Analysis Of Fluorescence Correlation Spectroscopy Data 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.

Statistical analysis of the autocorrelation function in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful method to measure concentration, mobility, and stoichiometry in solution and in living cells, but quantitative analysis of FCS data remains challenging due to the correlated noise in the autocorrelation function (ACF) of FCS. We demonstrate here that least-squares fitting of the conventional ACF is incompatible with the χ2 goodness-of-fit test and systematically underestimates the true fit parameter uncertainty. To overcome this challenge, a simple method to fit the ACF is introduced that allows proper calculation of goodness-of-fit statistics and that provides more tightly constrained parameter estimates than the conventional least-squares fitting method, achieving the theoretical minimum uncertainty. Because this method requires significantly more data than the standard method, we further introduce an approximate method that requires fewer data. We demonstrate both these new methods using experiments and simulations of diffusion. Finally, we apply our method to FCS data of the peripheral membrane protein HRas, which has a slow-diffusing membrane-bound population and a fast-diffusing cytoplasmic population. Despite the order-of-magnitude difference of the diffusion times, conventional FCS fails to reliably resolve the two species, whereas the new method identifies the correct model and provides robust estimates of the fit parameters for both species.

FCSNet and ImFCSNet, convolutional neural network approaches to FCS data analysis.

Fluorescence Correlation Spectroscopy (FCS) is a widely used tool to analyse molecular dynamics in biological samples. It analyses the correlation function of the fluorescence fluctuations in a defined observation volume to extract information about the underlying molecular processes. However, FCS faces a number of challenges. First, it requires the use of theoretical fit models that often cannot be solved exactly and thus require approximations. Second, the measurement times for FCS are comparatively long, on the order of a minute, to obtain accurate parameter estimates. Third, the data analysis can be computationally quite time consuming. We therefore explore deep learning approaches to address these issues. For this purpose, we focus on Imaging FCS, a camera-based FCS modality, that provides correlation functions at or between any pixels on a camera, without loss of generality. We developed two convolutional neural networks (CNNs). FCSNet and ImFCSNet use either correlation functions or raw intensity traces as input, respectively. Both networks are trained on simulated, synthetic data, as it is difficult to obtain ground truth data for FCS over wide parameter ranges. More importantly, it allows us to use arbitrary experimental geometries and molecular processes, even when analytic models are not available for conventional fitting, thus solving the first problem. We demonstrate that the two CNNs perform well on synthetic and experimental data and outperform conventional nonlinear least squares (NLS) fits by a) requiring about one order of magnitude less data, b) providing higher precision for parameter estimates, and c) being two orders of magnitude faster. To demonstrate the power of CNNs we present comparisons of data evaluations by conventional NLS fitting on lipid bilayers and cells and on data recorded on total internal reflection and light sheet microscopes.

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking.

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Bayesian Approach to Fluorescence Correlation Spectroscopy Data Analysis - The Danger of Least-Square Fitting

Bayesian Approach to Fluorescence Correlation Spectroscopy Data Analysis - The Danger of Least-Square Fitting

Reconceptualizing Fluorescence Correlation Spectroscopy for Monitoring and Analyzing Periodically Passing Objects.

Fluorescence correlation spectroscopy (FCS) is a sensitive technique commonly applied for studying the dynamics of nanoscale-labeled objects in solution. Current analysis of FCS data is largely based on the assumption that the labeled objects are stochastically displaced due to Brownian motion. However, this assumption is often invalid for microscale objects, since the motion of these objects is dominated by Stokes drag and settling or rising effects, rather than stochastic Brownian motion. To utilize the power of FCS for systems with nonstochastic displacements of objects, the collection and analysis of FCS data have to be reconceptualized. Here, we extended the applicability of FCS for the detection and analysis of periodically passing objects. Toward this end, we implemented droplet-based microfluidics, in which monodispersed droplets containing fluorescent marker are flowing equally spaced within microchannels. We show by simulations and experiments that FCS can sensitively quantify the flow-rates, variability, and content of rapidly passing droplets. This information can be derived at high temporal resolution, based on the intensity fluctuations generated by only 5–10 passing droplets. Moreover, by utilizing the periodicity of the flowing droplets for noise reduction by averaging, FCS can monitor accurately the droplets flow even if their fluorescence intensity is negligible. Hence, extending FCS for periodically passing objects converts it into a powerful analytical tool for high-throughput droplet-based microfluidics. Moreover, based on the principles described here, FCS can be straightforwardly applied for a variety of systems in which the passing of objects is periodic rather than stochastic.

