1H-NMR spin-spin relaxation time assessment of the reflection coefficient of the Triticale seed cell wall–plasmalemma barrier to mannitol

The ¹H-NMR spin-spin relaxation time (T₂) in Triticale seeds swelling in external osmotica, polyethylene glycol 8000 or mannitol can identify both bound and free water. At the same water content, the free water spin-spin relaxation time increases for seeds imbibed with the mannitol solution, demonstrating inadequate water potential adjustment. The exchange rate of free/bound water molecules is apparently influenced by the driving force for water flow. The reciprocal lifetime of free water molecules, as a measure of water flow through the main cell barrier, was obtained. From a model of the seed as a resistance–capacitor network for water flow, a method was derived for calculating the reflection coefficient σ as a lifetime ratio of the free water molecules in seeds imbibed with two different osmotica (one penetrating across the main cell barrier and one not penetrating) at the same water potential. The ¹H-NMR method and the classical method based on volume rate changes yielded reflection coefficients for mannitol for the cell wall–plasmalemma barrier of 0.78 ± 0.08 and 0.68 ± 0.06, respectively.     

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100 , 2678–2685] from ¹³C spin-lattice relaxation times (T₁) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T₁ of ¹³C nuclei to that of London is given. The formalism is illustrated through an example.     

On the question of hydronium binding to ATP-synthase membrane rotors

A recently determined atomic structure of an H⁺-coupled ATP-synthase membrane rotor has revived the long-standing question of whether protons may be bound to these structures in the form of a hydronium ion. Using both classical and quantum-mechanical simulations, we show that this notion is implausible. Ab initio molecular dynamics simulations of the binding site demonstrate that the putative H₃O⁺ deprotonates within femtoseconds. The bound proton is thus transferred irreversibly to the carboxylate side chain found in the ion-binding sites of all ATP-synthase rotors. This result is consistent with classical simulations of the rotor in a phospholipid membrane, on the 100-nanosecond timescale. These simulations show that the hydrogen-bond network seen in the crystal structure is incompatible with a bound hydronium. The observed coordination geometry is shown to correspond instead to a protonated carboxylate and a bound water molecule. In conclusion, this study underscores the notion that binding and transient storage of protons in the membrane rotors of ATP synthases occur through a common chemical mechanism, namely carboxylate protonation.     

Thermodynamic analysis of the physical state of water during freezing in plant tissue, based on the temperature dependence of proton spin-spin relaxation

Multi-proton spin-echo images were collected from cold-acclimated winter wheat crowns (Triticum aestivum L.) cv. Cappelle Desprez at 400 MHz between 4 and ?4 °C. Water proton relaxation by the spin-spin (T2) mechanism from individual voxels in image slices was found to be mono-exponential. The temperature dependence of these relaxation rates was found to obey Arrhenius or absolute rate theory expressions relating temperature, activation energies and relaxation rates, Images whose contrast is proportional to the Arrhenius activation energy (E_a), Gibb's free energy of activation (ΔG^?), and the entropy of activation (ΔS^?) for water relaxation on a voxel basis were constructed by post-image processing. These new images exhibit contrast based on activation energies rather than rules of proton relaxation. The temperature dependence of water proton T₂ relaxation rates permits prediction of changes in the physical state of water in this tissue over modest temperature ranges. A simple model is proposed to predict the freezing temperature kof various tissue in wheat crowns. The average E_a and ΔH^? for water proton T₂ relaxation over the above temperature range in winter wheat tissue were ?6.4 ± 14.8 and ?8.6 ± 14.8kj mol^?1, respectively. This barrier is considerably lower than the E_a for proton translation in ice at 0°C, which is reported to be between 46.0 and 56.5 kj mol^?1     

Influence of the energy of H-bond protons on the electron transfer rate in photosynthetic reaction centers

We present here a theoretical interpretation of the temperature dependence of the rate of dark recombination between a primary quinone (Q_A) and a bacteriochlorophyll dimer in the reaction center of Rhodobacter sphaeroides. We were able to describe qualitatively the nonmonotonous character of this dependence using the energy of interaction between an excess electron and H-bond protons. We considered a molecular model of Q_A and two reaction center fragments that make H-bonds with Q_A: His(M219) and Asn(M259)-Ala(M260). We used the two-center approach with regard for electron-phonon interaction in order to calculate the characteristic time of electron tunneling during the recombination reaction. The energy of the phonon emitted/ absorbed during the electron tunneling was determined by the relative shift of donor and acceptor energy levels, the detuning of levels. The detuning was shown to depend on temperature nonmonotonously for H-bonds with double-well potential energy surface. The characteristic time (or the reaction rate) depended on temperature parametrically. The computed dependence was in qualitative agreement with the experimental one.     

