Imaging & Photomanipulation  Approaches
The Imaging and Photomanipulation group is developing and expanding a variety of different kinds of imaging technologies for application to migration research both in vitro and in vivo.
Correlation Microscopy
Fluorescence Correlation Spectroscopy (FCS)
FCS was first described in the 1970's and was used to characterize the motion of fluorescent molecules in solution. It is a nonperturbing method used to gain molecular information to study particle diffusion, chemical kinetics, hybridization reaction and molecular aggregation (Magde et al., 1972; Koppel et al., 1976; Elson, 2001). Original experiments involved focusing a laser beam into a cuvette containing fluorescent molecules (Figure 4) and measuring fluctuations in the fluorescence intensity as molecules underwent Brownian motion moving in and out of the focused laser beam (Elson & Magde, 1975; Magde et al., 1974). The fluorescence fluctuation can originate from the diffusion of the fluorescent molecules through the observing volume, or the change of fluorescence quantum yield of the fluorophore due to chemical reaction. Data collected from the observed fluctuations of fluorescence intensity in a small volume (subfemtoliters) can be analyzed and two critical values can be derived: (i) the number of molecules in the excitation volume and (ii) the diffusion coefficient.
In a system where particles only undergo translational diffusion, the analysis of these fluctuations allows the determination of their diffusion coefficient (D) and the number of particles in the excitation volume (i.e. the concentration ) (Palmer & Thomson, 1987 ). Any changes in the diffusion coefficient of a particle in solution would reflect the change of its size (or shape) or the viscosity of the solution; any changes in the number of particles in the excitation volume would suggest particle association or dissociation. These parameters are critica l in analyzing molecules that behave as monomers or bound entities. Many researchers have found this technique to be very useful in analyzing particle diffusion and measuring diffusing rates of proteins in live cells (Berland et al., 1995; Schwille et al., 1999; Ruan et al., 2002).
An autocorrelation function can be calculated from a correlation analysis of the intensity fluctuations over time (Figure 4). The shape of the autocorrelation function provides dynamic information about the molecules while the magnitude of the function at zero time lag gives the average concentration of molecules in the laser beam volume, N (recent reviews Elson, 2001; Thompson et al., 2002).
Figure 4. The fluctuation of particles diffusing in and out of the excitation volume are detected and recorded as a function of Intensity (counts) vs time. The autocorrelation function is described in Eq.1 where N(t) is the fluorescence intensity at time t, tau is some absolute time separation, and the angle brackets denote a time average. At G(0) the autocorrelation function is inversely proportional to the average number of molecules in the excitation volume (Eq.2). In this equation as tau approaches infinity, for a stochastic, stationary system, the numerator approaches the product of the averages, and therefore G(t) approaches zero.
Figure 5Two photon excitation images of stable CHO cells expressing EGFP. Autocorrelation function of the cell using point FCS yields a diffusion coefficient of 19.3 micrometer square per second.
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Scanning SFCS
FCS measurements can be conducted by scanning the beam in a circular motion. This allows the simultaneous measurements of fast (point to point along the circle) and slow (same point at each pass as the laser scans) diffusing molecules while retaining spatial information by scanning the excitation beam periodically across the sample (Meyer et al., 1988; Rigler et al., 1993). Moving the laser beam at constant velocity (KisPetiková et al., 2000).
 Minimize photobleaching
 By monitoring several subvolumes in parallel, spatial averaging is achieved
 The peak heights in the autocorrelation function are free of the shot noise
Figure 6. Scanning FCS measures the fluctuation at a millisecond time resolution over a relatively large area
As the laser beam scans in a circle with a given radius, the data from each point (or subvolume) in the circle is collected. The fluctuations from one scanning period are recorded as a string of data for one cycle. Upon the second scanning period, the data is transposed beneath the first string and so on with subsequent data points.
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Figure 7 CHO cell expressing PaxEGFP in adhesions. Each line in the FCS carpet depicts fluctuations from one scanning period.
When the beam is scanned in a circular path with a specific radius, the intensity distribution of the laser beam is time dependent. The position of the center of the beam is displaced as a function of time by a scan vector. Hence, a fluorescence image is obtained after time on the vertical axis, which is referred to as the FCShyperspace or FCScarpet. An autocorrelation curve can be calculated from each column.
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Image Correlation Microscopy (ICM)
With the development of the scanning confocal microscope scanningFCS was brought to the 2D spatial regime of images as Image Correlation Spectroscopy (ICS) (Petersen et al., 1993). In this case an image is generated as the laser beam is scanned over a region of the sample (Figure 8). The 2D analysis of images rather than single line scans increases the amount of data acquired and gives better statistics for precise data. Newer confocal microscopes with faster more precise scan optics and sensitive detectors are ideal for correlation microscopy. The same mathematics follows as with an FCS experiment except now the fluctuations are in space rather than in time, and the number of molecules within the focal volume changes as the beam is moved. The main feature here is that the scanning rate must be faster then the rate of movement of the molecule being scanned.
Figure 8 The circles in the schematic represent the location of the focused laser beam as it scans over the surface of the cell. The image shown is of a transmembrane integrin protein labeled with GFP. Similarly to FCS, spatial ICM measures intensity fluctuations but in space, rather than in time, as the number of molecules in the laser beam focal volume change. Intensity fluctuations are now a function of distance, but the same mathematics follows as with FCS. Here the autocorrelation function looks like the intensity profile of the laser beam and the zero lag amplitude provides information on the concentration/distribution of molecules. The dynamic information is lost in the scanning but if it is on a long time scale can be seen by temporal ICM.
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Image Correlation Microscopy (ICM)
ICM combines both the temporal correlation of FCS and the spatial correlation of ICS. The average number of fluorescent entities, N (i.e. protein monomers or protein clusters), can be determined from the amplitude of the spatial autocorrelation function (g(0,0)) for a given image area (Eq. 3; Figure 8).
Equation (3)
If N provides the number of fluctuating entities and the average intensity (i) is a measure of the total amount ofprotein in the focal volume then the relative degree of aggregation (DA) of a protein can be determined using equation 4.
Equation (4)
where N_{m} is the total number of proteins. If changes in protein distribution occur the amplitude of the correlation function and the number of fluorescent entities will change accordingly. This allows the determination of the kinetics of protein aggregation or dispersion in real time on living cells.
From the temporal analysis of an image stack, protein diffusion rates and flow velocities can be determined(Figure 9). As things move, the amount of correlation between images will decay at a rate equal to the rate of movement of the proteins. If there is a flow of protein, that will show up in the shape of the temporal correlation function (Wiseman et al., 2000). The slow diffusion rates of transmembrane proteins can be determined this way (D ~ 1010 cm^{2}s^{1} and slower) where as for faster motion such as lipids (D = 10^{8} to 10^{9} cm^{2}s^{1}) and cytosolic proteins (D = 10^{7} to 10^{8} cm^{2}s^{1}) video rate imaging or line or point scanning must be used. If there is a flow of proteins, a more complex analysis for directional correlations can be conducted to determine the direction of flow from an image series (Wiseman and Hebert, in progress).
Figure 9. Temporal ICM measures intensity fluctuations in time through an image series as molecules move. The analysis can detect diffusion, flow and the immobile fraction of molecules for a given image subsection depending on the shape of the autocorrelationfunction decay. Concentration information is also contained in the zero lag amplitude of the function (schematics courtesy of Paul Wiseman).
Image Cross Correlation Microscopy (ICCM): ICM can also be extended to look at image cross correlation. If proteins are labeled with two different fluorophores the coincidence of intensity fluctuations can be determined from an ICCM analysis of image pairs. The cross correlation analysis provides all of the same spatial and temporal information for each protein as the auto correlation analysis, i.e. clustering, diffusion rates, flow rates and directions and immobile fractions for both proteins. In addition, it also provides the same information about any associated, codiffusing and/or coflowing proteins (Figure 10). This is very powerful because it not only tells you if proteins are interacting it also tells you if they are moving together. It is best to conduct ICCM analysis on images collected on a multiphoton microscope where the laser focal volumes are completely coincident, but we are developing methodsfor conducting the same experiments on a confocal microscope using two different lasers for fluorophore excitation.
Figure 10 Cross correlation measures the distribution and dynamics of each protein as well as the codistribution and codynamics of complexes. A spatial correlation function is determined for each protein (blue and yellow functions) and a cross correlation function for the coincident intensity fluctuations between the two proteins. This allows for the determination of the concentration of each protein as well as the protein complexes. There are also three temporal correlation functions. The two temporal autocorrelation functions provide information on the dynamics of each protein while the temporal cross correlation function provides information on the dynamics of protein complexes (schematics courtesy of Paul Wiseman).
Summary: ICM and ICCM provide the means to:

