Cucurbit[6]uril Hyperpolarized Chemical Exchange Saturation Transfer Pulse Sequence Parameter Optimization and Detectability Limit Assessment at 3.0T

Molecular imaging is the future of personalized medicine; however, it requires effective contrast agents. Hyperpolarized chemical exchange saturation transfer (HyperCEST) can boost the signal of Hyperpolarized ¹²⁹Xe MRI and render it a molecular imaging modality of high efficiency. Cucurbit[6]uril (CB6) has been successfully employed in vivo as a contrast agent for HyperCEST MRI, however its performance in a clinical MRI scanner has yet to be optimized. In this study, MRI pulse sequence parameter optimization was first performed in CB6 solutions in phosphate-buffered saline (PBS), and subsequently in whole sterile citrated bovine blood. The performance of four different depolarization pulse shapes (sinusoidal, 3-lobe sinc (3LS), rectangular (block), and hyperbolic secant (hypsec) was optimized. The detectability limits of CB6 in a clinical 3.0T MRI scanner was assessed using the optimized pulse sequences. The 3LS depolarization pulses performed best, and demonstrated 24 % depletion in a 25 μM solution of CB6 in PBS. It performed similarly in blood. The CB6 detectability limit was found to be 100 μM in citrated bovine blood with a correspondent HyperCEST depletion of 30 % ±9 %. For the first time, the HP ¹²⁹Xe HyperCEST effect was observed in red blood cells (RBC) and had a similar strength as HyperCEST in plasma.     

Hydroquinone clathrates and the theory of clathrate formation

The model of a clathrate solid solution, taking into account directed and nondirected guest-guest interactions, has been obtained using statistical thermodynamic methods in the approximation of the mean-field type for the general case (the formation of cavities of several types and the inclusion of different kinds of guest molecules by the host). Consideration of this interaction has been shown to improve the quantitative agreement between theory and experiment. When the guest-guest interaction is considerable in the case of guest molecules of the same type a phase transition (of a gas-liquid type) of the guest component may occur in the clathrate matrix. In the case of guests of two different types, the phase transition of the guest subsystem of the liquid-liquid type may also occur within one framework at the expense of a preferable interaction among guest molecules of the same type.We present the isothermal (20°C) section of the phase diagram of a hydroquinone-— formic acid — acetonitrile system. Clathrates, forming in the binary systems (with hydroquinone) produce restricted solid solutions (of type IV, according to Roozeboom). These and other experimental data are discussed in terms of the proposed theory.Dedicated to Professor H. M. Powell.     

NMR-spectroscopic mapping of an engineered cavity in the I14A mutant of HPr from Staphylococcus carnosus using xenon

The interaction between the histidine-containing phosphocarrier protein HPr and xenon atoms in solution is studied in the present paper. Wild-type HPr as well as the exchange mutant I14A have been studied. Specific binding of xenon into an engineered cavity created via the exchange of amino acid residue I14 by alanine could be shown using 1H-15N heteronuclear single-quantum coherence (HSQC) spectroscopy. Xenon binding results in pronounced changes of the 1H and 15N chemical shifts of amide groups close to the cavity. In addition to this observation which allows the NMR-spectroscopic mapping of such cavities, we have shown that the entire molecule is slightly rearranged as a result of xenon binding. In contrast, wild-type HPr only exhibits minor chemical shift changes due to the nonspecific interactions with the xenon atoms in solution.     

An application of the refined born approximation to the solution of coupled equations involved in electron-ion and electron-atom scattering problems

A new approach to the solution of coupled equations involved in electron-ion and electron-atom scattering problems is proposed. This method is a combination of iteration and variation procedures. The main advantage of this method is that exchange terms can be calculated in a direct and straightforward manner. The method is based on the Lippmann-Schwinger equation and does not require trial functions satisfying appropriate boundary conditions. Using the Volterra formulation one can find the solution on an interval determined by the range of the exchange potential and the long-range potential terms can be taken into account by a projection procedure giving the asymptotic value of the reactance matrix. The method is tested on the case of electron-hydrogen atom scattering in the 1s-2s and 1s-2s-2p approximation.We have adapted the method proposed originally by Rayski to obtain solutions of coupled equations involved in electron-ion and electron-atom scattering. As mentioned in section 1 the construction of the method secures an automatic fulfilment of the boundary conditions. It allows an easy calculation of the exchange potential as well as an estimation of the introduced approximation. It gives also a possibility of detecting any spurious convergence. Moreover, it is important that this formalism can be applied in the case of normalized as well as unnormalized initial integral equations. This fact is of special importance in the case of long-range interactions. When the method is used for unnormalized (Volterra) equations it allows application of a very convenient projection procedure for treating the long-range terms in the direct potential.Electron-hydrogen atom collisions are investigated as a numerical illustration of the method. In the 1s-2s approximation the normalized equations were solved, while in the 1s-2s-2p approximation the solution was obtained with the help of Volterra equations and the long-range terms of the direct potential were taken into account by the projection procedure. In both cases the calculations were performed in the first iteration step and the obtained solutions agree fairly well with the results obtained by a numerical integration. It is not clear which set of results is more accurate. The numbers of parameters needed to obtain these results was not too large (not more than twenty in each channel) and decreased with the increase of the values of angular momentum and energy. The calculations were performed without weight functions, although the use of an appropriate weight function can improve the effectiveness of the method. This effectiveness could also be improved through a more lucky choice of trial functions.     

