Development and verification of the method consisted of several steps. First, the point spread function (PSF) of the microscope was measured to use for the RICS analysis. Second, recordings of diffusion of Alexa Fluor 488 and fluorescent microspheres in water were used to verify the method. Third, a program was written to simulate the 3-D movement of molecules in isotropic and anisotropic media. The simulated data were then analyzed as normal image data to ensure that the method was sensitive enough to detect anisotropy in diffusion coefficients. Last, experiments with Alexa Fluor 647-ATP in solution and in rat cardiomyocytes were performed.
Adult Wistar rats of both sexes were used for the experiments. All animal procedures were approved by Estonian National Committee for Ethics in Animal Experimentation (Estonian Ministry of Agriculture).
Isolated ventricular rat cardiomyocytes were kindly provided by Tuuli Käämbre and Peeter Sikk. Intact ventricular cardiomyocytes were isolated from adult male Wistar rat heart as described previously (17
The measurement solution contained (in mM) 0.5 K2EGTA (Fluka), 3.0 Mg-acetate (Fluka), 3.0 KH2PO4 (Sigma), 20 taurine (Fluka), 20 HEPES (Roche), 170 sucrose (Sigma), 0.5 dithiothreitol (Sigma), 5 glutamate (Merck), 2 malate (Sigma), 3 ATP (Roche), and 10 PCr (Roche). In addition, 5 mg/ml BSA (Roche) and, for permeabilization, 50 μg/ml saponin (Roche) were added, and pH was adjusted at 25°C to 7.1.
The fluorescent dyes and spheres were purchased from Molecular Probes (Invitrogen). We used fluorescent microspheres for PSF determination (175-nm diameter, 540-nm excitation, 560-nm emission; PS-Speck, product no. P-7220), fluorescent microspheres (actual size reported by Molecular Probes of 24 nm, nominal size of 20 nm; FluoSpheres, product no. F-8782), Alexa Fluor 488 (Alexa 488, product no. A-20000), and Alexa Fluor 647-ATP (Alexa-ATP, product no. A-22362).
Raster image correlation spectroscopy.
To determine diffusion coefficients in the media, we used RICS (5
). In short, RICS uses spatial and temporal aspects of confocal images acquired using laser scanning. For simplicity, in the ideal case, the autocorrelation between fluctuations of intensities (F) in pixels of the image separated from each other by vector R is given by
where R is a spatial vector connecting two pixels, W
is the PSF with the integration performed in space surrounding both pixels, c is the concentration of fluorescent probe, τ(R) is a delay time between acquisition of two pixels,
is averaging over space with the point vector p, and
is a factor that depends on the properties of the fluorescent dye and confocal microscope. For the isometric case, the autocorrelation term
δc(p + r, 0)·δc(p + r′ + R, τ)p
for diffusing molecule is given by
is a diffusion coefficient. For the anisotropic case, this relationship is transferred to
where x, y
, and z
form the principal axes system for the diffusion tensor; x, y, z
are components of r (similar notation is used for r′ and R), and Dx
, and Dz
are diagonal components of the diffusion tensor in the coordinate system composed of the principal axes.
To determine the components of the diffusion tensor, the spatial and temporal aspects of RICS can be exploited. To get additional information on diffusion in anisotropic medium, we changed the angle of acquisition of confocal images (rotation angle in microscope software). By doing so, we changed the relationship between different spatial points and the delay of acquisition of the signal. Thus τ(R) was varied, and as a result, the autocorrelation relationship between fluctuations of fluorescence in different pixels varied as well. The method is illustrated in for rat cardiomyocytes. Rat cardiomyocytes were considered as cylindrical symmetric cells. In those cells, we assumed that diffusion tensor principal axes were along and across the myofibril orientation. In the plane perpendicular to myofibril orientation, the transverse direction, the diffusion was assumed to be equal. Thus the diffusion tensor is given by two constants, one longitudinal (y-axis) and the other transverse (x and z axes). As shown in , all cardiomyocytes were first rotated by changing the angle of image acquisition so that the cells were aligned along the y axis. The images were then acquired with different relative rotation angle, stored, and analyzed.
Fig. 1. Scheme showing the protocol of experiments on cardiomyocytes. Assuming that the cardiomyocyte has the shape of an elliptic cylinder (top left), the y-axis was defined as the longitudinal axis, the x-axis as the horizontal transverse axis, and the z-axis (more ...)
