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* Laboratory for Fluorescence Dynamics, University of Illinois at Urbana-Champaign, Urbana, Illinois; Department of Cell Biology, School of Medicine, University of Virginia, Charlottesville, Virginia; and Departments of Chemistry and Physics, McGill University, Montreal, Quebec, Canada
Correspondence: Address reprint requests to M. A. Digman, E-mail: mdigman{at}uiuc.edu; or E. Gratton, E-mail: enrico{at}scs.uiuc.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). New image analysis tools can provide dynamic information as a function of time and space-generating dynamic cellular maps throughout the cell (2). However, in developing these maps we need to move beyond simple averages for large regions of the cell and distinguish the underlying protein distributions that give rise to these averages, i.e., distinguish between a few aggregates containing a large number of molecules and many aggregates that contain a small number of molecules in a well-defined stoichiometry. More important is to have the ability to measure the dynamics of molecular aggregates with lifetimes that could range from small fractions of a second to many seconds.
Optical microscopy methods of increasing sensitivity, resolution and faster frame rate are being developed to generate this type of data. These methods include, among others, fluorescence resonance energy transfer, spectral decomposition, speckle fluorescence microscopy, and lifetime imaging, which can now be applied to living cells. Single-molecule methods have also reached an ultimate sensitivity and time resolution (3–5). However, while single-molecule techniques have had much success on immobilized and isolated systems, their application to molecules in living cells is still challenging. Instead, methods that provide average values, possibly on relatively few molecules in a small volume of the cell, are being used successfully. New developments in image correlation microscopy, based on laser scanning confocal methods and two-photon excitation, have begun to provide this information (2,6). These techniques have been used to develop detailed spatial maps of protein concentrations, dynamics, and interactions, and also to follow the development and dynamics of relatively large molecular assemblies in living cells (2).
Temporal and spatial resolution is a major consideration in correlation microscopy. Single-point fluorescence correlation spectroscopy (FCS), originally developed by Magde et al. (7) and Elson and Magde (8), for the study of molecules in solution, has been extended to two-photon excitation in cells (9) to provide information about protein concentrations and dynamics at high temporal resolution (microseconds) within a very small region of the cell (
1 fL). However, point FCS is limited to rapid processes occurring in a single location within the cell. Image correlation spectroscopy (ICS), developed by Petersen et al. (10), is a mathematical image-processing method that can be applied to any kind of microscope (or nonmicroscope) image or stack of images. The basis of the ICS method is to calculate the spatial autocorrelation function of an image using two-dimensional fast-Fourier transform algorithms. The number and size of aggregates is extracted from the analysis of the spatial power spectrum. ICS in cells provides the degree of aggregation and the average number of fluorescently labeled protein aggregates for an entire image. In a recent variation, ICS, termed image correlation microscopy, was expanded to allow temporal correlations between images collected in a time series (11) and to determine spatial correlations due to flow and other cellular processes in regions of the cell (2,6). Temporal ICS operates on image stacks and thus provides spatial maps of molecular interactions and dynamics with a spatial resolution theoretically equal to that of the original image and a time resolution that depends on the frame rate (usually on a timescale of seconds).
In this article we propose a method that has the potential to bridge the gap between the high temporal resolution of single-point FCS (microseconds) and the low temporal resolution of ICS (seconds). The original ICS theory was based on the assumption that the molecules being measured do not move substantially on the timescale of a single image frame acquisition (seconds). So it has been mostly used to study fixed sample or slowly moving transmembrane- or membrane-associated proteins (12). Here we demonstrate that images from laser scanning microscopes (LSM), including a standard commercial single photon confocal and a two-photon excitation microscope, contain a hidden temporal structure. A general mathematical method for analyzing spatial and temporal correlations within images from the rapid scanning of the laser is presented, and shows that LSM images can be exploited to extract fast dynamic information. Specifically methods are developed for the analysis of images generated by either 1), scanning repeated circular orbits or lines, or 2), raster-scanning images of larger areas. Simulations and experiments demonstrate the feasibility of the methods showing that the dynamics of fast molecular diffusion in solution and in the cell can be extracted directly from laser scanning microscopy (LSM) images.
