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, τ1,0, and locally with correlation time, τ2,0, where τ1,0 ≫ τ2,0. 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, Sk, both given by Peq = exp(-u). 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 τ2,0 = 0-170 ps for ligand-free MUP-I, whereas c02 ≅ 15 ± 4 and τ2,0 = 20-270 ps for ligand-bound MUP-I. β is in the 0-10° range. c02 and τ2,0 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 (τ2,0), geometry-related (β), and binding-related (Sk) 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 (τe) of the local motion, and a phenomenological exchange term (Rex). S2 is found to decrease (implying implicitly "global" increase in Sk) upon pheromone binding.