Determination of Equilibrium Constant and Relative Brightness in Fluorescence Correlation Spectroscopy by Considering Third-Order Correlations.

Fluorescence correlation spectroscopy (FCS) is a powerful tool to investigate molecular diffusion and relaxations, which may be utilized to study many problems such as molecular size and aggregation, chemical reaction, molecular transportation and motion, and various kinds of physical and chemical relaxations. This article focuses on a problem related to using the relaxation term to study a reaction. If two species with different fluorescence photon emission efficiencies are connected by a reaction, the kinetic and equilibrium properties will be manifested in the relaxation term of the FCS curve. However, the conventional FCS alone cannot simultaneously determine the equilibrium constant (K) and the relative fluorescence brightness (Q), both of which are indispensable in the extraction of thermodynamic and kinetic information from the experimental data. To circumvent the problem, an assumption of Q = 0 is often made for the weak fluorescent species, which may lead to numerous errors when the actual situation is not the case. We propose to combine the third-order FCS with the conventional second-order FCS to determine K and Q without invoking other resources. The strategy and formalism are verified by computer simulations and demonstrated in a classical example of the hairpin DNA-folding process.