One common and challenging problem in fluorescence microscopy is to determine the average number and brightness (aggregation) of molecules in images. This is a major challenge in cell biology as well, where both the concentration and clustering of proteins can differ in various locations in the cells and change during biological processes. For example, in vitro evidence suggests that membrane receptor aggregation triggers signaling responses. However, few direct demonstrations of aggregation have been reported and none have produced a map of this aggregation with high spatial resolution in vivo.
This determination has become feasible with the pervasive use of fluorescent proteins, and some recent studies have appeared that determine the state of aggregation of proteins in the membrane, the cytoplasm, or in the nucleus of live cells. These approaches use image correlation spectroscopy (1
), the photon counting histogram analysis (PCH) (3
), or fluorescence resonance energy transfer (FRET, both homo and hetero) with properly labeled protein partners (6
). A more common procedure widely used to evaluate the number of molecules in a pixel is to calibrate the fluorescence intensity using a solution of known concentration. This calibration procedure gives the total number of fluorophores, but it cannot provide information on the aggregation state of fluorophores since few bright aggregates or many dim molecules could give the same average intensity.
Using fluorescence correlation spectroscopy (FCS), it is possible to obtain separately the brightness of a particle from the number of particles in a given volume (22
) and therefore to determine the degree of aggregation of proteins in solution. This is due to the principle that the occupation number of particles in an open volume follows a Poisson distribution. The ratio of the variance to the square of the average intensity is proportional to 1/N
, where N
is the number of particles in the open volume. Once the number of particles has been determined using FCS, the brightness of the fluorescent particle can be obtained by the ratio of the average intensity to the number of particles. This analysis was originally proposed by Qian and Elson for particles in solution and it is known as the “moment analysis” (23
). For homogeneous systems composed of a single molecular species, the moment analysis is sufficient to provide the two quantities of interest, namely the number and brightness of the molecules. A limitation of the moment-analysis is that multiple species of different brightness cannot be resolved using only the first and second moments of the distribution; instead, higher moments are needed, which requires a much larger data set. Recently, a more general approach was proposed, known as the photon-counting histogram analysis (PCH) (3
). The PCH method considers the entire distribution of the photon counts in a given volume rather than only the first and second moments. Since the PCH approach uses the full distribution of photon counts, it is capable of resolving multiple species in a homogeneous solution. This method, originally developed for solutions, has been applied to obtain the state of aggregation of proteins in selected points in a cell, but has not yet been applied to entire fluorescence microscope images (25
). The PCH method requires a relatively large number of observations at each pixel, and it is computationally too slow for the analysis of all pixels in an image. Therefore, there is a need for a method capable of determining the state of aggregation of proteins simultaneously in the entire cell. If the method is fast (seconds), we could follow the aggregation of proteins in response to external signals and map the state of aggregation across the entire cell.
In this article, we describe the application of the moment analysis to relatively small image stacks. Our purpose is to use this approach to determine the aggregation state of proteins in a given region of the cell. Since the distribution of fluorophores in a cell is not spatially homogeneous and the size of aggregates is unknown, pixel moment analysis could provide a map of this distribution. However, the quantitative interpretation of the measured number of molecules and brightness is not trivial due to the presence of an immobile fraction either from intrinsic cellular features or background fluorescence. In this work, we specifically addressed the effects of the immobile fraction, bleaching, and slowly moving features, which are typical with cellular measurements. The moment analysis can be used in a wide range of concentrations, and it assumes that fluctuations are caused by the occupation number. In a cell, we have regions where proteins are immobile or regions with an autofluorescence or scattering background that contributes to the average intensity but not to the number fluctuations. We found that the ratio of the variance to the average intensity in a pixel is equal to 1 for the intensity fluctuations due to immobile components regardless of the brightness of the immobile features, while it depends on the brightness of the particles for the mobile components. This observation allowed us to separate these two contributions and to measure the brightness of the fast mobile components in the cell independently of the presence of immobile bright features.
We applied moment-analysis to study the process of binding and unbinding of a protein (paxillin-EGFP) to adhesions in CHO-K1 cells. We show that paxillin is monomeric in the cytoplasm but is aggregated when it unbinds from adhesions during disassembly. This is the first time, to our knowledge, that the binding-unbinding process was characterized at high spatial resolution simultaneously in several adhesions in a single cell. The paxillin example shows the potential of the fluctuation analysis performed in parallel using all pixels of an image for biophysical studies of protein-protein interactions in living cells.