13C-NMR off-resonance rotating frame spin-lattice relaxation studies of bovine lens γ-crystallin self association: effect of ‘macromolecular crowding’

The NMR technique of ¹³C off-resonance rotating frame spin-lattice relaxation, which provides an accurate assessment of the effective rotational correlation time (τ_0,eff) for macromolecular rotational diffusion, was applied to the study of γ-crystallin association as a function of protein concentration and temperature. Values of the effective rotational correlation time for γ-crystallin rotational diffusion were obtained at moderate to high protein concentrations (80–350 mg/ml) and at temperatures above, and below, the cold cataract phase transition temperature. With increasing concentration γ-crystallin was observed to increasingly associate as reflected by larger values of τ_0,eff Decreasing temperature in the range of 35 to 22°C was found to result in no change in the temperature corrected value of τ_0,eff at a γ-crystallin concentration of 80 mg/ml, whereas at temperatures of 18°C or below, this parameter was approx. twofold larger, suggesting the occurrence of a well defined phase transition, which correlated well with the cold cataract phase transition temperature. At higher protein concentrations, by contrast, τ_0,eff (temperature corrected) was found to increase by approx. 1.6- to 2-times in the temperature interval 35°C to 22°C, a result consistent with the dependence of the cold cataract phase transition temperature on γ-crystallin concentration. Analysis of intensity ratio dispersion curves, using an assumed model of isodesmic association, permitted the estimation of the association constant characterizing the aggregation under particular conditions of concentration and temperature. The significant increase in the value of the association constant with moderate increases in protein concentration was rationalized by invoking the effect of ‘macromolecular crowding’. The results obtained in this study suggest that in the intact lens, where high protein concentrations prevail, γ-crystallin is unlikely to be found in the monomeric state, but more likely, as a significantly aggregated species, representing a broad molecular weight distribution.     

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

The effective reproduction number R_eff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate R_eff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its R_eff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).     

Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution

Chemical (conformational) exchange on the ms-s time scale is reliably identified by the observation of transverse relaxation rates, R_ex, that depend upon the strength of the effective field (_1eff=B_1eff) used in spin lock or CPMG experiments. In order to determine if the exchange correlation time, _ex, is the fast or slow limit, measurements of (i) signal line shape and (ii) temperature dependence of R_ex have been commonly used in studies of stable, small molecules. However, these approaches are often not applicable to proteins, because sample stability and solubility, respectively, limit the temperature range and signal sensitivity of experiments. Herein we use a complex, but general, two-site exchange equation to show when the simple fast exchange equations for R_ex are good approximations, in the case of proteins. We then present a simple empirical equation that approximately predicts R_ex in all exchange regimes, and explains these results in a clear, straightforward manner. Finally we show how one can reliably determine whether _ex is in the fast or slow exchange limit.     

rnr gene from the antarctic bacterium Pseudomonas syringae Lz4W, encoding a psychrophilic RNase R

RNase R is a highly processive, hydrolytic 3′-5′ exoribonuclease belonging to the RNB/RNR superfamily which plays significant roles in RNA metabolism in bacteria. The enzyme was observed to be essential for growth of the psychrophilic Antarctic bacterium Pseudomonas syringae Lz4W at a low temperature. We present results here pertaining to the biochemical properties of RNase R and the RNase R-encoding gene (rnr) locus from this bacterium. By cloning and expressing a His₆-tagged form of the P. syringae RNase R (RNase R^Ps), we show that the enzyme is active at 0 to 4°C but exhibits optimum activity at ∼25°C. The enzyme is heat labile in nature, losing activity upon incubation at 37°C and above, a hallmark of many psychrophilic enzymes. The enzyme requires divalent cations (Mg²⁺ and Mn²⁺) for activity, and the activity is higher in 50 to 150 mM KCl when it largely remains as a monomer. On synthetic substrates, RNase R^Ps exhibited maximum activity on poly(A) and poly(U) in preference over poly(G) and poly(C). The enzyme also degraded structured malE-malF RNA substrates. Analysis of the cleavage products shows that the enzyme, apart from releasing 5′-nucleotide monophosphates by the processive exoribonuclease activity, produces four-nucleotide end products, as opposed to two-nucleotide products, of RNA chain by Escherichia coli RNase R. Interestingly, three ribonucleotides (ATP, GTP, and CTP) inhibited the activity of RNase R^Ps in vitro. The ability of the nonhydrolyzable ATP-γS to inhibit RNase R^Ps activity suggests that nucleotide hydrolysis is not required for inhibition. This is the first report on the biochemical property of a psychrophilic RNase R from any bacterium.     

