To Hop or not to Hop: Exceptions in the FCS Diffusion Law

Diffusion obstacles in membranes have not been directly visualized because of fast membrane dynamics and the occurrence of subresolution molecular complexes. To understand the obstacle characteristics, mobility-based methods are often used as an indirect way of assessing the membrane structure. Molecular movement in biological plasma membranes is often characterized by anomalous diffusion, but the exact underlying mechanisms are still elusive. Imaging total internal reflection fluorescence correlation spectroscopy (ITIR-FCS) is a well-established mobility-based method that provides spatially resolved diffusion coefficient maps and is combined with FCS diffusion law analysis to examine subresolution membrane organization. In recent years, although FCS diffusion law analysis has been instrumental in providing new insights into the membrane structure below the optical diffraction limit, there are certain exceptions and anomalies that require further clarification. To this end, we correlate the membrane structural features imaged by atomic force microscopy (AFM) with the dynamics measured using ITIR-FCS. We perform ITIR-FCS measurements on supported lipid bilayers (SLBs) of various lipid compositions to characterize the anomalous diffusion of lipid molecules in distinct obstacle configurations, along with the high-resolution imaging of the membrane structures with AFM. Furthermore, we validate our experimental results by performing simulations on image grids with experimentally determined obstacle configurations. This study demonstrates that FCS diffusion law analysis is a powerful tool to determine membrane heterogeneities implied from dynamics measurements. Our results corroborate the commonly accepted interpretations of imaging FCS diffusion law analysis, and we show that exceptions happen when domains reach the percolation threshold in a biphasic membrane and a network of domains behaves rather like a meshwork, resulting in hop diffusion.     

Phosphorus-31 two-dimensional solid-state exchange NMR. Application to model membrane and biological systems.

Two-dimensional solid-state 31P NMR has been used to investigate the orientational exchange of phospholipids in gel and liquid-crystalline aqueous multilamellar dispersions and oriented multibilayers, and in biological membranes. In liquid-crystalline L alpha multilamellar dispersions, orientational exchange originates from the lateral diffusion of phospholipid molecules over the curved surface of the liposomes and is manifest by an increase in off-diagonal intensity, which correlates the 90 and 0 degrees orientations of the membrane normal with respect to the magnetic field when the system is fully exchanged. Spectral simulations of the time evolution of exchange allowed determination of the correlation times tau d for lateral diffusion. For DMPC and DPPC at comparable reduced temperatures, tau d values of 44 and 8 ms were obtained, respectively. The nature and rate of exchange observed for POPE at 30 degrees C is similar to that of DMPC at the same temperature. The measured correlation times are consistent with diffusion rates obtained by FRAP for liposomes with radii in the 1 micron range. In the gel phase of DPPC (30 degrees C), little orientational exchange is observed at mixing times up to 200 ms, demonstrating that the lateral diffusion is very slow. The correlation time for orientational exchange obtained from spectral simulations was approximately 900 ms; thus, exchange in the gel state is at least two orders of magnitude slower than in the liquid-crystalline state. In the P beta (ripple) phase, at temperatures between 34 and 39 degrees C, significant exchange is observed for mixing times between 50 and 200 ms. Exchange is also observed in oriented samples of DPPC in the P beta phase for mixing times of 50 ms, but not for oriented liquid-crystalline samples for mixing times up to 100 ms. The exchange observed in the ripple phase could originate from rapid lateral diffusion of "fast" diffusing phospholipid within defect structures, and/or from "slow" lateral diffusion of ordered phospholipid over the ripples. 2D experiments were also performed on pig erythrocyte ghosts and on intact pig spinal cord. Significant orientational exchange was observed with the erythrocyte ghosts at a mixing time of 200 ms, but almost no exchange was observed with the spinal cord at the same mixing time. Spectral simulations suggest tau d values of approximately 400 ms and 1.3 s for the erythrocyte ghosts and spinal cord at 30 degrees C.(ABSTRACT TRUNCATED AT 400 WORDS)     

Two-Dimensional Continuum Percolation Threshold for Diffusing Particles of Nonzero Radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r¹² repulsion, the percolating diameter is ∼20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.     

