Quantifying lipid diffusion by fluorescence correlation spectroscopy: a critical treatise

Fluorescence correlation spectroscopy (FCS) measurements are widely used for determination of diffusion coefficients of lipids and proteins in biological membranes. In recent years, several variants of FCS have been introduced. However, a comprehensive comparison of these methods on identical systems has so far been lacking. In addition, there exist no consistent values of already determined diffusion coefficients for well-known or widely used membrane systems. This study aims to contribute to a better comparability of FCS experiments on membranes by determining the absolute diffusion coefficient of the fluorescent lipid analog 1,1'-dioctadecyl-3,3,3',3'-tetramethylindodicarbocyanine (DiD) in giant unilamellar vesicles (GUVs) made of dioleoylphosphatidylcholine (DOPC), which can in future studies be used as a reference value. For this purpose, five FCS variants, employing different calibration methods, were compared. Potential error sources for each particular FCS method and strategies to avoid them are discussed. The obtained absolute diffusion coefficients for DiD in DOPC were in good agreement for all investigated FCS variants. An average diffusion coefficient of D = 10.0 ± 0.4 μm(2) s(-1) at 23.5 ± 1.5 °C was obtained. The independent confirmation with different methods indicates that this value can be safely used for calibration purposes. Moreover, the comparability of the methods also in the case of slow diffusion was verified by measuring diffusion coefficients of DiD in GUVs consisting of DOPC and cholesterol.     

Molecular Diffusion Measurement in Lipid Bilayers over Wide Concentration Ranges: A Comparative Study

Molecular diffusion in biological membranes is a determining factor in cell signaling and cell function. In the past few decades, three main fluorescence spectroscopy techniques have emerged that are capable of measuring molecular diffusion in artificial and biological membranes at very different concentration ranges and spatial resolutions. The widely used methods of fluorescence recovery after photobleaching (FRAP) and single‐particle tracking (SPT) can determine absolute diffusion coefficients at high (>100 μm^?2) and very low surface concentrations (single‐molecule level), respectively. Fluorescence correlation spectroscopy (FCS), on the other hand, is well‐suited for the intermediate concentration range of about 0.1–100 μm^?2. However, FCS in general requires calibration with a standard dye of known diffusion coefficient, and yields only relative measurements with respect to the calibration. A variant of FCS, z‐scan FCS, is calibration‐free for membrane measurements, but requires several experiments at different well‐controlled focusing positions. A recently established FCS method, electron‐multiplying charge‐coupled‐device‐based total internal reflection FCS (TIR‐FCS), referred to here as imaging TIR‐FCS (ITIR–FCS), is also independent of calibration standards, but to our knowledge no direct comparison between these different methods has been made. Herein, we seek to establish a comparison between FRAP, SPT, FCS, and ITIR–FCS by measuring the lateral diffusion coefficients in two model systems, namely, supported lipid bilayers and giant unilamellar vesicles.     

Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements.

We present a new method to measure absolute diffusion coefficients at nanomolar concentrations with high precision. Based on a modified fluorescence correlation spectroscopy (FCS)-setup, this method is improved by introducing an external ruler for measuring the diffusion time by generating two laterally shifted and overlapping laser foci at a fixed and known distance. Data fitting is facilitated by a new two-parameter model to describe the molecule detection function (MDF). We present a recorded MDF and show the excellent agreement with the fitting model. We measure the diffusion coefficient of the red fluorescent dye Atto655 under various conditions and compare these values with a value achieved by gradient pulsed field NMR (GPF NMR). From these measurements we conclude, that the new measurement scheme is robust against optical and photophysical artefacts which are inherent to standard FCS. With two-focus-FCS, the diffusion coefficient of 4.26 x 10(-6) cm2s(-1) for Atto655 in water at 25 degrees C compares well with the GPF NMR value of 4.28 x 10(-6) cm2s(-1).     

