Relaxations times measuring dynamics

NMR possesses another facet, the nuclear relaxation times (Ti, T2, etc.), which allows measurement of dynamic parameters such as correlation times, activation energies, diffusion constants, etc. Relaxation times are linked to through  

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Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

NMR relaxation time measurements (7) and T2) can provide valuable information for investigating the molecular dynamics of water in food systems. However, a number of factors can seriously complicate the analysis... 

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

A unique feature of NMR is its sensitivity for dynamic processes. Using different techniques, from the well-known lineshape analysis to the application of relaxation time measurements, the correlation times of dynamic processes which can be studied span a... 

Macromolecule 3D structure Macromolecular dynamics Structure of articulated macromolecules (e.g. multimeric or membrane-bound receptors) 2D/3D/4D NMR Relaxation time measurements TROSY... 

Ligand- macromolecule complex Stoichiometry of complex Kinetics of binding Location of interacting sites Orientation of bound ligand Structure of complex Dynamics of complex Chemical shift titration Line width, titration analysis HSQC, isotope editing NOE docking 3D/4D NMR Relaxation time measurements... 

All together relaxation time measurements are a powerful tool to study the dynamic behaviour of polymers in the solid state. 

In early years of NMR, extensive studies of molecular dynamics were carried out using relaxation time measurements for spin 1/2 nuclei (mainly for 1H, 13C and 31P). However, difficulties associated with assignment of dipolar mechanisms and proper analysis of many-body dipole-dipole interactions for spin 1/2 nuclei have restricted their widespread application. Relaxation behaviour in the case of nuclei with spin greater than 1/2 on the other hand is mainly determined by the quadrupolar interaction and since the quadrupolar interaction is effectively a single nucleus property, few structural assumptions are required to analyse the relaxation behaviour. 

The temperature dependence of the quadrupole echo 2H NMR lineshape and 2H NMR spin-lattice relaxation time measurements demonstrated that the hydrogen bonding arrangement is dynamic. 

NMR is unique in that it can provide detailed and specific information on molecular dynamics in addition to structural information. The use of relaxation time measurements allows the relative mobility of individual atomic positions within a macromolecule to be determined. The d3mamic information obtained includes not only the rates or frequencies of internal motions but also their amplitudes. Such amplitudes are often expressed by order parameters. Not surprisingly, it is observed in many cases that the termini of proteins are more flexible than internal regions. More interestingly, NMR has provided a number of examples where internal loops in proteins have been shown to have dynamics that may be associated with their function. A good example of this is HIV protease, where NMR studies have identified reduced-order parameters in the flap region of the molecule that may reflect flexibility to allow entry of substrates or inhibitors into the active site. 

Two specific relaxation approaches are discussed the first approach involves measurement of the NMR longitudinal and transverse relaxation times (Ti and T2) wheareas the second approach involves measurement of transferred NOE intensities. In the relaxation time measurement approach, the distance information is assumed known and the focus is on dynamic information. In the transferred NOESY approach, the motion is considered constant and the focus is on the structural information. These are discussed in terms of two different biological systems. 

Analysis of the NMR parameters and the dynamic processes depends on the exchange rates. The basic one-dimensional band-shape analysis is best suited to intermediate rates (10—10 per s). Slow exchange rates (—0.1-10 per s) are most accurately measured by using magnetization transfer experiments and Ti-relaxation times. Fast dynamic processes (> 10 per s) can be elucidated by investigating the spin-spin relaxation times. 

J. Engelke and H. Ruterjans, Recent Developments in Studying the Dynamics of Protein Structures from N and C Relaxation Time Measurements , p. 357... 

Dynamics of nano- to picosecond proton transfer processes in the N labeled polycrystalline tetraaza[14]annulene have been studied by a combination of 9.1 MHz N Ti relaxation time measurements under CPMAS conditions and by 46 MHz H Ti relaxation time measurements of a static sample of a doubly deuterated sample. 

NMR spectroscopists are also interested in nuclear spin relaxation times. The relaxation time measures the time required for an excited nucleus to return to the ground state. Two types of relaxation times are involved spin-lattice relaxation time Ti, the time constant for thermal equilibrium between the nuclei and crystal lattice, and spin-spin relaxation time Tz, the time constant for thermal equilibrium between nuclei themselves. Information on molecular dynamics can be obtained from these relaxation times. Generally, T Tz for low-viscosity liquids and T Tz for solids. A combination of information in molecular dynamics (from relaxation times), molecular structure (from spin-spin interaction), molecular identification (from resonance frequency and chemical shift), and spin density (from signal intensity) make the NMR an extremely versatile tool. 

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