Anisotropy motions occur

Quantitative information can be obtained only if the time-scale of rotational motions is of the order of the excited-state lifetime r. In fact, if the motions are slow with respect to r(r ro) or rapid (r 0), no information on motions can be obtained from emission anisotropy measurements because these motions occur out of the experimental time window. 

Experiments involving anisotropy of phosphorescence or of the absorption of the triplet state rely upon the same principles as the measurement of fluorescence anisotropy. All are based upon the photoselection of molecules by polarized light and the randomization of polarization due to Brownian motion occurring on the time scale of the excited state. Anisotropy is defined as... 

In the case that the macromolecule is nonspherical or sidechain or segmental motions occur, then the anisotropy will decay as a sum of exponential functions. The work of Kinosita etal. deals with the case in which there are restricted motions. The anisotropy decay function becomes... 

In the review period there have been many studies of molecular motion using analysis of chemical shift anisotropy lineshapes. One that nicely illustrates what is currently possible concerns the motion of 13CO intercalated in C o.9 This is a particularly interesting example as both the CO and C6o molecules undergo reorientation, with the onset of motion occurring at different temperatures for the two species. Furthermore, the work uses a prior calculation of the potential... 

The correlation function, <-P2[am(0) ( )]>. provides a measure of the internal motions of particular residues in the protein.324 333 Figure 46 shows the results obtained for Trp-62 and Trp-63 from the stochastic boundary molecular dynamics simulations of lysozyme used to analyze the displacement and velocity autocorrelation functions. The net influence of the solvent for both Trp-62 and Trp-63 is to cause a slower decay in the anisotropy than occurs in vacuum. In vacuum, the anisotropy decays to a plateau value of 0.36 to 0.37 (relative to the initial value of 0.4) for both residues within a picosecond. In solution there is an initial rapid decay, corresponding to that found in vacuum, followed by a slower decay (without reaching a plateau value) that continues beyond the period (10 ps) over which the correlation function is ex-... 

Protein motions in single FlAsH-labeled CaM molecules tethered to glass slides have been measured by anisotropy using time-correlated single-photon counting in a confocal microscope [46]. Average anisotropy values were similar to bulk measurements but showed wide variability from molecule to molecule. Decay rates indicated that rapid-scale protein motions occur in the N-terminal domain on a nanosecond timescale but limited signal-to-noise levels precluded detailed analysis. Comparable experiments with CaM labeled with Texas Red failed to detect such motions because of faster dye rotation, independent of the protein motions. 

ANISOTROPY OF THE NMR RESPONSE WHEN MOLECULAR MOTIONS OCCUR... 

These earlier papers did not take into account the fact that the oriented polymers were partially oriented. It is therefore now necessary to extend the previous discussion of the aggregate model to the situation where molecular motion occurs. This has been done independently by Olf and Peterlin, McBrierty and Douglass, and Folkes and Ward. McBrierty and Douglass paper gives a formal theoretical treatment, as part of a general discussion of the influence of molecular motions on Tj, Tz and the other papers are particularly concerned with an analysis of the effects of molecular motion on the second moment anisotropy but nevertheless provide explicit results for special types of motion. The results are then applied to oriented mats of polyethylene single crystals and to... 

The chemical shift of a nuclear spin is a tensorial quantity. Its value depends on the orientation of the electronic distribution about the nucleus with respect to the external magnetic field. In a liquid, due to the rapid molecular motions, this interaction is averaged to zero and the observed chemical shift is the trace of the tensor. In contrast, in a powder, in the absence of motions, all the orientations have the same probability and the signal obtained for each carbon is the sum of the elementary chemical shifts corresponding to the different orientations. When local motions occur in the bulk below 7g, they usually induce a partial averaging of the chemical shift anisotropy. 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

Cross-polarization is more effective for rigid systems than for mobile structures. When extensive motion occurs, the C-H dipolar interactions are reduced, and this reduction causes a lower cross-polarization rate. In some systems, mobile components can exhibit sufficient motional anisotropy to permit cross-polarization because the anisotropy can impart a residual static component to the overall motion [69]. This appears to be the case for elastomeric systems. 

Equations (8.25) to (8.28) are no longer valid in the case of hindered rotations occurring in anisotropic media such as lipid bilayers and liquid crystals. In these media, the rotational motions of the probe are hindered and the emission anisotropy does not decay to zero but to a steady value rc0 (see Chapter 5). For isotropic rotations (rod-like probe), assuming a single correlation time, the emission anisotropy can be written in the following form ... 

Anisotropy of phosphorescence then becomes a powerful tool to study the overall rotation of large biological macromolecules and to study segmental motions which occur in these structures. 

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