Calibration and Limits of Camera‐Based Fluorescence Correlation Spectroscopy: A Supported Lipid Bilayer Study

Camera‐based fluorescence correlation spectroscopy (FCS) approaches allow the measurement of thousands of contiguous points yielding excellent statistics and details of sample structure. Imaging total internal reflection FCS (ITIR‐FCS) provides these measurements on lipid membranes. Herein, we determine the influence of the point spread function (PSF) of the optical system, the laser power used, and the time resolution of the camera on the accuracy of diffusion coefficient and concentration measurements. We demonstrate that the PSF can be accurately determined by ITIR‐FCS and that the laser power and time resolution can be varied over a wide range with limited influence on the measurement of the diffusion coefficient whereas the concentration measurements are sensitive to changes in the measurement parameters. One advantage of ITIR‐FCS is that the measurement of the PSF has to be performed only once for a given optical setup, in contrast to confocal FCS in which calibrations have to be performed at least once per measurement day. Using optimized experimental conditions we provide diffusion coefficients for over ten different lipid membranes consisting of one, two and three constituents, measured in over 200000 individual correlation functions. Using software binning and thus the inherent advantage of ITIR‐FCS of providing multiple observation areas in a single measurement we test the FCS diffusion law and show how they can be complemented by the local information provided by the difference in cross‐correlation functions (ΔCCF). With the determination of the PSF by ITIR‐FCS and the optimization of measurement conditions ITIR‐FCS becomes a calibration‐free method. This allows us to provide measurements of absolute diffusion coefficients for bilayers with different compositions, which were stable over many different bilayer preparations over a time of at least one year, using a single PSF calibration.     

Fluorescence correlation spectroscopy of water-in-oil microemulsions: an application in specific characterisation of droplets containing biomolecules

Fluorescence correlation spectroscopy (FCS) has been successfully used to characterise water-in-oil (w/o) microemulsions. The investigated systems were stabilised by sodium bis-2-ethylhexyl sulphosuccinate (AOT) and the measured diffusion times have been related to the radii of the aggregated species, which for some systems, were separately determined by small-angle neutron scattering (SANS). We demonstrate that FCS is capable of measuring hydrodynamic radii of microemulsions rapidly and at surfactant concentrations lower than previously reported for other techniques. FCS was also used to specifically interrogate microemulsion droplets containing a fluorescently-labelled biomolecule, specifically phalloidin, a peptide fungal toxin from Amanita phalloides, and the enzyme -chymotrypsin (-CT). The microemulsion droplets are only marginally increased in size if a small peptide (phalloidin) is included in the water phase, whereas the droplet size is significantly increased when a larger protein (-CT) is included.     

荧光关联光谱在高分子单链研究中的应用

荧光关联光谱(fluorescence correlation spectroscopy,FCS)是一项用于研究体系动力学性质的统计光谱技术,随着它被引入材料与化学研究领域,近年来取得了大量全新的研究成果.该技术在高分子科学研究中也逐渐发挥出越来越大的作用,特别是在聚合物结构和动力学方面,这表明它在高分子领域的巨大潜力.本文将从FCS的基本原理、实验技巧以及在一些具有挑战性体系中的应用等方面展开,着重介绍它在高分子溶液,如聚电解质溶液、高分子混致不溶现象,以及不同的表界面体系中取得的新成果,展示FCS区别于其他传统技术的特点和优势.     

Fluorescence correlation spectroscopy in colloid and interface science

In the last two decades fluorescence correlation spectroscopy (FCS) has been increasingly applied to analyze systems and processes relevant to colloid and interface science. The method has become a routine tool to measure the hydrodynamic radii of small fluorescent molecules, macromolecules and nanoparticles, characterize their interactions and follow a possible aggregation. It was also used to study the diffusion of such species in inhomogeneous media like polymer melts, solutions, gels or porous structures. The formation kinetics and size of micelles of surfactants or block copolymers has been quantified. FCS has also been applied to characterize diffusion of tracers at fluid–liquid and solid–liquid interfaces and study the hydrodynamic boundary condition. The review is intended to summarize these applications and highlight perspectives but also limits of FCS in colloid and interface science.     

