A theoretical study of rotational diffusion models for rod-shaped viruses. The influence of motion on 31P nuclear magnetic resonance lineshapes and transversal relaxation

RNA phosphodiester backbone dynamics of a perdeuterated cUUCGg tetraloop RNA from phosphorus-31 NMR relaxation analysis

We have analyzed the relaxation properties of all (31)P nuclei in an RNA cUUCGg tetraloop model hairpin at proton magnetic field strengths of 300, 600 and 900 MHz in solution. Significant H, P dipolar contributions to R (1) and R (2) relaxation are observed in a protonated RNA sample at 600 MHz. These contributions can be suppressed using a perdeuterated RNA sample. In order to interpret the (31)P relaxation data (R (1), R (2)), we measured the (31)P chemical shift anisotropy (CSA) by solid-state NMR spectroscopy under various salt and hydration conditions. A value of 178.5 ppm for the (31)P CSA in the static state (S (2) = 1) could be determined. In order to obtain information about fast time scale dynamics we performed a modelfree analysis on the basis of our relaxation data. The results show that subnanosecond dynamics detected around the phosphodiester backbone are more pronounced than the dynamics detected for the ribofuranosyl and nucleobase moieties of the individual nucleotides (Duchardt and Schwalbe, J Biomol NMR 32:295-308, 2005; Ferner et al., Nucleic Acids Res 36:1928-1940, 2008). Furthermore, the dynamics of the individual phosphate groups seem to be correlated to the 5' neighbouring nucleobases.

2D exchange 31P NMR spectroscopy of bacteriophage M13 and tobacco mosaic virus

Two-dimensional (2D) exchange 31P nuclear magnetic resonance spectroscopy is used to study the slow overall motion of the rod-shaped viruses M13 and tobacco mosaic virus in concentrated gels. Even for short mixing times, observed diagonal spectra differ remarkably from projection spectra and one-dimensional spectra. Our model readily explains this to be a consequence of the T2e anisotropy caused by slow overall rotation of the viruses about their length axis. 2D exchange spectra recorded for 30% (w/w) tobacco mosaic virus with mixing times < 1 s do not show any off-diagonal broadening, indicating that its overall motion occurs in the sub-Hz frequency range. In contrast, the exchange spectra obtained for 30% M13 show significant off-diagonal intensity for mixing times of 0.01 s and higher. A log-gaussian distribution around 25 Hz of overall diffusion coefficients mainly spread between 1 and 10(3) Hz faithfully reproduces the 2D exchange spectra of 30% M13 recorded at various mixing times in a consistent way. A small but notable change in diagonal spectra at increasing mixing time is not well accounted for by our model and is probably caused by 31P spin diffusion.

Analysis of 31P MAS NMR spectra and transversal relaxation of bacteriophage M13 and tobacco mosaic virus

Phosphorus magic angle spinning nuclear magnetic resonance (NMR) spectra and transversal relaxation of M13 and TMV are analyzed by use of a model, which includes both local backbone motions of the encapsulated nucleic acid molecules and overall rotational diffusion of the rod-shaped virions about their length axis. Backbone motions influence the sideband intensities by causing a fast restricted reorientation of the phosphodiesters. To evaluate their influence on the observed sideband patterns, we extend the model that we used previously to analyze nonspinning 31P NMR lineshapes (Magusin, P.C.M.M., and M. A. Hemminga. 1993a. Biophys. J. 64:1861-1868) to magic angle spinning NMR experiments. Backbone motions also influence the conformation of the phosphodiesters, causing conformational averaging of the isotropic chemical shift, which offers a possible explanation for the various linewidths of the centerband and the sidebands observed for M13 gels under various conditions. The change of the experimental lineshape of M13 as a function of temperature and hydration is interpreted in terms of fast restricted fluctuation of the dihedral angles between the POC and the OCH planes on both sides of the 31P nucleus in the nucleic acid backbone. Backbone motions also seem to be the main cause of transversal relaxation measured at spinning rates of 4 kHz or higher. At spinning rates less than 2 kHz, transversal relaxation is significantly faster. This effect is assigned to slow, overall rotation of the rod-shaped M13 phage about its length axis. Equations are derived to simulate the observed dependence of T2e on the spinning rate.

Analysis of 31P nuclear magnetic resonance lineshapes and transversal relaxation of bacteriophage M13 and tobacco mosaic virus

The experimentally observed 31P lineshapes and transversal relaxation of 15% (wt/wt) M13, 30% M13, and 30% tobacco mosaic virus (TMV) are compared with lineshapes and relaxation curves that are simulated for various types of rotational diffusion using the models discussed previously (Magusin, P. C. M. M., and M. A. Hemminga. 1993. Biophys. J. 64:1851-1860). It is found that isotropic diffusion cannot explain the observed lineshape effects. A rigid rod diffusion model is only successful in describing the experimental data obtained for 15% M13. For 30% M13 the experimental lineshape and relaxation curve cannot be interpreted consistently and the TMV lineshape cannot even be simulated alone, indicating that the rigid rod diffusion model does not generally apply. A combined diffusion model with fast isolated motions of the encapsulated nucleic acid dominating the lineshape and a slow overall rotation of the virion as a whole, which mainly is reflected in the transversal relaxation, is able to provide a consistent picture for the 15 and 30% M13 samples, but not for TMV. Strongly improved lineshape fits for TMV are obtained assuming that there are three binding sites with different mobilities. The presence of three binding sites is consistent with previous models of TMV. The best lineshapes are simulated for a combination of one mobile and two static sites. Although less markedly, the assumption that two fractions of DNA with different mobilities exist within M13 also improves the simulated lineshapes. The possible existence of two 31P fractions in M13 sheds new light on the nonintegral ratio 2.4:1 between the number of nucleotides and protein coat subunits in the phage: 83% of the viral DNA is less mobile, suggesting that the binding of the DNA molecule to the protein coat actually occurs at the integral ratio of two nucleotides per protein subunit.