Nuclear magnetic resonance relaxation methods

The use of computer simulations to study internal motions and thermodynamic properties is receiving increased attention. One important use of the method is to provide a more fundamental understanding of the molecular information contained in various kinds of experiments on these complex systems. In the first part of this paper we review recent work in our laboratory concerned with the use of computer simulations for the interpretation of experimental probes of molecular structure and dynamics of proteins and nucleic acids. The interplay between computer simulations and three experimental techniques is emphasized (1) nuclear magnetic resonance relaxation spectroscopy, (2) refinement of macro-molecular x-ray structures, and (3) vibrational spectroscopy. The treatment of solvent effects in biopolymer simulations is a difficult problem. It is not possible to study systematically the effect of solvent conditions, e.g. added salt concentration, on biopolymer properties by means of simulations alone. In the last part of the paper we review a more analytical approach we have developed to study polyelectrolyte properties of solvated biopolymers. The results are compared with computer simulations. 

Fushman, D. and D. Cowburn, Nuclear magnetic resonance relaxation in determination of residue-specific 1SN chemical shift tensors in proteins in solution protein dynamics, structure, and applications of transverse relaxation optimized spectroscopy, in Methods Enzymol. T. James, U. Schmitz, and V. Doetsch, Editors. 2001. p.109-126. 

Historically, hydrogen exchange experiments (i.e., the replacement of one isotope of hydrogen bound to an O, N, or S atom in the protein interior by another isotope from the solvent water) provided some of the earliest evidence for the existence of conformational fluctuations in proteins. More recently, a wide range of experimental methods (such as fluorescence quenching and depolarization, nuclear magnetic resonance relaxation, infrared and Raman spectroscopy, and X-ray and inelastic neutron scattering) have been used to study the motions in proteins. However, it is primarily the application of theoretical methods, particularly molecular dynamics simulations, that have... 

We define the hydration number as the average number of water molecules in the first sphere about the metal ion. The residence time of these molecules is determined generally by the nature of the bonding to the metal ion. For the f-element cations, ion-dipole interactions result in fast exchange between the hydration layer and the bulk solvent. The techniques for studying the nature (number and/or structure) of the hydration shell can be classified as either direct or indirect methods. The direct methods include X-ray and neutron diffraction, luminescence and NMR (nuclear magnetic resonance) relaxation measurements. The indirect methods involve compressibility, NMR exchange and absorption spectroscopy measurements. 

The experimental results obtained by the nuclear magnetic resonance (NMR) method can be used to determine the nature of the chemical bonding and, particularly, the susceptibility and the carrier density. Nuclear magnetic resonance can be used to deduce information on the structure of a substance from the resonance line width and profile, from the spin-lattice relaxation, and from the shift of the resonance frequency. We shall consider some results obtained from the shift of the NMR line. 

Before discussing some raultiexponential relaxation functions, we will consider some specific aspects of theoretical methods describing the relaxation phenomena in nuclear magnetic resonance. Various methods have been proposed in the literature since the work of Bloembergen, Purcell, and Pound (1). Many of them have some common features like the use of density matrix theory, correlation functions, and their associated spectral density functions. People interested in the foundations of these theories will find some excellent book chapters and review articles in the literature (7-9,21). Slichter s book (Chapter 5) contains a very good introduction to the density matrix which is of crucial importance in all these theories (3). On the other hand, Abragam s book (2) remains a "Bible" in this field. The more recent book of Lenk (5) contains very concise definitions of many terms and concepts widely used in all the relaxation theories. Moreover, this author presents an excellent overview of many recent theories, especially those based on irreversible thermodynamics ... 

A number of methods have been used for determining Kg values cation selective electrodes, pH-metric methods, conductimetry, calorimetry, temperature-jump relaxation measurements, membrane conductance measurements, nuclear magnetic resonance, optical rotatory dispersion. The results listed in Tables 7—10 have been obtained by various methods and at different ionic strengths so they may not always be strictly comparable. However, the corrections are probably small and the experimental accuracy is generally the same or very similar within a certain ligand type. 

Nuclear magnetic resonance (NMR) spectroscopy is a most effective and significant method for observing the structure and dynamics of polymer chains both in solution and in the solid state [1]. Undoubtedly the widest application of NMR spectroscopy is in the field of structure determination. The identification of certain atoms or groups in a molecule as well as their position relative to each other can be obtained by one-, two-, and three-dimensional NMR. Of importance to polymerization of vinyl monomers is the orientation of each vinyl monomer unit to the growing chain tacticity. The time scale involved in NMR measurements makes it possible to study certain rate processes, including chemical reaction rates. Other applications are isomerism, internal relaxation, conformational analysis, and tautomerism. 

Nuclear Magnetic Resonance (NMR) Spectroscopy. Longitudinal and transverse relaxation times (Ti and T2) of 1H and 23Na in the water-polyelectrolytes systems were measured using a Nicolet FT-NMR, model NT-200WB. T2 was measured by the Meiboom-Gill variant of the Carr-Purcell method (5). However, in the case of very rapid relaxation, the free induction decay (FID) method was applied. The sample temperature was changed from 30 to —70°C with the assistance of the 1180 system. The accuracy of the temperature control was 0.5°C. 

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

Electron spin resonance (ESR) measures the absorption spectra associated with the energy states produced from the ground state by interaction with the magnetic field. This review deals with the theory of these states, their description by a spin Hamiltonian and the transitions between these states induced by electromagnetic radiation. The dynamics of these transitions (spin-lattice relaxation times, etc.) are not considered. Also omitted are discussions of other methods of measuring spin Hamiltonian parameters such as nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR), although results obtained by these methods are included in Sec. VI. 

Methods such as nuclear magnetic resonance (NMR), electron spectroscopy for chemical analysis (ESCA), electron spin resonance (ESR), infrared (IR), and laser raman spectroscopy could be used in conjunction with rate studies to define mechanisms. Another alternative would be to use fast kinetic techniques such as pressure-jump relaxation, electric field pulse, or stopped flow (Chapter 4), where chemical kinetics are measured and mechanisms can be definitively established. 

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