Heterogeneity of diffusion inside microbial biofilms determined by fluorescence correlation spectroscopy under two-photon excitation

Fluorescence correlation spectroscopy (FCS) under two-photon excitation was applied successfully to characterize the penetration and diffusion capabilities of fluorescent probes (latex beads and fluorescein isothiocyanate-dextran) of different size and electrical charge in two models of monomicrobial biofilms with low (Lactococcus lactis biofilm) or high (Stenotrophonas maltophilia biofilm) contents of extracellular polymeric substance (EPS). FCS measurements performed on each biofilm can show deviation from Brownian diffusion, depending on the local structure of the biofilm and the fluorophore size. In this case, we fitted the data to an anomalous diffusion model and determined apparent diffusion coefficients, which can be 50 times smaller than the values in aqueous solutions. This result was interpreted as steric hindrance of the diffusion of the fluorescent particles within the biofilm that can lead to a total inhibition as observed particularly in the mushroom-like structure of the S. maltophilia biofilm. Alternatively, mechanisms for the absence of FCS signal behavior were related to attractive electrostatic interactions between cationic particles and negatively charged bacteria or to specific interactions between dextrans and EPS of the biofilm matrix.     

Local and average diffusion of nanosolutes in agarose gel: the effect of the gel/solution interface structure

Fluorescence correlation spectroscopy (FCS) has been used to study the diffusion of nanometric solutes in agarose gel, at microscopic and macroscopic scales. Agarose gel was prepared and put in contact with aqueous solution. Several factors were studied: (i) the role of gel relaxation after its preparation, (ii) the specific structure of the interfacial zone and its role on the local diffusion coefficient of solutes, and (iii) the comparison between the local diffusion coefficient and the average diffusion coefficient in the gel. Fluorescent dyes and labeled biomolecules were used to cover a size range of solutes of 1.5 to 15 nm. Their transport through the interface from the solution toward the gel was modeled by the first Fick's law based on either average diffusion coefficients or the knowledge of local diffusion coefficients in the system. Experimental results have shown that, at the liquid/gel interface, a gel layer with a thickness of 120 microm is formed with characteristics significantly different from the bulk gel. In particular, in this layer, the porosity of agarose fiber network is significantly lower than in the bulk gel. The diffusion coefficient of solutes in this layer is consequently decreased for steric reasons. Modeling of solute transport shows that, in the bulk gel, macroscopic diffusion satisfactorily follows the classical Fick's diffusion laws. For the tested solutes, the local diffusion coefficients in the bulk gel, measured at microscopic scale by FCS, were equal, within experimental errors, to the average diffusion coefficients applicable at macroscopic scales (>or=mm). This confirms that anomalous diffusion applies only to solutes with sizes close to the gel pore size and at short time (相似文献   

Size dependence of protein diffusion very close to membrane surfaces: measurement by total internal reflection with fluorescence correlation spectroscopy

The diffusion coefficients of nine fluorescently labeled antibodies, antibody fragments, and antibody complexes have been measured in solution very close to supported planar membranes by using total internal reflection with fluorescence correlation spectroscopy (TIR-FCS). The hydrodynamic radii (3-24 nm) of the nine antibody types were determined by comparing literature values with bulk diffusion coefficients measured by spot FCS. The diffusion coefficients very near membranes decreased significantly with molecular size, and the size dependence was greater than that predicted to occur in bulk solution. The observation that membrane surfaces slow the local diffusion coefficient of proteins in a size-dependent manner suggests that the primary effect is hydrodynamic as predicted for simple spheres diffusing close to planar walls. The TIR-FCS data are consistent with predictions derived from hydrodynamic theory. This work illustrates one factor that could contribute to previously observed nonideal ligand-receptor kinetics at model and natural cell membranes.     

