Proteins motional correlation time

The Perrin plot enables us to obtain information concerning fluorophore motion. When the fluorophore is tightly bound to the protein, its motion will correspond to that of the protein. In this case, r will be equal to the protein rotational correlation time p, and A0 obtained experimentally from the Perrin plot will be equal to that measured at —45°C (Figure 11.3). 

Figure 14.1. Dependence of the spin-spin relaxation time (T2) and spin-lattice relaxation time (7)) on the motional correlation time xc. Approximate values of the expected line widths for small organic molecules, proteins, and lipids in a bilayer are indicated.

Steinhoff et al. (1989) measured the temperature and hydration dependence of the ESR spectra of hemoglobin spin-labeled at cysteine )8-93. They observed the critical temperature near 200 K, as described above, and the sensitivity of the spectrum to hydration level. Spectrum simulations suggested that there were two types of motion in the dry protein, a fast vibration of the label within a limited motion cone upon the addition of water, a hydration-dependent motion assigned to the fluctuations of the protein, of correlation time 10 sec in samples of high hydration and at 300 K. The temperature dependence of the motional properties of a spin probe (TEMPONE), diffused into hydrated single crystals, closely paralleled the motional properties of the label. This was taken to be evidence for coupling between the dynamical properties of the protein and the adjacent solvent. 

It is well known that 2D NOESY is an effective method to study the three-dimensional (3D) structure of large molecules, such as proteins which have long motional correlation times.70-71 Cross-dipolar interaction peaks in a NOESY spectrum rely on the cross-relaxation of the longitudinal magnetization during the mixing time. One can extract valuable information about intermolecular distances from the intensity of the NOESY cross-peaks. The appearance of... 

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. 

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... 

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... 

The NMRD profile of the protein adduct shows a largely increased relaxivity, with the dispersion moved at about 1 MHz and a relaxivity peak in the high field region. This shape is clearly related to the fact that the field dependent electron relaxation time is now the correlation time for proton relaxation even at low fields. The difference in relaxivities before and after the dispersion is in this case very small, and therefore the profile cannot be well fit with the SBM theory, and the presence of a small static ZFS must be taken into account 103). The best fit parameters obtained with the Florence NMRD program are D = 0.01 cm , A = 0.017 cm , t = 18x10 s, and xji =0.56 X 10 s. Such values are clearly in agreement with those obtained with fast-motion theory 101). 

The importance of the magnetic coupling is easily seen in Fig. 17 which shows two water proton MRD profiles for serum albumin solutions at the same composition (89). The approximately Lorentzian dispersion is obtained for the solution, and reports the effective rotational correlation time for the protein. The magnetic coupling between the protein and the water protons carries the information on the slow reorientation of the protein to the water spins by chemical exchange of the water molecules and protons between the protein and the bulk solution. When the protein is cross-linked with itself at the same total concentration of protein, the rotational motion of the protein... 

Miscellaneous bRC. - The bRC of R. sphaeroides contains one accessible cysteine at the H subunit (His H-156). Poluektov et al.m have bound a specific nitroxide spin label to this Cys and used temperature-dependent multifrequency (9 and 130 GHz) EPR to determine the motion of the protein. It was found that the restricted dynamics can be described as fast libration in a cone with a correlation time of >10 9 s. Several dynamically nonequivalent sites were observed that indicate conformational substates of local protein structure. 

Globular proteins are found to rotate in solution at frequencies close to those calculated for rigid spheres. The frequencies are usually expressed in terms of a rotational correlation time, , which is the reciprocal of the rate constant for the randomization of the orientation of the molecule by Brownian motion. For a rigid sphere, 4> is given by... 

The correlation times of the a carbons in the native protein compared to those of the denaturated biomolecule are much larger, indicating an increased segmental motion in the backbone of denatured ribonuclease. 

Another study used H T, T2 and 13C T, T p measurements to assess the molecular dynamics in dry and wet solid proteins bacterial RNAase, lysozyme and bovine serum albumin.115 All relaxation time data were analysed assuming three components for the molecular motion methyl group rotation and slow and fast oscillations of all atoms. An inhomogeneous distribution of correlation times was found for all samples, not surprisingly given the inhomogeneous nature of the samples. Interestingly, it was found that dehydration affected only the slow internal motions of the proteins and that the fast ones remained unaltered. 

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