Quantitative characterization of the lateral distribution of membrane proteins within the lipid bilayer.

The dependence of the lateral distribution of membrane proteins on the size, protein/lipoid molar ratio, and the magnitude of the interaction potentials has been investigated by computer modeling protein-lipid distributions with Monte Carlo calculations. These results have allowed us to develop a quantitative characterization of the distribution of membrane proteins and to correlate these distributions with experimental observables. The topological arrangement of protein domains, protein plus annular lipid domains, and free lipid domains is described in terms of radial distribution, pair connectedness, and cluster distribution functions. The radial distribution functions are used to measure the distribution of intermolecular distances between protein molecules, whereas the pair connectedness functions are used to estimate the physical extension of compositional domains. It is shown that, at characteristic protein/lipid molar ratios, previously isolated domains become connected, forming domain networks that extend over the entire membrane surface. These changes in the lateral connectivity of compositional domains are paralleled by changes in the calculated lateral diffusion coefficients and might have important implications for the regulation of diffusion controlled processes within the membrane.     

Molecular origins of osmotic second virial coefficients of proteins.

The thermodynamic properties of protein solutions are determined by the molecular interactions involving both solvent and solute molecules. A quantitative understanding of the relationship would facilitate more systematic procedures for manipulating the properties in a process environment. In this work the molecular basis for the osmotic second virial coefficient, B22, is studied; osmotic effects are critical in membrane transport, and the value of B22 has also been shown to correlate with protein crystallization behavior. The calculations here account for steric, electrostatic, and short-range interactions, with the structural and functional anisotropy of the protein molecules explicitly accounted for. The orientational dependence of the protein interactions is seen to have a pronounced effect on the calculations; in particular, the relatively few protein-protein configurations in which the apposing surfaces display geometric complementarity contribute disproportionately strongly to B22. The importance of electrostatic interactions is also amplified in these high-complementarity configurations. The significance of molecular recognition in determining B22 can explain the correlation with crystallization behavior, and it suggests that alteration of local molecular geometry can help in manipulating protein solution behavior. The results also have implications for the role of protein interactions in biological self-organization.     

On the problem of dehydration and intracellular crystallization during freezing of cell suspensions.

The kinetic equation of the process of cell dehydration during freezing has been obtained. It is used to assess the degree of protoplasmic supercooling as a function of the cooling rate and cell parameters.The suggested model of dehydration cannot be applied to cells with permeability coefficients for water molecules more than 10^?5 cm/sec · bar, in particular to erythrocytes.The peculiarities of intracellular crystallization in red cells have been studied. The results show that red cells are likely to start freezing at cooling rates slower than those supposed from calculations of Mazur (9).     

Visualization and tracking of single protein molecules in the cell nucleus

A recently developed laser fluorescence videomicroscopy method was used to determine for the first time the intranuclear trajectories of single protein molecules. Using the recombinant Escherichia coli beta-galactosidase protein P4K, labeled with an average of 4.6 ALEXA 488 chromophores per tetramer, single P4K molecules could be localized and tracked in the nuclei of permeabilized 3T3 cells at a spatial accuracy of approximately 30 nm and a time resolution of 18 ms. Our previous photobleaching measurements indicated that P4K had two fractions inside the nucleus, a larger mobile and a smaller immobile fraction. The present study supported this observation but revealed a much larger variety of mobility classes. Thus, a fraction of P4K molecules appeared to be truly immobile while another fraction was mobile but confined to very small areas. In addition, a large fraction of the P4K molecules appeared to be mobile and to move over extended distances by diffusion. However, a quantitative analysis showed that at least two subpopulations were present differing widely in diffusion coefficients. Importantly, both the diffusion coefficients and the fractions of these subpopulations were time-dependent. Our results suggest that proteins can move inside the nucleus over extended distances by diffusion. However, intranuclear protein diffusion is severely restricted, most likely by multiple association-dissociation events and/or impermeable obstacles.     

