Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis

Abstract

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether CE (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Analytical form of the autocorrelation function for the fluorescence correlation spectroscopy

“…Finally, we note that to study biochemical systems also high-order fluorescence correlation analysis can be used, besides G(t). 18 In this theoretical work and the accompanying experimental paper, 19 we apply FCS to study the kinetics of binary reactions A + B $ C. The theoretical model of the autocorrelation function introduced by Elson and Magde, 3 modified later by Krichevsky and Bonnet, 1 is based on linearized reaction-diffusion equations. We use this model to derive an approximate formula for G(t), which is then applied to fit the experimental data.…”

“…We use this model to derive an approximate formula for G(t), which is then applied to fit the experimental data. 19 In our case, A is a surfactant micelle and B is a fluorescent dye that reacts with A to form complex C through noncovalent interactions. It is known that physical aggregation of the dye to the micelle can be used to study formation of micelles by FCS, in particular, the aggregate size and critical micelle concentration.…”

“…The value of o measured in our experimental studies was close to 5. 19 In principle, it is possible to change o by changing the diameter of the beam waist L. It can be achieved by means of stimulated emission depletion (STED) far-field fluorescence nanoscopy, which allows to spatially resolve heterogeneous dynamics in complex systems. 22,23 We return to this point in Section 3.…”

“…In fact, y was always very small (t10 À3 ) in our experimental studies. 19 The relation between the diffusion coefficients is expressed by a dimensionless parameter…”

“…the state A should be interchanged with B in eqn (19). Thus, K and b should be replaced with K À1 and 1 À b, respectively, whereas t AE and t D do not change.…”