Relationship between nonlinear pressure-induced chemical shift changes and thermodynamic parameters.

NMR chemical shift analysis is a powerful method to investigate local changes in the environment of the observed nuclear spin of a polypeptide that are induced by application of high hydrostatic pressure. Usually, in the fast exchange regime, the pressure dependence of chemical shifts is analyzed by a second order Taylor expansion providing the first- and second-order pressure coefficient B1 and B2. The coefficients then are interpreted in a qualitative manner. We show here that in a two-state model, the ratio of B2/B1 is related to thermodynamic parameters, namely the ratio of the difference of compressibility factors Δβ' and partial molar volumes ΔV. The analysis is applied to the random-coil model peptides Ac-Gly-Gly-Xxx-Ala-NH2, with Xxx being one of the 20 proteinogenic amino acids. The analysis gives an average Δβ'/ΔV ratio of 1.6 GPa(-1) provided the condition |ΔG(0)| ≪ 2RT holds for the difference of the Gibbs free energies (ΔG(0)) of the two states at the temperature (T0) and the pressure (p0). The amide proton and nitrogen B2/B1 of a given amino acid Xxx are strongly correlated, indicating that their pressure-dependent chemical shift changes are due to the same thermodynamic process. As a possible physical mechanism providing a two-state model, the hydrogen bonding of water with the corresponding amide protein was simulated for isoleucine in position Xxx. The obtained free energy could satisfy the relation |ΔG(0)| ≪ 2RT. The derived relation was applied to the β-amyloid peptide Aβ and the phosphocarrier protein HPr from S. carnosus. For the transition of state 1 to state 2' of Aβ, the derived relation of B2/B1 to Δβ'/ΔV can be confirmed experimentally. The HPr protein is characterized by substantially higher negative B2/B1 values than those found in the tetrapeptides with an average value of approximately -5.1 GPa(-1) (Δβ'/ΔV of 5.1 GPa(-1) provided |ΔG(0)| ≪ 2RT holds). Qualitatively, the B2/B1 ratio can be used to predict regions of the HPr protein involved in the interaction with enzyme I or HPr-kinase/phosphatase.