Fluorescence correlation spectroscopy. I. Conceptual basis and theory

We describe a method for determining chemical kinetic constants and diffusion coefficients by measuring the rates of decay of spontaneous concentration fluctuations. The equilibrium of the system is not disturbed during the measurement. We measure the number of molecules of a specified type in a defined open volume as a function of time and compute the time course of the deviations from the thermodynamic mean concentration. The method is based on the principle that the rates of decay of spontaneous microscopic fluctuations are determined by the same phenomenological rate coefficients as those of macroscopic departures from equilibrium which result from external perturbations. Hence, an analysis of fluctuations yields the same chemical rate constants and diffusion coefficients as are measured by conventional procedures. In practice the number of the specified molecules is measured by a property such as absorbance or fluorescence which is specific and sensitive to chemical change. The sample volume is defined by a light beam which traverses the cell. As the molecules appear in or disappear from the light beam, either due to diffusion or chemical reaction, their concentration fluctuations give rise to corresponding fluctuations of the intensity of absorbed or emitted light. This paper presents the theory needed to derive chemical rate constants and diffusion coefficients from these fluctuations in light intensity. The theory is applied to three examples of general interest: pure diffusion in the absence of chemical reaction; the binding of a small rapidly diffusing ligand to a larger slowly diffusing macromolecule; and a unimolecular isomerization. The method should be especially useful in studying highly cooperative systems, relatively noncooperative systems with intermediate states closely spaced in free energy, small systems, and systems not readily subject to perturbations of state.     

Raster image correlation spectroscopy in live cells

Raster image correlation spectroscopy (RICS) is a noninvasive technique to detect and quantify events in a live cell, including concentration of molecules and diffusion coefficients of molecules; in addition, by measuring changes in diffusion coefficients, RICS can indirectly detect binding. Any specimen containing fluorophores that can be imaged with a laser scanning microscope can be analyzed using RICS. There are other techniques to measure diffusion coefficients and binding; however, RICS fills a unique niche. It provides spatial information and can be performed in live cells using a conventional confocal microscope. It can measure a range of diffusion coefficients that is not accessible with any other single optical correlation-based technique. In this article we describe a protocol to obtain raster scanned images with an Olympus FluoView FV1000 confocal laser scanning microscope using Olympus FluoView software to acquire data and SimFCS software to perform RICS analysis. Each RICS measurement takes several minutes. The entire procedure can be completed in ～2 h. This procedure includes focal volume calibration using a solution of fluorophores with a known diffusion coefficient and measurement of the diffusion coefficients of cytosolic enhanced green fluorescent protein (EGFP) and EGFP-paxillin.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes.

Tracer diffusion coefficients of integral membrane proteins (IMPs) in intact plasma membranes are often much lower than those found in blebbed, organelle, and reconstituted membranes. We calculate the contribution of hydrodynamic interactions to the tracer, gradient, and rotational diffusion of IMPs in plasma membranes. Because of the presence of immobile IMPs, Brinkman's equation governs the hydrodynamics in plasma membranes. Solutions of Brinkman's equation enable the calculation of short-time diffusion coefficients of IMPs. There is a large reduction in particle mobilities when a fraction of them is immobile, and as the fraction increases, the mobilities of the mobile particles continue to decrease. Combination of the hydrodynamic mobilities with Monte Carlo simulation results, which incorporate excluded area effects, enable the calculation of long-time diffusion coefficients. We use our calculations to analyze results for tracer diffusivities in several different systems. In erythrocytes, we find that the hydrodynamic theory, when combined with excluded area effects, closes the gap between existing theory and experiment for the mobility of band 3, with the remaining discrepancy likely due to direct obstruction of band 3 lateral mobility by the spectrin network. In lymphocytes, the combined hydrodynamic-excluded area theory provides a plausible explanation for the reduced mobility of sIg molecules induced by binding concanavalin A-coated platelets. However, the theory does not explain all reported cases of "anchorage modulation" in all cell types in which receptor mobilities are reduced after binding by concanavalin A-coated platelets. The hydrodynamic theory provides an explanation of why protein lateral mobilities are restricted in plasma membranes and why, in many systems, deletion of the cytoplasmic tail of a receptor has little effect on diffusion rates. However, much more data are needed to test the theory definitively. We also predict that gradient and tracer diffusivities are the same to leading order. Finally, we have calculated rotational diffusion coefficients in plasma membranes. They decrease less rapidly than translational diffusion coefficients with increasing protein immobilization, and the results agree qualitatively with the limited experimental data available.     

