Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.     

Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes.

We report on the successful application of fluorescence correlation spectroscopy (FCS) to the analysis of single fluorescently labeled lipid analogue molecules diffusing laterally in lipid bilayers, as exemplified by time traces of fluorescence bursts of individual molecules entering and leaving the excitation area. FCS measurements performed on lipid probes in rat basophilic leukemia cell membranes showed deviations from two-dimensional Brownian motion with a single uniform diffusion constant. Giant unilamellar vesicles were employed as model systems to characterize diffusion of fluorescent lipid analogues in both homogeneous and mixed lipid phases with diffusion heterogeneity. Comparing the results of cell membrane diffusion with the findings on the model systems suggests possible explanations for the observations: (a) anomalous subdiffusion in which evanescent attractive interactions with disparate mobile molecules modifies the diffusion statistics; (b) alternatively, probe molecules are localized in microdomains of submicroscopic size, possibly in heterogeneous membrane phases.     

Fluorescence polarization in a planar array of pigment molecules: theoretical treatment and application to flavins incorporated into artificial membranes.

A quantitative fluorescence polarization theory of molecules bound to two-dimensional plane layers has been developed when the electronic transition moments of absorption and emission are parallel within the fluorescent molecules. The transition moments are assumed to be in preferred orientation with respect to the normal to the plane and to be randomly oriented within the plane (rotational symmetry with the normal as axis of symmetry). Three basic model distributions of transition moments are investigated quantitatively. These model distributions represent a simplification but in most cases may be expected to describe reality with sufficient accuracy. For all distributions, two cases of different mobility of molecules are treated: (a) the lifetime of fluorescence is small compared with the characteristic relaxation time of the distribution, and (b) the lifetime of fluorescence is long, so that a complete reorientation of transition moments during the excited state can take place. From the quantitative calculations four characteristic quantities are derived, which are appropriate for the analysis of experimental data. Experiments are carried out with phosphatidylcholine bilayer membranes which contain three differently substituted amphiphilic flavins. All three flavins yield similar data. Their analyses predict free and fast mobility of the flavin chromophore.     

Fluorescence photobleaching recovery using total internal reflection interference fringes

Lateral diffusion measurements on cell membrane molecules, most commonly accomplished through fluorescence photobleaching recovery (FPR or FRAP), provide information on such molecules' size, environment, and participation in intermolecular interactions. However, difficulties arise in FPR measurements of lateral dynamics of materials, such as visible fluorescent protein (VFP) fusion proteins, where fluorescent intracellular species contribute to the fluorescence recovery signal and thus distort measurements intended to reflect surface molecules only. A new method helps eliminate these difficulties. In total internal reflection interference fringe FPR, interfering laser beams enter a 1.65-numercial aperture (NA) Olympus objective at the periphery of the back focal plane where the NA exceeds 1.38. This creates an extended interference pattern totally internally reflected at the coverslip-medium interface which excites fluorescence only from fluorescent molecules located where the cell contacts the coverslip. The large illuminated area interrogates many more membrane receptors than spot methods and hence obtains more diffusion information per measurement while rejecting virtually all interfering intracellular fluorescence. We report successful measurements of membrane dynamics of both VFP-containing and conventionally labeled molecules by this technique and compare them with results of other FPR methods.     

Anisotropy of photosynthetic membranes and the degree of fluorescence polarization

The degree of fluoresence polarization, P, of unoriented and magnetically oriented spinach chloroplasts as a function of excitation (400–680 nm) and emission wavelengths (675–750 nm) is reported. For unoriented chloroplasts P can be divided into two contributions, P_IN and P_AN. The latter arises from the optical anisotropy of the membranes which is due to the orientation with respect to the membrane plane of pigment molecules in vivo. The intrinsic polarization P_IN, which reflects the energy transfer between different pigment molecules and their degree of mutual orientation, can be measured unambiguously only if (1) oriented membranes are used and the fluorescence is viewed along a direction normal to the membrane planes, and (2) the excitation is confined to the Q_y (≈ 660−680 nm) absorption band of chlorophyll in vivo. With 670–680 nm excitation, values of P using unoriented chloroplasts can be as high as +14%, mostly reflecting the orientational anisotropy of the pigments. Using oriented chloroplasts, P_IN is shown to be +5±1%. The excitation wavelength dependence studies of P_IN indicate that the carotenoid and chlorophyll Q_y transition moments tend to be partially oriented with respect to each other on a local level (within a given photosynthetic unit or its immediate neighbors).     

Phospholipid order in gel- and fluid-phase cell-size liposomes measured by digitized video fluorescence polarization microscopy.

