Slow rotational motion

G. B. Strambini and W. C. Galley, Detection of slow rotational motions of proteins by steady-state phosphorescence anisotropy, Nature 260, 554-555 (1976). 

As noted in Section III.C.2, the adiabatic method allows one to separate "slow" rotational motion from "fast" vibrational motion. The evaluation of vibrational distributions that has been described is based on this feature of adiabatic theory. In many cases one can also similarly ignore "slow" bending motion. However, advances in experimental methods have led to measurements of rotational distributions of photofragments (see Okabe and Jackson, this volume) and thus the evaluation of these distributions has become a timely and interesting problem. 

Very recently an anisotropic scattering pattern from photo-excited myoglobin was observed, including its temporal change from 100 ps to 1 ps [37]. The relatively slow rotational motion of myoglobin made this observation possible with the 100 ps time resolution available at a synchrotron source. 

With a slow rotating motion to avoid burning, the part to be buffed is pressed to the revolving buffing wheel to which an abrasive compound has been applied. Buffing operations are used on both thermoplastic and thermosetting materials, usually with two or three sized abrasives and at a controlled speed. 

Slow rotational motion short-time expansions... 

In accordance with the separation of fast vibrational from slow rotational motions, the unperturbed vibration is described by the Hamiltonian operator + Fh + Knh d it is driven by the... 

Nitrogen-15 and Deuterium Substituted Spin Labels for Studies of Very Slow Rotational Motion... 

CPI labeled with eosin-SCN in the non activated mode restored photophosphorylation in partially depleted EDTA-chloroplasts and fully depleted NaBr-particles (10). Wheras in the case of the EDTA-particles we could observe very slow rotational motion of the reconstituted eosin-CFI relative to the membrane, in NaBr-part ides we could not detect any rotational motion (up to 500 as) of reconstituted eosin-CFI. We also studied the rotational diffusion of another extrinsic protein of the thylakoid membrane, the ferredoxin-NADP-oxidoreductase (ll), which is probably located in the same stromal region of stacked chloroplasts as CPI and we found very rapid rotation (< 1/is). Only after addition of ferredoxin rotational correlation time decreased to 40 /is. This was interpreted to indicate formation of a ternary complex between ferredoxin-NADP-oxidoreductase ferredoxin and PSI. This revealed rather high lipid fluidy in thylakoids. We tend to assume that the low rotational mobility of the CP0-CF1 complex is caused either by self aggregation or strong interaction with other membrane proteins. 

Although the underlying physics and mathematics used to convert relaxation rates into molecular motions are rather complex (Lipari and Szabo, 1982), the most important parameter obtained from such analyses, the order parameter. S 2, has a simple interpretation. In approximate terms, it corresponds to the fraction of motion experienced by a bond vector that arises from slow rotation as a rigid body of roughly the size of the macromolecule. Thus, in the interior of folded proteins, S2 for Hn bonds is always close to 1.0. In very flexible loops, on the other hand, it may drop as low as 0.6 because subnanosecond motions partially randomize the bond vector before it rotates as a rigid body. 

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. 

Figure 5.11 Effect of a slowing of the rate of rotational motion on the simulated ESR spectrum of a typical nitroxide spin label. Broadening becomes even more pronounced and non-uniform as the rate is further decreased.

The optimization of the rotational motion of Gd111 complexes in the objective of increasing their proton relaxivity has been in the center of very intensive research in the last two decades. At intermediate magnetic fields typically used in the clinics (20-60 MHz), the SBM theory predicts a significant relaxivity increase with respect to small molecular weight chelates when the rotation is slowed down. In this perspective, a large number of macromolecular chelates have been investigated. The three... 

As an example, infrared spectroscopy has shown that the lowest stable hydration state for a Li-hectorite has a structure in which the lithium cation is partially keyed into the ditrigonal hole of the hectorite and has 3 water molecules coordinating the exposed part of the cation in a triangular arrangement (17), as proposed in the model of Mamy (J2.) The water molecules exhibit two kinds of motion a slow rotation of the whole hydration sphere about an axis through the triangle of the water molecules, and a faster rotation of each water molecule about its own C axis ( l8). A similar structure for adsorbed water at low water contents has been observed for Cu-hectorite, Ca-bentonite, and Ca-vermiculite (17). 

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. 

Rose and Benjamin studied the water dipole and the water H-H vector reorientation dynamics at the water/Pt( 100) interface and the results are reproduced in Fig. 4. As in the case of the translational diffusion, the effect of the surface is to significantly slow down the adsorbed water layer. We note that the effect is very short range, and that the rotational motion of water molecules in the second layer is already very close to the one in bulk water. 

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... 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

---