Study protein dynamics in the lamellipod and retracting regions of the cell as it migrates. Including determination of immobile fractions, diffusion rates and flow directions and velocities.

Determine the distribution of interacting proteins and how that distribution changes during cell migration.

Determine the dynamics of protein complexes containing two proteins. Including determination of the immobile fraction of colocalized proteins, diffusion of complexes and the flow of complexes containing both proteins.
The Photon Counting Histogram (PCH)
While Fluorescence Correlation Spectroscopy (FCS) can measure the diffusion coefficient and concentration of fluorophores, a complementary method, a photon counting histogram (PCH) analysis, can be used to differentiate etween species of similar diffusion coefficient through their molecular brightness (Chen et al, 1999, Kask et al, 1999, Thompson et al, 2002). In this manner, the PCH can also resolve aggregation through specie brightness levels. An attractive feature of this method is that the same data obtained to calculate the autocorrelation function can also be used to generate a histogram, although a time series is not required for the PCH.
The PCH is based on the probability distribution of photon counts in a small volume (~one femtoliter); these data can be used to measure:
1. The average photon counts ‹k›, i.e. concentration, of fluorescence species (where a monomer or oligomer is counted as a single species).
2. The molecular brightness (E ) : The average number of photons
per sampling time per molecule. The molecular brightness is proportional to
the product of the quantum yield, the excitation of the fluorophore (extinction
oefficient), and the instrument efficiency in measuring photons.
There are limitations to presenting extensive mathematical equations and symbols on the web, so the concept behind photon counting histograms is presented as a PDF file which can be obtained by clicking here.
Text References
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