The autocorrelation function C
computed from the images acquired from the microscope is different from G
due to the noise of the system and other simplifications done in Eq. 1
. Assuming that the noise (s
) is the main component modifying the autocorrelation function and that it depends only on delay between pixels (τ), the following formula was used in this work:
is the distance between pixels along the fastest scanning direction of the laser (horizontal lines in images) and Δy
is the distance between pixels in the direction perpendicular to x
(distance between lines).
When not specified, the autocorrelation function analyzed in this work was normalized by the standard deviation of the fluorescence signal, i.e., C
(0, 0). In our analysis, multiple (25–100) images were acquired with the same pixel size, dwell time, and scan rotation angle to calculate the autocorrelation function. When not specified otherwise, fluctuation of the fluorescence signal for each pixel was calculated relative to the average intensity of the pixels in the same position on all images. This allowed us to remove the influence of immobile intracellular structures on the autocorrelation function (7
Confocal images were acquired on an inverted confocal microscope (Zeiss LSM510 Duo) built around an Axio Observer Z1 with a ×63 water-immersion objective (1.2 NA) at room temperature. The signal was acquired via a high-voltage single photomultiplier tube (PMT) using 8-bit mode; the pinhole was set to one Airy disk. The imaging chamber consisted of a FlexiPERM silicone insert (Vivascience, Hanau, Germany) attached to a coverslip of 0.17 mm in thickness.
The microscope was characterized by measuring its PSF and determining the settings that would reduce the interference of acquisition noise and RICS analysis. To determine PSF, we used fluorescent microspheres with a diameter of 175 nm (540-nm excitation, 560-nm emission; PS-Speck, Molecular Probes, Invitrogen). The 3-D image stacks were acquired with several microspheres in focus, with the voxel size 0.027 × 0.027 × 0.191 μm. By averaging the intensity profiles acquired from different microspheres, we found the PSF of the system (). This PSF was used in the analysis of the autocorrelation functions and in Brownian simulations of freely diffusing particles in three dimensions.
Fig. 2. Characterization of the confocal microscope system used in this study, the Zeiss LSM510. Point spread function (PSF) measured using fluorescent beads is shown in A. The PSF is shown in the planes xy (z = 0 μm), xz (y = 0 μm), (more ...)
To estimate the noise component and find conditions where it is mainly influencing the standard deviation of the fluorescence signal [C
(0, 0)], we recorded the series of images either without any illumination from the laser or from pure water with laser illumination. In both cases, the offset and gain of the PMT was adjusted so that the noise signal would be visible and there would be no pixels with either minimal or maximal intensity allowed by the image format. The autocorrelation functions determined for both cases are shown in , B
. Similar to properties of the Olympus Fluoview 300 (5
), the use of fast scanning speeds with small pixel dwell times led to strong autocorrelation between the neighboring pixels. To avoid such interference with the analysis of diffusion, we used images acquired with slow scan speeds (pixel dwell times larger than or equal to 25.6 μs).
For RICS analysis, timing information of image acquisition is needed. According to Zeiss, the signal is acquired during almost the full-pixel dwell time in the fast acquisition modes. For scan speeds slower than 6, three-fourths of pixel dwell time is used for recording the signal. The time between acquisition of the last pixel in the line and the first pixel in the next line (fly-back time) depends on the speed of imaging. For fast acquisition speeds, fly-back time is 1.34 times larger than the time for acquisition of a line. However, the maximal fly-back time is limited to 9.38 ms. This timing information was used in the analysis through τ(R).
RICS analysis was used to estimate the diffusion of fluorescent microspheres and Alexa 488 in water and of Alexa-ATP in solution and inside permeabilized cardiomyocytes. Irrespective of the preparation, the imaging protocol was the same. Confocal images with a resolution of 128 × 128 pixels were recorded in a single plane. Recordings were done at three different zooms of 10, 20, and 40, resulting in pixel sizes of 0.1116, 0.0558, and 0.0279 μm, respectively. At each zoom setting, the pixel dwell time was varied among 25.6, 51.2, and 102.4 μs. For each of these nine settings, we rotated the scanning field to record images at three different angles: 0°, 45°, and 90° (). This gave a total of 27 settings at which a series of 25–100 images were recorded.
