The formation of a hydrophobic core of globular proteins is believed to be the consequence of exterior hydrophobic forces of entropic nature. This, together with the low occurrence of hydrogen bonds in the protein core, leads to the opinion that the energy contribution of core formation to protein folding and stability is negligible. We show that stabilization inside the hydrophobic core of a small protein, rubredoxin, determined by means of high-level correlated ab initio calculations (complete basis set limit of MP2 stabilization energy + CCSD(T) correction term), amounted to approximately 50 kcal/mol. These results clearly demonstrate strong attraction inside a hydrophobic core. This finding may lead to substantial changes in the current view of protein folding. We also point out the inability of the DFT/B3LYP method to describe a strong attraction between studied amino acids.

Correlated ab initio calculations on large systems, such as the popular MP2 (or RI-MP2) method, suffer from the intramolecular basis set superposition error (BSSE). This error is typically manifested in molecules with folded structures, characterized by intramolecular dispersion interactions. It can dramatically affect the energy differences between various conformers as well as intramolecular stabilities, and it can even impair the accuracy of the predictions of the equilibrium molecular structures. In this study, we will present two extreme cases of intramolecular BSSE, the internal stability of [n]helicene molecules and the relative energies of various conformers of phenylalanyl-glycyl-phenylalanine tripeptide (Phe-Gly-Phe), and compare the calculated data with benchmark values (experimental or high-level theoretical data). As a practical and cheap solution to the accurate treatment of the systems with large anticipated value of intramolecular BSSE, the recently developed density functional method augmented with an empirical dispersion term (DFT-D) is proposed and shown to provide very good results in both of the above described representative cases.

Activation and reaction energies for four model systems capturing the essential physicochemical features of the hydrolysis of the peptide bond have been calculated at various level of theory, including the presumably accurate CCSD(T) calculations. The models studied covered a part of the spectrum encountered in biological systems: the hydrolysis in the absence of metal ions (represented by formamide and Ala-Ala) and the hydrolysis in the presence of one and two zinc(II) ions, mimicking the active sites of mono- and dizinc metallopeptidases, respectively (by using thermolysin and glutamate carboxypeptidase II as the model catalytic systems and formamide as the model substrate). The results obtained using CCSD(T)/def2-TZVP and CCSD(T)/aug-cc-pVTZ calculations were used as the benchmark values to which the set of cheaper methods, such as (RI-)DFT, (RI-)MP2, and SCS-MP2, were referenced. It was shown that deviations of 3-5 kcal mol(-1) (translating to 2-3 orders in reaction constants) with respect to the reference CCSD(T) barriers are frequently encountered for many correlated methods and most of studied DFT functionals. It has been concluded that from the set of wave-function methods, both MP2 and SCS-MP2 methods can be recommended for smaller models (measured by the mean absolute deviation of the activation barriers over the four systems studied), whereas among the popular DFT functionals, B3LYP and especially M06-2X are likely to be reasonable choices for calculating the activation barriers of zinc metallopeptidases. Finally, with the model of glutamate carboxypeptidase II, issues related to the convergence of the calculated barriers with the size of the model system used as the representative of the enzyme active site were addressed. The intricacies related to system truncation are demonstrated, and suggest that the correlated wave-function methods may suffer from problems, such as intramolecular BSSE, which make their usage for the larger system questionable. Altogether, the presented data should contribute to efforts to understand enzymatic catalysis more deeply and to gain control of the accuracy and deficiencies of the available theoretical methods and computational approaches.

An analysis of the crystal structure of [BmPBP...bombykol] complex identified nine amino acid residues involved in a variety of intermolecular interactions binding the ligand. Using simple model fragments as the representatives of the residues, the interaction energies of their complexes with bombykol were calculated using high-level ab initio methods. The results were discussed in terms of the method and basis set dependence and were further corrected to account for their pair nonadditivities. This enabled us to describe quantitatively the nature and origin of the binding forces in terms of contribution of the individual amino acids and individual types of interaction to the overall stability. All of these interactions are well defined and cannot be considered as nonspecific hydrophobic interactions, one of the major conclusions of this work.