Statistical analysis of the autocorrelation function in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful method to measure concentration, mobility, and stoichiometry in solution and in living cells, but quantitative analysis of FCS data remains challenging due to the correlated noise in the autocorrelation function (ACF) of FCS. We demonstrate here that least-squares fitting of the conventional ACF is incompatible with the χ² goodness-of-fit test and systematically underestimates the true fit parameter uncertainty. To overcome this challenge, a simple method to fit the ACF is introduced that allows proper calculation of goodness-of-fit statistics and that provides more tightly constrained parameter estimates than the conventional least-squares fitting method, achieving the theoretical minimum uncertainty. Because this method requires significantly more data than the standard method, we further introduce an approximate method that requires fewer data. We demonstrate both these new methods using experiments and simulations of diffusion. Finally, we apply our method to FCS data of the peripheral membrane protein HRas, which has a slow-diffusing membrane-bound population and a fast-diffusing cytoplasmic population. Despite the order-of-magnitude difference of the diffusion times, conventional FCS fails to reliably resolve the two species, whereas the new method identifies the correct model and provides robust estimates of the fit parameters for both species.