THERMAL DEPOLARIZATION OF FLUORESCENCE FROM POLYTENE CHROMOSOMES STAINED WITH ACRIDINE ORANGE

The degree of polarization of fluorescence from stretched Chironomus thummi polytene chromosomes, stained with low concentrations of acridine orange (AO), decreases with increasing temperature. The "half temperature" of this decrease (T_½R) is lower than the expected DNA thermal denaturation temperature (T_m) by about 20°C. T_½R is lowered as histone is removed from chromosomes. Balbiani ring regions of the fourth chromosome have T_½R's much lower than other regions, and nearly as low as chromosomes which had been extensively pretreated with trypsin to remove histone and other proteins. Measurements of the thermal change in the rotational diffusion rate of AO in solution with DNA indicate that the temperature at which the DNA-AO bonding changes from a "rigid" to a "loose" mode varies with the GC percentage of the DNA, and in the same fashion as T_m, although 20°C lower.     

Characterization of human phosphodiesterase 12 and identification of a novel 2'-5' oligoadenylate nuclease - The ectonucleotide pyrophosphatase/phosphodiesterase 1

The vertebrate 2-5A system is part of the innate immune response and central to cellular antiviral activities. Upon activation by viral double-stranded RNA, 5′-triphosphorylated, 2′-5′-linked oligoadenylate polyribonucleotides (2-5As) are synthesized by one of several 2′-5′ oligoadenylate synthetases. The 2-5As bind and activate RNase L, an unspecific endoribonuclease, resulting in viral and cellular RNA decay. Given that most endogenous RNAs are degraded by RNase L, continued enzyme activity will eventually lead to cell growth arrest and cell death. This is averted, when 2-5As and their 5′-dephosphorylated forms, the so-called 2-5A core molecules, are cleaved and thus inactivated by 2′-5′-specific nuclease(s), e.g. phosphodiesterase 12, thereby turning RNase L into its latent form. In this study, we have characterized the human phosphodiesterase 12 in vitro focusing on its ability to degrade 2-5As and 2-5A core molecules. We have found that the enzyme activity is distributive and is influenced by temperature, pH and divalent cations. This allowed us to determine V_max and K_m kinetic parameters for the enzyme. We have also identified a novel 2′-5′-oligoadenylate nuclease; the human plasma membrane-bound ectonucleotide pyrophosphatase/phosphodiesterase 1, suggesting that 2-5A catabolism may be a multienzyme-regulated process.     

DNase and RNase Responses of Petunia × hybrida During Transition to Flowering as Affected by Light Treatments

The responses of DNase and RNase isoforms and their specific activities following transition to flowering (1 to 6 weeks) were examined in Petunia × hybrida under different light conditions. Petunia × hybrida plants formed flower buds at the 4^th week in the case of high light and at the 6^th week in the far-red light treatment, while no flower bud formation was observed upon red light and control light treatments. The DNase and RNase activities decreased from the 1^st to the 6^th week during transition to flowering. Native-PAGE analysis revealed the appearance of one DNase (D₁) and seven RNase (R₁ - R₇) isoforms in all light treatments. It is assumed that the progress of the flowering could be related to the disappearance or reduction of D₁ DNase band intensity and disappearance of R₁, R₂ and R₇ RNase isoforms. Consequently, these isoforms could be used as potent biochemical markers of flower bud formation under light intensity as well as light quality treatments.     