This new analysis, termed raster image correlation spectroscopy (RICS), successfully bridges the timescales of FCS and ICS and provides spatially resolved dynamic information in the microsecond-to-second time range. For raster-scan images the spatial resolution of this method depends on the diffusion coefficient of the molecules or molecular aggregates. The spatial resolution will be lower for rapidly diffusing molecules because they cannot be localized with high precision. To date, expensive and highly specialized instruments have been required for FCS measurements. In addition, the FCS measurements and imaging have to be done at two different times with different conditions. Since LSMs are readily available in almost all life science labs, the RICS method opens up the measurement of fast dynamics within the cell to the general microscope user. On a single instrument from a temporal stack of images one can obtain dynamic information anywhere from the microsecond-to-hours timescale. This includes dynamic processes ranging from that of diffusion of cytosolic proteins to slower processes such as the assembly and disassembly of large multiprotein complexes. The potential impact of RICS on the life science community is enormous, since it allows the determination of spatial maps of concentrations, aggregation, and dynamics in living cells using readily accessible instrumentation.
Temporal and spatial fluctuations in microscope images
We first describe how to measure fast diffusion dynamics of molecules in a dilute, homogenous solution using a conventional LSM. Although images appear uniform, there are hidden temporal and spatial fluctuations that can be analyzed to recover the diffusion coefficient and the number of molecules in the instantaneous (scanning) excitation volume.
Molecular processes such as conformational transitions, and quenching associated with aggregation and molecular rotations, as well as diffusion, can cause fluctuations in fluorescence intensity. However, for this mathematical derivation we only consider signal fluctuations due to diffusion of particles in a homogenous medium since most of the processes in the cell involve transport (either by diffusion or by directed motion) of particles from one location to another. Diffusion of a particle in a uniform medium can be described by the relationship below,
 | (1) |
). LSM using either line-scan or raster-scan modalities enables data acquisition from different spatial locations at different times. Spatial correlations for small diffusing particles depend on the spatial overlap and the time interval between adjacent pixels. Random diffusion of the particle and longer time intervals between data points decrease correlation at shorter spatial scales but increase correlation at distant pixels. It is precisely the change of shape of the spatial correlation function that contains information about molecular diffusion. For the most common scan configurations, circular or line-scan and raster-scan microscopy, the adjacent volumes along the scanning line are sampled very rapidly; but the adjacent volumes in two consecutive lines are sampled at a much slower rate. This difference in sampling time can be exploited to measure a range of diffusion coefficients, from very fast molecular diffusion through the illumination volume, which occurs in the microsecond range to slower diffusion, which can occur on the timescale of milliseconds or even seconds.
Starting from Eq. 1, the relationship between the concentration of a particle and fluorescence intensity F is given by
 | (2) |
is a factor that accounts for the instrument sensitivity, and W(r) describes the point-spread function (PSF) of the microscope system. In Eq. 2, the concentration of the particle as a function of time (Eq. 1) is convolved with the expression for the illumination profile W(r). The temporal autocorrelation function (ACF) is given by the expression below,
 | (3) |
F is the fluorescence intensity fluctuation with respect to the average, and 
is the delay time between successive sampling of the fluorescence signal. By inserting Eq. 2 into Eq. 3 and assuming time sampling at the same spatial locations (see, for example, Eq. 7 below), we can obtain the familiar autocorrelation function used in FCS for the analysis of a particle freely diffusing in a volume. To derive expressions for the spatial autocorrelations we need to specify the spatial sampling sequence used in the experiment. Equations for the spatiotemporal correlation function for data were generated using two common modalities, from which a circular (line) or raster scan pattern will be derived. These equations are then used to fit experimental spatiotemporal correlation functions and diffusion coefficients, and the concentrations of molecules in dilute samples are extracted.
