How the stabilization of INK4 tumor suppressor 3D structure evaluated by quantum chemical and molecular mechanics calculations corresponds well with experimental results: interplay of association enthalpy, entropy, and solvation effects

The folding free energy of the INK4c tumor suppressor core, consisting of 10 helices, was determined as the sum of gas-phase interaction enthalpy, gas-phase interaction entropy, and dehydration and hydration free energy. The interaction energy and the hydration free energy were determined using the nonempirical density functional theory (DFT) method, augmented by a dispersion-energy correction term, the semiempirical density-functional tight-binding method covering the dispersion energy, and the density functional theory/conductor-like screening model (DFT/COSMO) procedure, whereas the interaction entropy was calculated with the empirical Cornell et al. force field. Alternatively, all contributions were evaluated consistently using empirical methods. All the values of the interaction energy of helix pairs are stabilizing, and the dominant stabilizing terms stem from the London dispersion energy and, in the case of charged systems, the electrostatic energy. The stabilization energy of the core, determined as the difference of the energy of the core and 10 separate helices, amounts to approximately 450 kcal/mol. Systematically, the difference in the hydration free energy of a helix pair and its separate components is smaller in magnitude than the interaction energy, and it is negative for some pairs while positive for others. The average total free energy of a core formation amounts to -29.6 kcal/mol (yielded by scaled quantum-chemical methods) and +13.9 kcal/mol (resulting from empirical methods). These values are considerably smaller than their single components, which are dominated by the interaction energy. The computationally predicted interval encloses the experimental value of the folding free energy (-2.8 kcal/mol).