Effect of pH, Mg, CO(2) and Mercurials on the Circular Dichroism, Thermal Stability and Light Scattering of Ribulose 1,5-Bisphosphate Carboxylases from Alfalfa, Spinach and Tobacco

Circular dichroism, differential scanning calorimetry and light-scattering measurements of ribulose 1,5-bisphosphate carboxylase (E.C. 4.1.1.39) from alfalfa, spinach and tobacco show: a) The conformation and thermal stability of the native carboxylases are sensitive to changes in pH and to activation of the enzyme with Mg²⁺ and CO₂. The helical content, denaturation temperature (T_d) and specific enthalpy of denaturation (Δq) decreased with increase in pH. Addition of Mg²⁺ and CO₂ at pH 9 increased T_d by 4 to 5 C; at pH 7.5 the changes in T_d were smaller. b) Addition of mercurials produced changes in conformation and thermal stability. The decrease in helical content of the enzymes with increase in pH was enhanced by the addition of p-chloromercuribenzoate. At pH 9, addition of p-chloromercuribenzoate or of 1-(3-(chloromercuri)-2-methoxypropyl)urea decreased T_d by 11.4 to 20.2 C and Δq by 2.1 to 2.8 calories per gram. c) The spinach carboxylase undergoes the largest and the tobacco the smallest changes in conformation and thermal stability upon change in pH or treatment with mercurials. d) The calorimetric data suggest that the large and small subunits are heat denatured independently but at the same temperature. e) Light scattering measurements at pH 9 of p-chloromercuribenzoate treated tobacco enzyme showed that there is no dissociation into subunits upon heating to temperatures greater than T_d. A `ball and string' model for the carboxylase molecule is proposed to reconcile independence of subunit denaturation with apparent strong interactions between subunits.     

The biosynthesis of ribonuclease and its accumulation in protein bodies in the cotyledons of mung bean seedlings

Germination and seedling growth of mung bean are accompanied by a 7- to 10-fold increase in the ribonuclease content of the cotyledons. The increase occurs during the first 4 days of seedling growth and precedes the senescence of the cotyledons. Separation of the RNases in the cotyledons by polyacrylamide gel electrophoresis indicates the presence of several minor bands in seeds imbibed for 24 hr. On the second day of seedling growth a new major band with an R_f of 0.76 is present. In 4- to 5-day old seedlings this major band accounts for nearly all the RNase activity in the tissue. The characteristics of this RNase show that it is a plant ribonuclease I (pH optimum of 5.0; MW 16,000; activity preferentially inhibited by purine nucleotides; no activity toward DNA; no phosphodiesterase activity). When the seedlings are grown in 66% D₂O the RNase activity undergoes a density shift of 0.61% indicating that the increase in enzyme activity is due to the de novo synthesis of the enzyme molecules. A method is described for the isolation of protein bodies from protoplasts of storage parenchyma cells. Fractionation of protoplast lysates on Ficoll gradients results in the recovery of a high proportion (75%) of intact protein bodies. On these gradients RNase activity comigrates with α-mannosidase, a protein body marker enzyme indicating that the newly synthesized RNase accumulates in the protein bodies. We suggest that the synthesis of RNase in the cotyledons and its accumulation in the protein bodies indicates that protein bodies may function in the degradation of cellular macromolecules other than the reserves stored within them.     

Laser spectroscopy measurements of the effective temperature of argon ions in the PNX-U plasma neutralizer

Laser spectroscopy measurements of the effective temperature of Ar¹⁺ ions in the PNX-U multipole trap, in which argon plasma is ionized and heated by microwaves under electron-cyclotron-resonance conditions, are performed using a narrow-band tunable dye laser. The absorption profile of the 611.5-nm line is examined. In a microwave power range of 5–50 kW, the observed behavior of the effective temperature of argon ions T_{i, eff} indicates an anomalous mechanism for ion heating. It is shown that certain information about the electron temperature can be deduced from measurements by the laser-induced fluorescence (LIF) technique. The measurements performed also serve to test the laser technique and apparatus that is presently being developed for diagnosing additives to the ITER divertor plasma by the LIF method.     

