Thermodynamics of Ligand Binding to trp Repressor

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 ΔC_P° = −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 ΔC_P° = −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 ΔC_P° values were compared with ΔC_P° 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 ΔC_P°. Better agreement is obtained by incorporating solution data on repressor flexibility, suggesting that ΔC_P° 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 ΔC_P° values, despite clear limitations in calculating ΔC_P° for this type of reaction.