Temporal correlations in circular scanning
If the scanner performs a circular orbit of radius A and angular frequency 
around a center at x0 and y0, the relationship among x, y, and the time is given by the sine and cosine functions, respectively, as
 | (4) |
 | (5) |
) is the autocorrelation function due to scanning and G() the autocorrelation function without scanning. Assuming a three-dimensional Gaussian excitation profile with a radial waist w0 and axial waist wz, the S() term for circular scanning is given by
 | (6) |
) is the familiar autocorrelation function due to diffusion,
 | (7) |
of circular scanning (14). Note that Eqs. 6 and 7 contain only the time, . In this analysis the spatial correlation between adjacent points in the orbit and successive orbits is hidden.
Spatial correlations in circular, line, and raster scanning
To reveal the spatial part of the correlation function and to show the similarity between RICS and ICS we construct a transpose matrix from the time series in which each column represents points along the circular orbit (or line) and each row represents a different orbit (or line). This transpose matrix is a pseudo-image of the orbit because the vertical axis is not space but time. The entire time series is then divided into a pseudo-image stack of frames in a 2n format that is amenable for calculating the spatial autocorrelation using fast-Fourier transform methods, e.g., 128 x 128 or 256 x 256. The advantage of this image representation is that the spatial and temporal parts of the pseudo-image are separated. For orbit-scanned images, the time data is continuous along the scan and the division of the time series into images gives no particular advantages when studying solutions. However, for line scan or raster scan, the time series is not usually continuous in successive points due to line retracing; the image, in contrast, is contiguous among adjacent points. Therefore, we can apply the spatial correlation operation to the images (the points are equally separated in space), although we cannot apply the correlation operation to the time series obtained in the raster acquisition mode (the points are not equally separated in time). The spatial correlation function is defined as
 | (8) |
and 
are the spatial increments in the x and y directions, respectively, and the angle bracket indicates average over all the spatial locations in both x and y directions. We then calculate the spatial autocorrelation of the raster-scan pseudo-image. The two-dimensional spatial autocorrelation function for circular or line scan is given by
 | (9) |
 | (10) |
r is the distance between adjacent points in the line or along the orbit, and p and l are the pixel sampling time and time between lines, respectively. Analogous to Eq. 5, the overall spatial autocorrelation function is given by GS(,) = S(,) x G(,).
Raster-scan image correlation spectroscopy
To make RICS accessible to most researchers using standard confocal microscopes, we expanded the theory developed for circular (or line) scan to two-dimensional spatial raster-scan images. In this case, the spatial part of the correlation function is expressed directly in terms of the pixel size, r (typically in the range 0.05–0.2 µm); pixel resident time, p (typically in the range 2–100 µs); and the line repetition time, l, typically in the 3–100 ms range:
 | (11) |
,) = S(,) x G(,) where G(,) is given by Eq. 9. (Note: All terms containing the diffusion coefficient, D, in Eqs. 9–11 contain a factor of 4D, but for two-photon excitation this factor should be 8D. Also, w0 in all equations of this manuscript is the 1/e2 of the illumination Gaussian profile.) To test the validity of the expressions used to fit the two-dimensional autocorrelation functions, we performed simulations of particles diffusing in a three-dimensional grid. For particles moving at two different rates (diffusion constants of 100 and 6 µm2/s), simulations were performed for three illumination scenarios: 1), a stationary beam (standard FCS); 2), a beam rotating in a circular orbit; or 3), a beam moving in a raster-scan fashion. (The simulation program for FCS data has been previously described, and it can be downloaded from https://lfd.uiuc.edu.) Briefly, a number of particles are simultaneously moved in a random walk, at different rates, on a three-dimensional grid with 0.05 µm per grid step. The grid is illuminated with a selected illumination profile function either for one-photon or two-photon experiments. For all simulated data the input parameters were recovered within the noise using the equations presented above (Fig. 1 and Table 1). (See Table 3, later in this article, for an estimation of the noise under the conditions of the simulation for similar values of the total length of the experiment.)