Kinetics of adsorption of proteins at interfaces: role of protein conformation in diffusional adsorption

To elucidate the role of protein conformation in the kinetics of adsorption at interfaces, seven structural intermediates of bovine serum albumin were prepared and their adsorption at the air/water interface was studied. Molecular area calculations indicated two distinct molecular processes, the first being the creation of an area, delta A1, for anchoring the molecule during the initial phase of adsorption and the second being the delta A2 cleared during subsequent reorientation and rearrangement of adsorbed molecules at the interface. The delta A1 values for all the albumin intermediates were the same, indicating that the initial work pi delta A1 needed to anchor the molecule at the interface was independent of solution conformation of the protein. Unlike delta A1, delta A2 exhibited a bell-shaped relationship with the extent of refolded state of the intermediates. Calculation of diffusion coefficients indicated that greater the unfolded state of the albumin intermediate, the greater was the diffusion coefficient. It is shown that the simple diffusion theory is inadequate to explain quantitatively the kinetics of protein adsorption. Specific, conformation-dependent, solute-solvent and solute-interface interactions also seem to influence the kinetics of adsorption of proteins.     

Estimation of diffusion coefficients of proteins

A correlation for estimating the diffusion coefficients of protein molecules is presented. The correlation is based upon literature values of the protein diffusion coefficients and molal volumes for 143 proteins. The correlation can be used for the estimation of diffusion coefficients using only molecular weight. Accuracy is such that a linear regression on 301 proteins showed 75% of the diffusion coefficients estimated fell within 20% of the experimental values. The relationship between this correlation, the Stokes–Einstein equation, and the Wilke–Chang correlation is discussed.     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Line-FRAP,A Versatile Method to Measure Diffusion Rates In Vitro and In Vivo

The crowded cellular milieu affect molecular diffusion through hard (occluded space) and soft (weak, non-specific) interactions. Multiple methods have been developed to measure diffusion coefficients at physiological protein concentrations within cells, each with its limitations. Here, we show that Line-FRAP, combined with rigours data analysis, is able to determine diffusion coefficients in a variety of environments, from in vitro to in vivo. The use of Line mode greatly improves time resolution of FRAP data acquisition, from 20-100 Hz in the classical mode to 800 Hz in the line mode. This improves data analysis, as intensity and radius of the bleach at the first post-bleach frame is critical. We evaluated the method on different proteins labelled chemically or fused to YFP in a wide range of environments. The diffusion coefficients measured in HeLa and in E. coli were ~2.5-fold and 15-fold slower than in buffer, and were comparable to previously published data. Increasing the osmotic pressure on E. coli further decreases diffusion, to the point at which proteins virtually stop moving. The method presented here, which requires a confocal microscope equipped with dual scanners, can be applied to study a large range of molecules with different sizes, and provides robust results in a wide range of environments and protein concentrations for fast diffusing molecules.     

An enhanced sensitivity methyl <Superscript>1</Superscript>H triple-quantum pulse scheme for measuring diffusion constants of macromolecules

We present a pulse scheme that exploits methyl ¹H triple-quantum (TQ) coherences for the measurement of diffusion rates of slowly diffusing molecules in solution. It is based on the well-known stimulated echo experiment, with encoding and decoding of TQ coherences. The size of quantifiable diffusion coefficients is thus lowered by an order of magnitude with respect to single-quantum (SQ) approaches. Notably, the sensitivity of the scheme is high, approximately ¾ that of the corresponding single quantum experiment, neglecting relaxation losses, and on the order of a factor of 4 more sensitive than a previously published sequence for AX₃ spin systems (Zheng et al. in JMR 198:271–274, 2009) for molecules that are only ¹³C labeled at the methyl carbon position. Diffusion coefficients measured from TQ- and SQ-based experiments recorded on a range of protein samples are in excellent agreement. We present an application of this technique to the study of phase-separated proteins where protein concentrations in the condensed phase can exceed 400 mg/mL, diffusion coefficients can be as low as ~10^?9 cm²s^?1 and traditional SQ experiments fail.     

Comparative study of diffusion coefficients of alpha-lactalbumins and lysozyme using polarization interferometer

The method of macroscopic diffusion with polarization optics has been applied to compare the translational diffusion coefficients for three proteins with similar three-dimensional structures in different conformational states. It has been shown that the values of diffusion coefficients obtained by the method are almost the same as those obtained by quasielastic light scattering. However this method is more available since it is less sensitive to aggregation and requires less amount of protein for investigation.     

