On the dielectrically observable consequences of the diffusional motions of lipids and proteins in membranes

The dielectric properties of suspensions of intact cells of Methylophilus methylotrophus, Paracoccus denitrificans and Bacillus subtilis have been measured in the frequency range 1 kHz to 13 MHz. All possess a pronounced dispersion corresponding in magnitude and relaxation time to the "beta-dispersion" in a terminology defined by Schwan [Adv. Biol. Med. Phys. 5:147-209 (1957)]. The latter two strains, but not M. methylotrophus, also possess a substantial alpha-dispersion. The relaxation time of the beta-dispersion of B. subtilis is significantly lower than that of the other two strains, due to the higher internal K+ content of this Gram-positive organism. Treatment of P. denitrificans or B. subtilis with lysozyme greatly reduces the magnitude of the alpha-dispersion; in the latter case it is virtually abolished. The magnitude of both the alpha- and beta-dispersions of protoplasts of these organisms is significantly decreased by treatment with the cross-linking reagent glutaraldehyde, indicating that diffusional motions of the lipids and/or proteins in the protoplast membranes contribute to the dielectric relaxations observed in this frequency range. Such motions cannot be unrestricted, as in the "fluid mosaic" model, since the relaxation times of the lipids and proteins, if restricted by hydrodynamic forces alone, should then correspond, in protoplasts of this radius (0.4-0.5 micron), to approximately 10 Hz. Even after treatment of the (spherical) protoplasts with glutaraldehyde, the breadth of the remaining beta-dispersion is still significantly greater than (a) that of a pure Debye dispersion and (b) that to be expected solely from a classical Maxwell-Wagner-type mechanism. It is recognised that the surfaces of the protein complexes in such membranes extend significantly beyond the membrane surface as delineated by the phospholipid head-groups; such molecular granularity can in principle account for the broadened dielectric relaxations in the frequency range above 1 kHz, in terms of the impediment to genuinely tangential counterion relaxation caused by the protruding proteins themselves. The relaxation time of a previously observed, novel, low-frequency, glutaraldehyde-sensitive (mu-) dispersion in bacterial chromatophore suspensions, as well as that of their alpha-dispersion, is significantly increased by increasing the aqueous viscosity with glycerol. This finding is consistent with the view that, from a dielectric standpoint, the motions of charged proteins (and lipids) in biological membranes are rather tightly coupled to those of the adjacent ions and dipoles in the electric double layer.(ABSTRACT TRUNCATED AT 400 WORDS)     

Conformational change in the activation of lipase: an analysis in terms of low-frequency normal modes.

The interfacial activation of Rhizomucor miehei lipase (RmL) involves the motion of an alpha-helical region (residues 82-96) which acts as a "lid" over the active site of the enzyme, undergoing a displacement from a "closed" to an "open" conformation upon binding of substrate. Normal mode analyses performed in both low and high dielectric media reveal that low-frequency vibrational modes contribute significantly to the conformational transition between the closed and open conformations. In these modes, the lid displacement is coupled to local motions of active site loops as well as global breathing motions. Atomic fluctuations of the first hinge of the lid (residues 83-84) are substantially larger in the low dielectric medium than in the high dielectric medium. Our results also suggest that electrostatic interactions of Arg86 play an important role in terms of both the intrinsic stability of the lid and its displacement, through enhancement of hinge mobility in a high dielectric medium. Additional calculations demonstrate that the observed patterns of atomic fluctuations are an intrinsic feature of the protein structure and not dependent on the nature of specific energy minima.     

Reconstituted syntaxin1a/SNAP25 interacts with negatively charged lipids as measured by lateral diffusion in planar supported bilayers.

According to the soluble N-ethylmaleimide-sensitive factor (NSF)-attachment protein (SNAP) receptor hypothesis (SNARE hypothesis), interactions between target SNAREs and vesicle SNAREs (t- and v-SNAREs) are required for membrane fusion in intracellular vesicle transport and exocytosis. The precise role of the SNAREs in tethering, docking, and fusion is still disputed. Biophysical measurements of SNARE interactions in planar supported membranes could potentially resolve some of the key questions regarding the mechanism of SNARE-mediated membrane fusion. As a first step toward this goal, recombinant syntaxin1A/SNAP25 (t-SNARE) was reconstituted into polymer-supported planar lipid bilayers. Reconstituted t-SNAREs in supported bilayers bound soluble green fluorescent protein/vesicle-associated membrane protein (v-SNARE), and the SNARE complexes could be specifically dissociated by NSF/alpha-SNAP in the presence of ATP. The physiological activities of SNARE complex formation were thus well reproduced in this reconstituted planar model membrane system. A large fraction (~75%) of the reconstituted t-SNARE was laterally mobile with a lateral diffusion coefficient of 7.5 x 10(-9) cm(2)/s in a phosphatidylcholine lipid background. Negatively charged lipids reduced the mobile fraction of the t-SNARE and the lipids themselves. Phosphatidylinositol-4,5-bisphosphate was more effective than phosphatidylserine in reducing the lateral mobility of the complexes. A model of how acidic lipid-SNARE interactions might alter lipid fluidity is discussed.     

