Rotational diffusion small-molecule

While it is always possible to find the best-fit diffusion tensor from the correlation functions of a reorienting molecule, the rotational dynamics need not be diffusive. For example, the rotation of small molecules in solution can be much more inertial in character than one would ordinarily expect for a macromolecule [32]. A more relevant scenario to protein dynamics would be instances where a single diffusion tensor cannot describe global tumbling because of conformational transitions that change the shape of the protein. However, for the small, well-folded proteins considered in [13] (GB3, ubiquitin, binase and lysozyme), the overall rotation was well characterized as diffusion, as monitored by the comparisons between MD and diffusional estimates of dioc n, 1) for / = 1 to 8. 

Molecular dynamics and transport phenomena in isotropic liquids are reasonably well understood. In the case of small prolate, ellipsoidal molecules, the rotational diffusion of molecules is very fast. The rotational correlation time r corresponding to rates of diffusion about the ellipsoid s major axes is in the range 10 -10 s. Intramolecular transitions among conformers - isomers formed by rotating dihedral angles defined by three consecutive chemical bonds within flexible molecules -are also very fast (conformer lifetimes of 10 s). Center-of-mass translational... 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

Two solutes were used to study diffusion in liquids, methylbenzene, which is a small molecule that can be approximated as a sphere, and a liquid crystal that is long and rodlike. The two solutes were found to move and rotate in all directions to the same extent in benzene. In a liquid crystal solvent the methylbenzene again moved and rotated to the same extent in all directions, but the liquid crystal solute moved much more rapidly along the long axis of the molecule than it... 

Our approach is to use the two-dimensional relaxation and diffusion correlation experiments to further enhance the resolution of different components. It is important to note that the correlation experiment, e.g., the Ti-T2 experiment, is different from two experiments of and T2 separately. For instance, the separate Ti and T2 experiment, in general, cannot determine the T1(/T2 ratio for each component. On the contrary, a component with a particular Tj and T2 will appear as a peak in the 2D 7i-T2 and the Ti/T2 ratio can be obtained directly. For example, small molecules often exhibit rapid rotation and diffusion in a solution and Ti/T2 ratio tends to be close to 1. On the other hand, the rotational dynamics of larger molecules such as proteins can be significantly slow compared with the Larmor frequency and resulting in a Ti/T2 ratio significantly larger than 1. 

Small-step rotational diffusion is the model universally used for characterizing the overall molecular reorientation. If the molecule is of spherical symmetry (or approximately this is generally the case for molecules of important size), a single rotational diffusion coefficient is needed and the molecular tumbling is said isotropic. According to this model, correlation functions obey a diffusion type equation and we can write... 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

A small step rotational diffusion model has been used to describe molecular rotations (MR) of rigid molecules in the presence of a potential of mean torque.118 120,151 t0 calculate the orientation correlation functions, the rotational diffusion equation must be solved to give the conditional probability for the molecule in a certain orientation at time t given that it has a different orientation at t = 0, and the equilibrium probability for finding the molecule with a certain orientation. These orientation correlation functions were found as a sum of decaying exponentials.120 In the notation of Tarroni and Zannoni,123 the spectral denisities (m = 0, 1, 2) for a deuteron fixed on a reorienting symmetric top molecule are ... 

However, picosecond resolution is insufficient to fully describe solvation dynamics. In fact, computer simulations have shown that in small-molecule solvents (e.g. acetonitrile, water, methyl chloride), the ultrafast part of solvation dynamics (< 300 fs) can be assigned to inertial motion of solvent molecules belonging to the first solvation layer, and can be described by a Gaussian func-tiona) b). An exponential term (or a sum of exponentials) must be added to take into account the contribution of rotational and translational diffusion motions. Therefore, C(t) can be written in the following form ... 

For macromolecules (or small molecules in viscous solvents at a low temperature) in a high magnetic field, wqTc 3> 1. At this spin-diffusion limit the rotating-frame cross-relaxation rate is twice as fast as in the laboratory frame, and the rates are of the opposite sign, 5 = —1/2 (fig. 1, top). 

For chromophores that are part of small molecules, or that are located flexibly on large molecules, the depolarization is complete—i.e., P = 0. A protein of Mr = 25 kDa, however, has a rotational diffusion coefficient such that only limited rotation occurs before emission of fluorescence and only partial depolarization occurs, measured as 1 > P > 0. The depolarization can therefore provide access to the rotational diffusion coefficient and hence the asymmetry and/or degree of expansion of the protein molecule, its state of association, and its major conformational changes. This holds provided that the chromo-phore is firmly bound within the protein and not able to rotate independently. Chromophores can be either intrinsic—e.g., tryptophan—or extrinsic covalently bound fluorophores—e.g., the dansyl (5-dimethylamino-1-naphthalenesulfonyl) group. More detailed information can be obtained from time-resolved measurements of depolarization, in which the kinetics of rotation, rather than the average degree of rotation, are measured. For further details, see Lakowicz (1983) and Campbell and Dwek (1984). 

This study is the first where semiquantitative use of relaxation data was made for conformational questions. A similar computer program was written and applied to the Tl data of several small peptides and cyclic amino acids (Somorjai and Deslauriers, 1976). The results, however, are questionable since in all these calculations it is generally assumed that the principal axis of the rotation diffusion tensor coincides with the principal axis of the moment of inertia tensor. Only very restricted types of molecules can be expected to obey this assumption. There should be no large dipole moments nor large or polar substituents present. Furthermore, the molecule should have a rather rigid backbone, and only relaxation times of backbone carbon atoms can be used in this type of calculation. 

Macromolecules display continuous motions. These motions can be of two main types the molecule can rotate on itself, following the precise axis of rotation, and it can have a local flexibility. Local flexibility, also called internal motions, allows different small molecules, such as solvent molecules, to diffuse along the macromolecule. This diffusion is generally dependent on the importance of the local internal dynamics. Also, the fact that solvent molecules can reach the interior hydrophobic core of macromolecules such as proteins clearly means that the term hydrophobicity should be considered as relative and not as absolute. Internal dynamics of proteins allow and facilitate a permanent contact between protein core and the solvent. Also, this internal motion permits small molecules such as oxygen to diffuse within the protein core. Since oxygen is a collisional quencher, analyzing the fluorescence data in the presence of different oxygen concentrations yields information on the internal dynamics of macromolecules. 

In view of these results for binary glasses composed of molecules with different masses respectively different Tg, one may speculate that the isotropic reorientation of the small molecules results from translational diffusion in an essentially rigid glassy matrix formed by the large molecules, i.e., the diffusional process may be probed by 2H NMR via rotational-translational coupling.183 Finally, we note that the stimulated-echo technique was also applied to study the main relaxation in... 

Rotational Diffusion in a Shear Field Consider for a moment rod-shaped particle of unit length. The orientation of the rod, u, can be specified by a unit vector u directed along its axis with spherical polar coordinates, Q = (0, used to describe its orientation. Because the solvent molecules are expected to frequently collide with the rod, it should exhibit a random walk on the surface of the unit sphere (i.e., r = 1.0). Debye [15] in 1929 developed a model for the reorientation process based on the assumption that collisions are so frequent that a particle can rotate through only a very small angle before having another reorienting collision (i.e., small step diffusion). 

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