Amplitude correlation time

AAS acrylate-styrene-acrylonitrile ACT amplitude correlation time... 

Polycarbonate (PC) serves as a convenient example for both, the direct determination of the distribution of correlation times and the close connection of localized motions and mechanical properties. This material shows a pronounced P-relaxation in the glassy state, but the nature of the corresponding motional mechanism was not clear 76 80> before the advent of advanced NMR techniques. Meanwhile it has been shown both from 2H NMR 17) and later from 13C NMRSI) that only the phenyl groups exhibit major mobility, consisting in 180° flips augmented by substantial small angle fluctuations about the same axis, reaching an rms amplitude of 35° at 380 K, for details see Ref. 17). 

Figure 12. (a) Plots of the Rouse amplitude correlation functions for several modes versus time... 

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

The amplitude and correlation time tc of the libration in the stacked state were estimated by using the diffusion in a cone model. The semiangle of the cone 6c at 20° C were obtained to be 22° and 26° for the TiL component and PBG- d2 and PBLG- d2, respectively. The tc values were obtained to be about 10 12 s at 19°C in both states. The 6C of r1L component is 4° smaller than that of PBLG- d2, showing that the amplitude of the libration in the stacked state is smaller than that in the free state due to the steric hindrance between the adjacent side chains forming the stacking... 

The amplitude and correlation time rc of the libration in the stacked state are estimated by using the diffusion in a cone model. The semiangles of the cone 6C are obtained to be 17°, 18°, and 19° for the riL component at 20, 40, and 60°C, respectively, while 20°, 22°, and 22° for the PBLG-yd2 at 23, 40, and, 55°C, respectively. The 6C in the stacking structure is smaller by 3° to 4° than that in the free state at the y position. Comparing the 6C value at the y position with that at the position in the stacked state, the 6C value at the y position is 5° smaller than that at the position at 20° C. This is because the Cf 2H bond is located at a more terminal part of the side chain than is the Cy 2H bond. The rc values were obtained to be about 10 11 s for both stacked and free states in this temperature range. There is little difference in the correlation time between the stacked and free states. 

Recent progress in protein dynamics studies by NMR was greatly facilitated by the invention of the model-free formalism [28, 32]. In this approach, the local dynamics of a protein are characterized by an order parameter, S, measuring the amplitude of local motion on a scale from 0 to 1, and the correlation time of the motion, T oc. The model-free expression for the correlation function of local motion reads... 

Fig. 16.7 Theoretical curves of the CCR rate as a function of the ribose pseudorotation phase angle P for three different pucker amplitudes (i/m = 30, 35 and 40°. A rotational correlation time of 1.5 ns and a C-H distance of 1.07 A has been used for the calculation.

Lakowicz et al.(]7] VB) examined the intensity and anisotropy decays of the tyrosine fluorescence of oxytocin at pH 7 and 25 °C. They found that the fluorescence decay was best fit by a triple exponential having time constants of 80, 359, and 927 ps with respective amplitudes of 0.29, 0.27, and 0.43. It is difficult to compare these results with those of Ross et al,(68) because of the differences in pH (3 vs. 7) and temperature (5° vs. 25 °C). For example, whereas at pH 3 the amino terminus of oxytocin is fully protonated, at pH 7 it is partially ionized, and since the tyrosine is adjacent to the amino terminal residue, the state of ionization could affect the tyrosine emission. The anisotropy decay at 25 °C was well fit by a double exponential with rotational correlation times of 454 and 29 ps. Following the assumptions described previously for the anisotropy decay of enkephalin, the longer correlation time was ascribed to the overall rotational motion of oxytocin, and the shorter correlation time was ascribed to torsional motion of the tyrosine side chain. 

Recent results show large variations in intramolecular rotations of tryptophan residues in proteins on the nanosecond time scale, ranging from complete absence of mobility to motions of considerable angular amplitudes. Among native proteins with internal tryptophan residues, wide angular amplitude rotations were observed only in studies of azurin,(28 29) where the correlation time of the rapid component was x = 0.51 ns.(28) The existence of... 

This effective Q,t-range overlaps with that of DLS. DLS measures the dynamics of density or concentration fluctuations by autocorrelation of the scattered laser light intensity in time. The intensity fluctuations result from a change of the random interference pattern (speckle) from a small observation volume. The size of the observation volume and the width of the detector opening determine the contrast factor C of the fluctuations (coherence factor). The normalized intensity autocorrelation function g Q,t) relates to the field amplitude correlation function g (Q,t) in a simple way g t)=l+C g t) if Gaussian statistics holds [30]. g Q,t) represents the correlation function of the fluctuat-... 

The molecular reorientational correlation time tends to dominate the overall correlation time of low molecular weight Gd(III) chelates, particularly in the high field region, and therefore represents a key parameter in governing their relaxivity. The effect of the increase in x on the shape and amplitude of the NMRD profiles was understood in detail early on and, as a consequence, the attempts at optimizing the relaxivity were primarily focused on slowing down the rotation by increasing the size of the... 

Fig. 9. NMRD profiles (25° C) of [GdD0TA(B0M)3(H20)] (open circles), its inclusion complex with P-cyclodextrin (filled circles) and of [GdD0TA(B0M)3(H20)]-HSA adduct (squares). The different shapes and amplitudes of the profiles are primarily due to the different rotational correlation times of the paramagnetic complexes.

Akaganeite particles Both Ti and T2 are strongly pH-dependent (Pigs. 17 and 19). The amplitudes of the longitudinal NMRD profiles drastically decrease when the pH increases from 3.35 to 9.45. The correlation time associated with the first dispersion is only weakly pH dependent, consistent with its former interpretation as an electron relaxation time. However, T2, the correlation time characteristic of the second dispersion, increases from 30 8 ns at pH 3.35 to 280 32 ns at pH 9.45, which eliminates its interpretation as a diffusion time T2 can be identified as a proton exchange time. 

In addition to the semiquantitative approach, more quantitative analytical approaches have been reported. For example, in the fast motion regime (t 10 11—10 9 s at X-band), one can compute the nitroxide rotational correlation time based on the measured line-widths and amplitudes (Marsh, 1981 Qin et al., 2001 Xi et al., 2008). Furthermore, it is possible to simulate a nitroxide spectrum based on quantum mechanics and specific motional models (Columbus et al., 2001 Grant et al., 2009 Hustedt et al., 1993 Liang et al., 2000 Qin et al., 2006 Schneider and Freed, 1989). The details of these advanced analysis techniques are not discussed here, interested readers are instead referred to a recent review (Sowa and Qin, 2008) and the relevant literatures. 

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