simultaneous X²-tests.     

On the difference between gauss-markov and least squares estimates

For the usual full rank univariate least squares regression model y = XB + e, E(e) = 0, E(ee) = A, the equality of the estimates occurs when B-B^* = (XA^?1X)^?1XA^-1y-(XX)^?1Xy = 0. A necessary and sufficient condition for this equality is that A has some N - k + 1 roots equal where N is the rank of A and k is the rank of X.     

Enhanced electrotransformation of the ethanologen Zymomonas mobilis ZM4 with plasmids

The Zymomonas mobilis ZM4 strain with excellent ethanol‐producing capabilities was the first strain of Z. mobilis, which was sequenced. This strain is resistant to transformation, and no previous study has shown a detailed protocol for electrotransfer of ZM4 with foreign DNA. In this work, many electrical and biological parameters were selected and evaluated in order to optimize the electrotransformation of ZM4. First, improved transformation efficiencies of 11 896, 99, 96 and 5989 transformants/μg DNA were separately achieved with shuttle plasmid pZB21‐mini (3082 bp), pZB21 (5930 bp), pZA22 (6994 bp) and broad‐host‐range vector pBBR1MCS‐2 (5144 bp) all prepared from Escherichia coli JM110. The crucial factors affecting the transformation efficiency included the source of the plasmid (the best strain was ZM4), origin and size of the plasmids, growth phase of the cells (the most ideal phase was early log phase with OD₆₀₀ of 0.3–0.4), the electric field strength (generally 11.75 kV/cm–13.25 kV/cm) and the recovery time (3–24 h). Further, based upon the optimal transformation protocol mentioned above for replicative plasmids in ZM4, (i) the electrotransformation by recombinant plasmid pBBR1MCS‐2‐Pgap‐FLP (6880 bp) was an immediate success with the transformation efficiency 10² transformants/μg DNA; (ii) the site‐specific integration efficiencies (expressed in terms of “per μg of DNA”) of 3–6 integrating transformants was obtained using the integrating plasmid pBR328‐ldhR‐cml‐ldhL (7447 bp). This study will assist genetic and biotechnological research of ZM4 and other Z. mobilis strains by providing information about suitable vectors and a more universal and reliable procedure for introducing DNA into this strain.     

Using the QICAR Model to Correlate Metal Ion Characteristics with Toxicity Order Numbers

The quantitative ion character–activity relationship (QICAR) was used to correlate nine ion characteristics with ion toxicity order numbers (TON) in 19 metals. A multi-parameter regression model was used to simulate the metals toxicity order numbers after minimization of the multicollinearity among the ion characteristics using principal component analysis (PCA). The toxicity order numbers of the metals increased with the positively correlated variables AN, X_m ²r, AN/ΔIP, AW, and X_m , and decreased with the negatively correlated variables ΔE ₀, |logK _OH|, AR/AW, and σ _P . The regression model provided high prediction ability, with Nash-Suttcliffe simulation efficiency coefficients (NSC) of 0.93 for the modeling phase and 0.87 for the testing phases. The model may be successfully employed to predict the stability constants and metal toxicity and used as a first step in the further risk assessment modeling.     

Fluvoxamine rescues mitochondrial Ca transport and ATP production through σ1-receptor in hypertrophic cardiomyocytes

Aims

We previously reported that fluvoxamine, a selective serotonin reuptake inhibitor with high affinity for the σ₁-receptor (σ₁R), ameliorates cardiac hypertrophy and dysfunction via σ₁R stimulation. Although σ₁R on non-cardiomyocytes interacts with the IP₃ receptor (IP₃R) to promote mitochondrial Ca^2 + transport, little is known about its physiological and pathological relevance in cardiomyocytes.

Main methods

Here we performed Ca^2 + imaging and measured ATP production to define the role of σ₁Rs in regulating sarcoplasmic reticulum (SR)-mitochondrial Ca^2 + transport in neonatal rat ventricular cardiomyocytes treated with angiotensin II to promote hypertrophy.

Key finding

These cardiomyocytes exhibited imbalances in expression levels of σ₁R and IP₃R and impairments in both phenylephrine-induced mitochondrial Ca^2 + mobilization from the SR and ATP production. Interestingly, σ₁R stimulation with fluvoxamine rescued impaired mitochondrial Ca^2 + mobilization and ATP production, an effect abolished by treatment of cells with the σ₁R antagonist, NE-100. Under physiological conditions, fluvoxamine stimulation of σ₁Rs suppressed intracellular Ca^2 + mobilization through IP₃Rs and ryanodine receptors (RyRs). In vivo, chronic administration of fluvoxamine to TAC mice also rescued impaired ATP production.