Macromolecular pair correlation functions from fluorescence depolarization experiments

Depolarization of fluorescence resulting from the transport of electronic excitations in chromophore-containing polymers is investigated as a technique for detecting deviations from ideal-chain statistics. An approximate expression for the fluorescence anisotropy that depends only on the pair correlation function of chromophore labels is presented. This approximation is shown to be accurate for particular cases of long-range correlations, short-range correlations, and no correlations among chromophore positions. The formalism allows fluorescence depolarization experiments to be used as a probe of macromolecular pair correlation functions.     

Study of Relaxation in Micellar Solution by the Numerical Experiment

A numerical simulation of the relaxation process of surfactant micellar solution to a new equilibrium state is performed using model analytical representations for the main characteristics of micellar aggregates. Relaxation stages of molecular aggregate size distribution in the typical regions of aggregation number variations predicted by the analytical theory in two-flux approximation are revealed. Good agreement between the predicted values of the relaxation times of micellar solution and those obtained in numerical simulation is disclosed within the domain of applicability of two-flux approximation. Numerical algorithm proposed in this work makes it possible to study the relaxation process of micellar solution even in the case when two-flux approximation becomes inapplicable. The realization of numerical algorithm can be considered as a kind of experiment for studying the relaxation process of a model micellar solution.     

Determining the radius and the apparent charge of a micelle from electrical conductivity measurements by using a transport theory: explicit equations for practical use

We propose here a procedure which combines experiments and simple analytical formulas that allows us to determine good estimations of the size and charge of ionic micelles above the critical micellar concentration (cmc). First, the conductivity of n-tetradecyltrimethylammonium bromide and chloride (TTABr and TTACl, respectively) aqueous solutions was measured at 25 degrees C, before and above their cmc. Then, an analytical expression for the concentration dependence of the conductance of an ionic mixture with three species (monomers, micelles, and counterions) was developed and applied to the analysis of the experiments. The theoretical calculations use the mean spherical approximation (MSA) to describe equilibrium properties. Here, we propose new expressions for the electrical conductivity, adapted to the case of electrolytes that are dissymmetric in size, and applicable up to a total surfactant concentration of 0.1 mol L(-1). Moreover, we show that they are good approximations of the corresponding numerical results obtained from Brownian dynamics simulations. Since the analytical formulas given in the present paper involve a small number of unknown parameters, they allow one to derive the size and charge of macroions in solution from conductivity measurements.     

Energy eigenvalue spectroscopy

A wave function which is other than an exact eigenfunction, if it obeys appropriate analytical conditions, can be considered to represent the initial configuration of a nonstationary state. In the course of its subsequent time development the quantum system exhibits implicitly its entire eigenvalue spectrum. A method based, in principle, on Fourier analysis of the evolving quantum system is applied to the direct calculation of the energy eigenvalue spectrum. The spectral function is expressed as a moment expansion, in terms of expectation values of powers of the Hamiltonian. When the expansion is truncated, as it must be in any practical application, the corresponding spectral function represents a smeared-out eigenvalue spectrum. An alternative approximation leads to the quantum-mechanical method of moments. As the number of terms is increased, the computed spectrum becomes sharper and more accurate. In certain cases the moment expansion can be circumvented, if the action of the evolution operator can be evaluated in closed form. This is equivalent to finding some solution of the time-dependent Schrödinger equation. The various methods of eigenvalue spectroscopy are applied to the harmonic oscillator.     