The analysis of NMR relaxation data in terms of multiple internal motions

A novel formalism for estimating the complex motions of proteins and other flexible macromolecules from NMR relaxation measurements is applied to ¹³C NMR relaxation data on the Bovine Pancreatic Trypsin Inhibitor (M. W. 6,500). Six experimental parameters measured at two field strengths are accounted for by a minimum of three motions at each carbon group. Low frequency components make small but finite contribution to the relaxation of all resonances, suggesting a general low frequency distortion of the backbone. Rotational diffusion of the protein makes a relatively minor contribution to the relaxation process. For aliphatic groups, rotation of side chains dominates relaxation.     

Fast-time scale dynamics of outer membrane protein A by extended model-free analysis of NMR relaxation data

In order to better understand the dynamics of an integral membrane protein, backbone amide ¹⁵N NMR dynamics measurements of the β-barrel membrane protein OmpA have been performed at three magnetic fields. A total of nine relaxation data sets were globally analyzed using an extended model-free formalism. The diffusion tensor was found to be prolate axially symmetric with an axial ratio of 5.75, indicating a possible rotation of the protein within the micelle. The generalized order parameters gradually decreased from the mid-plane towards the two ends of the barrel, counteracting the dynamic gradient of the lipids in a matching bilayer, and were dramatically reduced in the extracellular loops. Large-scale internal motions on the ns time scale indicate that entire loops most likely undergo concerted (“sea anemone”-like) motions emanating from their anchoring points on the barrel. The case of OmpA in DPC micelles also illustrates inherent limitations of analyzing the data with even the most sophisticated current models of the model-free formalism. It is likely that conformational exchange processes on the ms-μs also play a role in describing the motions of some residues, but their analysis did not produce unique results that could be independently verified.     

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.     

Solid-state NMR approaches to measure topological equilibria and dynamics of membrane polypeptides

Biological membranes are characterized by a high degree of dynamics. In order to understand the function of membrane proteins and even more of membrane-associated peptides, these motional aspects have to be taken into consideration. Solid-state NMR spectroscopy is a method of choice when characterizing topological equilibria, molecular motions, lateral and rotational diffusion as well as dynamic oligomerization equilibria within fluid phase lipid bilayers. Here we show and review examples where the ¹⁵N chemical shift anisotropy, dipolar interactions and the deuterium quadrupolar splittings have been used to analyze motions of peptides such as peptaibols, antimicrobial sequences, Vpu, phospholamban or other channel domains. In particular, simulations of ¹⁵N and ²H-solid-state NMR spectra are shown of helical domains in uniaxially oriented membranes when rotation around the membrane normal or the helix long axis occurs.     

Radially softening diffusive motions in a globular protein

Molecular dynamics simulation, quasielastic neutron scattering and analytical theory are combined to characterize diffusive motions in a hydrated protein, C-phycocyanin. The simulation-derived scattering function is in approximate agreement with experiment and is decomposed to determine the essential contributions. It is found that the geometry of the atomic motions can be modeled as diffusion in spheres with a distribution of radii. The time dependence of the dynamics follows stretched exponential behavior, reflecting a distribution of relaxation times. The average side chain and backbone dynamics are quantified and compared. The dynamical parameters are shown to present a smooth variation with distance from the core of the protein. Moving outward from the center of the protein there is a progressive increase of the mean sphere size, accompanied by a narrowing and shifting to shorter times of the relaxation time distribution. This smooth, "radially softening" dynamics may have important consequences for protein function. It also raises the possibility that the dynamical or "glass" transition with temperature observed experimentally in proteins might be depth dependent, involving, as the temperature decreases, progressive freezing out of the anharmonic dynamics with increasing distance from the center of the protein.     