Determining diffusion coefficients in inhomogeneous tissues using fluorescence recovery after photobleaching

Diffusion plays an important role in the transport of nutrients and signaling molecules in cartilaginous tissues. Diffusion coefficients can be measured by fluorescence recovery after photobleaching (FRAP). Available methods to analyze FRAP data, however, assume homogeneity in the environment of the bleached area and neglect geometrical restrictions to diffusion. Hence, diffusion coefficients in inhomogeneous materials, such as most biological tissues, cannot be assessed accurately. In this study, a new method for analyzing data from FRAP measurements has been developed, which is applicable to inhomogeneous tissues. It is based on a fitting procedure of the intensity recovery after photobleaching with a two-dimensional finite element analysis, which includes Fick's law for diffusion. The finite element analysis can account for distinctive diffusivity in predefined zones, which allows determining diffusion coefficients in inhomogeneous samples. The method is validated theoretically and experimentally in both homogeneous and inhomogeneous tissues and subsequently applied to the proliferation zone of the growth plate. Finally, the importance of accounting for inhomogeneities, for appropriate assessment of diffusivity in inhomogeneous tissues, is illustrated.     

Lateral diffusion of gramicidin S, M-13 coat protein and glycophorin in bilayers of saturated phospholipids. Mean field and Monte Carlo studies

We have developed a general model that relates the lateral diffusion coefficient of one isolated large intrinsic molecule (mol. wt. greater than or approximately 1000) in a phosphatidylcholine bilayer to the static lipid hydrocarbon chain order. We have studied how protein lateral diffusion can depend upon protein-lipid interactions but have not investigated possible non-specific contributions from gel-state lattice defects. The model has been used in Monte Carlo simulations or in mean-field approximations to study the lateral diffusion coefficients of Gramicidin S, the M-13 coat protein and glycophorin in dimyristoyl- and dipalmitoylphosphatidylcholine (DMPC and DPPC) bilayers as functions of temperature. Our calculated lateral diffusion coefficients for Gramicidin S and the M-13 coat protein are in good agreement with what has been observed and suggest that Gramicidin S is in a dimeric form in DMPC bilayers. In the case of glycophorin we find that the 'ice breaker' effect can be understood as a consequence of perturbation of the lipid polar region around the protein. In order to understand this effect is necessary that the protein hydrophilic section perturb the polar regions of at least approx. 24 lipid molecules, in good agreement with the numbers of 29-30 measured using 31P-NMR. Because of lipid-lipid interactions this effect extends itself out to four or five lipid layers away from the protein so that the hydrocarbon chains of between approx. 74 and approx. 108 lipid molecules are more disordered in the gel phase, so contributing less to the transition enthalpy, in agreement with the numbers of 80-100 deduced from differential scanning calorimetry (DSC). An understanding of the abrupt change in the diffusion coefficient at a temperature below the main bilayer transition temperature requires an additional mechanism. We propose that this change may be a consequence of a 'coupling-uncoupling' transition involving the protein hydrophilic section and the lipid polar regions, which may be triggered by the lipid bilayer pretransition. Our calculation of the average number of gauche bonds per lipid chain as a function of temperature and distance away from an isolated polypeptide or integral protein shows the extent of statically disordered lipid around such molecules. The range of this disorder depends upon temperature, particularly near the main transition.     

Intracellular macromolecular mobility measured by fluorescence recovery after photobleaching with confocal laser scanning microscopes

Fluorescence recovery after photobleaching (FRAP) is a widely used tool for estimating mobility parameters of fluorescently tagged molecules in cells. Despite the widespread use of confocal laser scanning microscopes (CLSMs) to perform photobleaching experiments, quantitative data analysis has been limited by lack of appropriate practical models. Here, we present a new approximate FRAP model for use on any standard CLSM. The main novelty of the method is that it takes into account diffusion of highly mobile molecules during the bleach phase. In fact, we show that by the time the first postbleach image is acquired in a CLSM a significant fluorescence recovery of fast-moving molecules has already taken place. The model was tested by generating simulated FRAP recovery curves for a wide range of diffusion coefficients and immobile fractions. The method was further validated by an experimental determination of the diffusion coefficient of fluorescent dextrans and green fluorescent protein. The new FRAP method was used to compare the mobility rates of fluorescent dextrans of 20, 40, 70, and 500 kDa in aqueous solution and in the nucleus of living HeLa cells. Diffusion coefficients were lower in the nucleoplasm, particularly for higher molecular weight dextrans. This is most likely caused by a sterical hindrance effect imposed by nuclear components. Decreasing the temperature from 37 to 22 degrees C reduces the dextran diffusion rates by approximately 30% in aqueous solution but has little effect on mobility in the nucleoplasm. This suggests that spatial constraints to diffusion of dextrans inside the nucleus are insensitive to temperature.     