Excimer-forming lipids in membrane research

Pyrenedecanoic acid and pyrene lecithin are optical probes well suited to investigate lipid bilayer membranes. The method is based on the determination of the formation of excited dimers or excimers. The rate of excimer formation yields information on the dynamic molecular properties of artificial as well as of natural membranes. This article will review applications of the excimer-forming probes.Pyrene lipid probes are used to determine the coefficient of the lateral diffusion in fluid lipid membranes. Results in artificial membranes are comparable to the values obtained in erythrocyte membranes.Moreover, the excimer formation rate is a very sensitive measure of changes in membrane fluidity. Membrane fluidity is an important regulator of membrane functional proteins. For example, there is a correlation between membrane fluidity and enzyme activities of the adenylate cyclase system.The excimer formation technique is not restricted to the measurement of lateral mobility in membranes. It can also be used to determine the transversal mobility, that is, the lipid exchange between the lipid layers of one bilayer or between bilayers of different vesicles. Again, artificial as well as natural membranes can be investigated by this technique.Another important area of investigation in membrane research is the interaction between lipids and proteins. Lipids, in the presence of a protein, show a different dynamic behavior from free lipids. Because of changes in fluidity and a modified solubility of the pyrene probes within different membrane regions, our methods could also be applied to the examination of phase separation phenomena and to lipid-protein interactions.     

Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes

Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys⁴⁰, residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein dynamics but also protein-lipid interactions in detail.     

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.     

A milling crowd model for local and long-range obstructed lateral diffusion. Mobility of excimeric probes in the membrane of intact erythrocytes.

A new model for lateral diffusion, the milling crowd model (MC), is proposed and is used to derive the dependence of the monomeric and excimeric fluorescence yields of excimeric membrane probes on their concentration. According to the MC model, probes migrate by performing spatial exchanges with a randomly chosen nearest neighbor (lipid or probe). Only nearest neighbor probes, one of which is in the excited state, may form an excimer. The exchange frequency, and hence the local lateral diffusion coefficient, may then be determined from experiment with the aid of computer simulation of the excimer formation kinetics. The same model is also used to study the long-range lateral diffusion coefficient of probes in the presence of obstacles (e.g., membrane proteins). The dependence of the monomeric and excimeric fluorescence yields of 1-pyrene-dodecanoic acid probes on their concentration in the membranes of intact erythrocytes was measured and compared with the prediction of the MC model. The analysis yields an excimer formation rate for nearest neighbor molecules of approximately 1 X 10(7) s-1 and an exchange frequency of approximately greater than 2 X 10(7) s-1, corresponding to a local diffusion coefficient of greater than 3 X 10(-8) cm2 s-1. This value is several times larger than the long-range diffusion coefficient for a similar system measured in fluorescence photobleaching recovery experiments. The difference is explained by the fact that long-range diffusion is obstructed by dispersed membrane proteins and is therefore greatly reduced when compared to free diffusion. The dependence of the diffusion coefficient on the fractional area covered by obstacles and on their size is derived from MC simulations and is compared to those of other theories lateral diffusibility.     

Obstructed diffusion in phase-separated supported lipid bilayers: a combined atomic force microscopy and fluorescence recovery after photobleaching approach

Proteins and other macromolecules are believed to hinder molecular lateral diffusion in cellular membranes. We have constructed a well-characterized model system to better understand how obstacles in lipid bilayers obstruct diffusion. Fluorescence recovery after photobleaching was used to measure the lateral diffusion coefficient in single supported bilayers composed of mixtures of 1,2-dilauroylphosphotidylcholine (DLPC) and 1,2-distearoylphosphotidylcholine (DSPC). Because these lipids are immiscible and phase separate at room temperature, a novel quenching technique allowed us to construct fluid DLPC bilayers containing small disk-shaped gel-phase DSPC domains that acted as obstacles to lateral diffusion. Our experimental setup enabled us to analyze the same samples with atomic force microscopy and exactly characterize the size, shape, and number of gel-phase domains before measuring the obstacle-dependent diffusion coefficient. Lateral obstructed diffusion was found to be dependent on obstacle area fraction, size, and geometry. Analysis of our results using a free area diffusion model shows the possibility of unexpected long-range ordering of fluid-phase lipids around the gel-phase obstacles. This lipid ordering has implications for lipid-mediated protein interactions in cellular membranes.     

The Long and Viscous Road: Uncovering Nuclear Diffusion Barriers in Closed Mitosis

Diffusion barriers are effective means for constraining protein lateral exchange in cellular membranes. In Saccharomyces cerevisiae, they have been shown to sustain parental identity through asymmetric segregation of ageing factors during closed mitosis. Even though barriers have been extensively studied in the plasma membrane, their identity and organization within the nucleus remains poorly understood. Based on different lines of experimental evidence, we present a model of the composition and structural organization of a nuclear diffusion barrier during anaphase. By means of spatial stochastic simulations, we propose how specialised lipid domains, protein rings, and morphological changes of the nucleus may coordinate to restrict protein exchange between mother and daughter nuclear lobes. We explore distinct, plausible configurations of these diffusion barriers and offer testable predictions regarding their protein exclusion properties and the diffusion regimes they generate. Our model predicts that, while a specialised lipid domain and an immobile protein ring at the bud neck can compartmentalize the nucleus during early anaphase; a specialised lipid domain spanning the elongated bridge between lobes would be entirely sufficient during late anaphase. Our work shows how complex nuclear diffusion barriers in closed mitosis may arise from simple nanoscale biophysical interactions.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Identification of structural transitions in bacterial fatty acid binding proteins that permit ligand entry and exit at membranes

