Anisotropic rotation

Huntress WT 1970 The study of anisotropic rotation of molecules in liquids by NMR quadrupolar relaxation Adv. Magn. Reson. 4 1-37... 

Time Resolved Fluorescence Depolarization. In Equation 3, it is assumed that the polarization decays to zero as a single exponential function, which is equivalent to assuming that the molecular shape is spherical with isotropic rotational motion. Multiexponential decays arise from anisotropic rotational motion, which might indicate a nonspherical molecule, a molecule rotating in a nonuniform environment, a fluorophore bound to tbe molecule in a manner that binders its motion, or a mixture of fluorophores with different rotational rates. 

Another example comes from the work of Johnson, et a/.18 These workers studied spin labels dissolved in lipid bilayer dispersions of dipalmitoylphos-phatidylcholine and cholesterol (9 1 by weight) in the hope that anisotropic rotational diffusion of the spin label would mimic the motion of the bilayer components. In addition to 5-DS, which is sensitive to rotational motion about the NO bond, they used the steroidal nitroxide 8, which tends to rotate about an axis perpendicular to the N-O bond. ESR measurements were carried out at both 9 and 35 GHz and at temperatures ranging from 30 to 30 °C. Rather different results were obtained with the two spin labels, largely as a result of the different axes of rotation. Because the rotation rates were very slow, ESR spectra appeared as powder patterns rather than isotropic spectra and special methods were needed to extract the motional data. 

While the assumption of an isotropic rotational motion is reasonable for low molecular weight chelates, macromolecules have anisotropic rotation involving internal motions. In the Lipari-Szabo approach, two kinds of motion are assumed to affect relaxation a rapid, local motion, which lies in the extreme narrowing limit and a slower, global motion (86,87). Provided they are statistically independent and the global motion is isotropic, the reduced spectral density function can be written as ... 

In most cases, fluorescent molecules undergo anisotropic rotations because of their asymmetry. A totally asymmetric rotor has three different rotational diffusion coefficients, and in cases where the absorption and emission transition moments are not directed along one of the principal diffusion axes, the decay of r(t) is a sum of five exponentials (see Box 5.3). 

When determining QSC values of dimeric lithium phenolates in solution, the value has to be corrected for anisotropic rotational diffusion as the complexes have an oblate, non-spherical shape . The Li2A2S2 complex of 2,6-di-f-butylphenolate has a Li QSC value of ca 280 kHz in a number of different solvents. The 2,6-dimethylphenolate system is present as an Li2A2S4 complex in THF and apparently as an L12A2S2 complex in DEE. These complexes have QSC values of 170 and 270 kHz in the two solvents, respectively. 

Eq. (3.21) discussed in Section 3.3.2 is only valid if the motion of the molecules under study has no preferential orientation, i.e. is not anisotropic. Strictly speaking, this applies only for approximately spherical bodies such as adamantane. Even an ellipsoidal molecule like trans-decalin performs anisotropic motion in solution it will preferentially undergo rotation and translation such that it displaces as few as possible of the other molecules present. This anisotropic rotation during translation is described by the three diagonal components Rlt R2, and R3 of the rotational diffusion tensor. If the principal axes of this tensor coincide with those of the moment of inertia - as can frequently be assumed in practice - then Rl, R2, and R3 indicate the speed at which the molecule rotates about its three principal axes. 

Figure 4. Experimental (center) and best-fit simulated (right middle and left middle) H-NMR spectra of DABES on silica from a 2% treating solution (approximately monolayer coverage). On the right-hand side, the fractions of rigid and mobile components were varied from 30% rigid (upper) to 10% rigid (lower). On the left-hand side, the anisotropic rotational rates for the faster rotation

Explicit expressions for Tivr were derived from models for the interactions of a proton with the local magnetic fields of its environment. Two types of environments which are important in hemoproteins will be discussed. First, if the water molecule is in a diamagnetic environment, dipole-dipole coupling between the two protons modulated by the anisotropic rotational tumbling of the molecule will be the dominant relaxation mechanism. The resulting relaxation rate is (Solomon (102) Abragam (/))... 

V02+ substituted PCA (V02+ substituted for Gd3+,Mn2+, etc.) BPCA rotational motion, including specifics of anisotropic rotation (TR(XjyjZ)).Also details of BPCA-protein interactions. 

The interest in alkaloids of the nicotine group continues. Convenient syntheses of 7V-CD3-labelled nicotine and nicotine analogues have been described.38 The 13C n.m.r. spin-lattice relaxation times of nicotine have been analysed in terms of anisotropic rotational diffusion constants. The results agree best with a dihedral angle of H(2 )-C(2 )-C(3)-C(2) of ca 0°.39 Dithiodinicotyrine , obtained... 

Zhang J, Jonas J. NMR Study of the geometric confinement effects of the anisotropic rotational diffusion of acetonitrile-dj. J Phys Chem 1993 97 8812-8815. 

Figure 2. Theoretical spectra of NO2 anisotropically rotating about its x axis (b), y axis (c), and z axis (d). The spectra were calculated for Brownian rotational diffusion model by using R// = 5.27 X 10 sec- Rj = 5.27 x 10 sec and T2 =3.0 G. For isotropic rotation (a), R// = Rj = 1.67 X 10 sec l and T2 l=3.0 G were used. The rotational diffusion values used through (a) to (d) correspond to a constant value of r =l x 10 sec v, 9 167 GHz...

Membrane fluidity is determined by following anisotropic rotation of fluorescent or spin probes. Liquid-crystalline (or fluid) to gel thermotropic phase transition of lipids (Figure 1) (cf. Section 3.1.1 l)in liposomes or intact biomembranes can be followed by Fourier transform infrared (FTIR) spectroscopy or differential scanning calorimetry (DSC). 

When a molecule is rigid and rotates equally well in any direction (isotropically), all the carbon relaxation times (after correction for the number of attached protons) should be nearly the same. The nonspherical shape of a molecule, however, frequently leads to preferential rotation in solution around one or more axes (anisotropic rotation). For example, toluene prefers to rotate around the long axis that includes the methyl, ipso, and para carbons, so that less mass is in motion. As a result, on average, these carbons (and their attached protons) move less in solution than do the ortho and meta carbons, because atoms on the axis of rotation remain stationary during rotation. The more rapidly moving ortho and meta carbons... 

---