Determination of Equilibrium Constant and Relative Brightness in FRET-FCS by Including the Third-Order Correlations

Fluorescence correlation spectroscopy (FCS) encodes the information on the equilibrium constant (<i>K</i>), the relative fluorescence brightness of fluorophore (<i>Q</i>), and the forward and backward reaction rate constants (<i>k</i>₊ and <i>k</i>_–) on a physical or chemical relaxation. However, it has been a long-standing problem to completely resolve the FCS data to get the thermodynamic and kinetic information. Recently, we have solved the problem for fluorescence autocorrelation spectroscopy (FACS). Here, we extend the method to fluorescence cross-correlation spectroscopy (FCCS), which appears when FCS is coupled with fluorescence resonance energy transfer (FRET). Among 12 total second-order and third-order pre-exponential factors in a relaxation process probed by the FRET-FCS technique, 3 are independent. We presented and discussed 3 sets of explicit solutions to use these pre-exponential factors to calculate <i>K</i> and <i>Q</i>. Together with the relaxation time, the acquired <i>K</i> will allow people to obtain <i>k</i>₊ and <i>k</i>_–, so that the goal of deciphering the FRET-FCS data will be fully reached. The theory is verified by extensive computer simulations and tested experimentally on a system of oligonucleotide hybridization