Investigation of water bound to photosystem I with multiquantum filtered 17 O nuclear magnetic resonance

A new analytical approach was developed to characterize the properties of water molecules bound to macromolecules in solution using 17 O nuclear magnetic resonance (NMR) relaxation. A combination of conventional (single-quantum) and triple-quantum filtered Hahn echo and inversion recovery measurements was employed. From measured relaxation rate constants, the fraction and the correlation time of bound H2 17 O molecules and the relaxation rate constant of bulk water in solution were calculated. This was done by solving analytically a set of nonlinear equations describing the overall relaxation rate constants in the presence of chemical exchange between bulk and bound water. The analytical approach shows the uniqueness of the solution for a given set of three relaxation rate constants. This important result sheds light on the data reduction problem from 17 O NMR experiments on biological systems. Water bound in photosystem I isolated from the wild type and rubA variant of the cyanobacterium Synechocystis species PCC 7002 was investigated for the first time. The analysis revealed that photosystem I isolated from the wild type binds 1720+/-110 water molecules, whereas photosystem I isolated from the rubA variant binds only 1310+/-170. The accuracy of the method proposed can be increased by further 17 O enrichment. The methodology, established for the first time in this work, allows the study of a diverse range of biological samples regardless of their size and molecular weight. Applied initially to photosystem I, this novel method has important consequences for the future investigation of the assembly of biological molecules.     

Calibration by orthogonal and common least squares — Theoretical and practical aspects

Consequences resulting from a three-dimensional calibration model introduced in [5] are investigated. Accordingly, there exists a different statistical background for the calibration, the analytical evaluation and the validation step. If the errors of the concentration values are not negligible compared with the errors of the measured values, orthogonal calibration models have to be used instead of the common Gaussian least squares (GLS). Four different approximation models of orthogonal least squares, Wald's approximation (WA), Mandel's approximation (MA), Geometrical mean (GM), and Principal component estimation (PC) are investigated and compared with each other and with GLS by simulations and by real analytical applications. From the simulations it can be seen that GLS is affected by bias in the estimates of both slope and intercept in the case of increasing concentration error. On the other hand, the orthogonal models estimate the calibration parameter better. The best fit is obtained by Wald's approximation. It is shown by simulations and real analytical calibration problems that orthogonal calibration has to be used in all cases in which the concentration errors cannot be neglected compared to the errors of the measured values. This is in particular relevant in recovery experiments for validation by means of comparison of methods. In such cases orthogonal least squares methods have always to be applied where the use of WA is recommended. The situation is different in the case of ordinary calibration experiments. The examples considered show small existing differences between the classical GLS and the orthogonal procedures. In doubtful cases both GLS and WA should be computed where the latter should be used if significant differences appear.     

Analytic density-functional self-consistent-field theory of diblock copolymers near patterned surfaces

Analytical solutions are derived for the density profiles and the free energies of compressible diblock copolymer melts (or incompressible copolymer solutions) near patterned surfaces. The density-functional self-consistent-field theory is employed along with a Gaussian chain model for bonding constraints and a random mixing approximation for nonbonded interactions. An analytical solution is rendered possible by expanding the chain distribution function around an inhomogeneous reference state with a nontrivial analytical solution, by retaining the linear terms, and by requiring consistency with the homopolymer limit. The density profiles are determined by both real and complex roots of a sixth-degree polynomial that may easily be obtained by solving a generalized eigenvalue problem. This analytical formulation enables one to efficiently explore the large nine-dimensional parameter space and can serve as a first approximation to computationally intensive studies with more detailed models. Illustrative computations are provided for uniform and patterned surfaces above the order-disorder transition. The results are consistent with the previous self-consistent-field calculations in that lamellar ordering appears near the surface above the order-disorder transition and the lamella order perpendicular or parallel to the surface depending on the commensurability between the periods of the surface pattern and the density oscillations.     

Depolarization of light scattering by atomic and molecular solutions with strongly anisotropic translational-orientational fluctuations

Translational-orientational fluctuations are shown to raise or lower the depolarization of light scattered by solutions according to the structure of the near-order region of anisotropic molecules. In solutions of atoms, translational fluctuations induce anisotropic scattering already described in the bi-molecular radial correlations approximation; in accordance with the latest experiments, this scattering undergoes an increase or decrease depending on ternary radial correlations. A general expression for the effective optical anisotropy of the near-order region in solutions is applied to the dilute case permitting, in a novel manner, determination of both the value and sign of the anisotropy for isolated solute molecules.     

