Transverse Nuclear Spin Relaxation Studies of Viscoelastic Properties of Membrane Vesicles. I. Theory

Biophysics of Membrane Stiffening by Cholesterol and Phosphatidylinositol 4,5-bisphosphate (PIP2)

Cell membranes regulate a wide range of phenomena that are implicated in key cellular functions. Cholesterol, a critical component of eukaryotic cell membranes, is responsible for cellular organization, membrane elasticity, and other critical physicochemical parameters. Besides cholesterol, other lipid components such as phosphatidylinositol 4,5-bisphosphate (PIP2) are found in minor concentrations in cell membranes yet can also play a major regulatory role in various cell functions. In this chapter, we describe how solid-state deuterium nuclear magnetic resonance (²H NMR) spectroscopy together with neutron spin-echo (NSE) spectroscopy can inform synergetic changes to lipid molecular packing due to cholesterol and PIP2 that modulate the bending rigidity of lipid membranes. Fundamental structure-property relations of molecular self-assembly are illuminated and point toward a length and time-scale dependence of cell membrane mechanics, with significant implications for biological activity and membrane lipid-protein interactions.

Cholesterol Effects on the Physical Properties of Lipid Membranes Viewed by Solid-state NMR Spectroscopy

In this chapter, we review the physical properties of lipid/cholesterol mixtures involving studies of model membranes using solid-state NMR spectroscopy. The approach allows one to quantify the average membrane structure, fluctuations, and elastic deformation upon cholesterol interaction. Emphasis is placed on understanding the membrane structural deformation and emergent fluctuations at an atomistic level. Lineshape measurements using solid-state NMR spectroscopy give equilibrium structural properties, while relaxation time measurements study the molecular dynamics over a wide timescale range. The equilibrium properties of glycerophospholipids, sphingolipids, and their binary and tertiary mixtures with cholesterol are accessible. Nonideal mixing of cholesterol with other lipids explains the occurrence of liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids, and may drive formation of lipid rafts. The functional dependence of ²H NMR spin-lattice relaxation (R _1Z) rates on segmental order parameters (S _CD) for lipid membranes is indicative of emergent viscoelastic properties. Addition of cholesterol shows stiffening of the bilayer relative to the pure lipids and this effect is diminished for lanosterol. Opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale can potentially affect lipid raft formation in cellular membranes.

Brownian Translational Dynamics on a Flexible Surface: Nuclear Spin Relaxation of Fluid Membrane Phases

A general model for nuclear magnetic resonance (NMR) relaxation studies of fluid bilayer systems is introduced, combining a mesoscopic Brownian dynamics description of the bilayer with atomistic molecular dynamics (MD) simulations. An example is given for dipalmitoylphosphatidylcholine in 2H2O solvent and compared with the experiment. Experimental agreement is within a factor of 2 in the water relaxation rates, based on a postulated model with fixed parameters, which are largely available from the MD simulation. Relaxation rates are particularly sensitive to the translational diffusion of water perturbed by the interface dynamics and structure. Simulation results suggest that a notable deviation in the relaxation rates may follow from the commonly used small-angle approximation of bilayer undulation. The method has the potential to overcome the temporal and spatial limitations in computing NMR relaxation with atomistic MD, as well as the shortcomings of continuum models enabling a consistent description of experiments performed on a solvent lipid and added spin probes. This work opens for possibilities to understand relaxation processes involving systems such as micelles, multilamellar vesicles, red blood cells, and so forth at biologically relevant timescales in great detail.

Cholesterol-induced suppression of membrane elastic fluctuations at the atomistic level

Applications of solid-state NMR spectroscopy for investigating the influences of lipid-cholesterol interactions on membrane fluctuations are reviewed in this paper. Emphasis is placed on understanding the energy landscapes and fluctuations at an emergent atomistic level. Solid-state (2)H NMR spectroscopy directly measures residual quadrupolar couplings (RQCs) due to individual C-(2)H labeled segments of the lipid molecules. Moreover, residual dipolar couplings (RDCs) of (13)C-(1)H bonds are obtained in separated local-field NMR spectroscopy. The distributions of RQC or RDC values give nearly complete profiles of the order parameters as a function of acyl segment position. Measured equilibrium properties of glycerophospholipids and sphingolipids including their binary and tertiary mixtures with cholesterol show unequal mixing associated with liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids and may drive the formation of lipid rafts. In addition relaxation time measurements enable one to study the molecular dynamics over a wide time-scale range. For (2)H NMR the experimental spin-lattice (R1Z) relaxation rates follow a theoretical square-law dependence on segmental order parameters (SCD) due to collective slow dynamics over mesoscopic length scales. The functional dependence for the liquid-crystalline lipid membranes is indicative of viscoelastic properties as they emerge from atomistic-level interactions. A striking decrease in square-law slope upon addition of cholesterol denotes stiffening relative to the pure lipid bilayers that is diminished in the case of lanosterol. Measured equilibrium properties and relaxation rates infer opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale that potentially affects lipid raft formation in cellular membranes.

