¹⁵N NMR relaxation studies of free and inhibitor-bound 4-oxalocrotonate tautomerase: Backbone dynamics and entropy changes of an enzyme upon inhibitor binding

The solution secondary structure of 4-oxalocrotonate tautomerase (4-OT), a 41 kDa homohexamer with 62 residues per subunit, consists of an α-helix, two β-strands, a β-hairpin, two loops, two turns, and a C-terminal coil [Stivers et al. (1996) Protein Sci. 5, 729-741 ]. The general base, proline-1, as well as the two loops and the β-hairpin have been shown to comprise the active site [Stivers et al. (1996) Biochemistry 35, 814-823]. The backbone dynamics of both the free enzyme and its complex with a substrate analog have been studied by ¹H-detected ¹⁵N relaxation rates and NOE determinations at 500 and 600 MHz. Analysis of the data using the model-free formalism showed that the nanosecond to picosecond motion of 53 of the 60 backbone ¹⁵N-H vectors was highly restricted with a mean order parameter 〈S2〉 = 0.87 ± 0.03. The lowest backbone mobility (S² > 0.90) is found in the β1-strand, loop 2, and turn 2. Greater backbone mobility is found in the active site (0.5 < S ² ≤ 0.83) and at C-terminal residues 58-62 (0.03 ≤ S ² ≤ 0.70). A τ_m value for the free hexamer of 13.7 ns at 42 °C was determined, consistent with a compact globular molecule of 41 kDa. Saturation of 4-OT with the analog of the dienolic intermediate and linear competitive inhibitor cis.cis-muconate (4) (K_D = 0.59 mM) increased the backbone S ² of seven residues and decreased the backbone S ² of another eight residues, both at the active site and at the antiparallel β1-β1 interface. The S ² values of the other 44 detectable NH vectors were not altered by the binding of 4. The increases in S ², resulting from the "freezing" of the backbone NH vectors of seven residues upon the binding of 4, correspond to an unfavorable entropic contribution to ΔG_binding of 3.2 ± 1.1 kcal/mol. This freezing is partially compensated for by the mobilization of the other eight residues, since the decreases in S ² for these residues correspond to an entropic contribution to binding of -1.9 ± 0.1 kcal/mol. These entropy changes, resulting solely from alterations in highfrequency motion, are significant compared to the overall ΔG_binding = -4.6 kcal/mol for 4. Other effects of the binding of 4 include (1) changes in ¹⁵N and NH chemical shifts localized to the active site and (2) increases in the exchange contributions (R_ex) to 1/T₂ of backbone ¹⁵N resonances at the active site and at the subunit interface, reflecting microsecond to millisecond motions which may play a role in substrate binding (k_on ≥ 4 × 10⁶ M^-1 s^-1) and/or catalysis (k_cat = 10³ S^-1).