Applications of Fluorescence Correlation Spectroscopy: Polydispersity Measurements

The method of histograms is applied to the determination of polydispersity of particles and molecules in solution from fluorescence correlation spectroscopy (FCS) data. This is an ill-posed problem, which can be overcome by using a common strategy for imposed regularization and constraint conditions. The method developed for evaluating the polydispersity is tested on both computer-generated correlation curves and real FCS data. The results obtained show that FCS measurements can be successfully used for the determination of polydispersity of suspensions, with an efficiency comparable to that of photon correlation spectroscopy (PCS). The advantage of FCS, however, is its better sensitivity to small particles (size <50 nm) and molecules in dilute solutions, as well as its better selectivity. The usefulness of FCS for environmental chemistry is discussed with regard to the obtained results. Copyright 1999 Academic Press.     

Size and shape of fast-tumbling bicelles as determined by translational diffusion

In this study, the size and shape of an isotropic bicelle have been determined by measuring the translational diffusion as a function of the volume fraction of the lipids. A linear relation between the diffusion coefficients is obtained for both DMPC and DHPC in the bicelles. The slope of this linear function, which is strongly shape-dependent, is found to be different for the two molecules. This difference is direct evidence that the two molecules are not fully mixed in the bicelle. The shape- combined with the size-dependence of the diffusion coefficient allows us to calculate both the size and shape of the bicelle.     

Diffusivity of asphaltene molecules by fluorescence correlation spectroscopy

Using fluorescence correlation spectroscopy (FCS) we measure the translational diffusion coefficient of asphaltene molecules in toluene at extremely low concentrations (0.03-3.0 mg/L): where aggregation does not occur. We find that the translational diffusion coefficient of asphaltene molecules in toluene is about 0.35 x 10(-5) cm(2)/s at room temperature. This diffusion coefficient corresponds to a hydrodynamic radius of approximately 1 nm. These data confirm previously estimated size from rotational diffusion studied using fluorescence depolarization. The implication of this concurrence is that asphaltene molecular structures are monomeric, not polymeric.     

Measuring the mutual diffusion coefficient for dodecyl acrylate in low molecular weight poly(dodecyl acrylate) with laser line deflection (Wiener's Method) and the fluorescence of pyrene

Diffusion of small molecules into glassy polymers is quite complicated and almost always non-Fickian. Little work has been done with the diffusion of low molecular weight polymers that are liquids at room temperature (such as poly(dodecyl acrylate)) into their miscible monomers. We have studied three molecular weights under 20 000 to determine if poly(dodecyl acrylate) diffusion into dodecyl acrylate could be treated with Fick's law and if so to determine the values of the diffusion coefficients. We compare two methods for measuring the diffusion of dodecyl acrylate into poly(dodecyl acrylate): We used laser line deflection (Wiener's method) and improved upon the method from published reports. We also used the dependence of pyrene's fluorescence on the viscosity to measure the concentration distribution, and thus to extract the diffusion coefficient. After an initial relaxation period, diffusion in all cases followed Fick's law with a single concentration-independent diffusion coefficient. Comparison of the diffusion coefficients obtained by both methods yielded the same order of magnitude for the diffusion coefficients (10(-7) cm2/s) and showed the same trend in the dependence on the average molecular weight of the polymer (a decrease in the diffusion coefficient with an increase in the molecular weight).     

Self-diffusion of rodlike and spherical particles in a matrix of charged colloidal spheres: a comparison between fluorescence recovery after photobleaching and fluorescence correlation spectroscopy