Significance

These results suggest that σ₁R stimulation with fluvoxamine promotes SR-mitochondrial Ca^2 + transport and mitochondrial ATP production, whereas σ₁R stimulation suppresses intracellular Ca^2 + overload through IP₃Rs and RyRs. These mechanisms likely underlie in part the anti-hypertrophic and cardioprotective action of the σ₁R agonists including fluvoxamine.     

P2X7 receptor inhibition attenuated sympathetic nerve sprouting after myocardial infarction via the NLRP3/IL‐1β pathway

Mounting evidence supports the hypothesis that inflammation modulates sympathetic sprouting after myocardial infarction (MI). The myeloid P2X₇ signal has been shown to activate the nucleotide‐binding and oligomerization domain‐like receptor family pyrin domain‐containing 3 (NLRP3) inflammasome, a master regulator of inflammation. We investigated whether P2X₇ signal participated in the pathogenesis of sympathetic reinnervation after MI, and whether NLRP3/interleukin‐1β (IL‐1β) axis is involved in the process. We explored the relationship between P2X₇ receptor (P2X₇R) and IL‐1β in the heart tissue of lipopolysaccharide (LPS)‐primed naive rats. 3′‐O‐(4‐benzoyl) benzoyl adenosine 5′‐triphosphate (BzATP), a P2X₇R agonist, induced caspase‐1 activation and mature IL‐1β release, which was further neutralized by a NLRP3 inhibitor (16673‐34‐0). MI was induced by coronary artery ligation. Following infarction, a marked increase in P2X₇R was localized within infiltrated macrophages and observed in parallel with an up‐regulation of NLRP3 inflammasome levels and the release of IL‐1β in the left ventricle. The administration of A‐740003 (a P2X₇R antagonist) significantly prevented the NLRP3/IL‐1β increase. A‐740003 and/or Anakinra (an IL‐1 receptor antagonist) significantly reduced macrophage infiltration as well as macrophage‐based IL‐1β and NGF (nerve growth factor) production and eventually blunted sympathetic hyperinnervation, as assessed by the immunofluorescence of tyrosine hydroxylase (TH) and growth‐associated protein 43 (GAP 43). Moreover, the use of Anakinra partly attenuated sympathetic sprouting. This indicated that the effect of P2X₇ on neural remodelling was mediated at least partially by IL‐1β. The arrhythmia score of programmed electric stimulation was in accordance with the degree of sympathetic hyperinnervation. In vitro studies showed that BzATP up‐regulated secretion of nerve growth factor (NGF) in M1 macrophages via IL‐1β. Together, these data indicate that P2X₇R contributes to neural and cardiac remodelling, at least partly mediated by NLRP3/IL‐1β axis. Therapeutic interventions targeting P2X₇ signal may be a novel approach to ameliorate arrhythmia following MI.     

An Unbalanced Two-way Model With Random Effects Having Unequal Variances

Consider the model y_ijk=u ± a_i ± b_i ± c_ij ± e_ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n_ij where μ is a constant and a_i, b_i, c_ij are distributed independently and normally with zero means and variances Δ₂ Δ2/bd_ij and δ₂ respectively. It is assumed that d_i's, and d_ij's are known (positive) constants (for all i and j). In this paper procedures for estimating the variance components (Δ₂, Δ²_b and Δ²_a) and for testing the hypothesis H_oc:Δ²_c/Δ² = y₃ and H_oa:Δ²_b/Δ² = y₄ (where y₂, y₃, and y₄, are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.     

Interpretation of invertebrate photoreceptor potentials in terms of a quantitative model

