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 B-1 and B-2. The coefficients then are interpreted in a qualitative manner. We show here that in a two-state model, the ratio of B-2/B-1 is related to thermodynamic parameters, namely the ratio of the difference of compressibility factors Delta beta' and partial molar volumes Delta V. 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 Delta beta'/Delta V ratio of 1.6 GPa(-1) provided the condition vertical bar Delta G(0)vertical bar << 2RT holds for the difference of the Gibbs free energies (Delta G(0)) of the two states at the temperature (T-0) and the pressure (p(0)). The amide proton and nitrogen B-2/B-1 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 vertical bar Delta G(0)vertical bar << 2RT. The derived relation was applied to the beta-amyloid peptide A beta and the phosphocarrier protein HPr from S. carnosus. For the transition of state 1 to state 2' of A beta, the derived relation of B-2/B-1 to Delta beta'/Delta V can be confirmed experimentally. The HPr protein is characterized by substantially higher negative B-2/B-1 values than those found in the tetrapeptides with an average value of approximately -5.1 GPa-1 (Delta beta'/Delta V of 5.1 GPa(-1) provided vertical bar Delta G(0)vertical bar << 2RT holds). Qualitatively, the B-2/B-1 ratio can be used to predict regions of the HPr protein involved in the interaction with enzyme I or HPr-kinase/phosphatase.