Statistical Properties of the Site-Frequency Spectrum Associated with Λ-Coalescents

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.     

A New Interpretation of the Dynamic Changes of the Potassium Conductance in the Squid Giant Axon

The solutions, n(t), of the differential equation dn/dt = α (1 - n) n (4 - 6n + 4n² - n³) - βn² (4 - 6n + 4n² - n³) in which α and β are instantaneous functions of membrane potential, are shown to fit with good accuracy the time courses of the rise of potassium conductance during depolarizing steps in clamp potential, found experimentally by Hodgkin and Huxley and by Cole and Moore. The equation is derived by analysing the dynamic behaviour of a system consisting of a square array of interacting pores. The possible role of Ca⁺⁺ ions in this system is discussed.     

The convergence in distribution of some simple epidemics

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by [α²X_n(t){n −X_n(t) +X_n(0)}]^1/2, t[0, ∞), α(0, ∞). This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t(0, t₀), and t₀ is evaluated.     

Cross-Correlation Functions for a Neuronal Model

Cross-correlation functions, R_XY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, R_XY(t,τ) = f_U [θ-h(τ), t + τ] {h′(τ) + E_U [u′(t + τ)]} for positive values of this quantity, where f_U(u,t) is the probability density function of U(t) and E_U [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in R_XY(t,τ) for a neuron subjected only to excitation. (3) For large τ, R_XY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) R_XY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.     

Voltage and Current Clamp Transients with Membrane Dielectric Loss

Transient responses of a space-clamped squid axon membrane to step changes of voltage or current are often approximated by exponential functions of time, corresponding to a series resistance and a membrane capacity of 1.0 μF/cm². Curtis and Cole (1938, J. Gen. Physiol. 21:757) found, however, that the membrane had a constant phase angle impedance z = z₁(jωτ)^-α, with a mean α = 0.85. (α = 1.0 for an ideal capacitor; α < 1.0 may represent dielectric loss.) This result is supported by more recently published experimental data. For comparison with experiments, we have computed functions expressing voltage and current transients with constant phase angle capacitance, a parallel leakage conductance, and a series resistance, at nine values of α from 0.5 to 1.0. A series in powers of t^α provided a good approximation for short times; one in powers of t^-α, for long times; for intermediate times, a rational approximation matching both series for a finite number of terms was used. These computations may help in determining experimental series resistances and parallel leakage conductances from membrane voltage or current clamp data.     

Increasing the Amphiphilicity of an Amyloidogenic Peptide Changes the β-Sheet Structure in the Fibrils from Antiparallel to Parallel

Solid-state NMR measurements have been reported for four peptides derived from β-amyloid peptide Aβ(1–42): Aβ(1–40), Aβ(10–35), Aβ(16–22), and Aβ(34–42). Of these, the first two are predicted to be amphiphilic and were reported to form parallel β-sheets, whereas the latter two peptides appear nonamphiphilic and adopt an antiparallel β-sheet organization. These results suggest that amphiphilicity may be significant in determining fibril structure. Here, we demonstrate that acylation of Aβ(16–22) with octanoic acid increases its amphiphilicity and changes the organization of fibrillar β-sheet from antiparallel to parallel. Electron microscopy, Congo Red binding, and one-dimensional ¹³C NMR measurements demonstrate that octanoyl-Aβ(16–22) forms typical amyloid fibrils. Based on the stability of monolayers at the air-water interface, octanoyl-Aβ(16–22) is more amphiphilic than Aβ(16–22). Measurements of ¹³C-¹³C and ¹⁵N-¹³C nuclear magnetic dipole-dipole couplings in isotopically labeled fibril samples, using the constant-time finite-pulse radiofrequency-driven recoupling (fpRFDR-CT) and rotational echo double resonance (REDOR) solid-state NMR techniques, demonstrate that octanoyl-Aβ(16–22) fibrils are composed of parallel β-sheets, whereas Aβ(16–22) fibrils are composed of antiparallel β-sheets. These data demonstrate that amphiphilicity is critical in determining the structural organization of β-sheets in the amyloid fibril. This work also shows that all amyloid fibrils do not share a common supramolecular structure, and suggests a method for controlling the structure of amyloid fibrils.     

