Static Conformational Distributions in the Solid State: Analysis and Application to Angular Dispersion in Side Chain Orientations in Model Tyrosine in Aqueous Glass

The analysis of static conformational distributions in the solid state to reveal the equilibrium thermodynamic properties of the motion prior to rigidification is described. The analysis is applied to the angular distribution about the ring carbon (C 1 )−β-methylene carbon (C β ) bond in the side chain of the amino acid tyrosine trapped in a low-temperature 40% aqueous-NaOH glass. The model tyrosine exhibits an angular distribution about C 1 −C β of full extent 33°. Hindered torsional motion about the C 1 −C β bond prior to medium vitrification is treated classically as the overdamped Brownian motion of a harmonically-bound particle. A motional criterion based on the viscosity-dependent conditional probability for oscillator displacement is used to estimate that oscillator motion ceases at T s = 203 ± 2 K ( k B T s = 141 cm -1 ). The observed “frozen-in” rotamer population is assumed to represent the thermally-weighted (at T s ) Boltzmann distribution function for harmonic C 1 −C β oscillators. Both classical and quantum mechanical descriptions of the distribution are presented. The observed population density is fitted with the classical model by using three torsional modes with frequencies corresponding to h ν = 80, 95, and ∼300 cm -1 that make relative contributions of 1, 0.8, and 0.1 to the observed distribution. The relative populations and different equilibrium angles suggest that the three modes arise from the two gauche/anti (80 and 95 cm -1 ) and one gauche/gauche (∼300 cm -1 ) conformations about the adjacent C β −C γ bond. The harmonic potential energy curves, equilibrium positions, and oscillator frequencies, and the strong dependence of these equilibrium thermodynamic parameters on C β −C γ conformation, identify factors that influence the orientation and mobility of tyrosine sidechains in proteins.