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MATERIALS AND METHODS |
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The two-photon excitation scanning fluorescence microscope used in these experiments was assembled at the Laboratory for Fluorescence Dynamics (University of Illinois at Urbana-Champaign) and has been described previously (9). Basically, 100-fs pulses from a mode-locked titanium-sapphire laser (Tsunami; Spectra-Physics, Palo Alto, CA) were used for excitation. The laser was guided into the microscope by x,y galvano-scanner mirrors (Model 6350; Cambridge Technology, Cambridge, MA), which allowed the beam to move in both the x and y directions. The mirrors are driven in a preset scanning path using the ISS 3-axis card (ISS, Champaign, IL) and synchronized with data acquisition using the ISS-FCS dual-channel card. Data are acquired and processed by the SimFCS software developed at the University of Illinois. For scanning in a circular orbit, the x- and y-scan mirrors are driven by two identical sine waves with a 90° phase-shift. The radius and frequency of the circular scan was controlled by the amplitude and frequency of the sine wave. For a raster scan, the x- and y-scanner mirror was driven by two sawtooth signals at different frequencies. A photomultiplier tube (HC120-08, Hamamatsu Photonics, Bridgewater, NJ) was used for light detection in the photon-counting mode. A BG39 optical filter was placed before the photomultiplier for efficient suppression of IR excitation light. A 40x water immersion objective (Zeiss, Jena, Germany) with 1.2 NA was used for the measurement. The excitation wavelengths used in the study are 780 nm (for polystyrene beads) and 910 nm (for EGFP). Due to the possible variation in the laser alignment from day to day, the waist (w0) of the excitation beam was calibrated before each day's measurement. The calibration was achieved by measuring the autocorrelation curve of 10 nM fluorescein in 0.01M NaOH, which was in turn fit with a diffusion rate of 300 µm2/s; the typical values of w0 were in the range of 0.30–0.50 µm, depending on the laser wavelength. The value of wz for the one-photon experiment was assumed to be three-times the radial waist and five-times the radial waist for the two-photon measurements.
For two-photon excitation, scanning fluorescence imaging data were collected at the rate of 16–128 µs/pixel. The scan area for a full frame (256 x 256 pixels) corresponds to 32 x 32 µm. The average fluorescence intensity of the sample remained constant, indicating the fluorophore was not photobleached significantly during the measurement. Some diffusion measurements were made on 10-nm fluorescently-labeled polystyrene beads (Molecular Probes, Eugene, OR) that were diluted in nanopure water and sonicated for 2 h.
CHO-K1 cells stably transfected with paxillin-EGFP were cultured in a humidified, 8.5% CO2 atmosphere at 37°C in minimum essential medium supplemented with 10% FBS, non-essential amino acids, and glutamine, as well as 0.5 mg/mL neomycin (G418), to maintain selection of transfected cells. Cells were lifted with trypsin and plated on homemade 35-mm glass-bottomed dishes coated with 2–10 µg/mL fibronectin. Cells were maintained in CCM1 medium (HyClone, Logan, UT) at 37°C during imaging with a Warner Instruments heated stage insert (Warner Instruments, Hamden, CT), in combination with a Bioptechs (Bioptechs, Butler, PA) objective heater.
All data fits were performed according to Eqs. 9–11 using the SimFCS program (available at www.lfd.uiuc.edu). When possible, the data was weighted by the standard deviation of the correlation function at each pixel. When a stack of images was available, the spatial autocorrelation function was calculated for each image or image region. The average spatial correlation function was then calculated and for each point of the spatial correlation function the standard deviation was evaluated and used as the weighting factor. For the time correlation, the time series was broken in segments. The average correlation function was calculated from the autocorrelation function of each segment and the standard deviation of the average at each point was used as the weighting factor for the 
-square evaluation.
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RESULTS |
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6 µm2/s (Table 2). Similarly, the spatial autocorrelation function (Fig. 3 C) of the pseudo-image of the transposed data stream from circular scanning of the same 10-nm bead sample (Fig. 3 B) was fit according to according to Eqs. 6 and 7 (Fig. 3 D, Table 2). The fitting yields a D-value of 8 µm2/s (Table 2). Finally, raster-scan data of the same sample (not shown) yields a similar D-value (Table 2).
