Fluorescence Correlation Spectroscopy Autocorrelation Function Research Articles

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems.

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.

Fluorescence Correlation Spectroscopic Studies of Particle Properties for Colloidal Ceria Abrasives Used in Chemical-Mechanical Planarization

The application of fluorescence correlation spectroscopy (FCS) in the characterization of ceria abrasives used in chemical-mechanical planarization (CMP) slurries is described. A fluorescent dye, Rhodamine 110 (R110), is used for this purpose. R110 adsorption on ceria particles is found to be pH-dependent and colloidal ceria dispersions differing in mean hydrodynamic diameter are analyzed. A Langmuir isotherm is generated for R110 adsorption on ceria, and the magnitude of the Langmuir constant is found to be four-times smaller than the corresponding constant for R110 adsorption on colloidal silica CMP abrasives. R110-labeled ceria particles are generated to quantitatively determine the particle size distribution (PSD) of abrasive ceria dispersions. The Maximum Entropy Method is used reduce the FCS autocorrelation function of R110-labeled ceria particle dispersions thereby producing a PSD. These findings indicate that ceria size distributions containing particles as small as 5 to 10 nm in diameter can be readily characterized using FCS.

A universal model of restricted diffusion for fluorescence correlation spectroscopy.

Fluorescence correlation spectroscopy (FCS) is frequently used to study the processes of restricted diffusion. The most important quantity to determine is the size of the structures that hinder the Brownian motion of the molecules. We study three qualitatively different models of restricted diffusion, widely applied in biophysics and material science: Diffusion constrained by elastic force (i), walking confined diffusion (ii), and hop diffusion (iii). They cover the diversity of statistical behaviors, from purely Gaussian (i) to sharply non-Gaussian on intermediate time scales (ii) and, additionally, discrete (iii). We test whether one can use the Gaussian approximation of the FCS autocorrelation function to interpret the non-Gaussian data. We show that (i-iii) have approximately the same mean square displacements. Using simulations, we show that the FCS data suspected of restricted diffusion can be reliably interpreted using one archetypal model (i). Even if the underlying mechanism of the restriction is different or unknown, the accuracy of fitting the confinement size is excellent, and diffusion coefficients are also estimated with a good accuracy. This study gives a physical insight into the statistical behavior of different types of restricted diffusion and into the ability of fluorescence correlation spectroscopy to distinguish between them.

Fluorescence correlation spectroscopy analysis for accurate determination of proportion of doubly labeled DNA in fluorescent DNA pool for quantitative biochemical assays

Fluorescent double-stranded DNA (dsDNA) molecules labeled at both ends are commonly produced by annealing of complementary single-stranded DNA (ssDNA) molecules, labeled with fluorescent dyes at the same (3′ or 5′) end. Because the labeling efficiency of ssDNA is smaller than 100%, the resulting dsDNA have two, one or are without a dye. Existing methods are insufficient to measure the percentage of the doubly-labeled dsDNA component in the fluorescent DNA sample and it is even difficult to distinguish the doubly-labeled DNA component from the singly-labeled component. Accurate measurement of the percentage of such doubly labeled dsDNA component is a critical prerequisite for quantitative biochemical measurements, which has puzzled scientists for decades. We established a fluorescence correlation spectroscopy (FCS) system to measure the percentage of doubly labeled dsDNA (PDL) in the total fluorescent dsDNA pool. The method is based on comparative analysis of the given sample and a reference dsDNA sample prepared by adding certain amount of unlabeled ssDNA into the original ssDNA solution. From FCS autocorrelation functions, we obtain the number of fluorescent dsDNA molecules in the focal volume of the confocal microscope and PDL. We also calculate the labeling efficiency of ssDNA. The method requires minimal amount of material. The samples have the concentration of DNA in the nano-molar/L range and the volume of tens of microliters. We verify our method by using restriction enzyme Hind III to cleave the fluorescent dsDNA. The kinetics of the reaction depends strongly on PDL, a critical parameter for quantitative biochemical measurements.

Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media

Fluorescence correlation spectroscopy (FCS) is increasingly being used to assess the movement of particles diffusing in complex, optically dense surroundings, in which case measurement conditions may complicate data interpretation. It is considered how a single-photon FCS measurement can be affected if the sample properties result in scattering of the incident light. FCS autocorrelation functions of Atto 488 dye molecules diffusing in solutions of polystyrene beads are measured, which acted as scatterers. Data indicated that a scattering-linked increase in the illuminated volume, as much as two fold, resulted in minimal increase in diffusivity. To analyze the illuminated beam profile, Monte-Carlo simulations were employed, which indicated a larger broadening of the beam along the axial than the radial directions, and a reduction of the incident intensity at the focal point. The broadening of the volume in the axial direction has only negligible effect on the measured diffusion time, since intensity fluctuations due to diffusion events in the radial direction are dominant in FCS measurements. Collectively, results indicate that multiple scattering does not result in FCS measurement artifacts and thus, when sufficient signal intensity is attainable, single-photon FCS can be a useful technique for measuring probe diffusivity in optically dense media.