Optical response of Cu clusters in zeolite template

Optical properties of Cu clusters embedded in mordenite are studied experimentally and theoretically. In this work we discuss spectral features of the system at various reduction steps and compare then with the results of spectra obtained within a theoretical model. The model employed consists of Cu clusters embedded in a homogeneous matrix. A second model employed introduced further variation considering a three component system where air or water can be present. The macroscopic dielectric response of the system is obtained within the Maxwell Garnett approximation. In this approach the complex non-local in homogeneous dielectric response of the zeolite+copper system is replaced by an effective homogeneous dielectric function. Metallic clusters can occupy specific available cavities in the zeolite framework. The presence of clusters that are smaller than the cavities in which they reside can lead to an air-Cu or water-Cu interface which allows shifts in surface plasmon resonance energies. As observed experimentally the energy of the main resonance is seen to be insensitive to the filling fraction ratios and highly susceptible to the embedding matrix properties. Reflectance spectra have been obtained which can be explained within this model.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Kinetic analysis of solid-state reactions: A new integral method for nonisothermal kinetics with the dependence of the preexponential factor on the temperature (A = A0Tn)

In this study, we have proposed a new approximation for the general temperature integral, which frequently occurs in the nonisothermal kinetics with the dependence of the preexponential factor on the temperature and has no exact analytical solution. The validity of the new approximation has been tested by some numerical analyses. As the solution of the general temperature integral, the new approximation is more accurate than other approximations. Based on the newly proposed approximation, the corresponding integral method has been given. The precision of the integral methods for the determination of the activation energy has been calculated, and the results have shown that the relative error involved in the activation energy obtained from the new integral method is smaller than that from other integral methods. For applications, nonisothermal data obtained by theoretical simulation have been successfully processed using the new integral method.     

Effective generation of molecular cavities in polarizable continuum model by DefPol procedure

A new computational strategy for the building of molecular cavities (named DefPol) has been linked to the most recent implementation of the polarizable continuum model (PCM) for the representation of solvent effects on physicochemical properties of large molecules. Free energies, analytical gradients, and Hessians can be computed in this framework in the rigid cavity approximation. Coupling DefPol cavities with a number of other recent improvements of the standard algorithm (e.g., effective use of symmetry, iterative procedures with linear scaling) significantly enlarges the dimensions of systems amenable to refined computations and strongly reduces the gap between computations for isolated molecules and in solution. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1693–1701, 1999     

Relative binding affinities of molecular capsules investigated by ESI-mass spectrometry

ESI-MS(/MS) has been used as a method which allows the fast, unambiguous and sensitive simultaneous detection and relative stability approximation of supramolecular assemblies in mixtures. In spite of the obvious fundamental differences between solution and gas phase, ESI-MS in the case of self-assembled molecular capsules has been shown to produce very similar results to single binding experiments monitored by NMR titrations as well as conformational searches performed by Monte-Carlo simulations. MS/MS experiments reveal the same relative order of gas phase stabilities as previously found in solution. Moreover, proton transfer reactions which lead to new molecular capsules, are not detectable in the time-averaged NMR spectrum. However, the newly produced species are found in the complex mixtures by ESI-MS and can be conveniently characterized by subsequent MS/MS experiments: in a collision-induced dissociation the single half-spheres are easily discovered and structurally assigned. Thus, ESI-MS has worked as a valuable tool for the rapid screening of complex supramolecular mixtures and in combination with MS/MS experiments elucidated both the path of unexpected side reactions as well as the thermodynamic gas-phase stabilities of all components in the mixture.     

Fast quantitative 2D NMR for metabolomics and lipidomics: A tutorial

Nuclear magnetic resonance (NMR) is a well-known analytical technique for the analysis of complex mixtures. Its quantitative capability makes it ideally suited to metabolomics or lipidomics studies involving large sample collections of complex biological samples. To overcome the ubiquitous limitation of spectral overcrowding when recording 1D NMR spectra on such samples, the acquisition of 2D NMR spectra allows a better separation between overlapped resonances while yielding accurate quantitative data when appropriate analytical protocols are implemented. Moreover, the experiment duration can be considerably reduced by applying fast acquisition methods. Here, we describe the general workflow to acquire fast quantitative 2D NMR spectra in the “omics” context. It is illustrated on three representative and complementary experiments: UF COSY, ZF-TOCSY with nonuniform sampling, and HSQC with nonuniform sampling. After giving some details and recommendations on how to apply this protocol, its implementation in the case of targeted and untargeted metabolomics/lipidomics studies is described.     

Communication: equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval 0.584-0.605, respectively.