Elastic-Mathematical Theory of Cells and Mitochondria in Swelling Process: II. Effect of Temperature upon Modulus of Elasticity of Membranous Material of Egg Cells of Sea Urchin, Strongylocentrotus purpuratus, and of Oyster, Crassostrea virginica

The elastic behavior of the cell wall as a function of the temperature has been studied with particular attention being given to the swelling of egg cells of Strongylocentrotus purpuratus and Crassostrea virginica in different sea water concentrations at different temperatures. It was found that the modulus of elasticity is a nonlinear function of temperature. At about 12-13°C the modulus of elasticity (E) is constant, independent of the stress (σ) and strain (ε_ν) which exist at the cell wall; the membranous material follows Hooke's law, and E ≈ 3 × 10⁷ dyn/cm² for S. purpuratus and C. virginica. When the temperature is higher or lower than 12-13°C, the modulus of elasticity increases, and the membranous material does not follow Hooke's law, but is almost directly proportional to the stresses existing at the cell wall. On increasing the stress, the function E_σ = E(σ) approaches saturation. The corresponding stress-strain diagrams, σ = σ(ε_ν), and the graphs, E_σ = E(σ) and E_σ = E(t) are given. The cyto-elastic phenomena at the membrane are discussed.     

Chiral Ruthenium(II) Polypyridyl Complexes: Stabilization of G-Quadruplex DNA,Inhibition of Telomerase Activity and Cellular Uptake

Two ruthenium(II) complexes, Λ-[Ru(phen)₂(p-HPIP)]²⁺ and Δ-[Ru(phen)₂(p-HPIP)]²⁺, were synthesized and characterized via proton nuclear magnetic resonance spectroscopy, electrospray ionization-mass spectrometry, and circular dichroism spectroscopy. This study aims to clarify the anticancer effect of metal complexes as novel and potent telomerase inhibitors and cellular nucleus target drug. First, the chiral selectivity of the compounds and their ability to stabilize quadruplex DNA were studied via absorption and emission analyses, circular dichroism spectroscopy, fluorescence-resonance energy transfer melting assay, electrophoretic mobility shift assay, and polymerase chain reaction stop assay. The two chiral compounds selectively induced and stabilized the G-quadruplex of telomeric DNA with or without metal cations. These results provide new insights into the development of chiral anticancer agents for G-quadruplex DNA targeting. Telomerase repeat amplification protocol reveals the higher inhibitory activity of Λ-[Ru(phen)₂(p-HPIP)]²⁺ against telomerase, suggesting that Λ-[Ru(phen)₂(p-HPIP)]²⁺ may be a potential telomerase inhibitor for cancer chemotherapy. MTT assay results show that these chiral complexes have significant antitumor activities in HepG2 cells. More interestingly, cellular uptake and laser-scanning confocal microscopic studies reveal the efficient uptake of Λ-[Ru(phen)₂(p-HPIP)]²⁺ by HepG2 cells. This complex then enters the cytoplasm and tends to accumulate in the nucleus. This nuclear penetration of the ruthenium complexes and their subsequent accumulation are associated with the chirality of the isomers as well as with the subtle environment of the ruthenium complexes. Therefore, the nucleus can be the cellular target of chiral ruthenium complexes for anticancer therapy.     

Simple Uniaxial and Uniform Biaxial Deformation of Nearly Isotropic Incompressible Tissues

A method is developed for analyzing in a unified manner both uniaxial and uniform biaxial strain data obtained from nearly isotropic tissues. The formulation is a direct application of nonlinear elasticity theory pertaining to large deformations. The general relation between Eulerian stress (σ) and extension ratio (λ) in soft isotropic elastic bodies undergoing uniform deformation takes the simple form: σ = ((λ³ - 1)/λ) f(λ), where f(λ) must be determined for each material. The extension ratio may be either greater than 1.0 (uniaxial elongation), or lie between zero and 1.0 (uniform biaxial extension). Simple analytical functions for f(λ) are most readily found for each tissue by plotting all data as (λ³ - 1)/λσ vs. λ. Of those tissues investigated in this way (dog pericardium and pleura, and cat mesentery and dura), all but pleura could be adequately described by a parabola: 1/f(λ) = 1/k{[(λ_M - λ)(λ - λ_m)]/[λ_M - λ_m}. In these instances, three material constants per tissue (K, λ_M, λ_m) served to predict approximately the stresses attained during both small and large deformations, in strips and sheets alike. It was further found that the uniaxial strain asymptote (λ_M) was linearly related to the biaxial strain asymptote (Λ_M), thus effectively reducing the number of constants by one.     