Phospholipid chain immobilization and steriod rotational immobilization in acetylcholine receptor-rich membranes from torpedo marmorata

1. The ESR spectra of both phosphatidylcholine and phosphatidylethanolamine spin labels reveal an immobilized lipid component (τ_R ? 50 ns), in addition to a fluid component (τ_R ～ 1 ns), in acetylcholine receptorrich membranes prepared from Torpedo marmorata electroplax according to the method of Cohen et al. (Cohen, J.B., Weber, M., Huchet, M. and Changeux, J.P. (1972) FEBS Lett. 26, 43–47). 2. The ESR spectra of the androstanol spin label display a component corresponding to molecules which are immobilized with respect to rotation about the long molecular axis (

), in addition to the fluid lipid bilayer component in which the molecules are rotating rapidly about their long axes (

). This immobilized component is observed throughout the temperature range 2–22°C, at an approximately constant relative intensity of approx. 45% of the total, which is quantitatively the same as previously observed with fatty acid spin labels.     

Temperature-independent diel variation in soil respiration observed from a temperate deciduous forest

The response of soil respiration (R_s) to temperature depends largely on the temporal and spatial scales of interest and how other environmental factors interact with this response. They are often represented by empirical exponential equations in many ecosystem analyses because of the difficulties in separating covarying environmental responses and in observing below ground processes. The objective of this study was to quantify a soil temperature‐independent component in R_s by examining the diel variation of an R_s time series measured in a temperate deciduous forest located at Oak Ridge, TN, USA between March and December 2003. By fitting 2 hourly, continuous automatic chamber measurements of CO₂ efflux at the soil surface to a Q₁₀ function to obtain the temperature‐dependent respiration (R_t) and plotting the diel cycles of R_t, R_s, and their difference (R_i), we found that an obvious temperature‐independent component exists in R_s during the growing season. The diel cycle of this component has a distinct day/night pattern and agrees well with diel variations in photosynthetically active radiation (PAR) and air temperature. Elevated canopy CO₂ concentration resulted in similar patterns in the diel cycle of the temperature‐independent component but with different daily average rates in different stages of growing season. We speculate that photosynthesis of the stand is one of the main contributors to this temperature‐independent respiration component although more experiments are needed to draw a firm conclusion. We also found that despite its relatively small magnitude compared with the temperature‐dependent component, the diel variation in the temperature‐independent component can lead to significantly different estimates of the temperature sensitivity of soil respiration in the study forest. As a result, the common practice of using fitted temperature‐dependent function from night‐time measurements to extrapolate soil respiration during the daytime may underestimate daytime soil respiration.     

Photon buildup factors in some dosimetric materials for heterogeneous radiation sources

Effective photon energy absorption (EABF_eff) and exposure buildup factors (EBF_eff) have been calculated based on the effective energy concept, for some dosimetric materials such as water, polymethyl methacrylate (PMMA), polystyrene, solid water (WT1), RW3 (Goettingen Water 3), and ABS (acrylonitrile butadiene styrene), for MV X-rays and ⁶⁰Co gamma rays. Firstly, the equivalent atomic numbers (Z _eq) of the given materials have been determined using the effective photon energies (E _eff). Then, the five-parameter geometric progression (G-P) fitting approximation has been used to calculate both EABF_eff and EBF_eff values. Since the G-P fitting parameters are not available for the E _eff values of the given materials, a linear interpolation in which a function of the logarithm of the variable is used has been performed, in order to calculate the parameters in each E _eff, which will be further used for the determination of EABF_eff and EBF_eff. In the present paper, water equivalence properties of the given materials are also discussed based on the effective buildup factors. In this study, special emphasis is placed on the calculation of EABF_eff and EBF_eff values of different materials for photons that are not monoenergetic but heterogeneous in energy, to obtain an initial and prior knowledge of the probable energy and buildup of photons at locations of interest, i.e., to understand whether the real absorbed dose occurs at the surface or somewhere inside the medium of interest.     