Fatty acid (FA) transfer proteins extract FA from membranes and sequester them to facilitate their movement through the cytosol. Detailed structural information is available for these soluble protein–FA complexes, but the structure of the protein conformation responsible for FA exchange at the membrane is unknown. Staphylococcus aureus FakB1 is a prototypical bacterial FA transfer protein that binds palmitate within a narrow, buried tunnel. Here, we define the conformational change from a “closed” FakB1 state to an “open” state that associates with the membrane and provides a path for entry and egress of the FA. Using NMR spectroscopy, we identified a conformationally flexible dynamic region in FakB1, and X-ray crystallography of FakB1 mutants captured the conformation of the open state. In addition, molecular dynamics simulations show that the new amphipathic α-helix formed in the open state inserts below the phosphate plane of the bilayer to create a diffusion channel for the hydrophobic FA tail to access the hydrocarbon core and place the carboxyl group at the phosphate layer. The membrane binding and catalytic properties of site-directed mutants were consistent with the proposed membrane docked structure predicted by our molecular dynamics simulations. Finally, the structure of the bilayer-associated conformation of FakB1 has local similarities with mammalian FA binding proteins and provides a conceptual framework for how these proteins interact with the membrane to create a diffusion channel from the FA location in the bilayer to the protein interior.     

Molecular dynamics study of bipolar tetraether lipid membranes

Membranes composed of bipolar tetraether lipids have been studied by a series of 25-ns molecular dynamics simulations to understand the microscopic structure and dynamics as well as membrane area elasticity. By comparing macrocyclic and acyclic tetraether and diether archaeal lipids, the effect of tail linkage of the two phytanyl-chained lipids on the membrane properties is elucidated. Tetraether lipids show smaller molecular area and lateral mobility. For the latter, calculated diffusion coefficients are indeed one order-of-magnitude smaller than that of the diether lipid. These two tetraether membranes are alike in many physical properties except for membrane area elasticity. The macrocyclic tetraether membrane shows a higher elastic area expansion modulus than its acyclic counterpart by a factor of three. Free energy profiles of a water molecule crossing the membranes show no major difference in barrier height; however, a significant difference is observed near the membrane center due to the lack of the slip-plane in tetraether membranes.     

Assessing the nature of lipid raft membranes

The paradigm of biological membranes has recently gone through a major update. Instead of being fluid and homogeneous, recent studies suggest that membranes are characterized by transient domains with varying fluidity. In particular, a number of experimental studies have revealed the existence of highly ordered lateral domains rich in sphingomyelin and cholesterol (CHOL). These domains, called functional lipid rafts, have been suggested to take part in a variety of dynamic cellular processes such as membrane trafficking, signal transduction, and regulation of the activity of membrane proteins. However, despite the proposed importance of these domains, their properties, and even the precise nature of the lipid phases, have remained open issues mainly because the associated short time and length scales have posed a major challenge to experiments. In this work, we employ extensive atom-scale simulations to elucidate the properties of ternary raft mixtures with CHOL, palmitoylsphingomyelin (PSM), and palmitoyloleoylphosphatidylcholine. We simulate two bilayers of 1,024 lipids for 100 ns in the liquid-ordered phase and one system of the same size in the liquid-disordered phase. The studies provide evidence that the presence of PSM and CHOL in raft-like membranes leads to strongly packed and rigid bilayers. We also find that the simulated raft bilayers are characterized by nanoscale lateral heterogeneity, though the slow lateral diffusion renders the interpretation of the observed lateral heterogeneity more difficult. The findings reveal aspects of the role of favored (specific) lipid-lipid interactions within rafts and clarify the prominent role of CHOL in altering the properties of the membrane locally in its neighborhood. Also, we show that the presence of PSM and CHOL in rafts leads to intriguing lateral pressure profiles that are distinctly different from corresponding profiles in nonraft-like membranes. The results propose that the functioning of certain classes of membrane proteins is regulated by changes in the lateral pressure profile, which can be altered by a change in lipid content.     

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.     

