The thermodynamics of l-tryptophan and operator DNA binding to the tryptophan repressor of Escherichia coli were analyzed by titration microcalorimetry and van't Hoff analysis of footprinting titrations, respectively. At 25 °C in 10 mM sodium phosphate, pH 7.6, and 0.1 M NaCl, the binding of l-tryptophan to the repressor is characterized by values of ΔG° = −6.04, ΔH° = −14.7, and TΔS° = −8.67 kcal/mol. The temperature dependence of ΔH° yields ΔCP° = −0.46 ± 0.08 kcal/(mol•K) per dimer. The binding is noncooperative at all temperatures studied. At 23 °C in 2.5 mM sodium phosphate, pH 7.6, and 25 mM NaCl, the binding of operator DNA to the repressor is characterized by values of ΔG° =−13.3 kcal/mol, ΔH° = −1.55 kcal/mol, TΔS° = 11.8 kcal/mol, and ΔCP° = −0.54 ± 0.10kcal/(mol•K). Changes in water-accessible surface areas upon binding of l-tryptophan or DNA were calculated from X-ray crystal structures. The experimentally observed ΔCP° values were compared with ΔCP° values calculated according to several methods based on various proposed relationships between surface area changes and heat capacity changes. Regardless of which method is used, we find poor agreement between the calorimetric results for l-tryptophan binding and the surface areas calculated from X-ray data; the direction of the discrepancy is that the X-ray data underestimate the value of ΔCP°. Better agreement is obtained by incorporating solution data on repressor flexibility, suggesting that ΔCP° measurements may report on protein dynamical transitions accompanying ligand binding. For the case of DNA binding there is apparently fortuitous agreement between the measured and calculated ΔCP° values, despite clear limitations in calculating ΔCP° for this type of reaction.
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