It is known from voltage-clamp experiments on visual cells of Limulus and Balanus that the total membrane current can be separated approximately into a dark current J _D and a light-induced current J _L such that each part has a time-and intensity-independent reversal potential. In addition J _L can be represented approximately as a product of a nonlinear, time-independent current-voltage characteristics J ⁰ _L (V) and an activation factor x _A which depends on light intensity and time. J ⁰ _L (V) can be described by a simple electrodiffusion membrane model (for J _D we use the same model). A set of kinetic equations including amplification, latency and light adaptation leads to a determination of x _A for photoisomerization of single rhodospin molecules and for arbitrary light signals. The receptor potentials calculated show many features of the experiments on Limulus, Balanus and Astacus.List of the more Important Symbols A Adaptation factor - C ratio between slopes of current-voltage curves for maximum light-induced current and dark current - d one half the thickness of the membrane - F _i effective membrane permeability, cf. Eq. (7) - g _i electrochemical potential inside membrane - g _i electrochemical potential inside and outside cell - I light intensity (quanta/sec cm²) - i (index) refers to i-th ionic species - J total current leaving cell - J _D dark current - J _L light-induced current - j _i ionic current density inside membrane in x-direction - K cf. Eq. (21) - k Boltzmann's constant - k ₀ rate constant for chain reaction (production of X) - k ₁ rate constant for decay of X ₁ - k ₂ rate constant for decay of X (closing of sites) - M total number of sites controlling light conductance - N multiplication factor in dark adapted state (maximum of Z) - n _i density of ions iaside membrane - n _i density of ions inside and outside cell - p ₁, p ₂ rate constants for adaptation kinetics - p ₃ cf. Eq. (29) - q elementary charge - q _i ionic charges - r = (x, y, z) spatial variable - T temperature - t time - u cf. Eq. (28) - V membrane potential - V _D reversal potential for the dark current - V _L reversal potential for the light current - V _i diffusion potential, cf. Eq. (8) - V potential steps at the inner and outer membrane surface - V ₀ = V ^–V - X = x _a M, number of open sites - X ₁ = x ₁M number of molecules of agent whose decay initiates chain reactions - x _A degree of activation of light sensitive membrane - Y number of sites opened by individual chain reaction - Z multiplication factor (number of sites opened by one photoisomerized rhodopsin molecule) - _i activation energy inside membrane (measured with respect to surrounding solution) - electrostatic potential - ₀ flxed-charge distribution inside membrane - cross section for photoisomerization of one rhodopsin molecule by a photon - k ₁/k ₂     

MeCP2 R168X male and female mutant mice exhibit Rett‐like behavioral deficits

Rett syndrome (RTT) is a regressive developmental disorder characterized by motor and breathing abnormalities, anxiety, cognitive dysfunction and seizures. Approximately 95% of RTT cases are caused by more than 200 different mutations in the X‐linked gene encoding methyl‐CpG‐binding protein 2 (MeCP2). While numerous transgenic mice have been created modeling common mutations in MeCP2, the behavioral phenotype of many of these male and, especially, female mutant mice has not been well characterized. Thorough phenotyping of additional RTT mouse models will provide valuable insight into the effects of Mecp2 mutations on behavior and aid in the selection of appropriate models, ages, sexes and outcome measures for preclinical trials. In this study, we characterize the phenotype of male and female mice containing the early truncating MeCP2 R168X nonsense point mutation, one of the most common in RTT individuals, and compare the phenotypes to Mecp2 null mutants. Mecp2^R168X mutants mirror many clinical features of RTT. Mecp2^R168X/y males exhibit impaired motor and cognitive function and reduced anxiety. The behavioral phenotype is less severe and with later onset in Mecp2^R168X/+ females. Seizures were noted in 3.7% of Mecp2^R168X mutant females. The phenotype in Mecp2^R168X/y mutant males is remarkably similar to our previous characterizations of Mecp2 null males, whereas Mecp2^R168X/+ females exhibit a number of phenotypic differences from females heterozygous for a null Mecp2 mutation. This study describes a number of highly robust behavioral paradigms that can be used in preclinical drug trials and underscores the importance of including Mecp2 mutant females in preclinical studies .     

Increased CaVβ1a expression with aging contributes to skeletal muscle weakness

Ca²⁺ release from the sarcoplasmic reticulum (SR) into the cytosol is a crucial part of excitation–contraction (E‐C) coupling. Excitation–contraction uncoupling, a deficit in Ca²⁺ release from the SR, is thought to be responsible for at least some of the loss in specific force observed in aging skeletal muscle. Excitation–contraction uncoupling may be caused by alterations in expression of the voltage‐dependent calcium channel α_1s (Ca_V1.1) and β_1a (Ca_Vβ_1a) subunits, both of which are necessary for E‐C coupling to occur. While previous studies have found Ca_V1.1 expression declines in old rodents, Ca_Vβ_1a expression has not been previously examined in aging models. Western blot analysis shows a substantial increase of Ca_Vβ_1a expression over the full lifespan of Friend Virus B (FVB) mice. To examine the specific effects of Ca_Vβ_1a overexpression, a Ca_Vβ_1a‐YFP plasmid was electroporated in vivo into young animals. The resulting increase in expression of Ca_Vβ_1a corresponded to decline of Ca_V1.1 over the same time period. YFP fluorescence, used as a measure of Ca_Vβ_1a‐YFP expression in individual fibers, also showed an inverse relationship with charge movement, measured using the whole‐cell patch‐clamp technique. Specific force was significantly reduced in young Ca_Vβ_1a‐YFP electroporated muscle fibers compared with sham‐electroporated, age‐matched controls. siRNA interference of Ca_Vβ_1a in young muscles reduced charge movement, while charge movement in old was restored to young control levels. These studies imply Ca_Vβ_1a serves as both a positive and negative regulator Ca_V1.1 expression, and that endogenous overexpression of Ca_Vβ_1a during old age may play a role in the loss of specific force.