Inductive influence of 4′-terpyridyl substituents on redox and spin state properties of iron(II) and cobalt(II) bis-terpyridyl complexes

A series of iron and cobalt bis-terpyridine (terpy) complexes were prepared with the general formula [M(R-terpy)₂](PF₆)₂, where M represents Co(II) and Fe(II), and R is the following terpyridine substituents in order of increasing electron-withdrawing behavior [(C₄H₈)N, (C₄H₉)NH, HO, CH₃O, CH₃-phenyl, H, Cl, CH₃SO, CH₃SO₂]. The complexes were prepared to investigate the extent of redox and spin state control that is attainable by simply varying the electron donating/withdrawing influence using a single substituent site on the terpyridine ligand. Cyclic voltammetry was used to assess the substituents influence on the M(III/II) redox couple. A plot of the M(III/II) redox potential (E_1/2) versus the electron donating/withdrawing nature of the substituents (Hammett constants), shows a strong linear trend for both metals; however, the substituents were observed to have a stronger influence on the Fe(III/II) couple. Solution magnetic susceptibility measurements at room temperature were carried out using standard NMR methodology (modified Evans method) where all of the Fe(II) complexes exhibited a diamagnetic, low spin (S = 0) behavior. In the cobalt series where R = H for [Co(R-terpy)₂]²⁺, the complex is known to be near the spin cross-over where the room temperature effective magnetic moment (μ_eff) in solution is ≈3.1 Bohr magnetons; however, in this study the μ_eff is observed to vary between 2.7 and 4.1 Bohr magnetons depending on the R-substituent.     

On the Origin and the Signal-Shaping Mechanism of the Fast Photosignal in the Vertebrate Retina

Fast photosignals (FPS) with R₁ and R₂ components were measured in retinas of cattle, rat, and frog within a temperature range of 0° to 60°C. Except for temperatures near 0°C the signal rise of the R₁ component was determined by the duration of the exciting flash. The kinetics of the R₂ component and the meta transition of rhodopsin in the cattle and rat retina were compared. For the analysis of the FPS it is presupposed that the signal is produced by light-induced charges on the outer segment envelope membrane that spread onto the whole plasma membrane of the photoreceptor cell. To a good approximation, this mechanism can be described by a model circuit with two distinct capacitors. In this model, the charging capacitance of the pigmented outer segment envelope membrane and the capacitance of the receptor's nonpigmented plasma membrane are connected via the extra- and intracellular electrolyte resistances. The active charging is explained by two independent processes, both with exponential rise (R₁ and R₂), that are due to charge displacements within the pigmented envelope membrane. The time constant τ₂ of the R₂ membrane charging process shows a strong temperature dependence that of the charge redistribution, τ_r, a weak one. In frog and cattle retinas the active charging is much slower within a large temperature range than the passive charge redistribution. From the two-capacitor model it follows for τ_r « τ₂ that the rise of the R₂ component is determined by τ_r, whereas the decay is given by τ₂. For the rat retina, however, τ₂ approaches τ_r at physiological temperatures and becomes <τ_r above 45°C. In this temperature range where τ₂ ≈ τ_r, both processes affect rise and decay of the photosignal. The absolute values of τ_r are in good accordance with the known electric parameters of the photoreceptors. At least in the cattle retina, the time constant τ₂ is identical with that of the slow component of the meta II formation. The strong temperature dependence of the meta transition time gives rise to the marked decrease of the R₂ amplitude with falling temperature. As the R₁ rise could not be fully time resolved the signal analysis does not yield the time constant τ₁ of the R₁ generating process. It could be established, however, within the whole temperature range that the decay of the R₁ component is determined by τ_r. Using an extended model that allows for membrane leakage, we show that in normal ringer solution the membrane time constant does not influence the signal time-course and amplitude.     

