Change in vibrational entropy with change in protein volume estimated with mode Grüneisen parameters

For a small adjustment in average volume, due to a change in state of a protein or other macromolecule at constant temperature, the change in vibrational entropy is related to the mode Grüneisen parameters, which relate shifts in frequency to a small volume change. We report here values of mode Grüneisen parameters computed for two hydrated proteins, cytochrome c and myoglobin, which exhibit trends with mode frequency resembling those of glassy systems. We use the mode Grüneisen parameters to relate volumetric thermal expansion to previously computed values of the isothermal compressibility for several proteins. We also estimate changes in vibrational entropy resulting from the change in volume upon ligand bonding of myoglobin and the homodimeric hemoglobin from Scapharca inaequivalvis (HbI). We compare estimates of the change in entropy upon ligation obtained in terms of mode Grüneisen parameters with the results of normal mode analysis for myoglobin and earlier molecular dynamics simulations of HbI. The results illustrate how small changes in average volume can yield changes in entropy that contribute to ligand binding and allostery.