Mapping Diffusion in a Living Cell via the Phasor Approach

Diffusion of a fluorescent protein within a cell has been measured using either fluctuation-based techniques (fluorescence correlation spectroscopy (FCS) or raster-scan image correlation spectroscopy) or particle tracking. However, none of these methods enables us to measure the diffusion of the fluorescent particle at each pixel of the image. Measurement using conventional single-point FCS at every individual pixel results in continuous long exposure of the cell to the laser and eventual bleaching of the sample. To overcome this limitation, we have developed what we believe to be a new method of scanning with simultaneous construction of a fluorescent image of the cell. In this believed new method of modified raster scanning, as it acquires the image, the laser scans each individual line multiple times before moving to the next line. This continues until the entire area is scanned. This is different from the original raster-scan image correlation spectroscopy approach, where data are acquired by scanning each frame once and then scanning the image multiple times. The total time of data acquisition needed for this method is much shorter than the time required for traditional FCS analysis at each pixel. However, at a single pixel, the acquired intensity time sequence is short; requiring nonconventional analysis of the correlation function to extract information about the diffusion. These correlation data have been analyzed using the phasor approach, a fit-free method that was originally developed for analysis of FLIM images. Analysis using this method results in an estimation of the average diffusion coefficient of the fluorescent species at each pixel of an image, and thus, a detailed diffusion map of the cell can be created.     

Scanning image correlation spectroscopy

Molecular interactions are at the origin of life. How molecules get at different locations in the cell and how they locate their partners is a major and partially unresolved question in biology that is paramount to signaling. Spatio-temporal correlations of fluctuating fluorescently tagged molecules reveal how they move, interact, and bind in the different cellular compartments. Methods based on fluctuations represent a remarkable technical advancement in biological imaging. Here we discuss image analysis methods based on spatial and temporal correlation of fluctuations, raster image correlation spectroscopy, number and brightness, and spatial cross-correlations that give us information about how individual molecules move in cells and interact with partners at the single molecule level. These methods can be implemented with a standard laser scanning microscope and produce a cellular level spatio-temporal map of molecular interactions.     

Raster image correlation spectroscopy in live cells

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

Measuring fast dynamics in solutions and cells with a laser scanning microscope

Single-point fluorescence correlation spectroscopy (FCS) allows measurements of fast diffusion and dynamic processes in the microsecond-to-millisecond time range. For measurements on living cells, image correlation spectroscopy (ICS) and temporal ICS extend the FCS approach to diffusion times as long as seconds to minutes and simultaneously provide spatially resolved dynamic information. However, ICS is limited to very slow dynamics due to the frame acquisition rate. Here we develop novel extensions to ICS that probe spatial correlations in previously inaccessible temporal windows. We show that using standard laser confocal imaging techniques (raster-scan mode) not only can we reach the temporal scales of single-point FCS, but also have the advantages of ICS in providing spatial information. This novel method, called raster image correlation spectroscopy (RICS), rapidly measures during the scan many focal points within the cell providing the same concentration and dynamic information of FCS as well as information on the spatial correlation between points along the scanning path. Longer time dynamics are recovered from the information in successive lines and frames. We exploit the hidden time structure of the scan method in which adjacent pixels are a few microseconds apart thereby accurately measuring dynamic processes such as molecular diffusion in the microseconds-to-seconds timescale. In conjunction with simulated data, we show that a wide range of diffusion coefficients and concentrations can be measured by RICS. We used RICS to determine for the first time spatially resolved diffusions of paxillin-EGFP stably expressed in CHOK1 cells. This new type of data analysis has a broad application in biology and it provides a powerful tool for measuring fast as well as slower dynamic processes in cellular systems using any standard laser confocal microscope.     

Position-sensitive scanning fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) uses a stationary laser beam to illuminate a small sample volume and analyze the temporal behavior of the fluorescence fluctuations within the stationary observation volume. In contrast, scanning FCS (SFCS) collects the fluorescence signal from a moving observation volume by scanning the laser beam. The fluctuations now contain both temporal and spatial information about the sample. To access the spatial information we synchronize scanning and data acquisition. Synchronization allows us to evaluate correlations for every position along the scanned trajectory. We use a circular scan trajectory in this study. Because the scan radius is constant, the phase angle is sufficient to characterize the position of the beam. We introduce position-sensitive SFCS (PSFCS), where correlations are calculated as a function of lag time and phase. We present the theory of PSFCS and derive expressions for diffusion, diffusion in the presence of flow, and for immobilization. To test PSFCS we compare experimental data with theory. We determine the direction and speed of a flowing dye solution and the position of an immobilized particle. To demonstrate the feasibility of the technique for applications in living cells we present data of enhanced green fluorescent protein measured in the nucleus of COS cells.     

