Over thirty years ago, fluorescence correlation spectroscopy (FCS) was developed to measure the mobility of fluorescent molecules in solution (Magde et al., 1974
). With this technique, fluctuations of a fluorescent signal from a laser beam focus are detected on a photomultiplier tube. These fluctuations provide insight into the dynamics of fluorescent particles in solution. The change in signal is due to temporal variations in the number of fluorescent particles residing within the focal volume. The correlation of these fluctuations in time can be used to calculate diffusion coefficients as well as reaction kinetics (Elson & Magde, 1974
, Magde et al., 1974
). FCS was later extended to scanning systems where the sample was translated across the beam in either a line or circle (Petersen, 1986
). Later yet, a laser scanning confocal microscope was used to create an image analog of FCS (Petersen et al., 1993
). This technique, called image correlation spectroscopy (ICS), quantitatively characterized the distribution, density and aggregation of fluorescent domains or features in an image using spatial autocorrelation functions. ICS was further extended to study slow mobility of fluorescent domains in images by analyzing the temporal decay of the correlation function. This analysis was initially called image cross correlation spectroscopy (ICCS), but has recently been referred to as temporal image correlation spectroscopy (TICS) (Kolin & Wiseman, 2007
) and is used to study receptor domain diffusion in cell membranes (Srivastava & Petersen, 1998
The extension of FCS to ICS and TICS enabled study of whole image dynamics using the mathematical foundations of the single laser focus developed for FCS. By continuing to use a Gaussian illumination source, the fundamental characteristic length (e−2
radius) to calculate the diffusion coefficient in FCS is preserved. Additional extensions and variations have been added to this suite of tools that we will refer to collectively as image correlation microscopy (ICM): notably, spatial image cross-correlation spectroscopy (ICCS) (Petersen et al., 1998
) to measure transport and co-localization of two differently labeled molecules, applications in two-photon microscopy (Wiseman et al., 2000
), and spatiotemporal image correlation spectroscopy (STICS) (Hebert et al., 2005
) to measure both diffusion coefficients and vector velocities of fluorescent domains in cell membranes. All of these tools build on the mathematical foundation of FCS to create an array of options for the biophysical researcher.
To date, the applications of ICM techniques have been primarily limited to laser-scanning microscopes because of its evolution from laser-based FCS. However, there is a recent report that used ICM techniques with brightfield microscopy by blurring images with a Gaussian filter to prepare them for the traditional laser-scanning based ICM analysis (Immerstrand et al., 2007
). Additionally, pixel-by-pixel analysis of total internal reflection fluorescence (TIRF) using ICM methods was used to create color maps of receptor dynamics on cell surfaces (Digman et al., 2008
), Furthermore, another report investigated ICM using spinning disk confocal microscopy (Sisan et al., 2006
). The authors developed a correction factor for low spatial resolution systems where the pixel size is more than two times greater than the effective illumination radius. These publications continue to extend ICM techniques beyond laser-scanning systems, but do not yet include a framework for determining molecular diffusion coefficients.
In this report, we set out to expand ICM to high-resolution uniform illumination or wide-field microscopy with a mathematical framework that does not require image manipulation. Uniform illumination fluorescence microscopy is more common than laser-scanning microscopy because of its simplicity, reduced cost and potential for greater temporal resolution. Application to uniform illumination systems is useful because it provides broader access to ICM analysis. Historically, ICM has been limited to laser-scanning systems primarily for two reasons. First, the observation volume, and thus the characteristic diffusion distance is defined and controlled by the focus of the excitation laser beam. Second, if the beam has a Gaussian profile, there exists a concise closed form solution of the spatial and temporal autocorrelation functions. Here we build on the original correlation spectroscopy literature to extend the mathematical framework of ICM to uniform illumination ICM (UI-ICM). Specifically, we show that the characteristic diffusion distance is weakly dependent on the beam profile in the original FCS analysis. We establish that in the absence of a laser in UI-ICM, the characteristic diffusion length is defined by the size of the feature itself, which can be estimated from the spatial autocorrelation function. We demonstrate these principles with simulated diffusion of both uniform disks and Gaussian particles and thus establish that particle shape is not an important consideration.
Finally, we confirm UI-ICM diffusion measurements of fluorescent beads in thin chambers using particle tracking as an alternative method. As an example application we study the motion and size of receptor domains on the surface of spherical resting human neutrophils. We find that diffusion measurements of L-selectin domains on the cell surface using UI-ICM are nearly identical to values previously obtained using fluorescence recovery after photobleaching (FRAP) (Gaborski et al., 2008
Another report using spinning disk confocal microscopy investigated the limits of using low spatial resolution and developed a correction factor for when the pixel size is more than two times greater than the effective illumination radius. In our work presented here, the pixel size is just a fraction of the effective illumination radius or characteristic length.