Synthesis, spectral and magnetical characterization of monomeric [Cu(2-NO2bz)2(nia)2(H2O)2] and structural analysis of similar [Cu(RCOO)2(L-N)2(H2O)2] complexes

A new complex of composition [Cu(2-NO₂bz)₂(nia)₂(H₂O)₂] (1) (nia = nicotinamide, 2-NO₂bz = 2-nitrobenzoate) has been prepared and its composition and stereochemistry as well as coordination mode have been determined by elemental analysis, electronic, infrared and EPR spectroscopy, magnetization measurements over the temperature range 1.8-300 K, and its structure has been solved, as well. The complex structure consists of the centrosymmetric molecules with Cu(II) atom monodentately coordinated by the pair of 2-nitrobenzoato anions and by the pair of nicotinamide molecules, forming nearly tetragonal basal plane, and by a pair of water molecules that complete tetragonal-bipyramidal coordination polyhedron about the copper atom. The complex 1 exhibits magnetic moment μ_eff = 1.86 B.M. at 300 K which decreases to μ_eff = 1.83 B.M. at 1.8 K. The magnetic susceptibility temperature dependence obeys Curie-Weiss law with Curie constant of 0.442 cm³ K mol⁻¹ and with Weiss constant of −1.0 K. EPR spectra at room temperature as well as at 77 K are of axial type with g_⊥ = 2.065 and g_∥ = 2.280 and exhibit clearly, but partially resolved parallel hyperfine splitting with A_II = 160 G, that is consistent with the determined molecular structure of 1. In order to analyze the factors influencing the degree of tetragonal distortion of coordination polyhedron, the dataset of 72 structures similar to that of 1 was extracted from CCD and analyzed. A significant correlation between the average Cu-O_ax bond length and tetragonality parameter τ which was found as a consequence of the Jahn-Teller effect.     

Distinct binding interactions of HIV-1 Gag to Psi and non-Psi RNAs: Implications for viral genomic RNA packaging

Despite the vast excess of cellular RNAs, precisely two copies of viral genomic RNA (gRNA) are selectively packaged into new human immunodeficiency type 1 (HIV-1) particles via specific interactions between the HIV-1 Gag and the gRNA psi (ψ) packaging signal. Gag consists of the matrix (MA), capsid, nucleocapsid (NC), and p6 domains. Binding of the Gag NC domain to ψ is necessary for gRNA packaging, but the mechanism by which Gag selectively interacts with ψ is unclear. Here, we investigate the binding of NC and Gag variants to an RNA derived from ψ (Psi RNA), as well as to a non-ψ region (TARPolyA). Binding was measured as a function of salt to obtain the effective charge (Z_eff) and nonelectrostatic (i.e., specific) component of binding, K_d(1M). Gag binds to Psi RNA with a dramatically reduced K_d(1M) and lower Z_eff relative to TARPolyA. NC, GagΔMA, and a dimerization mutant of Gag bind TARPolyA with reduced Z_eff relative to WT Gag. Mutations involving the NC zinc finger motifs of Gag or changes to the G-rich NC-binding regions of Psi RNA significantly reduce the nonelectrostatic component of binding, leading to an increase in Z_eff. These results show that Gag interacts with gRNA using different binding modes; both the NC and MA domains are bound to RNA in the case of TARPolyA, whereas binding to Psi RNA involves only the NC domain. Taken together, these results suggest a novel mechanism for selective gRNA encapsidation.     

Conductance studies on the interaction of symmetrical tetraalkylammonium iodides with non-electrolytes – sucrose and urea – in N,N-dimethylformamide

The interaction of sucrose and urea with symmetrical tetraalkylammonium iodides in N,N-dimethylformamide (1) has been studied by employing conductance measurements. These studies involved the use of a rather simple, unique technique developed for study of the solute-solute and solute-solvent interactions in non-electrolyte solutions. Our results showed a break at the saturation temperature, indicating a transition in the conductance values. This behavior is explained in terms of the solute-solvent interactions involved in electrolyte-solvent-non-electrolyte systems. The results have been interpreted on the basis of the special, structure-promoting features of the (large) tetraalkylammonium (R₄N⁺) ions, the hydrogen-bonding capabilities of sucrose and urea, the salting-in behavior of R₄NI salts with sucrose and urea, and the one-dimensional, hydrogen-bonded structure of molecules of 1.