Spatial-temporal studies of membrane dynamics: scanning fluorescence correlation spectroscopy (SFCS)

Giant unilamellar vesicles (GUVs) have been widely used as a model membrane system to study membrane organization, dynamics, and protein-membrane interactions. Most recent studies have relied on imaging methods, which require good contrast for image resolution. Multiple sequential image processing only detects slow components of membrane dynamics. We have developed a new fluorescence correlation spectroscopy (FCS) technique, termed scanning FCS (i.e., SFCS), which performs multiple FCS measurements simultaneously by rapidly directing the excitation laser beam in a uniform (circular) scan across the bilayer of the GUVs in a repetitive fashion. The scan rate is fast compared to the diffusion of the membrane proteins and even small molecules in the GUVs. Scanning FCS outputs a "carpet" of timed fluorescence intensity fluctuations at specific points along the scan. In this study, GUVs were assembled from rat kidney brush border membranes, which included the integral membrane proteins. Scanning FCS measurements on GUVs allowed for a straightforward detection of spatial-temporal interactions between the protein and the membrane based on the diffusion rate of the protein. To test for protein incorporation into the bilayers of the GUVs, antibodies against one specific membrane protein (NaPi II cotransporter) were labeled with ALEXA-488. Fluorescence images of the GUVs in the presence of the labeled antibody showed marginal fluorescence enhancement on the GUV membrane bilayers (poor image contrast and resolution). With the application of scanning FCS, the binding of the antibody to the GUVs was detected directly from the analysis of diffusion rates of the fluorescent antibody. The diffusion coefficient of the antibody bound to NaPi II in the GUVs was approximately 200-fold smaller than that in solution. Scanning FCS provided a simple, quantitative, yet highly sensitive method to study protein-membrane interactions.     

Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells

We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.     

Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy

We have investigated spatial variations of the diffusion behavior of the green fluorescent protein mutant EGFP (F64L/S65T) and of the EGFP-beta-galactosidase fusion protein in living cells with fluorescence correlation spectroscopy. Our fluorescence correlation spectroscopy device, in connection with a precision x-y translation stage, provides submicron spatial resolution and a detection volume smaller than a femtoliter. The fluorescence fluctuations in cell lines expressing EGFP are caused by molecular diffusion as well as a possible internal and a pH-dependent external protonation process of the EGFP chromophore. The latter processes result in two apparent nonfluorescent states that have to be taken into account when evaluating the fluorescence correlation spectroscopy data. The diffusional contribution deviates from ideal behavior and depends on the position in the cell. The fluorescence correlation spectroscopy data can either be evaluated as a two component model with one fraction of the molecules undergoing free Brownian motion with a diffusion coefficient approximately five times smaller than in aqueous solution, and another fraction diffusing one or two orders of magnitude slower. This latter component is especially noticeable in the nuclei. Alternatively, we can fit the data to an anomalous diffusion model where the time dependence of the diffusion serves as a measure for the degree of obstruction, which is large especially in nuclei. Possible mechanisms for this long tail behavior include corralling, immobile obstacles, and binding with a broad distribution of binding affinities. The results are consistent with recent numerical models of the chromosome territory structure in the cell nucleus.     

Lateral diffusion measurement at high spatial resolution by scanning microphotolysis in a confocal microscope.

Fluorescence photobleaching methods have been widely used to study diffusion processes in the plasma membrane of single living cells and other membrane systems. Here we describe the application of a new photobleaching technique, scanning microphotolysis. Employing a recently developed extension module to a commercial confocal microscope, an intensive laser beam was switched on and off during scanning according to a user definable image mask. Thereby the location, geometry, and number of photolysed spots could be chosen arbitrarily, their size ranging from tens of micrometers down to the diffraction limit. Therewith we bleached circular areas on the surface of single living 3T3 cells labeled with the fluorescent lipid analog NBD-HPC. Subsequently, the fluorescence recovery process was observed using the attenuated laser beam for excitation. This yielded image stacks representing snapshots of the spatial distribution of fluorescent molecules. From these we computed the radial distribution functions of the photobleached dye molecules. The variance of these distributions is linearly related to the diffusion constant, time, and the mobile fraction of the diffusing species. Furthermore, we compared directly the theoretically expected and measured distribution functions, and could thus determine the diffusion coefficient from each single image. The results of these two new evaluation methods (D = 0.3 +/- 0.1 micron 2/s) agreed well with the outcome of conventional fluorescence recovery measurements. We show that by scanning microphotolysis information on dynamical processes such as diffusion of lipids or proteins can be acquired at the superior spatial resolution of a confocal laser scanning microscope.     

