Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media

A new method for the measurement of diffusion in thick samples is introduced, based upon the spatial Fourier analysis of Tsay and Jacobson (Biophys. J. 60: 360-368, 1991) for the video image analysis of fluorescence recovery after photobleaching (FRAP). In this approach, the diffusion coefficient is calculated from the decay of Fourier transform coefficients in successive fluorescence images. Previously, the application of FRAP in thick samples has been confounded by the optical effects of out-of-focus light and scattering and absorption by the sample. The theory of image formation is invoked to show that the decay rate is the same for both the observed fluorescence intensity and the true concentration distribution in the tissue. The method was tested in a series of macromolecular diffusion measurements in aqueous solution, in agarose gel, and in simulated tissue consisting of tumor cells (45% v/v) and blood cells (5% v/v) in an agarose gel. For a range of fluorescently labeled proteins (MW = 14 to 600 kD) and dextrans (MW = 4.4 to 147.8 kD), the diffusion coefficients in aqueous solution were comparable to previously published values. A comparison of the spatial Fourier analysis with a conventional direct photometric method revealed that even for the weakly scattering agarose sample, the conventional method gives a result that is inaccurate and dependent on sample thickness whereas the diffusion coefficient calculated by the spatial Fourier method agreed with published values and was independent of sample thickness. The diffusion coefficient of albumin in the simulated tissue samples, as determined by the spatial Fourier analysis, varied slightly with sample thickness. In contrast, when the same video images were analyzed by direct photometric analysis, the calculated diffusion coefficients were grossly inaccurate and highly dependent on sample thickness. No simple correction could be devised to ensure the accuracy of the direct photometric method of analysis.These in vitro experiments demonstrate the advantage of our new analysis for obtaining an accurate measure of the local diffusion coefficient in microscopic samples that are thick (thickness greater than the microscope depth of focus) and scatter light.