No 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.

We measure the activation energy E a for the diffusion of molecular probes (dyes and proteins of radii from 0.52 to 6.9 nm) and for macroscopic flow in a model complex liquid-aqueous solutions of polyethylene glycol. We cover a broad range of polymer molecular weights, concentrations, and temperatures. Fluorescence correlation spectroscopy and rheometry experiments reveal a relationship between the excess of the activation energy in polymer solutions over the one in pure solvent ÁE a and simple parameters describing the structure of the system: probe radius, polymer hydrodynamic radius, and correlation length. ÁE a varies by more than an order of magnitude in the investigated systems (in the range of ca. 1-15 kJ=mol) and for probes significantly larger than the polymer hydrodynamic radius approaches the value measured for macroscopic flow. We develop an explicit formula describing the smooth transition of ÁE a from the diffusion of molecular probes to macroscopic flow. This formula is a reference for the quantitative analysis of specific interactions of moving nano-objects with their environment as well as active transport. For instance, the power developed by a molecular motor moving at constant velocity u is proportional to u 2 expðE a =RTÞ.