  In recent years, thermophoresis has emerged as a promising tool for
quantifying biomolecular interactions. The underlying physical effect is still
not understood. To gain deeper insight, we investigate whether non-equilibrium
coefficients can be related to equilibrium properties. Therefore, we compare
thermophoretic data measured by thermal diffusion forced Rayleigh scattering
(TDFRS) (which is a non-equilibrium process) with thermodynamic data obtained
by isothermal titration calorimetry (ITC) (which is an equilibrium process). As
a reference system, we studied chelation reaction between
ethylenediaminetetraacetic acid (EDTA) and calcium chloride (CaCl$_2$) to
relate the thermophoretic behavior quantified by the Soret coefficient
$S_{\mathrm T}$ to the Gibb's free energy $\Delta G$ determined in the ITC
experiment using an expression proposed by Eastman [J. Am. Chem. Soc. 50, 283
(1928)]. Finally, we have studied the binding of the protein Bovine Carbonic
Anhydrase I (BCA I) to two different benzenesulfonamide derivatives:
4-fluorobenzenesulfonamide (4FBS) and pentafluorobenzenesulfonamide (PFBS). For
all three systems, we find that the Gibb' free energies calculated from
$S_{\mathrm T}$ agree with $\Delta G$ from the ITC experiment. In addition, we
also investigate the influence of fluorescent labeling, which allows
measurements in a thermophoretic microfluidic cell. Re-examination of the
fluorescently labeled system using ITC showed a strong influence of the dye on
the binding behavior.