Approximate quantum trajectory dynamics for reactive processes in condensed phase

A method of molecular dynamics with quantum corrections, practical for studies of large molecular systems, is reviewed. The approach is based on the Bohmian formulation of the time-dependent Schrödinger equation in which a wavefunction is represented by an ensemble of interdependent trajectories. The quantum effects come from the quantum potential acting on trajectories on par with the usual classical potential. The quantum potential is determined from the evolving nuclear wavefunction, i.e. from the quantum trajectory (QT) ensemble itself. For practical and conceptual reasons the quantum potential and corresponding quantum nuclear effect are computed only for the selected light nuclei. For studies of reactive chemical processes, the classical potential is computed on-the-fly using the density functional tight binding method of electronic structure. A massively parallel implementation, based on the message passing interface allows for efficient simulations of ensembles of thousands of trajectories describing systems of up to 200 atoms. As a biochemical application, the approximate QT approach is used to model the tunnelling-dominated proton transfer in soybean-lipoxygenase-1. A materials science application is represented by a study of the nuclear quantum effect on adsorption of hydrogen and deuterium on a C₃₇H₁₅ molecule, which is a model ‘flake’ of graphene.     

Two-dimensional model of a double-well potential: Proton transfer upon hydrogen bond deformation

Proton tunneling in a hydrogen bond can only take place if the potential energy surface has two minima; this is known as a double-well potential. The aim of this work was (i) to present a simple enough 2D model of H-bond double-well potential in harmonic approximation and (ii) to assess how proton transfer therein is affected by H-bond deformations (shifts and turns such as result from conformational motion of molecular structures carrying the donor and the acceptor). It is shown that even small stretching of the H-bond and reorientation of its covalent part (‘bending’) increase the characteristic time of proton tunneling by orders of magnitude. On the other hand, the model, being two-dimensional, demonstrates that different types of deformation not only can aggravate each other but in some cases can be mutually compensatory in terms of proton transfer efficiency. The properties of the model and some implications of the results are discussed.     

A deuteron and proton magnetic resonance relaxation study of beta-lactoglobulin a association: some approaches to the Scatchard hydration of globular proteins

A general expression for the concentration-dependent relaxation increment, $\text{(}\text{dR}\text{dc}\text{)}{}_{\mathrm{\mu }}$, (where R may be R₁, the spin-lattice, or R₂, the spin-spin relaxation rate of water), has been derived from multicomponent theory for a protein in salt solution. Emphasis is placed on the addition of salt to the aqueous protein to minimize potentially high virial effects due to charge repulsion or to the charge fluctuations predicted by the Kirkwood-Shumaker theory; under conditions where the protein has a high net charge-to-mass ratio the calculation of relaxation increments must employ protein activities in place of concentrations. This treatment was applied to the molecular states of β-lactoglobulin A under associating and nonassociating conditions. In contrast to data in the literature obtained in the absence of salt, where correlation times τ_c were excessively high and hydration values too low, here values of τ_c from ²H NMR were in quantitative agreement with those expected from parameters of the known structural states of this protein. With these values, hydrations were obtained by three different ways of calculating the relaxation rate of the bound water from ¹H and ²H NMR data. Preferential hydrations, derived from linked functions, for the association of the protein at pH 4.65 were obtained from sedimentation velocity measurements. Combination of the results from the temperature dependence of the deuteron NMR and the linked functions, on the basis of a three-state model, yields slow-tumbling hydration values and correlation times comparable to those obtained from the two-state model. Based on either an isotropic bound-water mechanism or an anisotropic orientational distribution of the water molecules, enthalpies of hydration determined from the three-state model are in accord with those calculated from the two-state model.     