Local dielectric properties around polar region of lipid bilayer membranes

Summary Local dielectric constant was evaluated from the Stokes shifts of fluorescence spectra ofl--dansylphosphatidylethanolamine (DPE) incorporated into liposomes made of synthetic phosphatidylcholine (dipalmitoyl or distearoyl) or bovine brain phosphatidylserine. The evaluation was established as follows. First, the Stokes shift of DPE was assured to follow Mataga-Lippert's equation and was a function of the dielectric constant and the refractive index in some standard organic solvents. Second, the change of the refractive index did not contribute much to the change in the Stokes shift. Third, the time resolved fluorescence depolarization of DPE in liposomes showed that the cone wobbling diffusion was rapid relative to the fluorescence lifetime and therefore that the dielectric relaxation did not affect the evaluation of the constant in the polar region of membranes. We then investigated the characteristics of the local dielectric constant in the polar region of the lipid bilayer and found that the dielectric constant varies between 4 and 34 depending upon calcium binding and also gel/liquid-crystal phase transition. Such large changes of the local dielectric constant were further correlated with the dynamic structure of lipid bilayer membranes measured by conventional fluorescence depolarization techniques. The large changes of dielectric constant around the polar region suggest that electrostatic interactions at this region can be altered 10-fold by such ionic or thermotropic factors and therefore that local dielectric properties can play crucial roles in membrane functions.     

Protein diffusion and macromolecular crowding in thylakoid membranes

The photosynthetic light reactions of green plants are mediated by chlorophyll-binding protein complexes located in the thylakoid membranes within the chloroplasts. Thylakoid membranes have a complex structure, with lateral segregation of protein complexes into distinct membrane regions known as the grana and the stroma lamellae. It has long been clear that some protein complexes can diffuse between the grana and the stroma lamellae, and that this movement is important for processes including membrane biogenesis, regulation of light harvesting, and turnover and repair of the photosynthetic complexes. In the grana membranes, diffusion may be problematic because the protein complexes are very densely packed (approximately 75% area occupation) and semicrystalline protein arrays are often observed. To date, direct measurements of protein diffusion in green plant thylakoids have been lacking. We have developed a form of fluorescence recovery after photobleaching that allows direct measurement of the diffusion of chlorophyll-protein complexes in isolated grana membranes from Spinacia oleracea. We show that about 75% of fluorophores are immobile within our measuring period of a few minutes. We suggest that this immobility is due to a protein network covering a whole grana disc. However, the remaining fraction is surprisingly mobile (diffusion coefficient 4.6 +/- 0.4 x 10(-11) cm(2) s(-1)), which suggests that it is associated with mobile proteins that exchange between the grana and stroma lamellae within a few seconds. Manipulation of the protein-lipid ratio and the ionic strength of the buffer reveals the roles of macromolecular crowding and protein-protein interactions in restricting the mobility of grana proteins.     

The Fluid—Mosaic Model of Membrane Structure: Still relevant to understanding the structure,function and dynamics of biological membranes after more than 40 years

In 1972 the Fluid—Mosaic Membrane Model of membrane structure was proposed based on thermodynamic principals of organization of membrane lipids and proteins and available evidence of asymmetry and lateral mobility within the membrane matrix [S. J. Singer and G. L. Nicolson, Science 175 (1972) 720–731]. After over 40 years, this basic model of the cell membrane remains relevant for describing the basic nano-structures of a variety of intracellular and cellular membranes of plant and animal cells and lower forms of life. In the intervening years, however, new information has documented the importance and roles of specialized membrane domains, such as lipid rafts and protein/glycoprotein complexes, in describing the macrostructure, dynamics and functions of cellular membranes as well as the roles of membrane-associated cytoskeletal fences and extracellular matrix structures in limiting the lateral diffusion and range of motion of membrane components. These newer data build on the foundation of the original model and add new layers of complexity and hierarchy, but the concepts described in the original model are still applicable today. In updated versions of the model more emphasis has been placed on the mosaic nature of the macrostructure of cellular membranes where many protein and lipid components are limited in their rotational and lateral motilities in the membrane plane, especially in their natural states where lipid–lipid, protein–protein and lipid–protein interactions as well as cell–matrix, cell–cell and intracellular membrane-associated protein and cytoskeletal interactions are important in restraining the lateral motility and range of motion of particular membrane components. The formation of specialized membrane domains and the presence of tightly packed integral membrane protein complexes due to membrane-associated fences, fenceposts and other structures are considered very important in describing membrane dynamics and architecture. These structures along with membrane-associated cytoskeletal and extracellular structures maintain the long-range, non-random mosaic macro-organization of membranes, while smaller membrane nano- and submicro-sized domains, such as lipid rafts and protein complexes, are important in maintaining specialized membrane structures that are in cooperative dynamic flux in a crowded membrane plane. This Article is Part of a Special Issue Entitled: Membrane Structure and Function: Relevance in the Cell's Physiology, Pathology and Therapy.     