Probabilistic Model of Microbial Cell Growth,Division, and Mortality

After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability P_d(t)δt, dead with probability P_m(t)δt, or alive but undivided with the probability 1 − [P_d(t) + P_m(t)]δt, where t is time, P_d(t) expresses the probability of division for an individual cell per unit of time, and P_m(t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat''s properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population''s size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With P_d(t) and P_m(t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data.     

Water transport in the midrib tissue of maize leaves : direct measurement of the propagation of changes in cell turgor across a plant tissue

Water movement across plant tissues occurs along two paths: from cell-to-cell and in the apoplasm. We examined the contribution of these two paths to the kinetics of water transport across the parenchymatous midrib tissue of the maize (Zea mays L.) leaf. Water relations parameters (hydraulic conductivity, Lp; cell elastic coefficient, ε; half-time of water exchange for individual cells, T_½) of individual parenchyma cells determined with the pressure probe varied in different regions of the midrib. In the adaxial region, Lp = (0.3 ± 0.3)·10⁻⁵ centimeters per second per bar, ε = 103 ± 72 bar, and T_½ = 7.9 ± 4.8 seconds (n = seven cells); whereas, in the abaxial region, Lp = (2.5 ± 0.9)·10⁻⁵ centimeters per second per bar, ε = 41 ± 9 bar, and T_½ = 1.3 ± 0.5 seconds (n = 7). This zonal variation in Lp, ε, and T_½ indicates that tissue inhomogeneities exist for these parameters and could have an effect on the kinetics of water transport across the tissue.

The diffusivity of the tissue to water (D_t) obtained from the sorption kinetics of rehydrating tissue was D_t = (1.1 ± 0.4)·10⁻⁶ square centimeters per second (n = 6). The diffusivity of the cell-to-cell path (D_c) calculated from pressure probe data ranged from D_c = 0.4·10⁻⁶ square centimeters per second in the adaxial region to D_c = 6.1·10⁻⁶ square centimeters per second in the abaxial region of the tissue. D_t D_c suggests substantial cell-to-cell transport of water occurred during rehydration. However, the tissue diffusivity calculated from the kinetics of pressure-propagation across the tissue (D_t′) was D_t′ = (33.1 ± 8.0)·10⁻⁶ square centimeters per second (n = 8) and more than 1 order of magnitude larger than D_t. Also, the hydraulic conductance of the midrib tissue (Lp_m per square centimeter of surface) estimated from pressure-induced flows across several parenchyma cell layers was Lp_m = (8.9 ± 5.6)·10⁻⁵ centimeters per second per bar (n = 5) and much larger than Lp.

These results indicate that the preferential path for water transport across the midrib tissue depends on the nature of the driving forces present within the tissue. Under osmotic conditions, the cell-to-cell path dominates, whereas under hydrostatic conditions water moves primarily in the apoplasm.

     

Identification of Novel α1,3-Galactosyltransferase and Elimination of α-Galactose-containing Glycans by Disruption of Multiple α-Galactosyltransferase Genes in Schizosaccharomyces pombe

The oligosaccharides from fission yeast Schizosaccharomyces pombe contain large amounts of d-galactose (Gal) in addition to d-mannose (Man), in contrast to the budding yeast Saccharomyces cerevisiae. Detailed structural analysis has revealed that the Gal residues are attached to the N- and O-linked oligosaccharides via α1,2- or α1,3-linkages. Previously we constructed and characterized a septuple α-galactosyltransferase disruptant (7GalTΔ) anticipating a complete lack of α-Gal residues. However, the 7GalTΔ strain still contained oligosaccharides consisting of α1,3-linked Gal residues, indicating the presence of at least one more additional unidentified α1,3-galactosyltransferase. In this study we searched for unidentified putative glycosyltransferases in the S. pombe genome sequence and identified three novel genes, named otg1⁺–otg3⁺ (α one, three-galactosyltransferase), that belong to glycosyltransferase gene family 8 in the Carbohydrate Active EnZymes (CAZY) database. Gal-recognizing lectin blotting and HPLC analyses of pyridylaminated oligosaccharides after deletion of these three additional genes from 7GalTΔ strain demonstrated that the resultant disruptant missing 10 α-galactosyltransferase genes, 10GalTΔ, exhibited a complete loss of galactosylation. In an in vitro galactosylation assay, the otg2⁺ gene product had Gal transfer activity toward a pyridylaminated Man₉GlcNAc₂ oligosaccharide and pyridylaminated Manα1,2-Manα1,2-Man oligosaccharide. In addition, the otg3⁺ gene product exhibited Gal transfer activity toward the pyridylaminated Man₉GlcNAc₂ oligosaccharide. Generation of an α1,3-linkage was confirmed by HPLC analysis, α-galactosidase digestion analysis, ¹H NMR spectroscopy, and LC-MS/MS analysis. These results indicate that Otg2p and Otg3p are involved in α1,3-galactosylation of S. pombe oligosaccharides.     