A Brillouin scattering study of the hydration of Li- and Na-DNA films

We have used Brillouin spectroscopy to study the velocities and attenuation of acoustic phonons in wet-spun films of Na-DNA and Li-DNA as a function of the degree of hydration at room temperature. Our data for the longitudinal acoustic (LA) phonon velocity vs water content display several interesting features and reveal effects that we can model at the atomic level as interhelical bond softening and relaxation of the hydration shell. The model for interhelical softening makes use of other physical parameters of these films, which we have determined by gravimetric, x-ray, and optical microscopy studies. We extract intrinsic elastic constants for hydrated Na-DNA molecules of c₁₁ ? 8.0 × 10¹⁰ dynes/cm² and c₃₃ ? 5.7 × 10¹⁰ dynes/cm², which corresponds to a Young's modulus, E ? 1.1 × 10¹⁰ dynes/cm² (with Poisson's ratio, σ = 0.44). The negative velocity anisotropy of the LA phonons indicates that neighboring DNA molecules are held together by strong interhelical bonds in the solid state. The LA phonon attenuation data can be understood by the relaxational model in which the acoustic phonon is coupled to a relaxation mode of the water molecules. Na-DNA undergoes the A to B phase transition at a relative humidity (rh) of 92% while Li-DNA (which remains in the B form in this range) decrystallizes at an rh of 84%. We find that our Brillouin results for Na- and Li-DNA are remarkably similar, indicating that the A to B phase transition does not play an important role in determining the acoustic properties of these two types of DNA.     

Refinement of protein structure against non-redundant carbonyl <Superscript>13</Superscript>C NMR relaxation

Carbonyl ¹³C′ relaxation is dominated by the contribution from the ¹³C′ chemical shift anisotropy (CSA). The relaxation rates provide useful and non-redundant structural information in addition to dynamic parameters. It is straightforward to acquire, and offers complimentary structural information to the ¹⁵N relaxation data. Furthermore, the non-axial nature of the ¹³C′ CSA tensor results in a T₁/T₂ value that depends on an additional angular variable even when the diffusion tensor of the protein molecule is axially symmetric. This dependence on an extra degree of freedom provides new geometrical information that is not available from the NH dipolar relaxation. A protocol that incorporates such structural restraints into NMR structure calculation was developed within the program Xplor-NIH. Its application was illustrated with the yeast Fis1 NMR structure. Refinement against the ¹³C′ T₁/T₂ improved the overall quality of the structure, as evaluated by cross-validation against the residual dipolar coupling as well as the ¹⁵N relaxation data. In addition, possible variations of the CSA tensor were addressed. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A 13C-NMR study on the conformational and dynamical properties of a cereal seed storage protein,C-hordein,and its model peptides

We have recorded the ¹³C CP-MAS and DD-MAS nmr spectra of dry and hydrated barley storage protein, C-hordein, as a model for wheat S-poor prolamins, together with those of model synthetic peptides (Pro)₂(Gln)₆(I) and (Pro-Gln-Gln-Pro-Phe-Pro-Gln-Gln)₃(II) under dry or hydrated conditions. The spectral features of C-hordein as well as these peptides were appreciably different from each other depending on the extent of hydration, reflecting different domains that adopt different types of conformations as well as dynamics. In particular, considerable proportions of the peak intensities were lost in the CP-MAS spectra, and well-resolved ¹³C-nmr signals emerged in DD-MAS nmr spectra owing to acquisition of molecular motions by swelling. It was shown that local β-turn or (Pro)_n type II conformation is more preferable for individual Pro residues and β-sheet type conformation is dominant for individual Gln residues in the dry and hydrated systems. In addition, two types of Gln environments are originated in C-hordein that differ in their mobility. Further, ¹³C spin-lattice relaxation times (T₁'s) of C- hordein and peptide II were reduced by more than one order of magnitude by hydration, reflecting the presence of well-swollen molecular chains. In contrast, theT₁ values of peptide I upon hydration remained one third of those in the dry state. Carbon-resolved proton spin-lattice relaxation times in the rotating frame (T_1ρ's) were also decreased by about 50% upon hydration, although these parameters were less sensitive as compared to T₁ values. In addition, the ¹³C-nmr signals of the aromatic side chain of Phe residues disappeared on hydration owing to interference between the frequency of the acquired flip-flop motion and the proton decoupling frequency. This information gives a new insight into establishing the structural properties of the studied protein system. A model may be put forward for a gel-type structure in which the more rigid part of the system involves intermolecular hydrogen-bonded Gln side chains as well as some hydrophobic “pockets” involving Pro and Phe residues. The liquid-like domain is characterized by considerable backbone and side-chain motion as well as rapid ring-puckering motion in Pro residues. © 1997 John Wiley & Sons, Inc.     

