Quasiharmonic analysis of protein energy landscapes from pressure-temperature molecular dynamics simulations

Positional fluctuations of an atom in a protein can be described as motion in an effective local energy minimum created by the surrounding protein atoms. The dependence of atomic fluctuations on both temperature (T) and pressure (P) has been used to probe the nature of these minima, which are generally described as harmonic in experiments such as x-ray crystallography and neutron scattering. Here, a quasiharmonic analysis method is presented in which the P-T dependence of atomic fluctuations is in terms of an intrinsic isobaric thermal expansivity α_P and an intrinsic isothermal compressibility κ_T. The method is tested on previously reported mean-square displacements from P-T molecular dynamics simulations of lysozyme, which were interpreted to have a pressure-independent dynamical transition T_g near 200 K and a change in the pressure dependence near 480 MPa. Our quasiharmonic analysis of the same data shows that the P-T dependence can be described in terms of α_P and κ_T where below T_g, the temperature dependence is frozen at the T_g value. In addition, the purported transition at 480 MPa is reinterpreted as a consequence of the pressure dependence of T_g and the quasiharmonic frequencies. The former also indicates that barrier heights between substates are pressure dependent in these data. Furthermore, the insights gained from this quasiharmonic analysis, which was of the energy landscape near the native state of a protein, suggest that similar analyses of other simulations may be useful in understanding such phenomena as pressure-induced protein unfolding.