Comparison between the backbone dynamics of an 11-amino acid peptide sequence in alpha-helical and beta-hairpin structural contexts

To investigate the relationship between backbone motions and the structural environment of a peptide sequence, we have used (15)N NMR relaxation data to characterize the backbone motions of the "chameleon-alpha" (Chm-alpha) and "chameleon-beta" (Chm-beta) proteins designed previously by Minor and Kim [Minor, D. L., Jr., and Kim, P. S. (1996) Nature 380, 730-734]. These two proteins contain an identical 11-amino acid sequence (dubbed the "chameleon" peptide sequence) in alpha-helix and beta-hairpin conformations, respectively, within the B1 domain of protein G. When placed in an alpha-helical context, the chameleon peptide shows very limited backbone motions, but some remote regions of the protein are induced to undergo conformational exchange motions, apparently due to modification of packing interactions with the chameleon peptide. In contrast, within a beta-hairpin context, the chameleon peptide displays substantial motions on both picosecond and microsecond-to-millisecond time scales, suggesting that it cannot be readily accommodated within the native reverse turn structure. These observations are consistent with the relatively low stability of the Chm-beta protein and can be rationalized in terms of native turn-stabilizing interactions that may be disrupted in the Chm-beta protein.     

Elbow‐ and hinge‐bending motions of IgG: Dielectric response and dynamic feature

Immunoglobulin G (IgG) is a Y‐shaped globular protein consisting of two Fab segments connecting to an Fc segment with a flexible hinge region, in which the Fab segments show secondary flexibility at an “elbow” region. In the present work, the hinge‐bending and elbow‐bending motions of aqueous solutions of IgG by microwave dielectric measurements below the freezing point of bulk water was observed. The presence of unfreezable water around the macromolecules reduced the effects of steric hindrance normally generated by ice and enabled the intramolecular motions of IgG. At the same time, the overall IgG molecule rotation was restricted by ice. Papain digestion and reduction of the disulfide linkage at the hinge region was used to generate Fab and Fc fragments. In solutions of these fragments, the dielectric relaxation process of the hinge‐bending motion was absent, although the elbow‐bending motion remained. Three relaxation processes were observed for papain‐digested IgG. The high, middle, and low frequency processes were attributed to unfrozen water, local peptide motions cooperating with bound water, and the elbow‐bending motion, respectively. In the case of the intact IgG, an additional relaxation process due to the hinge‐bending motion was observed at frequencies lower than that of the elbow‐bending motion. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 626–632, 2016.     

Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex

Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and molecular interactions. It is assumed that the membrane-associated cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin density and reduction in mobility was observed for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addition of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the analysis of the experimental FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner.     

Excitation wavelength dependent fluorescence anisotropy of eosin-myosin adducts. Evidence for anisotropic rotations.

Steady-state and time-resolved fluorescence anisotropy measurements of eosin in solution and eosin-5-maleimide bound to purified myosin were made to study localized motions of the "head region" of this protein. The lifetime and apparent Debye rotational relaxation times of eosin in aqueous solution are essentially invariant with changes in excitation wavelength. In more viscous solvents, such as propylene glycol/water mixtures, the apparent Debye rotational relaxation times of eosin differ upon excitation in the regions of positive and negative anisotropy. Using eosin attached to the SH-1 thiol of the myosin head differing rotational modes of the bound probe were detected, dependent upon excitation wavelength. The main features of the anisotropy data for eosin-myosin are consistent with the existence of a 'crevice' or 'pocket' in the myosin head. A model is presented which allows estimation of the ratio of distinct rotational diffusion terms (selected by different excitation wavelengths) that produce both the observed steady-state anisotropy and differential phase results.     

1H NMR relaxation studies of protein-polysaccharide mixtures

NMR water proton relaxation was used to characterize the structure of plant proteins and plant protein-polysaccharide mixtures in aqueous solutions. The method is based on the mobility determination of the water molecules in the biopolymer environment in solutions through relaxation time measurements. Differences of conformation between pea globulin and alpha gliadin seem to control the water molecules mobility in their environment. As deduced from the study of complexes, the electrostatic interactions may also play a major role in the water molecule motions. The phase separation induced under specific conditions seems to promote the translational diffusion of structured water molecules whereas the rotational motion was more restricted.     

