Protein rotational correlation time

Berliner, L. J. 1978. Spin labeling in enzymology Spin-labeled enzymes and proteins. Rotational correlation times calculation. Methods Enzymol. 49 466 170. 

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. 

Figure 6 Effect of the increased rotational correlation time on the proton relaxivity of MP2269, a Gd111 chelate capable of noncovalent protein binding (Scheme 2). The lower NMRD curve was measured in water, whereas the upper curve was obtained in a 10%w/v bovine serum albumin solution in which the chelate is completely bound to the protein. The rotational correlation times calculated are rR=105ps in the nonbound state, and rR= 1,000 ps in the protein-bound state (t=35°C). For this chelate, the water exchange...

Fig. 11. HN(CO)CANH-TROSY experiment for establishing sequential 13Ca(t—1), 15N(/), Hn(0 connectivity in 13C/15N/2H labelled proteins. Delay durations A = l/ (4JHn) 2Tn = 23 33 ms, 2Ta = 22-28 ms, depending on rotational correlation time of the protein Tc= 1/(47C/C ) S = gradient + field recovery delay 0 < k < Ta/t2jmax-Phase cycling i = x = x, — x + States-TPPI 03 = x 4>rec. = x, — x.

When the protein rotational correlation time exceeds 15 ns, the upfield component of the JNH doublet broadens. In such cases the amide JNH coupling can be obtained from the displacement of the 15N chemical shift of the TROSY component (see Chapt. 10) relative to the one from a XH-decoupled HSQC experiment. 

In a protein-ligand complex the correlation time rc of the vector connecting the electron and nuclear spins, depends on the rotational correlation time of the protein-ligand complex, Tr, on the electron relaxation time, rs, and on the lifetime of the complex, rm [6, 9] ... 

Bo is the measurement frequency. Rapid exchange between the different fractions is assumed the bulk, water at the protein surface (s) and interior water molecules, buried in the protein and responsible for dispersion (i). In fact, protons from the protein surface exchanging with water lead to dispersion as well and should fall into this category Bulk and s are relevant to extreme narrowing conditions and cannot be separated unless additional data or estimations are available (for instance, an estimation of fg from some knowledge of the protein surface). As far as quadrupolar nuclei are concerned (i.e., and O), dispersion of Rj is relevant of Eqs. (62) and (63) (this evolves according to a Lorentzian function as in Fig. 9) and yield information about the number of water molecules inside the protein and about the protein dynamics (sensed by the buried water molecules). Two important points must be noted about Eqs. (62) and (63). First, the effective correlation time Tc is composed of the protein rotational correlation time and of the residence time iw at the hydration site so that... 

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... 

Reticulum ATPase [105,106], Owing to the long-lived nature of the triplet state, Eosin derivatives are suitable to study protein dynamics in the microsecond-millisecond range. Rotational correlation times are obtained by monitoring the time-dependent anisotropy of the probe s phosphorescence [107-112] and/or the recovery of the ground state absorption [113— 118] or fluorescence [119-122], The decay of the anisotropy allows determination of the mobility of the protein chain that cover the binding site and the rotational diffusion of the protein, the latter being a function of the size and shape of the protein, the viscosity of the medium, and the temperature. 

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... 

Fig. 5.45 shows the NMRD profiles obtained with Mn(II) bound to the protein concanavalin A. Both contact and dipolar relaxation are now dispersed at the same frequency, the rotational correlation time being longer than the electron relaxation time. After the beginning of the cos dispersion, the profile is dominated by the... 

The 2,2,6,6-tetramethylpiperidinoxyl radical (TEMPO) was first prepared in 1960 by Lebedev and Kazarnovskii by oxidation of its piperidine precursor.18 The steric hindrance of the NO bond in TEMPO makes it a highly stable radical species, resistant to air and moisture. Paramagnetic TEMPO radicals can be employed as powerful spin probes for elucidating the structure and dynamics of both synthetic and biopolymers (e.g., proteins and DNA) by ESR spectroscopy.19 Unlike solid-phase 1H-NMR where magic angle spinning is required in order to reduce the anisotropic effects in the solid-phase environment, solid-phase ESR spectroscopy can be conducted without specialized equipment. Thus, we conducted comparative ESR studies of various polymers with persistent radical labels, and we also determined rotational correlation times as a function of... 

Gd(III) chelates, the relatively low relaxivity is the consequence of the flexibility of the linker group between the Gd(III) chelate and the rigid dendrimer molecule (slow water exchange is also limitative). Internal flexibility has been also proved for certain non-covalently bound Gd(III) chelate - protein adducts. The tr value determined for MP-2269 bound to bovine serum albumin is 1.0 ns, one order of magnitude lower than the rotational correlation time of the protein molecule [50]. 

When the rotation of the Gd(III) chelate is substantially slowed down, one observes the typical high field peak around 20-60 MHz in the NMRD profiles. As an example, Fig. 10 shows the effect of non-covalent protein binding on the relaxivity under the experimental conditions applied, the small molecular weight chelate MP2269 is totally bound to bovine serum albumin which results in an increase in the rotational correlation time, and consequently in proton relaxivity [50]. 

In this section, some of the approaches described above for enhancing the sensitivity and information content of protein-ligand NOEs are demonstrated for relatively large protein-inhibitor complexes. In addition, we demonstrate that a medium-quality 3D X-filtered NOESY spectrum can be obtained for a large protein-inhibitor complex by using a stabilized, uniformly 13C/15N-labeled protein sample in conjunction with an elevated experimental temperature to increase the rotational correlation time of the protein-ligand complex. 

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