Brief overview on 2H NMR studies of polysiloxane-based side-chain nematic elastomers

This is a brief overview on recent studies on liquid crystalline elastomers (LCEs) based on polysiloxane chain, in the form of monodomain films, selectively (2)H-labeled in different parts of the LCE samples, i.e. on the crosslinker or mesogenic units. (2)H NMR spectroscopic techniques were used to measure the temperature dependence of the quadrupolar splittings, line widths and relaxation times, T(1) and T(2). From these data, several information about the orientational order parameter, S, of various LCE fragments, thermodynamic features of the isotropic-nematic transition and main motional processes could be generalized for this type of elastomers.

The effect of cholesterol on membrane dynamics on different timescales in lipid bilayers from fast field-cycling NMR relaxometry studies of unilamellar vesicles

The general applicability of fast field-cycling nuclear magnetic resonance relaxometry in the study of dynamics in lipid bilayers is demonstrated through analysis of binary unilamellar liposomes composed of 1,2-dioleoyl-sn-glycero-3-posphocholine (DOPC) and cholesterol. We extend an evidence-based method to simulating the NMR relaxation response, previously validated for single-component membranes, to evaluate the effect of the sterol molecule on local ordering and dynamics over multiple timescales. The relaxometric results are found to be most consistent with the partitioning of the lipid molecules into affected and unaffected portions, rather than a single averaged phase. Our analysis suggests that up to 25 mol%, each cholesterol molecule orders three DOPC molecules, providing experimental backup to the findings of many molecular dynamics studies. A methodology is established for studying dynamics on multiple timescales in unilamellar membranes of more complex compositions.

Effects of cholesterol on membrane molecular dynamics studied by fast field cycling NMR relaxometry

Biological membranes are complex structures composed of various lipids and proteins. Different membrane compositions affect viscoelastic and hydrodynamic properties of membranes, which are critical to their functions. Lipid bilayer vesicles inserted by cholesterol not only enhance membrane surface motional behavior but also strengthen vesicle stability. Cholesterol-rich vesicles are similar to cell membranes in structure and composition. Therefore, cholesterol-rich vesicles can represent a typical model for studying membrane dynamics and functions. In this study, nuclear magnetic relaxation dispersion was used to investigate the detailed molecular dynamics of membrane differences between vesicles and cholesterol vesicles in the temperature range of 278-298 K. Vesicles of two different sizes were prepared. The effect of cholesterol mainly affected the order fluctuation of membranes and the diffusional motion of lipid molecules. In addition, phase variations were also observed in liposomes that contained cholesterol from analyses of the distances between lipid molecules.

An NMR database for simulations of membrane dynamics

Computational methods are powerful in capturing the results of experimental studies in terms of force fields that both explain and predict biological structures. Validation of molecular simulations requires comparison with experimental data to test and confirm computational predictions. Here we report a comprehensive database of NMR results for membrane phospholipids with interpretations intended to be accessible by non-NMR specialists. Experimental ¹³C-¹H and ²H NMR segmental order parameters (S(CH) or S(CD)) and spin-lattice (Zeeman) relaxation times (T(1Z)) are summarized in convenient tabular form for various saturated, unsaturated, and biological membrane phospholipids. Segmental order parameters give direct information about bilayer structural properties, including the area per lipid and volumetric hydrocarbon thickness. In addition, relaxation rates provide complementary information about molecular dynamics. Particular attention is paid to the magnetic field dependence (frequency dispersion) of the NMR relaxation rates in terms of various simplified power laws. Model-free reduction of the T(1Z) studies in terms of a power-law formalism shows that the relaxation rates for saturated phosphatidylcholines follow a single frequency-dispersive trend within the MHz regime. We show how analytical models can guide the continued development of atomistic and coarse-grained force fields. Our interpretation suggests that lipid diffusion and collective order fluctuations are implicitly governed by the viscoelastic nature of the liquid-crystalline ensemble. Collective bilayer excitations are emergent over mesoscopic length scales that fall between the molecular and bilayer dimensions, and are important for lipid organization and lipid-protein interactions. Future conceptual advances and theoretical reductions will foster understanding of biomembrane structural dynamics through a synergy of NMR measurements and molecular simulations.