Advances in Image Correlation Spectroscopy: Measuring Number Densities,Aggregation States,and Dynamics of Fluorescently labeled Macromolecules in Cells

A brief historical outline of fluorescence fluctuation correlation techniques is presented, followed by an in-depth review of the theory and development of image correlation techniques, including: image correlation spectroscopy (ICS), temporal ICS (TICS), image cross-correlation spectroscopy (ICCS), spatiotemporal ICS (STICS), k-space ICS (kICS), raster ICS (RICS), and particle ICS (PICS). These techniques can be applied to analyze image series acquired on commercially available laser scanning or total internal reflection fluorescence microscopes, and are used to determine the number density, aggregation state, diffusion coefficient, velocity, and interaction fraction of fluorescently labeled molecules or particles. A comprehensive review of the application of ICS techniques to a number of systems, including cell adhesion, membrane receptor aggregation and dynamics, virus particle fusion, and fluorophore photophysics, is presented.     

Accuracy and dynamic range of spatial image correlation and cross-correlation spectroscopy

We present a comprehensive study of the accuracy and dynamic range of spatial image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS). We use simulations to model laser scanning microscopy imaging of static subdiffraction limit fluorescent proteins or protein clusters in a cell membrane. The simulation programs allow us to control the spatial imaging sampling variables and the particle population densities and interactions and introduce and vary background and counting noise typical of what is encountered in digital optical microscopy. We systematically calculate how the accuracy of both image correlation methods depends on practical experimental collection parameters and characteristics of the sample. The results of this study provide a guide to appropriately plan spatial image correlation measurements on proteins in biological membranes in real cells. The data presented map regimes where the spatial ICS and ICCS provide accurate results as well as clearly showing the conditions where they systematically deviate from acceptable accuracy. Finally, we compare the simulated data with standard confocal microscopy using live CHO cells expressing the epidermal growth factor receptor fused with green fluorescent protein (GFP/EGFR) to obtain typical values for the experimental variables that were investigated in our study. We used our simulation results to estimate a relative precision of 20% for the ICS measured receptor density of 64 microm(-2) within a 121 x 98 pixel subregion of a single cell.     

Translational diffusion of fluorescent proteins by molecular fourier imaging correlation spectroscopy

The ability to noninvasively observe translational diffusion of proteins and protein complexes is important to many biophysical problems. We report high signal/noise (>or=250) measurements of the translational diffusion in viscous solution of the fluorescent protein, DsRed. This is carried out using a new technique: molecular Fourier imaging correlation spectroscopy (M-FICS). M-FICS is an interferometric method that detects a collective Fourier component of the fluctuating density of a small population of fluorescent molecules, and provides information about the distribution of molecular diffusivities. A theoretical analysis is presented that expresses the detected signal fluctuations in terms of the relevant time-correlation functions for molecular translational diffusion. Furthermore, the role played by optical orientational degrees of freedom is established. We report Fickian self-diffusion of the DsRed tetramer at short timescales. The long-time deviation of our data from Fickian behavior is used to determine the variance of the distribution of the protein self-diffusion coefficient. We compare our results to the expected outcomes for 1), a bi-disperse distribution of protein species, and 2), dynamic disorder of the host solvent.     