Low-light digitized video fluorescence microscopy has been utilized to measure the steady-state polarized fluorescence from the membrane probe diphenylhexatriene (DPH) and its cationic and phosphatidylcholine derivatives 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene (TMA-DPH) and 2-[3-(diphenylhexatrienyl)propanoyl]-3-palmitoyl-L-alpha-phosphati dylcholine (DPH-PC), respectively, in cell-size (10-70 microns) unilamellar vesicles composed of gel-or fluid-phase phospholipid. Using an inverted microscope with epi-illumination optics and an intensified silicon intensified target camera interfaced to a minicomputer, fluorescence images of single vesicles were obtained at emission polarizer orientations of 0 degrees, 45 degrees, 90 degrees, and 135 degrees relative to the excitation light polarization direction. Fluorescence intensity ratios F90 degrees/F0 degrees (= F perpendicular/F parallel) and F135 degrees/F45 degrees were calculated on a pixel-by-pixel basis from digitized image pairs. Theoretical expressions were derived for collected polarized fluorescence as a function of position on the membrane surface as well as the degree of lipid order, in terms of the fluorophore's maximum angular motional freedom in the bilayer (identical to theta max), using a modification of the method of D. Axelrod (1979. Biophys. J. 26:557-574) together with the "wobbling-in-a-cone" model of probe rotational diffusion. Comparison of experimental polarization ratios with theoretical ratios yielded the following results. In gel-phase dipalmitoyl-phosphatidylcholine, the data for all three probes correspond to a model in which the cone angle theta max = 17 +/- 2 degrees and there exists a collective tilt of the phospholipid acyl chains of 30 degrees relative to the bilayer normal. In addition, approximately 5% of DPH and TMA-DPH molecules are aligned parallel to the plane of the bilayer. In fluid-phase palmitoyloleoyl-phosphatidylcholine, the data are well fit by models in which theta max = 60 +/- 2 degrees for DPH and DPH-PC and 32 +/- 4 degrees for TMA-DPH, with approximately 20% of DPH molecules and 10% of TMA-DPH molecules aligned parallel to the bilayer plane, and a net phospholipid tilt at or near the headgroup region of approximately 30 degrees. The results demonstrate that lipid order can be measured with a spatial resolution of approximately 1 micron2 in cell-size vesicles even with high aperture observation through a microscope.     

Cholesterol depletion induces dynamic confinement of the G-protein coupled serotonin(1A) receptor in the plasma membrane of living cells

Cholesterol is an essential constituent of eukaryotic membranes and plays a crucial role in membrane organization, dynamics, function, and sorting. It is often found distributed non-randomly in domains or pools in biological and model membranes and is thought to contribute to a segregated distribution of membrane constituents. Signal transduction events mediated by seven transmembrane domain G-protein coupled receptors (GPCRs) are the primary means by which cells communicate with and respond to their external environment. We analyzed the role of cholesterol in the plasma membrane organization of the G-protein coupled serotonin(1A) receptor by fluorescence recovery after photobleaching (FRAP) measurements with varying bleach spot sizes. Our results show that lateral diffusion parameters of serotonin(1A) receptors in normal cells are consistent with models describing diffusion of molecules in a homogenous membrane. Interestingly, these characteristics are altered in cholesterol-depleted cells in a manner that is consistent with dynamic confinement of serotonin(1A) receptors in the plasma membrane. Importantly, analysis of ligand binding and downstream signaling of the serotonin(1A) receptor suggests that receptor function is affected in a significantly different manner when intact cells or isolated membranes are depleted of cholesterol. These results assume significance in the context of interpreting effects of cholesterol depletion on diffusion characteristics of membrane proteins in particular, and cholesterol-dependent cellular processes in general.     

Simulations of (an)isotropic diffusion on curved biological surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of approximately 4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of approximately 2 in different ER samples.     

Cholesterol depletion induces dynamic confinement of the G-protein coupled serotonin1A receptor in the plasma membrane of living cells

Cholesterol is an essential constituent of eukaryotic membranes and plays a crucial role in membrane organization, dynamics, function, and sorting. It is often found distributed non-randomly in domains or pools in biological and model membranes and is thought to contribute to a segregated distribution of membrane constituents. Signal transduction events mediated by seven transmembrane domain G-protein coupled receptors (GPCRs) are the primary means by which cells communicate with and respond to their external environment. We analyzed the role of cholesterol in the plasma membrane organization of the G-protein coupled serotonin_1A receptor by fluorescence recovery after photobleaching (FRAP) measurements with varying bleach spot sizes. Our results show that lateral diffusion parameters of serotonin_1A receptors in normal cells are consistent with models describing diffusion of molecules in a homogenous membrane. Interestingly, these characteristics are altered in cholesterol-depleted cells in a manner that is consistent with dynamic confinement of serotonin_1A receptors in the plasma membrane. Importantly, analysis of ligand binding and downstream signaling of the serotonin_1A receptor suggests that receptor function is affected in a significantly different manner when intact cells or isolated membranes are depleted of cholesterol. These results assume significance in the context of interpreting effects of cholesterol depletion on diffusion characteristics of membrane proteins in particular, and cholesterol-dependent cellular processes in general.     