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Paxillin-EGFP in CHOK1 cells localizes to bright fingerlike features that are cellular adhesions (Fig. 5 A). A subregion of the cell where most of the paxillin protein is soluble in the cytosol was analyzed (Fig. 5 B). There is a contribution in this image from small paxillin-containing adhesions in the central regions of the cell that will dominate the spatial ACF so that the fast dynamics of soluble paxillin cannot be extracted (Fig. 5 C). However, after applying the subtraction algorithm, the spatial ACF only reveals the fast moving components (Fig. 5 D) and that function can be fit (Fig. 5 E) yielding a diffusion coefficient of D = 8.3 µm2/s (comparable to point-scan FCS measurements, not shown). Different regions of the cell with various shapes, brightness, and total number of dim organized structures were analyzed using the subtraction method and similar D-values were obtained. These regions did not contain bright structures due to large elongated focal adhesions.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). When circular- (or line-) scan FCS is applied to cells, it is possible to extract spatiotemporal correlations to obtain very high temporal and spatial resolution maps of intracellular dynamics. For data acquired with the raster technique, we must first represent the data in a contiguous image (or pseudo-image in the case of line scan) and then apply the spatial correlation method. We were able to derive analytical equations for spatial correlations that contain explicitly the effect of molecular diffusion. These equations are then used to fit the experimental spatial correlation functions to extract the diffusion of molecules and molecular aggregates. The range of diffusion coefficients that can be measured is determined by the sampling rates, which are in the microsecond range in common LSM systems, a value adequate to recover the diffusion of a small protein in solution such as EGFP. Therefore, they are more than fast enough to detect the dynamics of proteins within the cell. The form of the equations describing spatial correlations is somewhat similar to the equations used for fitting FCS data in the presence of flow (15). This is not a surprise since either moving the sample or moving the laser beam at a constant velocity should be equivalent. The main difference is that a volume adjacent to the original volume can be explored during the next line of the raster-scan pattern in the RICS method opening up another intermediate timescale.
When the RICS technique is applied to cells, spatial correlations can be dominated by immobile features in the image. A simple algorithm that subtracts the immobile features is sufficient to eliminate the effect of these structures even if they are bright. This is the equivalent of performing a highpass filter operation on the image before applying the spatial correlation algorithm. The highpass filter cutoff can be tuned to subtract slowly moving features. Bright immobile cellular features are characterized by large shot noise. Dim, fast diffusing particles in the presence of large noise are difficult to see. However, shot noise per se has neither spatial nor temporal correlation so that it can be effectively subtracted without affecting the dynamic information. To account for slowly moving features in the cell, the highpass filter must be tuned to slightly higher frequencies. This filtering operation introduces additional correlations into the data that will be discussed elsewhere. Also in this article we have not examined spatiotemporal correlations to obtain information regarding flow, aggregation, and other dynamic processes such as binding equilibrium occurring in cells. Flow and aggregation processes have been discussed previously in the context of FCS and ICS (2,6).
Comparison of diffusion constants obtained by single-point FCS versus RICS
An important technical question is whether or not the RICS technique is equivalent to standard FCS performed at specific points in solution or in a cell. The time series provided by a laser-scanning microscope, when properly analyzed using the spatial correlation algorithm, basically gives the same information. The RICS technique provides very similar information in regard to the dynamics but is better suited for very low concentrations because it has better S/N, since many spatial points are sampled in rapid succession. Table 3 shows the results of repeating a simulation of 100 particles diffusing in a plane and detected either by single-point FCS, circular scanning, or raster scanning. Due to the enhanced S/N the standard deviation of D and G(0) from 10 independent measurements is lower when the RICS technique is applied (Table 3).