Medicinal value of asiaticoside for Alzheimer's disease as assessed using single-molecule-detection fluorescence correlation spectroscopy, laser-scanning microscopy, transmission electron microscopy, and in silico docking.

BackgroundIdentifying agents that inhibit amyloid beta peptide (Aβ) aggregation is the ultimate goal for slowing Alzheimer’s disease (AD) progression. This study investigated whether the glycoside asiaticoside inhibits Aβ1–42 fibrillation in vitro.MethodsFluorescence correlation spectroscopy (FCS), evaluating the Brownian diffusion times of moving particles in a small confocal volume at the single-molecule level, was used. If asiaticoside inhibits early Aβ1–42 fibrillation steps, more Aβs would remain free and rapidly diffuse in the confocal volume. In contrast, “weaker or no inhibition” permits a greater number of Aβs to polymerize into oligomers, leading to fibers and gives rise to slow diffusion times in the solution. Trace amounts of 5-carboxytetramethylrhodamine (TAMRA)-labeled Aβ1–42 in the presence of excess unlabeled Aβ1–42 (10 μM) was used as a fluorescent probe. Steady-state and kinetic-Thioflavin T (ThT) fluorospectroscopy, laser-scanning fluorescence microscopy (LSM), and transmission electron microscopy (TEM) were also used to monitor fibrillation. Binding of asiaticoside with Aβ1–42 at the atomic level was computationally examined using the Molegro Virtual Docker and PatchDock.ResultsWith 1 h of incubation time for aggregation, FCS data analysis revealed that the diffusion time of TAMRA-Aβ1–42 was 208 ± 4 μs, which decreased to 164 ± 8.0 μs in the presence of asiaticoside, clearly indicating that asiaticoside inhibited the early stages Aβ1–42 of fibrillation, leaving more free Aβs in the solution and permitting their rapid diffusion in the confocal volume. The inhibitory effects were also evidenced by reduced fiber formation as assessed by steady-state and kinetic ThT fluorospectroscopy, LSM, and TEM. Asiaticoside elongated the lag phase of Aβ1–42 fibrillation, indicating the formation of smaller amyloid species were impaired in the presence of asiaticoside. Molecular docking revealed that asiaticoside binds with amyloid intra- and inter-molecular amino acid residues, which are responsible for β-sheet formation and longitudinal extension of fibrils.ConclusionFinally, asiaticoside prevents amyloidogenesis that precedes neurodegeneration in patients with Alzheimer’s disease.

Bayesian model selection applied to the analysis of fluorescence correlation spectroscopy data of fluorescent proteins in vitro and in vivo.

Fluorescence correlation spectroscopy (FCS) is a powerful technique to investigate molecular dynamics with single molecule sensitivity. In particular, in the life sciences it has found widespread application using fluorescent proteins as molecularly specific labels. However, FCS data analysis and interpretation using fluorescent proteins remains challenging due to typically low signal-to-noise ratio of FCS data and correlated noise in autocorrelated data sets. As a result, naive fitting procedures that ignore these important issues typically provide similarly good fits for multiple competing models without clear distinction of which model is preferred given the signal-to-noise ratio present in the data. Recently, we introduced a Bayesian model selection procedure to overcome this issue with FCS data analysis. The method accounts for the highly correlated noise that is present in FCS data sets and additionally penalizes model complexity to prevent over interpretation of FCS data. Here, we apply this procedure to evaluate FCS data from fluorescent proteins assayed in vitro and in vivo. Consistent with previous work, we demonstrate that model selection is strongly dependent on the signal-to-noise ratio of the measurement, namely, excitation intensity and measurement time, and is sensitive to saturation artifacts. Under fixed, low intensity excitation conditions, physical transport models can unambiguously be identified. However, at excitation intensities that are considered moderate in many studies, unwanted artifacts are introduced that result in nonphysical models to be preferred. We also determined the appropriate fitting models of a GFP tagged secreted signaling protein, Wnt3, in live zebrafish embryos, which is necessary for the investigation of Wnt3 expression and secretion in development. Bayes model selection therefore provides a robust procedure to determine appropriate transport and photophysical models for fluorescent proteins when appropriate models are provided, to help detect and eliminate experimental artifacts in solution, cells, and in living organisms.

Protein oligomerization equilibria and kinetics investigated by fluorescence correlation spectroscopy: a mathematical treatment.

