Theoretical methods in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a valuable tool in the study of reaction kinetics, diffusion, and photo-physics of bio-molecules. FCS utilizes correlation-function analysis of fluorescence intensity fluctuations from a small number of laser-excited molecules in a confocal optical system. The theoretical foundation of FCS was established in 1974 by Madge and Elson (ME). From this foundation, equations necessary to fit experimental correlations and extract parameters of interest are obtained.;The SPT technique furnishes other possibilities not available in the ME technique. First, the SPT approach yields an efficient means of calculating spatial correlation-functions. While such functions have been derived previously, the approach in this work provides a means to obtain them in a direct and logical manner. Second, a power spectrum can be written in terms of the white noise driving the system. This allows one to easily derive the integrals for the FCS power spectrum for use in analysis of the data.;Also, a method is presented to eliminate the effect of diffusion in experimental correlation-functions of conformational reaction studies by means of auto/cross-correlation ratios. This method eliminates the need to utilize a separate diffusion-characterizing sample in a second experiment. Changes in confocal volume shape between experiments are also eliminated, providing more reliable parameter extraction.;It can be shown that ME theory does not yield steady-state solutions, contradicting observed continuous intensity fluctuations from solutions in thermodynamic equilibrium. In this work, the contradiction is corrected through the application of stochastic process theory (SPT). To accomplish this, the master equation for a chemical reaction can be written; manipulations permit derivation of all equations necessary for FCS analysis and solve the contradiction. This new approach dispenses with the assumptions required in ME theory to write the reaction/diffusion equations and conditions on correlations at zero lag-time. These can be derived through SPT whereas ME methodology requires their assumption. It can be shown for non-linear reactions (at least for the types of non-linear, non-reversible reactions presented in this work) that the zero-time correlation conditions and correlation-functions from ME theory and SPT yield divergent results, converging for vanishing non-linearity.