Anomalous transport resolved in space and time by fluorescence correlation spectroscopy

A ubiquitous observation in crowded cell membranes is that molecular transport does not follow Fickian diffusion but exhibits subdiffusion. The microscopic origin of such a behaviour is not understood and highly debated. Here we discuss the spatio-temporal dynamics for two models of subdiffusion: fractional Brownian motion and hindered motion due to immobile obstacles. We show that the different microscopic mechanisms can be distinguished using fluorescence correlation spectroscopy (FCS) by systematic variation of the confocal detection area. We provide a theoretical framework for space-resolved FCS by generalising FCS theory beyond the common assumption of spatially Gaussian transport. We derive a master formula for the FCS autocorrelation function, from which it is evident that the beam waist of an FCS experiment is a similarly important parameter as the wavenumber of scattering experiments. These results lead to scaling properties of the FCS correlation for both models, which are tested by in silico experiments. Further, our scaling prediction is compatible with the FCS half-value times reported by Wawrezinieck et al. [Biophys. J. 89, 4029 (2005)] for in vivo experiments on a transmembrane protein.

How does sensitivity to dynamical heterogeneity in supercooled colloidal liquids depend on tracer size?

Few experimental investigations have examined the dependence of probe length scale on the evolution of dynamical heterogeneity in supercooled liquids. In this study, we use fluorescent tracer probes, which are smaller than that of the constituent unlabeled particles in the matrix suspension, to investigate the tracer size sensitivity to the onset of dynamical heterogeneity in model hard-sphere colloidal suspensions close to the glass transition. The dynamics of poly(methyl methacrylate) (PMMA) tracer particles of radii a(S) = 137 nm embedded into constituent PMMA particles of a(L) = 212 and 637 nm with bulk volume fraction phi varied from 0.50 to 0.57 is examined using fluorescence correlation spectroscopy (FCS). Upon increasing phi for the largest tracer size ratio explored, f (= a(S)/a(L)) = 0.646, the onset of dynamic heterogeneity is observed from the broad distribution of characteristic decay times of the tracers, which is extracted from the measured FCS autocorrelation functions. The strong coupling between tracer size and its sensitivity to dynamical heterogeneity is reflected in the dynamic susceptibility, where dynamic correlation lengths are immeasurable for the smallest size ratio and show a marked increase to five tracer particle diameters for the largest size ratio.

Stick-and-Diffuse and Caged Diffusion: A Comparison of Two Models of Synaptic Vesicle Dynamics

Two models were recently proposed to enable us to understand the dynamics of synaptic vesicles in hippocampal neurons. In the caged diffusion model, the vesicles diffuse in small circular cages located randomly in the bouton, while in the stick-and-diffuse model the vesicles bind and release from a cellular cytomatrix. In this article, we obtain analytic expressions for the fluorescence correlation spectroscopy (FCS) autocorrelation function for the two models and test their predictions against our earlier FCS measurements of the vesicle dynamics. We find that the stick-and-diffuse model agrees much better with the experiment. We find also that, due to the slow dynamics of the vesicles, the finite experimental integration time has an important effect on the FCS autocorrelation function and demonstrate its effect for the different models. The two models of the dynamics are also relevant to other cellular environments where mobile species undergo slow diffusionlike motion in restricted spaces or bind and release from a stationary substrate.

Microphotonic control of single molecule fluorescence correlation spectroscopy using planar optofluidics

We demonstrate the implementation of fluorescence correlation spectroscopy (FCS) on a chip. Full planar integration is achieved by lithographic definition of sub-picoliter excitation volumes using intersecting solid and liquid-core optical waveguides. Concentration dependent measurements on dye molecules with single molecule resolution are demonstrated. Theoretical modeling of the FCS autocorrelation function in microstructured geometries shows that the FCS behavior can be controlled over a wide range by tailoring the micro-photonic environment. The ability to perform correlation spectroscopy using silicon photonics without the need for free-space microscopy permits implementation of numerous diagnostic applications on compact planar optofluidic devices.