Fluorescence correlation spectroscopy (FCS) is a technique that is increasingly being used to investigate protein oligomerization equilibria and dynamics. Each individual FCS decay is characterized by its amplitude and a characteristic diffusion time, both of which are sensitive to the degree of dissociation of the protein. Here, we provide a mathematical treatment that relates these observables with the parameters of interest: the equilibrium constants of the different protein dissociation steps and their corresponding dissociation and association kinetic rate constants. We focused on the two most common types of protein homooligomers (dimers and tetramers) and on the experimental variables relevant for the design of the experiment (protein concentration, fractional concentration of labeled protein). The analysis of the theoretical expectations for proteins with different dissociation constants is a key aspect of experiment design and data analysis and cannot be performed without a physically accurate treatment of the system. In particular, we show that the analysis of FCS data using some commonly used empirical models may result in a serious misinterpretation of the experimental results.

Fluorescence correlation spectroscopy: principles and applications.

Fluorescence correlation spectroscopy (FCS) is used to study the movements and the interactions of biomolecules at extremely dilute concentrations, yielding results with good spatial and temporal resolutions. Using a number of technical developments, FCS has become a versatile technique that can be used to study a variety of sample types and can be advantageously combined with other methods. Unlike other fluorescence-based techniques, the analysis of FCS data is not based on the average intensity of the fluorescence emission but examines the minute intensity fluctuations caused by spontaneous deviations from the mean at thermal equilibrium. These fluctuations can result from variations in local concentrations owing to molecular mobility or from characteristic intermolecular or intramolecular reactions of fluorescently labeled biomolecules present at low concentrations. Here, we provide a basic introduction to FCS, including its technical development and theoretical basis, experimental setup of an FCS system, adjustment of a setup, data acquisition, and analysis of FCS measurements. Finally, the application of FCS to the study of lipid bilayer membranes and to living cells is discussed.

Fluorescence Correlation Spectroscopic Investigation of Surface Adsorption of CMP Slurry Additives on Abrasive Particles

ABSTRACTAdditive-abrasive interactions in chemical-mechanical planarization (CMP) slurries are investigated using fluorescence correlation spectroscopy (FCS). The FCS technique provides quantitative determinations of the interaction between additives and abrasive particles by characterizing the competitive adsorption of the additive and a fluorescent probe molecule by an abrasive particle. Adsorption of the CMP additives glycine and benzotriazole (BTA) on precipitated and sol-gel colloidal silica abrasives are characterized. Significant differences in the fluorescent probe’s adsorption to the different silica abrasives in the presence of the additives suggest surface chemistry differences between the different types of silica. Extensions of the analysis of FCS data are proposed for improving the quantitative determination of the competitive adsorption of fluorescent probe dyes and CMP additives on abrasive particles.

Amplitude of Relaxations in Fluorescence Correlation Spectroscopy for Fluorophores That Diffuse Together.

The amplitude of chemical relaxations in fluorescence correlation spectroscopy (FCS) is an important parameter that directly relates to not only the equilibrium constant of the relaxations but also the number of individual fluorophores that diffuse together. In this Letter we answer the question how exactly the amplitude of the relaxations in FCS changes with respect to the number of identical fluorophores on one cargo. We anchored tetramethylrhodamine molecules onto each arm of a DNA Holliday junction molecule so that the codiffusing dyes were capable of performing independent fluorescent fluctuations. We found that the amplitudes of the relaxations were inversely proportional to the number of the dyes on each cargo molecule, well agreeing with the theoretical prediction derived in this Letter. The result provides a guideline for the FCS data analysis and points out a simple way to determine the number of molecules that a cargo carries.

Bayesian Fluorescence Correlation Microscopy to Resolve Heterogeneity in Membrane Protein Dynamics

Fluorescence Correlation Spectroscopy (FCS) is a powerful tool to measure molecular dynamics with single molecule sensitivity, including local concentrations, aggregation states, and transport mechanisms. Due to its high spatial-temporal resolution and non-invasive nature, FCS has been widely used to probe molecular dynamics in living systems. In contrast to single point detection in traditional confocal FCS, advances in Electron-Multiplying Charge-Coupled Device (EM-CCD) camera technology, Total Internal Reflection Fluorescence Microscopy (TIRFM), and Single-Plane Illumination Microscopy (SPIM) now enable parallel measurements at hundreds to thousands of spatial locations either on cell surface membranes or within tissues. However, objective, automated Multiple Hypothesis Testing (MHT) for such highly parallel FCS measurements is challenging due to sampling limitations, sample heterogeneity, and the lack of automated procedures to accurately estimate the highly correlated noise that is present in Temporal Autocorrelation Functions (TACFs). Thus, automated, unbiased MHT procedures are critical for the proper analysis and interpretation of highly parallel FCS measurements as obtained from TIRFM and SPIM. Here, we apply a Bayesian inference procedure for MHT of competing models for FCS datasets. Simulated FCS measurements demonstrate that the Bayesian procedure selects the simplest model that describes the observed data, thereby capturing heterogeneity in the sample while avoiding over-fitting. Further, model probabilities provide a reliability test for the downstream interpretation of measured parameter values. We apply the procedure to TIRFM FCS data of phase-separated supported lipid bilayers and also Epidermal Growth Factor Receptor (EGFR), demonstrating that membrane and receptor heterogeneity and dynamics are captured when noise is sufficiently low. Our results demonstrate that the Bayesian approach provides an automated, unbiased procedure for FCS data analysis and interpretation with broad applicability to resolving heterogeneous molecular dynamics in biological processes interrogated using TIRFM and SPIM.