Influence of DPH on the structure and dynamics of a DPPC bilayer

We have conducted extensive molecular dynamics (MD) simulations together with differential scanning calorimetry (DSC) and nuclear magnetic resonance (NMR) experiments to quantify the influence of free 1,6-diphenyl-1,3,5-hexatriene (DPH) fluorescent probes on the structure and dynamics of a dipalmitoylphosphatidylcholine bilayer. Atomistic MD simulations show that in the membrane-water interface the influence of DPH is minor, whereas in the acyl-chain region DPH gives rise to major perturbations. In the latter case, DPH is found to influence a wide range of membrane properties, such as the packing and ordering of hydrocarbon tails and the lateral diffusion of lipid molecules. The effects are prominent but of local nature, i.e., the changes observed in the properties of lipid molecules are significant in the vicinity of DPH, but reduce rapidly as the distance from the probe increases. Long-range perturbations due to DPH are hence not expected. Detailed DSC and (2)H NMR measurements support this view. DSC shows only subtle perturbation to the cooperative behavior of the membrane system in the presence of DPH, and (2)H NMR shows that DPH gives rise to a slight increase in the lipid chain order, in agreement with MD simulations. Potential effects of other probes such as pyrene are briefly discussed.     

Segregated Phases in Pulmonary Surfactant Membranes Do Not Show Coexistence of Lipid Populations with Differentiated Dynamic Properties

The composition of pulmonary surfactant membranes and films has evolved to support a complex lateral structure, including segregation of ordered/disordered phases maintained up to physiological temperatures. In this study, we have analyzed the temperature-dependent dynamic properties of native surfactant membranes and membranes reconstituted from two surfactant hydrophobic fractions (i.e., all the lipids plus the hydrophobic proteins SP-B and SP-C, or only the total lipid fraction). These preparations show micrometer-sized fluid ordered/disordered phase coexistence, associated with a broad endothermic transition ending close to 37°C. However, both types of membrane exhibit uniform lipid mobility when analyzed by electron paramagnetic resonance with different spin-labeled phospholipids. A similar feature is observed with pulse-field gradient NMR experiments on oriented membranes reconstituted from the two types of surfactant hydrophobic extract. These latter results suggest that lipid dynamics are similar in the coexisting fluid phases observed by fluorescence microscopy. Additionally, it is found that surfactant proteins significantly reduce the average intramolecular lipid mobility and translational diffusion of phospholipids in the membranes, and that removal of cholesterol has a profound impact on both the lateral structure and dynamics of surfactant lipid membranes. We believe that the particular lipid composition of surfactant imposes a highly dynamic framework on the membrane structure, as well as maintains a lateral organization that is poised at the edge of critical transitions occurring under physiological conditions.     

Water diffusion permeability of human erythrocytes studied by a pulsed gradient NMR technique

Water diffusion permeability of human erythrocytes has been measured by NMR using a pulsed magnetic field gradient technique. The measurement of exchange rates was based on restricted diffusion of water molecules within red blood cells. This method avoids addition of paramagnetic ions, such as Mn²⁺ and is used in vivo.The mean lifetime of water inside human erythrocytes was found to be 17 ms at 24°C. A sulfhydryl reagent, known to inhibit water osmotic permeability, reduced significantly water diffusion across the red cell membrane.     

Influence of Hydrophobic Mismatch and Amino Acid Composition on the Lateral Diffusion of Transmembrane Peptides

We investigated the effect of amino acid composition and hydrophobic length of α-helical transmembrane peptides and the role of electrostatic interactions on the lateral diffusion of the peptides in lipid membranes. Model peptides of varying length and composition, and either tryptophans or lysines as flanking residues, were synthesized. The peptides were labeled with the fluorescent label Alexa Fluor 488 and incorporated into phospholipid bilayers of different hydrophobic thickness and composition. Giant unilamellar vesicles were formed by electroformation, and the lateral diffusion of the transmembrane peptides (and lipids) was determined by fluorescence correlation spectroscopy. In addition, we performed coarse-grained molecular-dynamics simulations of single peptides of different hydrophobic lengths embedded in planar membranes of different thicknesses. Both the experimental and simulation results indicate that lateral diffusion is sensitive to membrane thickness between the peptides and surrounding lipids. We did not observe a difference in the lateral diffusion of the peptides with respect to the presence of tryptophans or lysines as flanking residues. The specific lipid headgroup composition of the membrane has a much less pronounced impact on the diffusion of the peptides than does the hydrophobic thickness.     

Water diffusion permeability of human erythrocytes studied by a pulsed gradient NMR technique.

Water diffusion permeability of human erythrocytes has been measured by NMR using a pulsed magnetic field gradient technique. The measurement of exchange rates was based on restricted diffusion of water molecules within red blood cells. This method avoids addition of paramagnetic ions, such as Mn2+, and is used in vivo. The mean lifetime of water insed human erythrocytes was found to be 17 ms at 24 degrees C. A sulfhydryl reagent, known to inhibit water osmotic permeability, reduced significantly water diffusion across the red cell membrane.