Combining Small Angle Neutron Scattering (SANS) and Fluorescence Correlation Spectroscopy (FCS) Measurements To Relate Diffusion in Agarose Gels to Structure

Small angle neutron scattering (SANS) and fluorescence correlation spectroscopy (FCS) measurements were carried out on agarose hydrogels to link their microscopic structure to the diffusivity of solutes at different scales. SANS allowed for the determination of the distribution of void volumes within the gels. They were shown to be compatible with a random network of cylindrical fibers as described by the Ogston model. FCS measured solute diffusivity in spaces similar in size to the void volumes, and thus, the results reflected the gel heterogeneity. Solute diffusivity was predicted by modeling the gel as microscopic geometrical cells. Variations in the diffusivity of solutes of different sizes could be predicted from the structural parameters of the gel using theory, taking into account obstruction by cylindrical cells and solute hydrodynamics. Prediction of the FCS autocorrelation functions for solutes from a cell model demonstrated a lack of sensitivity of this technique for multicomponent analysis.

Ligand binding by estrogen receptor beta attached to nanospheres measured by fluorescence correlation spectroscopy

Although many indirect methods have been chosen to study the system of estrogen receptor ligand binding, an ideal method is fluorescence correlation spectroscopy (FCS). FCS is nondestructive to the sample, uses very small sample volumes, and operates well within physiological concentration ranges. The methodology was developed to biotinylate the estrogen receptor beta-ligand binding domain (ERbeta-LBD) using biotin with a very short spacer and to then attach this protein to a 40 nm neutravidin-coated bead (nanosphere). Diffusional FCS data were obtained for a fluorescently labeled coactivator peptide, steroid receptor coactivator peptide-1 (A-SRC-1(2)), in the absence and presence of bead-bound ERbeta-LBD. Data were also acquired in the presence of one of the endogenous ligands for ERbeta, 17beta-estradiol, and with tamoxifen. The bead strategy resulted in a decreased receptor diffusion coefficient and consequent increase in the decay time of the FCS autocorrelation functions for receptor-bound, labeled SRC-1(2). Thus, free and bound coactivators were much more readily distinguished by FCS. Discrimination between the fluorescently labeled unbound and bound species could be determined in autocorrelation functions obtained in as few as 30 s. The advantage of using FCS with the ERbeta-LBD: bead methodology is the ability to obtain reliable and reproducible data in a short time frame.

Noise on Fluorescence Correlation Spectroscopy

The time dependence of the noise and the signal-to-noise (SN) ratio of the fluorescence correlation spectroscopy (FCS) autocorrelation function is obtained from replica measurements of standard dextran solutions. The noise dependence on the delay time is fitted by a hyperbolic function with two fitting parameters. The dependence of these parameters on concentration, fluorescence intensity, and accumulation time is obtained experimentally. The behavior of SN at zero delay time agrees well with the theoretical predictions reported in the literature. The obtained data are useful for the quantitative evaluation of the FCS data fits, as well as for simulation of the FCS autocorrelation functions.

Applications of Fluorescence Correlation Spectroscopy— Particle Size Effect

Both computer simulations and experiments have been employed to study the fluorescence correlation spectroscopy autocorrelation function of particles with size comparable to the size of the light beam. When such particles are labeled by several fluorophores the characteristic time of diffusion and the particle number in the light beam are larger than those expected from the existing theory developed for the case of a point size diffuser. The resulting effect is described by simple equations.

On the measurement of particle number and mobility in nonideal solutions by fluorescence correlation spectroscopy

Interparticle interactions are incorporated into the theoretical description of the initial amplitude, G(0), of the normalized fluorescence correlation spectroscopy autocorrelation function. Measurements of particle number, aggregate size, and interaction-dependent diffusion are then analyzed in the context of this generalized theory. It is shown that the neglect of interactions can introduce order-of-magnitude errors into estimates of particle number and aggregate size. It is also shown that measurement of G(0) provides an essentially unique method for testing the validity of theories of interaction-dependent membrane protein diffusion.

Theory of sample translation in fluorescence correlation spectroscopy

New applications of the technique of fluorescence correlation spectroscopy (FCS) require lateral translation of the sample through a focused laser beam (Peterson, N.O., D.C. Johnson, and M.J. Schlesinger, 1986, Biophys. J., 49:817-820). Here, the effect of sample translation on the shape of the FCS autocorrelation function is examined in general. It is found that if the lateral diffusion coefficients of the fluorescent species obey certain conditions, then the FCS autocorrelation function is a simple product of one function that depends only on transport coefficients and another function that depends only on the rate constants of chemical reactions that occur in the sample. This simple form should allow manageable data analyses in new FCS experiments that involve sample translation.