Omega 1-decoupled 1H homonuclear shift-correlated nuclear magnetic resonance spectroscopy (COSYDEC) applied to steroids

Problems of cross-peak overlap in two-dimensional 1H homonuclear shift-correlated (COSY) spectra of steroids can often be avoided by use of the omega 1-decoupled COSY (COSYDEC) method. The selection of experimental parameters is discussed, and COSYDEC spectra are illustrated for 17a-oxa-D-homoandrost-4-ene-3,17-dione (testololactone), testosterone, and 17 alpha-hydroxyprogesterone. In a good case, a COSYDEC spectrum obtained at 250 MHz allows cross-peak recognition and assignment with facility comparable to that available only at 500 MHz for normal COSY spectra.     

Properties of the DREAM scheme and its optimization for application to proteins

The DREAM scheme is an efficient adiabatic homonuclear polarization-transfer method suitable for multi-dimensional experiments in biomolecular solid-state NMR. The bandwidth and dynamics of the polarization transfer in the DREAM experiment depend on a number of experimental and spin-system parameters. In order to obtain optimal results, the dependence of the cross-peak intensity on these parameters needs to be understood and carefully controlled. We introduce a simplified model to semi-quantitatively describe the polarization-transfer patterns for the relevant spin systems. Numerical simulations for all natural amino acids (except tryptophane) show the dependence of the cross-peak intensities as a function of the radio-frequency-carrier position. This dependency can be used as a guide to select the desired conditions in protein spectroscopy. Practical guidelines are given on how to set up a DREAM experiment for optimized Cα/Cβ transfer, which is important in sequential assignment experiments.     

RFDR with Adiabatic Inversion Pulses: Application to Internuclear Distance Measurements

In the context of the structural characterisation of biomolecular systems via MAS solid state NMR, the potential utility of homonuclear dipolar recoupling with adiabatic inversion pulses has been assessed via numerical simulations and experimental measurements. The results obtained suggest that it is possible to obtain reliable estimates of internuclear distances via an analysis of the initial cross-peak intensity buildup curves generated from two-dimensional adiabatic inversion pulse driven longitudinal magnetisation exchange experiments.     

Phosphorus-31 studies on lecithin in ethanol solutions

³¹P relaxation times of lecithin in ethanol solutions have been measured in dependence on temperature and water concentration. Trial calculations have been carried out on the assumption of a 2-site exchange model. The results suggest first, the relaxation behaviour is determined by various motional and exchange processes; second, at 29 MHz the dipole-dipole interaction between ³¹P and protons provides the dominant contribution; third, in general we are not concerned with the case of “extreme narrowing”. Moreover, there are no negligible intermolecular contributions to relaxation.     

Determination of time-constants in cables of finite length

Current flow in cylindrical nerve and muscle fibre has been analysed in terms of a mathematical model leading to a linear partial differential equation for the voltage as a function of both position and time. In the case of a one-dimensional cable subject to a step input of current, the solution will consist of a steady-state behaviour preceded by an initial transient. The electrical properties of the fibre or cable itself determine a length-constant, λ, which can be determined experimentally from the steady-state response, and a time-constant, τ, which must be found from the initial transient. When the cable is infinite and when there is a single input electrode, an exact solution can be produced which enables ready determination of the time-constant τ. Two complications arise in experimental practice, however. In the first place, the fibre has finite length, and in the second, two spatially separated stimulation electrodes are often required. We thus analyse a more complicated and more general situation. The linearity of the membrane properties, however, allows the solution to the more general case to be built up by superposition of solutions from the simpler case (equivalent to the classical method of images). We also approximate the Hodgkin and Rushton solution by asymptotic formulae in order to allow more tractable expressions for the exact solution. We are thus able to give a method for the ready evaluation of the time constant τ under more general conditions.     

Reconstruction of NOESY maps. A requirement for a reliable conformational analysis of biomolecules using 2D NMR

The modelling of the conformation of a biomolecule in solution is based mainly on the internuclear distances deduced from measurements of nuclear Overhauser effects (nOe) in NOESY correlation maps. The distances are then used as restraints in the energy minimization procedure, which leads to one or several optimized conformations. A general and safe technique for validating these structures with respect to the experimental data is here proposed: from the internuclear distances, the relaxation matrix can be computed under the assumption of a unique rotational correlation time. By stepwise integration of these relaxation equations, the NOESY maps can be accurately reconstructed for any mixing time. Because multi-spin effects are correctly taken into account, any difference between the experimental and theoretical maps can be easily interpreted in terms of conformation, and possible inconsistencies due to conformational averaging can be pointed out. The technique is illustrated for a bacterial lipopeptide, mycosubtilin, the spectrum of which is completely assigned.     

Designing matrix models for fluorescence energy transfer between moving donors and acceptors.

