Statistical-Mechanics Analyses on Thermodynamics of Protein Folding Constructed by Privalov and Co-Workers.

Privalov and co-workers estimated the changes in hydration enthalpy and entropy upon ubiquitin unfolding and their temperature dependences denoted by Δ H ^hyd ( T ) and Δ S ^hyd ( T ), respectively, from experimentally measured enthalpies and entropies of transfer of various model compounds from gaseous phase to water. We calculate Δ H ^hyd ( T ) and Δ S ^hyd ( T ) for ubiquitin by our statistical-mechanics theory where molecular and atomistic models are employed for water and protein structure, respectively. Δ H ^hyd ( T ) and Δ S ^hyd ( T ) calculated are in remarkably good agreement with those estimated by Privalov and co-workers. By examining relative magnitudes and signs of the changes in a variety of constituents of Δ H ^hyd ( T ) and Δ S ^hyd ( T ), we confirm that the hydrophobic effect is an essential force driving a protein to fold. Detailed and comprehensive explanations are given for our claim that the prevailing views of the hydrophobic effect are not capable of elucidating its weakening at low temperatures, whereas our updated view is. We find out problematic points of the changes in enthalpy and entropy upon protein unfolding denoted by Δ H °( T ) and Δ S °( T ), respectively, which are measured using the differential scanning calorimetry at low pH, suggesting a theoretical method of calculating Δ H °( T ) and Δ S °( T ) at pH ∼ 7.