Anisotropic rotational diffusion in model-free analysis for a ternary DHFR complex

Model-free analysis has been extensively used to extract information on motions in proteins over a wide range of timescales from NMR relaxation data. We present a detailed analysis of the effects of rotational anisotropy on the model-free analysis of a ternary complex for dihydrofolate reductase (DHFR). Our findings show that the small degree of anisotropy exhibited by DHFR (D_||/D=1.18) introduces erroneous motional models, mostly exchange terms, to over 50% of the NH spins analyzed when isotropic tumbling is assumed. Moreover, there is a systematic change in S², as large as 0.08 for some residues. The significant effects of anisotropic rotational diffusion on model-free motional parameters are in marked contrast to previous studies and are accentuated by lowering of the effective correlation time using isotropic tumbling methods. This is caused by the preponderance of NH vectors aligned perpendicular to the principal diffusion tensor axis and is readily detected because of the high quality of the relaxation data. A novel procedure, COPED (COmparison of Predicted and Experimental Diffusion tensors) is presented for distinguishing genuine motions from the effects of anisotropy by comparing experimental relaxation data and data predicted from hydrodynamic analyses. The procedure shows excellent agreement with the slow motions detected from the axially symmetric model-free analysis and represents an independent procedure for determining rotational diffusion and slow motions that can confirm or refute established procedures that rely on relaxation data. Our findings show that neglect of even small degrees of rotational diffusion anisotropy can introduce significant errors in model-free analysis when the data is of high quality. These errors can hinder our understanding of the role of internal motions in protein function.     

Effect of complement on the lateral mobility of erythrocyte membrane proteins. Evidence for terminal complex interaction with cytoskeletal components

The lateral mobilities of erythrocyte membrane proteins and terminal complement complexes (TCC) were measured on C-treated erythrocyte ghosts by the technique of fluorescence redistribution after photobleaching. Results showed that the lateral diffusion coefficient of the bulk membrane proteins decreased with the assembly of TCC on the membrane at low C dose and was significantly reduced with assembly of the full membrane attack complex (C5b-9), even in the absence of cell lysis. At high serum doses, the mobility of the membrane proteins increased slightly above that of the control cells. The diffusion coefficients of the TCC on the erythrocyte membrane range from 1.18 to 4.37 x 10(-11) cm2/s, values characteristic of anchored membrane proteins. Spectrin-depletion of the C-lysed erythrocytes results in 25- and 45-fold increases in the diffusion coefficients of the membrane proteins and the C5b-9 complex, respectively. Conversely, oxidative cross-linking of spectrin by diamide reduced the diffusion coefficients of both membrane and C proteins. These studies indicate that the deposition of TCC on an erythrocyte can result in a substantial change in the physical and structural properties of the target membrane, aside from the creation of functional lesions. The low mobilities of the terminal complexes on the target membrane suggest possible interactions with cytoskeletal elements or with anchored membrane proteins.     

Dielectric relaxation of water and water-plasticized biomolecules in relation to cellular water organization, cytoplasmic viscosity, and desiccation tolerance in recalcitrant seed tissues

To understand the relationship between the organization of cellular water, molecular interactions, and desiccation tolerance, dielectric behaviors of water and water-plasticized biomolecules in red oak (Quercus rubra) seeds were studied during dehydration. The thermally stimulated current study showed three dielectric dispersions: (a) the relaxation of loosely-bound water and small polar groups, (b) the relaxation of tightly-bound water, carbohydrate chains, large polar groups of macromolecules, and (c) the "freezing in" of molecular mobility (glassy state). Seven discrete hydration levels (water contents of 1.40, 0.55, 0.41, 0.31, 0.21, 0.13, and 0.08 g/g dry weight, corresponding to -1.5, -8, -11, -14, -24, -74, and -195 MPa, respectively) were identified according to the changes in thermodynamic and dielectric properties of water and water-plasticized biomolecules during dehydration. The implications of intracellular water organization for desiccation tolerance were discussed. Cytoplasmic viscosity increased exponentially at water content < 0.40 g/g dry weight, which was correlated with the great relaxation slowdown of water-plasticized biomolecules, supporting a role for viscosity in metabolic shutdown during dehydration.     

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

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.