The epithelial sodium channel in the Australian lungfish,Neoceratodus forsteri (Osteichthyes: Dipnoi)

Epithelial sodium channel (ENaC) is a Na⁺-selective, aldosterone-stimulated ion channel involved in sodium transport homeostasis. ENaC is rate-limiting for Na⁺ absorption in the epithelia of osmoregulatory organs of tetrapods. Although the ENaC/degenerin gene family is proposed to be present in metazoans, no orthologues or paralogues for ENaC have been found in the genome databases of teleosts. We studied full-length cDNA cloning and tissue distributions of ENaCα, β and γ subunits in the Australian lungfish, Neoceratodus forsteri, which is the closest living relative of tetrapods. Neoceratodus ENaC (nENaC) comprised three subunits: nENaCα, β and γ proteins. The nENaCα, β and γ subunits are closely related to amphibian ENaCα, β and γ subunits, respectively. Three ENaC subunit mRNAs were highly expressed in the gills, kidney and rectum. Amiloride-sensitive sodium current was recorded from Xenopus oocytes injected with the nENaCαβγ subunit complementary RNAs under a two-electrode voltage clamp. nENaCα immunoreactivity was observed in the apical cell membrane of the gills, kidney and rectum. Thus, nENaC may play a role in regulating sodium transport of the lungfish, which has a renin–angiotensin–aldosterone system. This is interesting because there may have been an ENaC sodium absorption system controlled by aldosterone before the conquest of land by vertebrates.     

The Formation of beta, 1 --> 4 Glucan from UDP-alpha-d-Glucose Catalyzed by a Phaseolus aureus Enzyme

Particulate enzyme preparations from Phaseolus aureus hypocotyls catalyze the formation of an alkali insoluble β, 1 → 4 linked [¹⁴C]-glucan using UDP-α-d [¹⁴C]-glucose as substrate. Particulate enzymes prepared from root tissue also catalyzed the production of β, 1 → 4 glucan. UDP-β-d-[¹⁴C]-glucose would not serve as a substrate for these enzymes. The presence or absence of β, 1 → 4 glucan synthetase activity was independent of tissue source, substrate concentration, or homogenization method.     

Immobilised Histidine Tagged β 2-Adrenoceptor Oriented by a Diazonium Salt Reaction and Its Application in Exploring Drug-Protein Interaction Using Ephedrine and Pseudoephedrine as Probes

A new oriented method using a diazonium salt reaction was developed for linking β ₂-adrenoceptor (β ₂-AR) on the surface of macroporous silica gel. Stationary phase containing the immobilised receptor was used to investigate the interaction between β ₂-AR and ephedrine plus pseudoephedrine by zonal elution. The isotherms of the two drugs best fit the Langmuir model. Only one type of binding site was found for ephedrine and pseudoephedrine targeting β ₂-AR. At 37 °C, the association constants during the binding were (5.94±0.05)×10³/M for ephedrine and (3.80±0.02) ×10³/M for pseudoephedrine, with the binding sites of (8.92±0.06) ×10⁻⁴ M. Thermodynamic studies showed that the binding of the two compounds to β ₂-AR was a spontaneous reaction with exothermal processes. The ΔG^θ, ΔH^θ and ΔS^θ for the interaction between ephedrine and β ₂-AR were −(22.33±0.04) kJ/mol, −(6.51±0.69) kJ/mol and 50.94±0.31 J/mol·K, respectively. For the binding of pseudoephedrine to the receptor, these values were −(21.17±0.02) kJ/mol, −(7.48±0.56) kJ/mol and 44.13±0.01 J/mol·K. Electrostatic interaction proved to be the driving force during the binding of the two drugs to β ₂-AR. The proposed immobilised method will have great potential for attaching protein to solid substrates and realizing the interactions between proteins and drugs.     

