Conformational Entropy from Slowly Relaxing Local Structure Analysis of ¹⁵N-H Relaxation in Proteins: Application to Pheromone Binding to MUP-I in the 283-308 K Temperature Range

The slowly relaxing local structure (SRLS) approach is applied to ¹⁵N-H relaxation from the major urinary protein I (MUP-I), and its complex with pheromone 2-sec-butyl-4,5-dihydrothiazol. The objective is to elucidate dynamics, and binding-induced changes in conformational entropy. Experimental data acquired previously in the 283-308 K temperature range are used. The N-H bond is found to reorient globally with correlation time, I_1,0, and locally with correlation time, I_2,0, where I_1,0 I_2,0. The local motion is restricted by the potential u = c0₂D00₂, where D00₂ is the Wigner rotation matrix element for L = 2, K = 0, and c0₂ evaluates the strength of the potential. u yields straightforwardly the order parameter, D00₂, and the conformational entropy, S_k, both given by P_eq = exp(). The deviation of the local ordering/local diffusion axis from the N-H bond, given by the angle β, is also determined. We find that c0₂ 18 ± 4 and I_2,0 = 0-170 ps for ligand-free MUP-I, whereas c0₂ 15 ± 4 and I_2,0 = 20-270 ps for ligand-bound MUP-I. β is in the 0-10° range. c0₂ and I_2,0 decrease, whereas β increases, when the temperature is increased from 283 to 308 K. Thus, SRLS provides physically well-defined structure-related (c0₂ and D00₂), motion-related (I_2,0), geometry-related (β), and binding-related (S_k) local parameters, and their temperature-dependences. Intriguingly, upon pheromone binding the conformational entropy of MUP-I decreases at high temperature and increases at low temperature. The very same experimental data were analyzed previously with the model-free (MF) method which yielded "global" (in this context, "relating to the entire 283-308 K range") amplitude (S²) and rate (I_e) of the local motion, and a phenomenological exchange term (R_ex). S² is found to decrease (implying implicitly "global" increase in S_k) upon pheromone binding.