Understanding Ligand Interaction with Different Structures of G-Quadruplex DNA: Evidence of Kinetically Controlled Ligand Binding and Binding-Mode Assisted Quadruplex Structure Alteration

The study of ligand interaction with G-quadruplex DNA is an active research area, because many ligands are shown to bind G-quadruplex structures, showing anticancer effects. Here, we show, for the first time, how fluorescence correlation spectroscopy (FCS) can be used to study binding kinetics of ligands with G-quadruplex DNA at the single molecule level. As an example, we study interaction of a benzo-phenoxazine ligand (Cresyl Violet, CV) with antiparallel and (3 + 1) hybrid G-quadruplex structures formed by human telomeric sequence. By using simple modifications in FCS setup, we describe how one can extract the reaction kinetics from diffusion-coupled correlation curves. It is found that the ligand (CV) binds stronger, by an order of magnitude, to a (3 + 1) hybrid structure, compared to an antiparallel one. Ensemble-averaged time-resolved fluorescence experiments are also carried out to obtain the binding equilibrium constants (K) of ligand-quadruplex interactions in bulk solution for the first time, which are found to match very well with FCS results. Global analysis of FCS data provides association (k(+)) and dissociation (k(-)) rates of the ligand in the two structures. Results indicate that stronger ligand binding to the (3 + 1) hybrid structure is controlled by the dissociation rate, rather than the association rate of ligand in the quadruplexes. Circular dichroism (CD) and induced-CD spectra show that the ligand not only binds at different conformations in the quadruplexes, but also induces antiparallel structure to form a mixed-type hybrid structure in Na(+) solution. However, in K(+) solution, the ligand stabilizes the (3 + 1) hybrid structure. Molecular docking studies predict the possible differences in binding sites of the ligand inside two quadruplexes, which strongly support the experimental observations. Results suggest that different binding modes of the ligand to the quadruplex structures actually assist the alteration of structures differently.

Probing the Role of Chain Length on the Diffusion Dynamics of π-Conjugated Polymers by Fluorescence Correlation Spectroscopy

We investigate the role of the chain length and molecular weight distribution on the diffusion dynamics of freshly synthesized MEH-PPV polymer chains. For the above purpose, a new technique based on combination of size exclusion chromatography (SEC) with fluorescence correlation spectroscopy (FCS) is developed to probe the diffusion dynamics of a narrow molecular weight distribution of fractionated samples of 20-500 kDa. The narrow dispersed samples were characterized by absorbance, emission, and time-resolved fluorescence decay techniques. The results revealed that the properties of fractionated samples were almost uniform for a wide range of molecular weights. A maximum entropy based method for FCS data analysis is employed to obtain the correct diffusion coefficients of the polymer chains with heterogeneous dynamics. The FCS experiment on the unfractionated broad molecular weight sample is not enough to establish the correlation between the molecular weight of the chains with diffusion dynamics and emphasized the need for relatively monodispersed π-conjugated polymers. FCS results show that higher molecular weight chains diffuse much faster than shorter ones. Atomic force microscopy revealed that 300 kDa polymers produced 130 nm particles, whereas 50 kDa polymer chains formed micrometer size aggregates. At higher molecular weights, the strong chain interactions promote the formation of globular (or tightly packed) particles which diffuse faster in solution. The low molecular weight chains experience strong interparticle interaction; as a consequence, the diffusion of chains becomes slower. In the present investigation, we demonstrate the need for the narrow polydisperse sample for establishing the correlation between diffusion dynamics and chain length (or molecular weights) of π-conjugated polymers using a single molecule spectroscopy technique such as FCS.

