Dual-focus fluorescence correlation spectroscopy of colloidal solutions: influence of particle size

Fluorescence correlation spectroscopy (FCS) is a powerful technique for measuring diffusion coefficients of small fluorescent molecules at pico- to nanomolar concentrations. Recently, a modified version of FCS, dual-focus FCS (2fFCS), was introduced that significantly improves the reliability and accuracy of FCS measurements and allows for obtaining absolute values of diffusion coefficients without the need of referencing again a known standard. It was shown that 2fFCS gives excellent results for measuring the diffusion of small molecules. However, when measuring colloids or macromolecules, the size of these objects can no longer be neglected with respect to the excitation laser focus. Here, we analyze how 2fFCS data evaluation has to be modified for correctly taking into a count these finite size effects. We exemplify the new method of measuring the absolute size of polymeric particles with simple and complex fluorophore distributions.     

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.     

Perfusive flow and intraparticle distribution of a neutral analyte in capillary electrochromatography

The relevance and magnitude of an electroosmotic perfusion mechanism in electrochromatography is analyzed. To systemize our studies we first considered the transport of an electroneutral and nonadsorbing tracer. Based on the refractive index matching in a microfluidic setup containing fixed spherical porous particles, we conducted a quantitative analysis in real time of the spatio-temporal distribution of fluorescent tracer molecules during their uptake by (and a release from) single particles using confocal laser scanning microscopy. Even under conditions of a significant electrical double layer overlap the intraparticle electroosmotic flow produces due to its unidirectional nature and in striking contrast to the symmetric (spherical) distributions typical for purely diffusive transport strongly asymmetric concentration profiles inside spherical particles as the locally charged pore liquid begins to respond to the externally applied electrical field. The profiles retain an axisymmetric nature, i.e., rotational symmetry with respect to the field direction. Results of our measurements could be successfully interpreted and further analyzed by a compact mathematical model. Intraparticle Peclet numbers of up to 150 have been realized and found to significantly enhance the mass transport on particle scale towards the convection-dominated regime when compared to a conventional (diffusion-limited) kinetics.     

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).     

Accurate sizing of nanoparticles using confocal correlation spectroscopy

The ability to accurately size low concentrations of nanoscale particles in small volumes is useful for a broad range of disciplines. Here, we characterize confocal correlation spectroscopy (CCS), which is capable of measuring the sizes of both fluorescent and nonfluorescent particles, such as quantum dots, gold colloids, latex spheres, and fluorescent beads. We accurately measured particles ranging in diameter from 11 to 300 nm, a size range that had been difficult to probe, owing to a phenomenon coined biased diffusion that causes diffusion times, or particle size, to deviate as a function of laser power. At low powers, artifacts mimicking biased diffusion are caused by saturation of the detector, which is especially problematic when probing highly fluorescent or highly scattering nanoparticles. However, at higher powers (>1 mW), autocorrelation curves in both resonant and nonresonant conditions show a structure indicative of an increased contribution from longer correlation times coupled with a decrease in shorter correlation times. We propose that this change in the autocorrelation curve is due to the partial trapping of the particles as they transit the probe volume. Furthermore, we found only a slight difference in the effect of biased diffusion when comparing resonant and nonresonant conditions. Simulations suggest the depth of trapping potential necessary for biased diffusion is > 1 k(B)T. Overcoming artifacts from detector saturation and biased diffusion, CCS is particularly advantageous due to its ability to size particles in the small volumes characteristic of microfluidic channels and aqueous microdroplets. We believe the method will find increasing use in a wide range of applications in measuring nanoparticles and macromolecular systems.     

Transport in polymer-gel composites: response to a bulk concentration gradient

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. An electrokinetic model was presented in an earlier publication, and the response of homogeneous composites to a weak electric field was calculated. In this work, the influence of the inclusions on bulk ion fluxes and the strength of an electric field (or membrane diffusion potential) induced by the bulk electrolyte concentration gradient are computed. Effective ion diffusion coefficients are significantly altered by the inclusions, so-depending on the inclusion surface charge or zeta potential-asymmetric electrolytes can behave as symmetrical electrolytes and vice versa. The theory also quantifies the strength of flow driven by concentration-gradient-induced perturbations to the equilibrium diffuse double layers. Similarly to diffusiophoresis, the flow may be either up or down the applied concentration gradient.     

