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

Abstract

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.

Microsecond sub-domain motions and the folding and misfolding of the mouse prion protein

“…The amplitudes of the exponential quenching processes observed by PET-FCS correspond to the equilibrium constants between two conformations only when the fluorescence of one of the conformations is completely quenched (Sauer and Neuweiler, 2014; Wu et al, 2016). In the case of the two faster exponential processes corresponding to fluctuations between N and N*, and between N and N**, this criterion appears to be approximately met (see above).…”

Affinity of Skp to OmpC revealed by single-molecule detection

“…The Monte-Carlo simulation was performed as described previously 34 , 35 and simplified by putting 6 diffusing molecules into the box. Each fluorescence trace was tracked and calculated to obtain the smFRET histograms in which the contribution from each molecule was known.…”

Statistical Methodology in Single-Molecule Experiments

“…When multiple molecular species with various concentrations and brightness levels are present, a conventional approach based on the autocorrelation function alone can be insufficient for distinguishing molecular species. In this scenario, it is necessary to consider higher-order moments of intensity signal Elson, 1990a, 1990b) or the higher-order correlation functions (Melnykov and Hall, 2009;Wu et al, 2016).…”