The rotational diffusion of chloroplast phosphate translocator and of lipid molecules in bilayer membranes

The rotational mobility of the phosphate translocator from the chloroplast envelope and of lipid molecules in the membrane of unilamellar azolectin liposomes has been investigated. The rotational dynamics of the liposome membrane were investigated by measuring the rotational diffusion of eosin-5-isothiocyanate(EITC)-labeled L-alpha-dipalmitoylglycerophosphoethanolamine (Pam2 GroPEtn) in the lipid phase of the vesicles, either in the presence or absence of the reconstituted phosphate translocator. The temperature dependence of the anisotropy decay showed that above 25 degrees C the main contribution to the anisotropy decay was caused by uniaxial anisotropic rotation of the labelled lipid molecules around the axis normal to the membrane plane. The rate of rotation of the labelled lipid molecules was strongly dependent on the viscosity of the medium (eta 1). Extrapolation to eta 1 = 0 Pa.s yielded a correlation time of phi = 20 +/- 5 ns, t = 30 degrees C, for lipid rotation with respect to the membrane normal. The rotational diffusion coefficient of the lipid molecules was calculated to be Dr = 2.0 x 10(9) rad2.s-1 and the apparent microviscosity in the vesicle membrane, as derived from the rotational correlation time, was eta 2 approximately 12 mPa.s. The rotational correlation time of the phosphate translocator in the membrane was only slightly dependent on the viscosity of the medium. The temperature dependence of the protein rotation also indicated that the rotation of the protein in the membrane was largely restricted and occurred mainly about the axis normal to the membrane plane. Measurements at a medium viscosity of eta 1 = 1 mPa.s yielded a value of phi r approximately 450 ns corresponding to Dr = 8.8 x 10(7) rad2.s-1 for protein rotation with respect to the membrane normal. From this value and the data of the lipid rotation, the cross-sectional area of the protein part embedded in the membrane was calculated to be approximately 9 nm2. This cross-sectional area is large enough to include at most 14 membrane-spanning helices. Our results also indicated that at lipid/protein molar ratios greater than or equal to 1.5 x 10(4): 1 aggregation occurred in the model membranes below 30 degrees C. However, above 30 degrees C and at a high dilution of the protein in the membrane it appeared that the membrane viscosity monitored by lipid and protein rotational diffusion were identical.     

Theory of fluorescence polarization of oriented pigment molecules in spherical arrays.

Theoretical results are presented which are appropriate for the analysis of the static polarized fluorescence experiment with oriented pigment molecules in spherical arrays (vesicles). Though the global orientation mediated over the whole sphere is isotropic, the fluorescent molecules may have preferred local orientation with respect to the local plane. As in a former paper, concerning fluroescence polarization in planar arrays, three basic (local) orientation distributions of the electronic transition moments are investigated, which may be expected to describe a wide class of real cases with sufficient accuracy. Analytic expressions for the degree of polarization are derived. One important result is that the degree of polarization may be extremely dependent on the local orientation of transition moments. Hence the usual method of determination of microviscosities from experiments with vesicles with the use of the theory of fluorescence polarization for macromolecules in solutions should be regarded with great caution.     

All-trans retinol in rod photoreceptor outer segments moves unrestrictedly by passive diffusion