Extended photon counting histogram and fluorescence intensity distribution analysis approaches for optically biased photon counting statistics

A gradient potential induced by a strongly focused laser beam can perturb the diffusion dynamics of particles in solutions and result in biased photon counting statistics in fluorescence fluctuation spectroscopy (FFS). In this paper, the theories of the photon counting histogram (PCH) and fluorescence intensity distribution analysis (FIDA) approaches are extended independently to fit the biased experimental data and retrieve the unbiased parameters, i.e., the average number of the sample particles in the focal volume N, their brightness epsilon, and polarizability alpha. The extended theories are tested using Monte Carlo simulations for single- and double-component systems. It is also proved numerically and analytically that the extended PCH and FIDA approaches are completely equivalent. Practical implementations and possible applications of extended PCH and FIDA are discussed.     

On the performance of bioanalytical fluorescence correlation spectroscopy measurements in a multiparameter photon-counting microscope

Fluorescence correlation spectroscopy (FCS) data acquisition and analysis routines were developed and implemented in a home-built, multiparameter photon-counting microscope. Laser excitation conditions were investigated for two representative fluorescent probes, Rhodamine110 and enhanced green fluorescent protein (EGFP). Reliable local concentrations and diffusion constants were obtained by fitting measured FCS curves, provided that the excitation intensity did not exceed 20% of the saturation level for each fluorophore. Accurate results were obtained from FCS measurements for sample concentrations varying from pM to μM range, as well as for conditions of high background signals. These experimental constraints were found to be determined by characteristics of the detection system and by the saturation behavior of the fluorescent probes. These factors actually limit the average number of photons that can be collected from a single fluorophore passing through the detection volume. The versatility of our setup and the data analysis capabilities were tested by measuring the mobility of EGFP in the nucleus of Drosophila cells under conditions of high concentration and molecular crowding. As a bioanalytical application, we studied by FCS the binding affinity of a novel peptide-based drug to the cancer-regulating STAT3 protein and corroborated the results with fluorescence polarization analysis derived from the same photon data.     

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.     

Fluorescence Correlation Spectroscopy Study of Probe Diffusion in Poly(vinyl alcohol) Solutions and Gels

In this study, we demonstrate how the diffusion of probe particles in aqueous poly(vinyl alcohol) (PVA) solutions and gels is affected by: (i) the presence of cross-links, (ii) the cross-link density, (iii) the polymer concentration. We apply fluorescence correlation spectroscopy (FCS) to measure the diffusion time of a rhodamine-based fluorescent particle (TAMRA) and TAMRA-labeled dextran in PVA solutions and gels prepared at various polymer concentrations (1% to 8.6% w/v) and cross-link densities (1/400 to 1/50 cross-link monomers per PVA monomers). The measurements indicate that the probe particles are slowed down with increasing polymer concentration and with increasing cross-link density. Also, FCS can detect differences in the diffusion times measured in “fresh” and “aged” PVA solutions. We find that FCS provides a quantitative measure of network inhomogeneities.     

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.     

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.     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Application of fluorescence correlation spectroscopy to the measurement of local temperature in solutions under optical trapping condition

Fluorescence correlation spectroscopy (FCS) was applied to the quantitative evaluation of the local heating in small domains <1 microm in solutions under the laser trapping condition in the presence of a near-infrared (NIR) laser beam at 1064 nm. On the basis of the translational diffusion coefficient of fluorescent molecules obtained by FCS, the relationship between temperature rise and the incident NIR laser power, DeltaT/DeltaP, were determined to be 62 +/- 6, 49 +/- 7, and 23 +/- 1 deg K/W in ethylene glycol, ethanol, and water, respectively, while no remarkable temperature increase was observed for deuterated water. The value of DeltaT/DeltaP linearly increased as a function of alpha/lambda (alpha is the extinction coefficient of solvent at the wavelength and lambda is the thermal conductivity of the medium). The validity and the applicability of the present method for the measurement of the local temperature increase were discussed by comparing the present results with previous ones by other various methods.     

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.     

