Measuring size distribution in highly heterogeneous systems with fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a sensitive and widely used technique for measuring diffusion. FCS data are conventionally modeled with a finite number of diffusing components and fit with a least-square fitting algorithm. This approach is inadequate for analyzing data obtained from highly heterogeneous systems. We introduce a Maximum Entropy Method based fitting routine (MEMFCS) that analyzes FCS data in terms of a quasicontinuous distribution of diffusing components, and also guarantees a maximally wide distribution that is consistent with the data. We verify that for a homogeneous specimen (green fluorescent protein in dilute aqueous solution), both MEMFCS and conventional fitting yield similar results. Further, we incorporate an appropriate goodness of fit criterion in MEMFCS. We show that for errors estimated from a large number of repeated measurements, the reduced X-2 value in MEMFCS analysis does approach unity. We find that the theoretical prediction for errors in FCS experiments overestimates the actual error, but can be empirically modified to serve as a guide for estimating the goodness of the fit where reliable error estimates are unavailable. Finally, we compare the performance of MEMFCS with that of a conventional fitting routine for analyzing simulated data describing a highly heterogeneous distribution containing 41 diffusing species. Both methods fit the data well. However, the conventional fit fails to reproduce the essential features of the input distribution, whereas MEMFCS yields a distribution close to the actual input.