Isolation of bright aggregate fluctuations in a multipopulation image correlation spectroscopy system using intensity subtraction

Image correlation spectroscopy allows sensitive measurement of the spatial distribution and aggregation state of fluorescent membrane macro molecules. When studying a single population system (i.e., aggregates of similar brightness), an accurate measure can be made of the aggregate number per observation area, but this measurement becomes much more complex in a distributed population system (i.e., bright and faint aggregates). This article describes an alternate solution that involves extraction of the bright aggregate population information. This novel development for image correlation spectroscopy, termed intensity subtraction analysis, uses sequential uniform intensity subtraction from raw confocal images. Sequential intensity subtraction results in loss of faint aggregate fluctuations that are smaller in magnitude than fluctuations due to the brightest aggregates. The resulting image has correlatable fluctuations originating from only the brightest population, permitting quantification of this population's distribution and further cross-correlation measurements. The feasibility of this technique is demonstrated using fluorescent microsphere images and biological samples. The technique is further used to examine the spatial distribution of a plasma-membrane-labeled fluorescent synthetic ganglioside, and to cross-correlate this probe with various membrane markers. The evidence provided demonstrates that bright aggregates of the fluorescent ganglioside are associated with clathrin-coated pits, membrane microvilli, and detergent-resistant membranes.     

3-d image analysis of fluorescent drug binding

Fluorescent ligands provide the means of studying receptors in whole tissues using confocal laser scanning microscopy and have advantages over antibody- or non-fluorescence-based method. Confocal microscopy provides large volumes of images to be measured. Histogram analysis of 3-D image volumes is proposed as a method of graphically displaying large amounts of volumetric image data to be quickly analyzed and compared. The fluorescent ligand BODIFY FL-prazosin (QAPB) was used in mouse aorta. Histogram analysis reports the amount of ligand-receptor binding under different conditions and the technique is sensitive enough to detect changes in receptor availability after antagonist incubation or generic manipulations. QAPB binding was concentration dependent, causing concentration-related rightward shifts in histogram. In the presence of 10 microM phenoxybenzamine (blocking agent), the QAPB (50 nM) histogram overlaps the autofluorescence curve. The histogram obtained for the 1D knockout aorta lay to the left of that control and 1B knockout aorta, indicating a reduction in 1D receptors. We have shown, for the first time, that it is possible to graphically display binding of a fluorescent drug to a biological tissue. Although our application is specific to adrenergic receptors, the general method could be applied to any volumetric, fluorescence-image-based assay.     

Imaging technique implemented in CellTracks system

BACKGROUND: We developed the CellTracks cell analysis system that, similar to flow cytometry, yields multiparameter information by which the cells can be differentiated. We describe the implementation of a laser scanning imaging method in the system. Image analysis of the cells improves the specificity of cell classification, especially in cases where the particular cells are found relatively infrequently and one has to discriminate between artifacts and real events. METHODS: Fluorescent images of immunomagnetically labeled and aligned cells are obtained by passing the cells through a laser focus. The laser focus is smaller than the objects and subsequent frames captured by a regular surveillance CCD camera with a frame grabber board represent different parts of the cells. Complete images of the cells are constructed by shifting each image with respect to each other and adding individual pixel values. RESULTS: The power of combining a fluorescent image with multiparametric data is demonstrated by imaging fluorescent and magnetically labeled beads and cells. The image gives additional information about the dye distribution across the objects. Changes in dye distribution as a function of time were observed in leukocytes labeled with the red fluorescent label, Oxazine750, which are imaged at different time intervals. CONCLUSIONS: An imaging technique implemented in the CellTracks system provides high-resolution fluorescent images of events previously identified by the system. The images of the fluorescent cells enhance the ability to classify rare events.     

Quantitation of membrane receptor distributions by image correlation spectroscopy: concept and application.

Measurement of receptor distributions on cell surfaces is one important aspect of understanding the mechanism whereby receptors function. In recent years, scanning fluorescence correlation spectroscopy has emerged as an excellent tool for making quantitative measurements of cluster sizes and densities. However, the measurements are slow and usually require fixed preparations. Moreover, while the precision is good, the accuracy is limited by the relatively small amount of information in each measurement, such that many are required. Here we present a novel extension of the scanning correlation spectroscopy that solves a number of the present problems. The new technique, which we call image correlation spectroscopy, is based on quantitative analysis of confocal scanning laser microscopy images. Since these can be generated in a matter of a second or so, the measurements become more rapid. The image is collected over a large cell area so that more sampling is done, improving the accuracy. The sacrifice is a lower resolution in the sampling, which leads to a lower precision. This compromise of precision in favor of speed and accuracy still provides an enormous advantage for image correlation spectroscopy over scanning correlation spectroscopy. The present work demonstrates the underlying theory, showing how the principles can be applied to measurements on standard fluorescent beads and changes in distribution of receptors for platelet-derived growth factor on human foreskin fibroblasts.     