A recipe is given for designing theoretical models for donor-acceptor systems in which fluorescence energy transfer and motion takes place simultaneously. This recipe is based on the idea that a system exhibiting both motion and fluorescence energy transfer can be modeled by specifying a number of "states" and the rates of transitions between them. A state in this context is a set of specific coordinates and conditions that describe the system at a certain moment in time. As time goes on, the coordinates and conditions for the system change, and this evolution can be described as a series of transitions from one state to the next. The recipe is applied to a number of example systems in which the donors and/or acceptors undergo either rotational or translational motion. In each example, fluorescence intensities and anisotropies for the donor and acceptor are calculated from solutions of eigensystems. The proposed method allows for analyzing time-resolved fluorescence energy transfer data without restrictive assumptions for motional averaging regimes and the orientation factor. It is shown that the fluorescence quantities depend on the size of the motional step (i.e., on the number of states), only if fluorescence energy transfer occurs. This finding indicates that fluorescence energy transfer studies may reveal whether the dynamics of a system (e.g., a protein) is better described in terms of transitions between a relatively small number of discrete states (jumping) or a large number of dense states (diffusion).     

Accurate estimation of inter-atomic distances in large proteins by NMR.

Recently a method was proposed which permits the extraction of the exact interatomic distance information from the measurement of the evolution of a single cross-peak relative to the mixing time in a NOESY experiment. This is performed through a careful multi-exponential analysis allowing the extraction of the relaxation parameter, and, consequently, the inter-proton distance. We investigate in the present paper whether this technique, already evaluated theoretically, can be used in a real experimental case. We have recorded and analyzed a set of 56 NOESY experiments on a lysozyme sample. Some 81 nOe build-up curves obtained from these data were analyzed in terms of distance. It is shown that the correlation between the measured distances and the reference distances obtained from crystallographic studies, is quite good. An accuracy of the order of 10% is obtained.     

Determination of local conformation of proteins from 1H-NMR spectroscopy data

A method is proposed to determine conformations of amino acid residues of the protein and effective correlation time tau c from cross-peak intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra. The method consists in fitting complete relaxation matrix of dipeptide unit protons to experimental cross-peak intensities by varying phi, psi, chi torsional angles and tau c. To verify the method, NOESY spectra of basic pancreatic trypsin inhibitor (BPTI) were theoretically generated at mixing times tau m = 25-300 ms and tau c = 4 ns and used for local structure determination. The method works well with optimum for measurement of NOE intensities tau m 100-200 ms. As a result, the backbone phi, psi torsion angles were unambiguously determined at tau m = 100 ms for all but Gly residues of BPTI, and chi 1 angles were determined for the majority of side chains. The obtained dipeptide unit conformations are very close to the BPTI crystallographic structure: root mean square deviation (RMSD) of interproton distances within dipeptide units, on the average, is 0.08 A (maximal deviation 0.44 A), and RMSD of phi and psi angles are 18 and 9 degrees, respectively (maximal deviations are 44 and 22 degrees).     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

Determination of interproton distances in peptides by two-dimensional nuclear Overhauser effect spectroscopy (NOESY). Conformation of a cyclic analog of substance P in a solution

Quantitative method is developed for evaluation interproton distances in peptides in solution. The method is based on the measurement of the relative intensities of the cross-peaks in the pure-phase absorption NOESY spectra. The ratios of the cross-peak intensities IN alpha/I alpha N and INN/I alpha N enable to determine the corresponding interproton distances dN alpha, d alpha N and dNN for several amino acid residues. These distances can be used to estimate other distances with cross-peaks in NOESY spectra. As example, the interproton distances are determined in a cyclic hexapeptide, namely cyclic analogue of substance P: cyclo [H-Glu-Phe-Phe-Gly-Leu-Met-NH(CH2)3-NH-]. The spatial structure of the molecule in dimethylsulphoxide solution is established.     

On the evaluation of data from flow-dialysis experiments

Flow dialysis can be used to measure (i) ligand binding to macromolecules and (ii) the size of transmembrane ion gradients. Generally an approximate method is used to calculate the binding or gradient parameters from the raw data. Here we present a simple but exact method and evaluate the errors that may arise when the approximate method is used to calculate the magnitude of ion gradients. In addition, equations are presented that allow for a correction for sampling from or additions to the upper compartment of a flow-dialysis vessel during the measurements. Setty and Hendler [(1982) J. Biochem. Biophys. Methods 7, 35-46] have reported artifacts in the measurement of ion-gradients caused by the addition of electron donors to the upper compartment of a flow-dialysis cell. Here we extend their observations and suggest additional methods to prevent such artifacts.     

An analytical method for investigating transient potentials in neurons with branching dendritic trees.