Host�Cguest association studied by fluorescence correlation spectroscopy

Fluorescence Correlation Spectroscopy (FCS) is a powerful single molecule technique for the study of the stability and the association dynamics of supramolecular systems and, in particular, of host?Cguest inclusion complexes. With FCS the host?Cguest binding equilibrium constant is determined analysing the variation in the diffusion coefficient of the fluorescent guest or host with no need for a change in the photophysical properties of the fluorescent probe. FCS gives also access to the association/dissociation rate constants of the host?Cguest inclusion providing that the fluorescence intensity of host or guest changes upon complexation. These rate constants can be compared with that of a diffusion-controlled process estimated from the same FCS experiment allowing for a better understanding of the association dynamics. The results show that cyclodextrin cavities act as ??hard?? cages which put geometric and orientational restrictions on the inclusion of a hydrophobic guest, whereas micelles behave as ??soft?? cages without geometrical requirements. In our contribution to this special issue we review briefly the application of FCS to the study of host?Cguest inclusion complexes with an emphasis on practical aspects and relevant bibliographic references.     

Continuous hydrophoretic separation and sizing of microparticles using slanted obstacles in a microchannel

We report a microfluidic separation and sizing method of microparticles with hydrophoresis--the movement of suspended particles under the influence of a microstructure-induced pressure field. By exploiting slanted obstacles in a microchannel, we can generate a lateral pressure gradient so that microparticles can be deflected and arranged along the lateral flows induced by the gradient. Using such movements of particles, we completely separated polystyrene microbeads with 9 and 12 microm diameters. Also, we discriminated polystyrene microbeads with diameter differences of approximately 7.3%. Additionally, we measured the diameter of 10.4 microm beads with high coefficient of variation and compared the result with a conventional laser diffraction method. The slanted obstacle as a microfluidic control element in a microchannel is analogous to the electric, magnetic, optical, or acoustic counterparts in that their function is to generate a field gradient. Since our method is based on intrinsic pressure fields, we could eliminate the need for external potential fields to induce the movement of particles. Therefore, our hydrophoretic method will offer a new opportunity for power-free and biocompatible particle control within integrated microfluidic devices.     

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.     

Phase behavior of a simple dipolar fluid under shear flow in an electric field

Nonequilibrium molecular dynamics simulations are performed on a dense simple dipolar fluid under a planar Couette shear flow. Shear generates heat, which is removed by thermostatting terms added to the equations of motion of the fluid particles. The spatial structure of simple fluids at high shear rates is known to depend strongly on the thermostatting mechanism chosen. Kinetic thermostats are either biased or unbiased: biased thermostats neglect the existence of secondary flows that appear at high shear rates superimposed upon the linear velocity profile of the fluid. Simulations that employ a biased thermostat produce a string phase where particles align in strings with hexagonal symmetry along the direction of the flow. This phase is known to be a simulation artifact of biased thermostatting, and has not been observed by experiments on colloidal suspensions under shear flow. In this paper, we investigate the possibility of using a suitably directed electric field, which is coupled to the dipole moments of the fluid particles, to stabilize the string phase. We explore several thermostatting mechanisms where either the kinetic or configurational fluid degrees of freedom are thermostated. Some of these mechanisms do not yield a string phase, but rather a shear-thickening phase; in this case, we find the influence of the dipolar interactions and external field on the packing structure, and in turn their influence on the shear viscosity at the onset of this shear-thickening regime.     

General bottom-up construction of spherical particles by pulsed laser irradiation of colloidal nanoparticles: a case study on CuO

The development of a general method to fabricate spherical semiconductor and metal particles advances their promising electrical, optical, magnetic, plasmonic, thermoelectric, and optoelectric applications. Herein, by using CuO as an example, we systematically demonstrate a general bottom-up laser processing technique for the synthesis of submicrometer semiconductor and metal colloidal spheres, in which the unique selective pulsed heating assures the formation of spherical particles. Importantly, we can easily control the size and phase of resultant colloidal spheres by simply tuning the input laser fluence. The heating-melting-fusion mechanism is proposed to be responsible for the size evolution of the spherical particles. We have systematically investigated the influence of experimental parameters, including laser fluence, laser wavelength, laser irradiation time, dispersing liquid, and starting material concentration on the formation of colloidal spheres. We believe that this facile laser irradiation approach represents a major step not only for the fabrication of colloidal spheres but also in the practical application of laser processing for micro- and nanomaterial synthesis.