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0.6 ms for a PSF of 0.5 µm full-width at half-maximum. If we sample at 2 µs per pixel and the pixel size is large, the beam could be out of the volume occupied by the molecule before there is appreciable change of the molecule's position. And if the line repetition time is greater than several milliseconds, the particle will not be there when the beam returns on the next line. In general, this effect is important only for fast moving particles and long line lengths. For slower particles there is always a chance to observe the particle again at the next line. If particles are moving very slowly, then the particle motion can be analyzed by correlating successive image frames (11). Table 4 reports the possible correlations and timescales that can be achieved by LSM. In regard to spatial resolution for the determination of dynamics, if the dynamic is slow enough that we can use temporal correlation at one pixel (in the millisecond range or slower); then the spatial resolution is the pixel or the PSF (<0.5 µm). Instead, if the dynamics (diffusion) is very fast (in the microsecond to millisecond range), we can use the spatial-correlation approach. This approach uses an area (for example, 16 x 16 pixels or 32 x 32 pixels, typically 0.092 µm/pixel) to recover the diffusion parameters, thereby reducing the spatial resolution to the size of that area (limit of 1.6–3.2 µm). The size of the selected area over which the diffusion coefficient is averaged depends on the value of the diffusion coefficient and of the speed of scanning.
Line (or circular) scan versus raster images
The main advantage of the circular scan pattern is that it gives the fastest possible sustained scan motion that can be obtained with mechanical scanners. It gives a continuous stream of data in time. Extracting diffusion coefficients from the continuous data time series and looking at single locations for successive scan orbits has been described (9,16). What has not been described previously is the information that can be extracted by performing spatial correlation of points along the scan orbit. We presented two different aspects of the spatiotemporal correlation approach, one for line scanning and the other for raster-scan images. Although the two methods are mathematically treated in the same framework and the equations describing spatial autocorrelation functions are similar for line scan and for raster scan, there is an important practical difference between the two. Line scan allows very high temporal and spatial resolution. At the pixel level resolution, the temporal resolution of the line-scan method depends on the scan-line repetition time. For raster images, high spatial resolution (pixel level resolution) for dynamic processes can only be obtained for millisecond dynamics. However, information on the fast dynamics can be obtained from the pixels along a line, but the spatial resolution is reduced. Table 5 describes the spatial resolution that can be obtained for different methods of data acquisition. In principle, both methods (line scan and raster image) can be implemented in any commercial LSM. In regard to the total time of data acquisition needed for this technique, the data set used for Figs. 5 and 6 has 23 frames taken at 512 x 512 frame size with a pixel time of 8 µs, giving a total acquisition time of <1 min. The data set used to analyze the dynamics in Fig. 7 along one line has 10,000 lines for a total acquisition time of 54 s.
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The focus of this article is to illustrate how different methods can be used to obtain diffusion and dynamics. However, the fluorophore concentration can also be extracted from solution samples if we know the focal volume from the inverse of the autocorrelation function amplitude, G(0), obtained using the different methods. Table 2 shows that the same value of G(0) is obtained applying the different equations for data analysis. In the presence of bright immobile structures, when the subtraction algorithm is applied the relationship between G(0) and number of particles is no longer valid.
Other dynamic processes
There are large intensity fluctuations at the immobile spots in an image. These fluctuations can be due to shot noise or to other dynamic processes such as binding equilibria, dynamic quenching, changes in conformations, rotational dynamics, dynamic fluorescence resonance energy transfer, and many other process that alter the fluorescence. By measuring the temporal and spatial correlation at the bright spots we can distinguish between shot noise and fluctuations due to dynamic processes. For example, it is probable that the dynamics we observe for paxillin-EGFP localized in adhesions are due to binding equilibria rather than diffusion of large aggregates. We are developing models to fit the data to distinguish among the different physical processes occurring at the adhesions. For example, binding equilibria have an exponential correlation (in time) rather than the characteristic form for diffusion (Eq. 7). Preliminary fits of the correlation functions obtained from the experiment in Fig. 7 show that, indeed, at the adhesions this model was a better fit to the experimental data. The best approach to distinguish between diffusion and localized processes is to change the waist of the excitation beam. Distinguishing diffusion from binding is beyond the scope of this article and will be discussed in detail elsewhere.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Submitted on March 13, 2005; accepted for publication May 10, 2005.
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REFERENCES |
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