An analytical method is developed that allows one to explore the way in which the geometrical structure of a neuron's dendritic tree affects the time-course and amplitude of transient potentials generated at different locations on dendritic branches. The method requires that, for a given dendritic arborization, one associates a symmetric geometry for which exact mathematical expressions for time-varying dendritic potentials can be calculated. The value of the dendritic potential for the asymmetric geometry is evaluated by adding correction terms to the results for the symmetric geometry. Several model trees are examined, and in each case the analytical results are expressed in terms of two closely related families of functions. These functions provide a precise formulation for systematically analyzing the way in which the voltage transient at a given point depends upon the geometrical structure of the dentritic tree. Several numerical examples are presented. A discussion of how to generalize the method and of some potential applications are given.     

Determination of the orientation distribution of adsorbed fluorophores using TIRF. I. Theory.

The spectroscopic technique total internal reflection fluorescence can be used for determination of the orientation of adsorbed fluorescent molecules. The underlying theory is presented in general terms and elaborated in detail for the case that the fluorescent group is a porphyrin ring. It is shown that order parameters of the orientation distribution can be obtained if both the fluorescence intensity and its polarization are measured as functions of the polarization of the incident laser beam. From these order parameters an approximation of the orientation distribution can be derived by the maximum-entropy method.     

The value of chemical shift parameters in the description of protein solution structures

An increasing number of protein solution structures, calculated on the basis of nuclear Overhauser enhancement cross-peak intensities observed in two- or higher dimensional NOESY experiments, are becoming available. Among these structures regions of uncertainty are frequently observed particularly with respect to loops and surface side chains. These are commonly ascribed to either a lack of NOE constraints or to some intrinsic mobility within the protein. A powerful method of structural analysis which may resolve this problem is based on the information content of the chemical shift. The value of such an analysis is illustrated here with cytochromes b5 and c, proteins for which high-quality crystallographic and NMR data are available. Comparison of these using a pseudocontact shift-based analysis indicates that NOE data should be combined with the chemical shift data in order to uncover fully the ensemble of protein states and their dynamics in solution.     

Solving the chemical master equation for monomolecular reaction systems analytically

The stochastic dynamics of a well-stirred mixture of molecular species interacting through different biochemical reactions can be accurately modelled by the chemical master equation (CME). Research in the biology and scientific computing community has concentrated mostly on the development of numerical techniques to approximate the solution of the CME via many realizations of the associated Markov jump process. The domain of exact and/or efficient methods for directly solving the CME is still widely open, which is due to its large dimension that grows exponentially with the number of molecular species involved. In this article, we present an exact solution formula of the CME for arbitrary initial conditions in the case where the underlying system is governed by monomolecular reactions. The solution can be expressed in terms of the convolution of multinomial and product Poisson distributions with time-dependent parameters evolving according to the traditional reaction-rate equations. This very structured representation allows to deduce easily many properties of the solution. The model class includes many interesting examples. For more complex reaction systems, our results can be seen as a first step towards the construction of new numerical integrators, because solutions to the monomolecular case provide promising ansatz functions for Galerkin-type methods.     

Pré-traitement d’un volume IRM par filtrage anisotrope robuste pour la segmentation de l’épaule

A novel pre-treatment process for image segmentation, based on anisotropic diffusion and robust statistics, is presented in this paper. Image smoothing with edge preservation is shown to help upper limb segmentation (shoulder segmentation in particular) in MRI datasets. The anisotropic diffusion process is mainly controlled by an automated stopping function that depends on the values of voxel gradient. Voxel gradients are divided into two classes: one for high values, corresponding to edge voxels or noisy voxels, one for low values. The anisotropic diffusion process is also controlled by a threshold on voxel gradients that separates both classes. A global estimation of this threshold parameter is classically used. In this paper, we propose a new method based on a local robust estimation. It allows a better removing of noise while preserving edges in the images. An entropy criterion is used to quantify the ability of the algorithm to remove noise with different signal to noise ratios in synthetic images. Another quantitative evaluation criterion based on the Pratt Figure of Merit (FOM) is proposed to evaluate the edge preservation and their location accuracy with respect to a manual segmentation. The results on synthetic and MRI data of shoulder show the assets of the local model in terms of areas homogeneity and edges locations.     

Measurement analysis of two radials with a common‐origin point and its application

In spectral analysis, a chemical component is usually identified by its characteristic spectra, especially the peaks. If two components have overlapping spectral peaks, they are generally considered to be indiscriminate in current analytical chemistry textbooks and related literature. However, if the intensities of the overlapping major spectral peaks are additive, and have different rates of change with respect to variations in the concentration of the individual components, a simple method, named the ‘common‐origin ray’, for the simultaneous determination of two components can be established. Several case studies highlighting its applications are presented.