The recordings of fluorescent dyes suspended in water and solution were straightforward. The recordings in rat cardiomyocytes were performed as follows. First, cardiomyocytes were suspended in 200 μl of measurement solution containing ~0.25 μM Alexa-ATP. When saponin (50 μg/ml) was added to permeabilize the sarcolemma, Alexa-ATP diffused into the cell cytosol. As has been shown previously, saponin skinning leaves the cellular structure well preserved (22
). For each cardiomyocyte, the scanning field was rotated so that the cell was positioned vertically in the field of view. Before the images were recorded for RICS analysis, imaging of mitochondrial autofluorescence with the 488-laser line ensured that the plane of scanning was inside the cell and in a region where mitochondria were organized in a highly ordered, crystal-like pattern (3
). Thus regions around the nuclei, where mitochondria appear smaller and not as organized, were avoided. When an appropriate region was found, RICS recordings of Alexa-ATP diffusion were commenced.
Calculation of autocorrelation functions and estimation of diffusion coefficients were done using software programs written in C++ and Python. First, images from each acquired time series were extracted from Zeiss LSM format by ImageJ (2
) to a directory with raw files using a LSM Reader plug-in. During this extraction, scanning parameters were taken from the Zeiss LSM file and saved in a text file in the same directory. Second, the extracted raw files were processed by our program to calculate two-dimensional autocorrelation function from the fluctuations of pixel intensities (first part of Eq. 4
). The found autocorrelation function was stored for further analysis.
Since the pixel dwell times used in this work were rather long, we assumed that the noise interfered with the autocorrelation function only at the value C
(0, 0). With this assumption, the autocorrelation functions were normalized by C
(0, 0) and fitted by minimizing the residuals (Res
) as follows:
is the autocorrelation found from images obtained by the confocal microscope, G
is calculated on the basis of the second part of Eq. 1
, and α is a shot noise contribution that depends only on pixel dwell time tpixel
. In this formula, the summation was performed over all autocorrelations considered in a particular fit. In this work, the fit was performed using autocorrelation functions determined for images acquired at different zooms (pixel sizes), pixel dwell times, and image orientation (rotation angles). Since the studied fluorescent probes were fast-moving ones and the pixel dwell time was rather large, only the autocorrelation between pixels in the same line was considered in this work, i.e., Δy
To fit the autocorrelation functions determined from acquired images, diffusion coefficient D (or diffusion tensor components Dx,z and Dy in the anisotropic case) and shot noise component contribution α (different for different pixel dwell times) were varied. In addition, experimentally determined PSF was scaled to improve the fits by taking into account the variation in microscope settings and differences in wavelength used to determine PSF and RICS acquisitions. The PSF scaling factor was the same in all directions and considered to be the same for all images used in the fit (independent of pixel time, dwell time, and image orientation). The PSF scaling factor was usually 1.2–1.3 in the experiments performed in this study. When autocorrelation functions were normalized by C(1, 0) (autocorrelation between neighboring pixels in the same line), the shot noise component was ignored (α = 0).
The integral required to find G
was calculated using the experimentally determined PSF (W
in Eq. 1
). Within each voxel used to measure PSF, PSF was considered constant. With this assumption, the integration was replaced by summation over all possible voxel combinations with the contribution of other components found using analytical expression for an integral within a voxel derived by Maple (Maplesoft, Waterloo, Ontario, Canada). The minimization of residual Res
was performed using the Levenberg-Marquardt algorithm (25
For testing the method, Brownian simulations were performed. For that, a program was written that simulates the movement of particles in three dimensions using Gaussian probability distribution to find the coordinates of the particle after each time step. The particle step was determined by floating point pseudo-random number with the mean zero and standard deviation of
(component along the coordinate axis n
). To generate a simulated confocal image, experimentally determined PSF was used as well as spatial and temporal information of the laser scanning of Zeiss LSM510. The generated images were analyzed the same way as experimental images to find autocorrelation functions.
Fitting and Brownian simulations were paralleled for use in an available computer cluster. On average, simulations were performed using ~100 parallel processes.
Values are means ± SD. A Welsh two-sample t
-test was used to determine the significance of the differences between mean values of diffusion coefficients as well as mean values of ratios of diffusion coefficients using the statistical software package R (http://www.r-project.org