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

Abstract

Information about the interaction between nucleic acids and coat proteins in intact virus particles may be obtained by studying the restricted backbone dynamics of the incapsulated nucleic acids using 31P nuclear magnetic resonance (NMR) spectroscopy. In this article, simulations are carried out to investigate how reorientation of a rod-shaped virus particle as a whole and isolated nucleic acid motions within the virion influence the 31P NMR lineshape and transversal relaxation dominated by the phosphorus chemical shift anisotropy. Two opposite cases are considered on a theoretical level. First, isotropic rotational diffusion is used as a model for mobile nucleic acids that are loosely or partially bound to the protein coat. The effect of this type of diffusion on lineshape and transversal relaxation is calculated by solving the stochastic Liouville equation by an expansion in spherical functions. Next, uniaxial rotational diffusion is assumed to represent the mobility of phosphorus in a virion that rotates as a rigid rod about its length axis. This type of diffusion is approximated by an exchange process among discrete sites. As turns out from these simulations, the amplitude and the frequency of the motion can only be unequivocally determined from experimental data by a combined analysis of the lineshape and the transversal relaxation. In the fast motional region both the isotropic and the uniaxial diffusion model predict the same transversal relaxation as the Redfield theory. For very slow motion, transversal relaxation resembles the nonexponential relaxation as observed for water molecules undergoing translational diffusion in a magnetic field gradient. In this frequency region T2e is inversely proportional to the cube root of the diffusion coefficient. In addition to the isotropic and uniaxial diffusion models, a third model is presented, in which fast restricted nucleic acid backbone motions dominating the lineshape are superimposed on a slow rotation of the virion about its length axis, dominating transversal relaxation. In an accompanying article the models are applied to the 31P NMR results obtained for bacteriophage M13 and tobacco mosaic virus.

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

“…6. The static relaxation decay measured for 70% M13, can also be simulated for D = 1.4 Hz by using a previously discussed model (Magusin and Hemminga, 1993b). This shows that the outcome of spinning and nonspinning relaxation experiments can be interpreted consistently in terms of our models.…”

“…3 cannot be solved analytically and some approximation must be made. Theoretical investigation of the influence of rotational diffusion on transversal relaxation under nonspinning conditions, has shown that for very slow diffusion the relaxation rate may be much larger than the diffusion coefficient (Magusin and Hemminga, 1993b). In such cases, most spin density stays close to its initial orientation within times comparable with the transversal relaxation time.…”

“…From the general formula lIT2. AM2 T which relates T2e to the portion of the second moment AM2 modulated by motion with a short correlation time T (Pauls et al, 1985), we previously derived for fast restricted uniaxial diffusion about the length axis of the virus particle an approximate contribution 1/T'sA to the transversal relaxation rate under nonspinning conditions as (Magusin and Hemminga, 1993b)…”

“…The occurrence of motions can also explain the fact that Herzfeld and Berger's theory does not apply to the sideband intensities of dilute M13 gels. By analogy with motional narrowing under nonspinning conditions (Magusin and Hemminga, 1993b), it may be reasonably assumed that motions with frequencies less than 103 would not be able to significantly alter the sideband pattern caused by the 31p chemical shift anisotropy with a "size" (o/27r) 0-33 -11 of 34 kHz at 202.5 MHz. In contrast, dramatic line-broadening effects would be expected for motions in the 103 Hz region, because their frequencies would be in the order of the spinning rates applied (Schmidt et al, 1986;Schmidt and Vega, 1987).…”

“…As all M13 spectra recorded at various spinning rates, temperatures, and water contents contain well resolved sidebands, the motions that modify the sideband intensities should therefore have frequencies greater than 104 Hz. To extract motional information from the sideband pattern more quantitatively, the previously used model (Magusin and Hemminga, 1993b), in which the fast motions of the nucleic acid phosphodiesters are collectively described as restricted rotation about the virion length axis, is extended to MAS NMR experiments (Eq. 2).…”