The visual pigment protein of vertebrate rod photoreceptors, rhodopsin, contains an 11-cis retinyl moiety that is isomerized to all-trans upon light absorption. Subsequently, all-trans retinal is released from the protein and reduced to all-trans retinol, the first step in the recycling of rhodopsin's chromophore group through the series of reactions that constitute the visual cycle. The concentration of all-trans retinol in photoreceptor outer segments can be monitored from its fluorescence. We have used two-photon excitation (720 nm) of retinol fluorescence and fluorescence recovery after photobleaching to characterize the mobility of all-trans retinol in frog photoreceptor outer segments. Retinol produced after rhodopsin bleaching moved laterally in the disk membrane bilayer with an apparent diffusion coefficient of 2.5 +/- 0.3 micro m(2) s(-1). The diffusion coefficient of exogenously added retinol was 3.2 +/- 0.5 micro m(2) s(-1). These diffusion coefficients are in close agreement with those reported for lipids, suggesting that retinol is not tightly bound to protein sites that would be diffusing much more slowly in the plane of the membrane. In agreement with this interpretation, a fluorescent-labeled C-16 fatty acid diffused laterally with a similar diffusion coefficient, 2.2 +/- 0.2 micro m(2) s(-1). Retinol also moved along the length of the rod outer segment, with an apparent diffusion coefficient of 0.07 +/- 0.01 micro m(2) s(-1), again suggesting that it is not tightly bound to proteins that would confine it to the disks. The axial diffusion coefficient of exogenously added retinol was 0.05 +/- 0.01 micro m(2) s(-1). In agreement with passive diffusion, the rate of axial movement was inversely proportional to the square of the length of the rod outer segment. Diffusion of retinol on the plasma membrane of the outer segment can readily account for the measured value of the axial diffusion coefficient, as the plasma membrane comprises approximately 1% of the total outer-segment membrane. The values of both the lateral and axial diffusion coefficients are consistent with most of the all-trans retinol in the outer segments moving unrestricted and not being bound to carrier proteins. Therefore, and in contrast to other steps of the visual cycle, there does not appear to be any specialized processing for all-trans retinol within the rod outer segment.     

Lowering the barriers to random walks on the cell surface

We used fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT) techniques to compare diffusion of class I major histocompatibility complex molecules (MHC) on normal and alpha-spectrin-deficient murine erythroleukemia (MEL) cells. Because the cytoskeleton mesh acts as a barrier to lateral mobility of membrane proteins, we expected that diffusion of membrane proteins in alpha-spectrin-deficient MEL cells would differ greatly from that in normal MEL cells. In the event, diffusion coefficients derived from either FRAP or SPT analysis were similar for alpha-spectrin-deficient and normal MEL cells, differing by a factor of approximately 2, on three different timescales: tens of seconds, 1-10 s, and 100 ms. SPT analysis showed that the diffusion of most class I MHC molecules was confined on both cell types. On the normal MEL cells, the mean diagonal length of the confined area was 330 nm with a mean residency time of 40s. On the alpha-spectrin-deficient MEL cells, the mean diagonal length was 650 nm with a mean residency time of 45s. Thus there are fewer barriers to lateral diffusion on cytoskeleton mutant MEL cells than on normal MEL cells, but this difference does not strongly affect lateral diffusion on the scales measured here.     

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.     

Compartmentalized structure of the plasma membrane for receptor movements as revealed by a nanometer-level motion analysis

Movements of transferrin and alpha 2-macroglobulin receptor molecules in the plasma membrane of cultured normal rat kidney (NRK) fibroblastic cells were investigated by video-enhanced contrast optical microscopy with 1.8 nm spatial precision and 33 ms temporal resolution by labeling the receptors with the ligand-coated nanometer-sized colloidal gold particles. For both receptor species, most of the movement trajectories are of the confined diffusion type, within domains of approximately 0.25 microns2 (500-700 nm in diagonal length). Movement within the domains is random with a diffusion coefficient approximately 10(-9) cm2/s, which is consistent with that expected for free Brownian diffusion of proteins in the plasma membrane. The receptor molecules move from one domain to one of the adjacent domains at an average frequency of 0.034 s-1 (the residence time within a domain approximately 29 s), indicating that the plasma membrane is compartmentalized for diffusion of membrane receptors and that long- range diffusion is the result of successive intercompartmental jumps. The macroscopic diffusion coefficients for these two receptor molecules calculated on the basis of the compartment size and the intercompartmental jump rate are approximately 2.4 x 10(-11) cm2/s, which is consistent with those determined by averaging the long-term movements of many particles. Partial destruction of the cytoskeleton decreased the confined diffusion mode, increased the simple diffusion mode, and induced the directed diffusion (transport) mode. These results suggest that the boundaries between compartments are made of dynamically fluctuating membrane skeletons (membrane-skeleton fence model).     

Anomalous diffusion of major histocompatibility complex class I molecules on HeLa cells determined by single particle tracking.