The fluorescence recovery after photobleaching (FRAP) method and the fluorescence correlation spectroscopy (FCS) have been applied on suspensions of highly charged colloidal spheres with a small content of rod-shaped tobacco mosaic virus (TMV) particles. Since these methods only determine the self-diffusion coefficient of the fluorescently labeled species, D(S) of the rods and the spheres could independently be measured. The ionic strength of the dispersion medium has been varied to measure self-diffusion of rods and spheres in dependence on the degree of order of the matrix spheres. In contrast to FRAP, which allows the determination of the long-time self-diffusion coefficient D(S) (L), FCS measures self-diffusion on a shorter time scale. Thus a comparison of the results that were obtained by FCS and FRAP, in combination with Brownian Dynamics simulations, gives insight into the time dependence of the self-diffusion coefficient of an interacting colloidal system. As the mean interparticle distance of the matrix is of the same order of magnitude as the length of a TMV rod, the rotational motion is influenced by the assembly of spheres around a TMV particle. Since FCS is sensitive both to translational and rotational motion, whereas FRAP, which probes the diffusion at much larger length scales, is only sensitive to the translational motion of TMV, the comparison of diffusion coefficients measured employing FRAP and FCS can give some insights in the rotational diffusion: the experimental data indicate a slowing down of the rotational motion of a TMV rod with increasing structural order of the matrix spheres.     

Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.     

The characterization of polymer interfaces by fluorescence decay measurements

Fluorescence decay measurements of energy transfer between donor (D) and acceptor (A) chromophores covalently attached to polymers can provide rich information about a polymer system. Here we use these techniques to study two quite different polymer phenomena. The first involves the diffusion of polymer molecules across the interfaces created during latex film formation. We are able to determine diffusion coefficients for this process. The second involves the phase separation which occurs in mixtures of homopolymers and graft copolymers. Here we are able to show that where a component of the graft is highly incompatible with the homopolymer matrix, interconnected domains of very small size can form. Under certain circumstances fluorescence decay measurements in conjunction with the recent model for “energy transfer in restricted geometrics” can be used to map out the size and shape of these domains.     

Correlation of transverse and rotational diffusion coefficient: a probe of chemical composition in hydrocarbon oils

Measurements of relaxation time and diffusion coefficient by nuclear magnetic resonance are well-established techniques to study molecular motions in fluids. Diffusion measurements sense the translational diffusion coefficients of the molecules, whereas relaxation times measured at low magnetic fields probe predominantly the rotational diffusion of the molecules. Many complex fluids are composed of a mixture of molecules with a wide distribution of sizes and chemical properties. This results in correspondingly wide distributions of measured diffusion coefficients and relaxation times. To first order, these distributions are determined by the distribution of molecular sizes. Here we show that additional information can be obtained on the chemical composition by measuring two-dimensional diffusion-relaxation distribution functions, a quantity that depends also on the shape and chemical interactions of molecules. We illustrate this with experimental results of diffusion-relaxation distribution functions on a series of hydrocarbon mixtures. For oils without significant amounts of asphaltenes, the diffusion-relaxation distribution functions follow a power-law behavior with an exponent that depends on the relative abundance of saturates and aromatics. Oils with asphaltene deviate from this trend, as asphaltene molecules act as relaxation contrast agent for other molecules without affecting their diffusion coefficient significantly. In waxy oils below the wax appearance temperature a gel forms. This is reflected in the measured diffusion-relaxation distribution functions, where the restrictions due to the gel network reduce the diffusion coefficients without affecting the relaxation rates significantly.     

Atomistic simulations of hydrated nafion and temperature effects on hydronium ion mobility

The effects of hydration level and temperature on the nanostructure of an atomistic model of a Nafion (DuPont) membrane and the vehicular transport of hydronium ions and water molecules were examined using classical molecular dynamics simulations. Through the determination and analysis of structural and dynamical parameters such as density, radial distribution functions, coordination numbers, mean square deviations, and diffusion coefficients, we identify that hydronium ions play an important role in modifying the hydration structure near the sulfonate groups. In the regime of low level of hydration, short hydrogen bonded linkages made of water molecules and sometimes hydronium ions alone give a more constrained structure among the sulfonate side chains. The diffusion coefficient for water was found to be in good accord with experimental data. The diffusion coefficient for the hydronium ions was determined to be much smaller (6-10 times) than that for water. Temperature was found to have a significant effect on the absolute value of the diffusion coefficients for both water and hydronium ions.