Pigmentation and Soluble Peroxidase Isozyme Patterns of Leaves of Pedilanthus tithymaloides L. variegatus as a Result of Daily Temperature Differences

In a constant environment with a narrow (less than 8°C) daily temperature difference (δt), leaves of Pedilanthus tithymaloides L. variegatus usually appeared green. After at least two days of δt > 10°C, new leaves had become green-white, and a red pigmentation appeared and increased if high δt conditions were maintained. If plants were returned to a narrow δt, new green leaves reappeared. Electrophoretic patterns of soluble peroxidase isozymes changed during the color changes. Three groups of electrophoretic bands occurred, and each was related to a characteristic tissue. The development of red color was correlated with the appearance of the group with the fastest electrophoretic mobility and the highest peroxidase activity.     

Distinguishing Closely Related Amyloid Precursors Using an RNA Aptamer

Although amyloid fibrils assembled in vitro commonly involve a single protein, fibrils formed in vivo can contain multiple protein sequences. The amyloidogenic protein human β₂-microglobulin (hβ₂m) can co-polymerize with its N-terminally truncated variant (ΔN6) in vitro to form hetero-polymeric fibrils that differ from their homo-polymeric counterparts. Discrimination between the different assembly precursors, for example by binding of a biomolecule to one species in a mixture of conformers, offers an opportunity to alter the course of co-assembly and the properties of the fibrils formed. Here, using hβ₂m and its amyloidogenic counterpart, ΔΝ6, we describe selection of a 2′F-modified RNA aptamer able to distinguish between these very similar proteins. SELEX with a N30 RNA pool yielded an aptamer (B6) that binds hβ₂m with an EC₅₀ of ∼200 nm. NMR spectroscopy was used to assign the ¹H-¹⁵N HSQC spectrum of the B6-hβ₂m complex, revealing that the aptamer binds to the face of hβ₂m containing the A, B, E, and D β-strands. In contrast, binding of B6 to ΔN6 is weak and less specific. Kinetic analysis of the effect of B6 on co-polymerization of hβ₂m and ΔN6 revealed that the aptamer alters the kinetics of co-polymerization of the two proteins. The results reveal the potential of RNA aptamers as tools for elucidating the mechanisms of co-assembly in amyloid formation and as reagents able to discriminate between very similar protein conformers with different amyloid propensity.     

The β1-Subunit of the MaxiK Channel Associates with the Thromboxane A2 Receptor and Reduces Thromboxane A2 Functional Effects

The large conductance voltage- and Ca²⁺-activated K⁺ channel (MaxiK, BK_Ca, BK) is composed of four pore-forming α-subunits and can be associated with regulatory β-subunits. One of the functional roles of MaxiK is to regulate vascular tone. We recently found that the MaxiK channel from coronary smooth muscle is trans-inhibited by activation of the vasoconstricting thromboxane A₂ prostanoid receptor (TP), a mechanism supported by MaxiK α-subunit (MaxiKα)-TP physical interaction. Here, we examined the role of the MaxiK β1-subunit in TP-MaxiK association. We found that the β1-subunit can by itself interact with TP and that this association can occur independently of MaxiKα. Subcellular localization analysis revealed that β1 and TP are closely associated at the cell periphery. The molecular mechanism of β1-TP interaction involves predominantly the β1 extracellular loop. As reported previously, TP activation by the thromboxane A₂ analog U46619 caused inhibition of MaxiKα macroscopic conductance or fractional open probability (FP_o) as a function of voltage. However, the positive shift of the FP_o versus voltage curve by U46619 relative to the control was less prominent when β1 was coexpressed with TP and MaxiKα proteins (20 ± 6 mV, n = 7) than in cells expressing TP and MaxiKα alone (51 ± 7 mV, n = 7). Finally, β1 gene ablation reduced the EC₅₀ of the U46619 agonist in mediating aortic contraction from 18 ± 1 nm (n = 12) to 9 ± 1 nm (n = 12). The results indicate that the β1-subunit can form a tripartite complex with TP and MaxiKα, has the ability to associate with each protein independently, and diminishes U46619-induced MaxiK channel trans-inhibition as well as vasoconstriction.