Single-particle tracking (SPT) was used to determine the mobility characteristics of MHC (major histocompatibility complex) class I molecules at the surface of HeLa cells at 22 degrees C and on different time scales. MHC class I was labeled using the Fab fragment of a monoclonal antibody (W6/32), covalently bound to either R-phycoerythrin or fluorescent microspheres, and the particles were tracked using high-sensitivity fluorescence imaging. Analysis of the data for a fixed time interval suggests a reasonable fit to a random diffusion model. The best fit values of the diffusion coefficient D decreased markedly, however, with increasing time interval, demonstrating the existence of anomalous diffusion. Further analysis of the data shows that the diffusion is anomalous over the complete time range investigated, 4-300 s. Fitting the results obtained with the R-phycoerythrin probe to D = D0talpha-1, where Do is a constant and t is the time, gave D0 = (6.7 +/- 4.5) x 10(-11) cm2 s-1 and alpha = 0.49 +/- 0.16. Experiments with fluorescent microspheres were less reproducible and gave slower anomalous diffusion. The R-phycoerythrin probe is considered more reliable for fluorescent SPT because it is small (11 x 8 nm) and monovalent. The type of motion exhibited by the class I molecules will greatly affect their ability to migrate in the plane of the membrane. Anomalous diffusion, in particular, greatly reduces the distance a class I molecule can travel on the time scale of minutes. The present data are discussed in relation to the possible role of diffusion and clustering in T-cell activation.     

Theory of fluorescence polarization of oriented pigment molecules in spherical arrays

Summary Theoretical results are presented which are appropriate for the analysis of the static polarized fluorescence experiment with oriented pigment molecules in spherical arrays (vesicles). Though the global orientation mediated over the whole sphere is isotropic, the fluorescent molecules may have preferred local orientation with respect to the local plane. As in a former paper, concerning fluorescence polarization in planar arrays, three basic (local) orientation distributions of the electronic transition moments are investigated, which may be expected to describe a wide class of real cases with sufficient accuracy. Analytic expressions for the degree of polarization are derived. One important result is that the degree of polarization may be extremely dependent on the local orientation of transition moments. Hence the usual method of determination of microviscosities from experiments with vesicles with the use of the theory of fluorescence polarization for macromolecules in solutions should be regarded with great caution.I wish to thank prof. P. LÄuger and Dr. G. Pohl for interesting discussions. This work has been financially supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 138).     

Bacteriorhodospin: a trans-membrane pump containing alpha-helix.

The probable arrangement of the bacteriorhodopsin molecules in the purple membrane of Halobacterium halobium is in clusters of three, with a 3-fold axis at the centre of each cluster; the axis is at right angles to the plane of the membrane. The proposed arrangement and the results of model calculations together indicate that each protein molecule spans the entire thickness of the membrane. An earlier proposal for the structure had the protein molecules in two layers, and it was symmetric in projection onto the profile-axis. This model is now rejected since it would be difficult to account for the recently discovered function of pumping protons. There remains a discrepancy in that the calculated number of protein molecules in the unit-cell is 3.4 compared to the three expected.The X-ray diffraction patterns from dispersions of the lipids extracted from the red and purple membranes of H. halobium are described.Model calculations are reported, which are based on the bilayer profile calculated for the extracted lipids and on two simple profiles for the protein. The calculations favour a structure for the purple membrane having the lipid molecules in two layers, as in a bilayer, although there may be more of the lipid on one side of the membrane than on the other. Assuming bilayer structure, the diffraction nearest the centre of the oriented pattern suggests that the lipid molecules may be located mainly in a few discrete regions, roughly 20 Å across, between the protein molecules. An uninterrupted monolayer of the lipid on one surface of a sheet of the protein molecules gives poor agreement with the observed profile-diffraction.The X-ray diffraction pattern from the oriented membranes suggested α-helix in the bacteriorhodopsin, and this has been confirmed by recording a 1.5 Å-reflection oriented on the profile-axis. There appear to be at least two segments of α-helix, which are somewhat inclined to one another, and the two may be packed together. Prominent diffraction on the in-plane axis near 10 Å is consistent with the segments lying more or less perpendicular to the plane of the membrane.     

Expanding the scope of quantitative FRAP analysis

In this study, new mathematical models were developed for analysis of fluorescence recovery after photobleaching (FRAP) data to account for features not represented in previous analysis: conical photobleaching geometry, spatial variations in binding of fluorescent molecules, and directed transport of fluorescent molecules. To facilitate computations in conical geometry, a fast computational method for calculation of fluorescence recovery is presented. Two approximations are presented to aid in FRAP analysis when binding varies spatially, one applying to cases of relatively fast diffusion and slow binding and the other to binding of molecules to small cellular structures. Numerical results show that using a model that represents the influential physical processes and that is formulated in the appropriate geometry can substantially improve the accuracy of FRAP calculations.