Fluorescence energy transfer in two dimensions. A numeric solution for random and nonrandom distributions.

A method of Monte Carlo calculations has been applied to the problem of fluorescence energy transfer in two dimensions in order to provide a quantitative measure of the effects of nonideal mixing of lipid and protein molecules on the quenching profiles of membrane systems. These numerical techniques permit the formulation of a detailed set of equations that describes in a precise manner the quenching and depolarization properties of planar donor-acceptor distributions as a function of specific spectroscopic and organizational parameters. Because of the exact nature of the present numeric method, these results are used to evaluate critically the validity of previous approximate treatments existing in the literature. This method is also used to examine the effects of excluded volume interactions and distinct lattice structures on the expected transfer efficiencies. As a specific application, representative quenching profiles for protein-lipid mixtures, in which donor groups are covalently linked to the protein molecules and acceptor species are randomly distributed within lipid domains, have been obtained. It is found that the existence of phase-separated protein domains gives rise to a shielding effect that significantly decreases the transfer efficiencies with respect to those expected for an ideal distribution of protein molecules. The results from the present numerical study indicate that the experimental application of fluorescence energy transfer measurements in multicomponent membrane systems can be used to obtain organizational parameters that accurately reflect the lateral distribution of protein and lipid molecules within the bilayer membrane.     

Tracer diffusion coefficients of oxyhemoglobin a and oxyhemoglobin s in blood cells as determined by pulsed field gradient NMR

It is demonstrated that tracer diffusion coefficients can be determined for oxyhemoglobin A (HbA-O₂) and oxyhemoglobin S (HbS-O₂) in intact blood cells by means of pulsed field gradient NMR (PFG-NMR). This is possible because the method discriminates between both rapidly moving water molecules and molecules having small proton transverse relaxation times (T₂). The results indicate that only hemoglobin molecules contribute to the echo signals when large field gradients are used. The dependence of the measured diffusion coefficients on osmolarity and pH are attributed to changes in hemoglobin concentration resulting from changes in cell volume.     

Physicochemical studies on turnip-yellow-mosaic virus. Homogeneity, relative molecular masses, hydrodynamic radii and concentration-dependence of parameters in non-dissociating solvents.

Turnip-yellow-mosaic virus, with its stable, highly spherical and monodisperse character, was chosen as a suitable model substance with which to test hydrodynamic theories of transport. Sedimentation coefficients, diffusion coefficients (obtained through photon correlation spectroscopy) and viscosities were measured accurately as a function of concentration in well-defined and nearly neutral buffer systems. Ancillary information was also obtained from very-low-speed sedimentation-equilibrium experiments. The coefficients expressing the variation in sedimentation and diffusion coefficients with weight concentration were obtained, and by combination with other data it was possible to avoid assumptions concerning solvation and transform such regression coefficients into the form appropriate to volume fractions. Some measure of support for Batchelor's [(1972) J. Fluid Mech. 52, 245-268] calculations was thus obtained, but over most of the pH range the coefficients were significantly smaller than those calculated from his theory. It seems likely that electrostatic interactions are responsible for the discrepancies. Hydrodynamic radii (from diffusion coefficients) were in very fair agreement with those calculated from the thermodynamic excluded-volume term, but were higher than indicated by electron microscopy and X-ray diffraction, a discrepancy ascribable to solvation.     

Diffusion and electrophoretic mobility of single-stranded RNA from molecular dynamics simulations

Hydrodynamic properties of small single-stranded RNA homopolymers with three and six nucleotides in free solution are determined from molecular dynamics simulations in explicit solvent. We find that the electrophoretic mobility increases with increasing RNA length, consistent with experiment. Diffusion coefficients of RNA, corrected for finite-size effects and solvent viscosity, agree well with those estimated from experiments and hydrodynamic calculations. The diffusion coefficients and electrophoretic mobilities satisfy a Nernst-Einstein relation in which the effective charge of RNA is reduced by the charge of transiently bound counterions. Fluctuations in the counterion atmosphere are shown to enhance the diffusive spread of RNA molecules drifting along the direction of the external electric field. As a consequence, apparent diffusion coefficients measured by capillary zone electrophoresis can be significantly larger than the actual values at certain experimental conditions.