Dynamic studies of a fibronectin type I module pair at three frequencies: Anisotropic modelling and direct determination of conformational exchange

Summary A detailed analysis of the ¹⁵N relaxation of a pair of modules from fibronectin is presented. The overall dimensions of the protein structure can be approximated by a cylinder with an axial ratio D/D of 1.9. T₁, T₂ and NOE data, collected at three ¹⁵M frequencies (50.6, 60.8 and 76 MHz), can be fitted satisfactorily to a Lipari-Szabo model, taking anisotropy into account. A method for analysing the exchange contribution to relaxation is presented. This contribution depends upon the predicted B _inf0 ^sup2 frequency dependence in the fast exchange limit of these exchange terms. Using this analysis, relatively slow conformational exchange contributions are detected around one of the disulphide bonds in the first module of the pair.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

MD Simulations of Liquids with Td,Oh Molecular Symmetry

Abstract

A new method is proposed for the calculation of intermolecular interactions in Molecular Dynamics simulations of liquids with T_d, O_h molecular symmetry. The new algorithm is based on the separation of the pair potential into a short-range and a long-range contribution described by a site-site and a spherical centre-centre potential model respectively using an additional cutoff distance. Test calculations for the Lennard-Jones fluids CCl₄ and SF₆ show significant savings in CPU time. We compare thermodynamic properties, pair correlation functions and a few dynamic autocorrelation functions obtained with the novel strategy with results of the commonly used algorithm for systems containing 864 molecules. Since no significant differences appear the new algorithm may be suggested as a useful contribution to the area of Molecular Dynamics simulation of liquids with these rather high molecular symmetries.     

CALCULATIONS OF BIOELECTRIC POTENTIALS : V. POTENTIALS IN HALICYSTIS

Interest in the study of Halicystis and of Valonia has been stimulated by discoveries of marked contrasts and striking similarities existing side by side. This is illustrated by new experiments with the alkali metals and alkaline earths. In Halicystis the apparent mobilities of K⁺, Rb⁺, Cs⁺, and Li⁺ (calculated by means of Henderson''s equation from changes in P.D. produced by replacing sea water by a mixture of equal parts of sea water and 0.6 M of various chlorides) are as follows, u _K, = 16, u _Rb = 16, u _Cs = 4.4, and u _Li = 0.2; u _Na is taken as 0.2. These values resemble those in Valonia except that in the latter u _Cs is about 0.2. No calculation is made for u _NHNH4, because in these experiments even at low pH so much NH₃ is present that the sign of the P.D. may reverse. This does not happen with Valonia. According to Blinks, NH₄ ⁺ at pH 5 in low concentrations acts like K⁺. The calculation gives u _Mg = 1.9 which is similar to the value found for Valonia. No calculation can be made for CaCl₂ since it produces protoplasmic alterations and in consequence Henderson''s equation does not apply. This differs from Valonia. Evidently these plants agree closely in some aspects of electrical behavior but differ widely in others.     

High resolution nuclear magnetic resonance studies of nigeran

Polymer motion in solution can be studied by ¹³CNMR relaxation methods, which provide information about the correlation time for C-H vectors. ¹³C-Relaxation and Nuclear Overhauser Enhancement (NOE) data may frequently be combined to determine the dipole-dipole relaxation contribution. An alternative method is proposed based on a comparison of the proton spin-lattice relaxation rates of the centre proton resonances of an unlabelled molecule with the relaxation rates of the ¹³C satellites (from ¹³C labelled molecules).Selectively labelled nigeran which is an alternating $\text{1 → 3 and 1 → 4 α-}\text{d}\text{-glucan}$ has been investigated. The discussion in terms of the occurrence of different motions for each of the two units of the polymer requires an unambiguous assignment of the two anomeric carbons. For this reason a detailed assignment of the ¹H and ¹³C Nuclear Magnetic Resonance (NMR) spectra of nigeran in dimethylsulphoxide-d₆ is described, based on T₁ and NOE measurements in addition to selective homonuclear and heteronuclear spin decoupling experiments. These values are correlated with a conformation estimated by HSEA hard-spheres calculation. The measurements of the relaxation parameters for labelled and unlabelled compounds which provide an alternative determination of the ¹³C-¹H dipole-dipole relaxation contribution in a macromolecule agree well with ¹³C-{¹H} NOE experiments.     

Kinetic studies of the helix–coil transition in aqueous solutions of poly(L-lysine)

The rate of conformational change of aqueous poly(α-L -lysine) solutions was measured using the electric field pulse relaxation method with conductivity detection. The relaxation time as a function of pH exhibits two maxima. One is assigned to a proton transfer reaction and the other to the helix–coil conformational transition. The helix nucleation parameter and the maximum relaxation time yield the rate constant of helix growth process (k_F) according to Schwarz's kinetic theory as k_F = 2 × 10⁷ sec^?1, which is comparable to that of the poly(glutamic acid) solution. The thermodynamic parameters of the helix growth process are compared with those of poly(glutamic acid).