ImFCS: A software for Imaging FCS data analysis and visualization

The multiplexing of fluorescence correlation spectroscopy (FCS), especially in imaging FCS using fast, sensitive array detectors, requires the handling of large amounts of data. One can easily collect in excess of 100,000 FCS curves a day, too many to be treated manually. Therefore, ImFCS, an open-source software which relies on standard image files was developed and provides a wide range of options for the calculation of spatial and temporal auto- and cross-correlations, as well as differences in Cross-Correlation Functions (ΔCCF). ImFCS permits fitting of standard models to correlation functions and provides optimized histograms of fitted parameters. Applications include the measurement of diffusion and flow with Imaging Total Internal Reflection FCS (ITIR-FCS) and Single Plane Illumination Microscopy FCS (SPIM-FCS) in biologically relevant samples. As a compromise between ITIR-FCS and SPIM-FCS, we extend the applications to Imaging Variable Angle-FCS (IVA-FCS) where sub-critical oblique illumination provides sample sectioning close to the cover slide.

Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy

Fluorescence Correlation Spectroscopy (FCS) in cells often suffers from artifacts caused by bright aggregates or vesicles, depletion of fluorophores or bleaching of a fluorescent background. The common practice of manually discarding distorted curves is time consuming and subjective. Here we demonstrate the feasibility of automated FCS data analysis with efficient rejection of corrupted parts of the signal. As test systems we use a solution of fluorescent molecules, contaminated with bright fluorescent beads, as well as cells expressing a fluorescent protein (ICA512-EGFP), which partitions into bright secretory granules. This approach improves the accuracy of FCS measurements in biological samples, extends its applicability to especially challenging systems and greatly simplifies and accelerates the data analysis.

Maximum Entropy Method for Analyses of Fluorescence Correlation Spectra of Oligonucleotide Intra-Chain Collision

It has been a challenge to accurately extract dynamic information from experimental fluorescence correlation spectroscopy (FCS) data. In this paper, we compare three major fitting methods: the model-dependent multiple exponential function (MultiExp), the empirical stretched exponential function (StreExp), and the exponential function based on the model-free maximum entropy method (MemExp). MultiExp has straight forward physical significance but it is difficult to implement and interpret in a complex system. StreExp has simple form and is easy to use but its physical picture is obscure. MultiExp is model free but its results are sensitive to experimental noise. A good choice seems to be a combination of MemExp and MultiExp. In our example, we have unraveled that two independent processes exist in the intra-chain collision of a single-stranded DNA when base pair formation is possible, which has not been observed by previous investigators. MemExp is recommended for the FCS data analysis, although caution should be exercised in the practice.

Direct Evidence That Neural Cell Adhesion Molecule (NCAM) Polysialylation Increases Intermembrane Repulsion and Abrogates Adhesion

Molecular force measurements quantified the impact of polysialylation on the adhesive properties both of membrane-bound neural cell adhesion molecule (NCAM) and of other proteins on the same membrane. These results show quantitatively that NCAM polysialylation increases the range and magnitude of intermembrane repulsion. The repulsion is sufficient to overwhelm both homophilic NCAM and cadherin attraction at physiological ionic strength, and it abrogates the protein-mediated intermembrane adhesion. The steric repulsion is ionic strength dependent and decreases substantially at high monovalent salt concentrations with a concomitant increase in the intermembrane attraction. The magnitude of the repulsion also depends on the amount of polysialic acid (PSA) on the membranes, and the PSA-dependent attenuation of cadherin adhesion increases with increasing PSA-NCAM:cadherin ratios. These findings agree qualitatively with independent reports based on cell adhesion studies and reveal the likely molecular mechanism by which NCAM polysialylation regulates cell adhesion and intermembrane space.

Measuring antibody affinity and performing immunoassay at the single molecule level

Fluorescence correlation spectroscopy (FCS) enables direct observation of the translational diffusion of single fluorescent molecules in solution. When fluorescent hapten binds to antibody, analysis of FCS data yields the fractional amounts of free and bound hapten, allowing determination of the equilibrium binding constant. Equilibrium dissociation constants of anti-digoxin antibodies and corresponding fluorescein-labeled digoxigenin obtained by FCS and fluorescence polarization measurements are identical. It is also possible to follow a competitive displacement of the tracer from the antibody by unlabeled hapten using FCS in an immunoassay format. The fluorescence polarization immunoassay for vancomycin detection was used to test the FCS approach. Fitting of the FCS data for the molar fractions of free and bound fluorescein-labeled vancomycin yielded a calibration curve which could serve for determination of the vancomycin concentration in biological samples.