Dynamics of partially oriented L-phenylalanine-d(8) in the CsPFO/H(2)O lyotropic system via (2)H NMR relaxation studies

Dynamics of the l-phenylalanine-d(8) has been here investigated by analyzing the (2)H NMR spin-lattice relaxation times of this selectively deuterium enriched amino acid diluted in the cesium pentadecafluorooctanoate/water (CsPFO/H(2)O) lyotropic system both in the nematic (N(+)(D)) and in the lamellar (L(D)) phases. Information on the internal and overall molecular motions as well as on collective motions has been achieved by a global fitting procedure. The dynamic processes affecting this probe molecule reflect its particular conformational and interaction properties with respect to the lyotropic environment. The best reproduction of the experimental data is obtained by assuming free internal reorientations of the benzylic moiety, which results in diffusion constants of the same order of magnitude of the overall molecular spinning motion. Moreover, the contribution of collective motions (order director fluctuations and layer undulations) is estimated to be greater than that commonly observed by other techniques in lyotropic systems.

Inhomogeneous NMR line shape as a probe of microscopic organization of bicontinuous cubic phases

NMR line shapes of the lipid and aqueous species in bicontinuous cubic phase (BCP) samples prepared by centrifugation are inhomogeneously broadened. The broadening of the lipid peaks is removed by magic-angle spinning (MAS). In this work, we studied the mechanism of this broadening using (1)H and (13)C NMR spectroscopy of a myverol/water BCP. It is demonstrated that the inhomogeneity possesses an intrinsic contribution that is independent of instrumental or setup factors and can be attributed to the microscopic organization of the BCP bilayer. A mechanism of the inhomogeneous broadening is proposed, which involves a spatially nonuniform diamagnetically induced magnetic field determined by the mesoscopic structure and the diamagnetic susceptibilities of the two BCP domains. The proposed mechanism does not require that molecular reorientation of the lipid be slow for the inhomogeneous broadening to survive. We discuss how this inhomogeneous broadening can be employed as a probe of compositional uniformity and microscopic organization of BCP samples.

Collective Fluctuations in Ordered Fluids Investigated by Two-Dimensional Electron−Electron Double Resonance Spectroscopy

Two-dimensional electron-electron double resonance (2D-ELDOR) is a technique that is sensitive to the dynamical processes affecting spin labels in complex fluid environments. In ordered fluids, such as membrane vesicles, the 2D-ELDOR experiment is affected by the molecular tumbling in the locally ordered environment. This motion occurs on two different time scales, the faster molecular motion relative to the local director, and the slower collective fluctuations of the director field. In the experimental study of Patyal, Crepeau, and Freed (Biophys. J. 1997, 73, 2201), it was found that the widths of the autopeaks of the 2D-ELDOR spectrum increased as a function of the mixing time. In the present work, a theory is developed for the effects of director fluctuations on the autopeaks in the 2D-ELDOR experiment by employing an analytical solution of the stochastic Liouville equation for which the director field is treated as a multidimensional Gaussian process, as previously developed by Frezzato, Kothe, and Moro (J. Phys. Chem. B 2001, 105, 1281 and J. Phys. Chem. B 2004, 108, 9505). Good agreement is found between theory and experiment, notably the only adjustable parameter is k, the bending elastic modulus of the membrane. The values of k = 11 x 10(-20) J for 1,2-dipalmitoyl-sn-glycero-phosphatidylcholine (DPPC) vesicles and k = 15 x 10(-20) J for DPPC/gramicidin A (5:1) vesicles, both at 45 degrees C, were found from the analysis and agree well with previous related measurements by other physical techniques. This establishes 2D-ELDOR as a useful technique to study the elastic properties of biological membranes.

NMR relaxation study of molecular dynamics in columnar and smectic phases of a PAMAM liquid-crystalline co-dendrimer

We present the first results obtained by proton ((1)H) nuclear magnetic relaxation studies of molecular dynamics in a supermolecular liquid-crystal dendrimer exhibiting columnar rectangular and smectic-A phases. The (1)H spin-lattice relaxation time (T(1)) dispersions are interpreted using two relaxation mechanisms associated with collective motions and local molecular reorientations of the dendritic segments in the low- and high-frequency ranges, respectively. The T(1) values show a drop around 2.3 MHz that is attributed to a contribution coming from cross-relaxation between (1)H and nitrogen nuclear spins. In the high-frequency range the motions appear to be of similar nature in both mesophases and are ascribed to reorientations of dendritic segments (belonging to the core and/or to the mesogenic units) characterized by two correlation times. Notable differences in the dynamics between the columnar and layered phases are observed in the low-frequency range. Depending on the mesophase they are discussed in terms of elastic deformations of the columns and layer undulations. In this study we find that the dendritic core influences the dynamics of the mesogenic units both for local and collective motions. These results can be understood in terms of spatial constraints imposed by the dendritic architecture and by the supermolecular arrangement in the mesophases.