Pulsed Interleaved Excitation Fluctuation Imaging

Fluorescence fluctuation imaging is a powerful means to investigate dynamics, interactions, and stoichiometry of proteins inside living cells. Pulsed interleaved excitation (PIE) is the method of nanosecond alternating excitation with time-resolved detection and allows accurate, independent, and quasi-simultaneous determination of fluorescence intensities and lifetimes of different fluorophores. In this work, we combine pulsed interleaved excitation with fluctuation imaging methods (PIE-FI) such as raster image correlation spectroscopy (RICS) or number and brightness analysis (N&B). More specifically, we show that quantitative measurements of diffusion and molecular brightness of Venus fluorescent protein (FP) can be performed in solution with PIE-RICS and compare PIE-RICS with single-point PIE-FCS measurements. We discuss the advantages of cross-talk free dual-color PIE-RICS and illustrate its proficiency by quantitatively comparing two commonly used FP pairs for dual-color microscopy, eGFP/mCherry and mVenus/mCherry. For N&B analysis, we implement dead-time correction to the PIE-FI data analysis to allow accurate molecular brightness determination with PIE-NB. We then use PIE-NB to investigate the effect of eGFP tandem oligomerization on the intracellular maturation efficiency of the fluorophore. Finally, we explore the possibilities of using the available fluorescence lifetime information in PIE-FI experiments. We perform lifetime-based weighting of confocal images, allowing us to quantitatively determine molecular concentrations from 100 nM down to <30 pM with PIE-raster lifetime image correlation spectroscopy (RLICS). We use the fluorescence lifetime information to perform a robust dual-color lifetime-based FRET analysis of tandem fluorescent protein dimers. Lastly, we investigate the use of dual-color RLICS to resolve codiffusing FRET species from non-FRET species in cells. The enhanced capabilities and quantitative results provided by PIE-FI make it a powerful method that is broadly applicable to a large number of interesting biophysical studies.     

k-Space image correlation spectroscopy: a method for accurate transport measurements independent of fluorophore photophysics

We present the theory and application of reciprocal space image correlation spectroscopy (kICS). This technique measures the number density, diffusion coefficient, and velocity of fluorescently labeled macromolecules in a cell membrane imaged on a confocal, two-photon, or total internal reflection fluorescence microscope. In contrast to r-space correlation techniques, we show kICS can recover accurate dynamics even in the presence of complex fluorophore photobleaching and/or "blinking". Furthermore, these quantities can be calculated without nonlinear curve fitting, or any knowledge of the beam radius of the exciting laser. The number densities calculated by kICS are less sensitive to spatial inhomogeneity of the fluorophore distribution than densities measured using image correlation spectroscopy. We use simulations as a proof-of-principle to show that number densities and transport coefficients can be extracted using this technique. We present calibration measurements with fluorescent microspheres imaged on a confocal microscope, which recover Stokes-Einstein diffusion coefficients, and flow velocities that agree with single particle tracking measurements. We also show the application of kICS to measurements of the transport dynamics of alpha5-integrin/enhanced green fluorescent protein constructs in a transfected CHO cell imaged on a total internal reflection fluorescence microscope using charge-coupled device area detection.     

Detection and correction of blinking bias in image correlation transport measurements of quantum dot tagged macromolecules

Semiconductor nanocrystals or quantum dots (QDs) are becoming widely used as fluorescent labels for biological applications. Here we demonstrate that fluorescence fluctuation analysis of their diffusional mobility using temporal image correlation spectroscopy is highly susceptible to systematic errors caused by fluorescence blinking of the nanoparticles. Temporal correlation analysis of fluorescence microscopy image time series of streptavidin-functionalized (CdSe)ZnS QDs freely diffusing in two dimensions shows that the correlation functions are fit well to a commonly used diffusion decay model, but the transport coefficients can have significant systematic errors in the measurements due to blinking. Image correlation measurements of the diffusing QD samples measured at different laser excitation powers and analysis of computer simulated image time series verified that the effect we observe is caused by fluorescence intermittency. We show that reciprocal space image correlation analysis can be used for mobility measurements in the presence of blinking emission because it separates the contributions of fluctuations due to photophysics from those due to transport. We also demonstrate application of the image correlation methods for measurement of the diffusion coefficient of glycosyl phosphatidylinositol-anchored proteins tagged with QDs as imaged on living fibroblasts.