No abstract

The conformational potential energy surface (PES) of a molecule provides insights into the relative stability of the possible foldamers. However, the time and space complexity of electronic structure calculations, commonly used to generate PES, increases exponentially with an increasing number of atoms. The use of mathematical functions to model the topology of conformational PES is an alternative to more computer-intensive quantum chemical calculations, but the choice and complexity of functions used are crucial in achieving more accurate results. This paper presents a method to illustrate the topology of amino acid diamide PESs through a linear combination of a Fourier series and a mixture of Gaussian functions. Results yield a significantly small error, with an average RMSE of 4.9946 kJ mol−1 for all fits, which suggest that these functions may be used to represent the topology of the PESs, with around twofold order of magnitude decrease in computational time, with respect to DFT electronic structure calculations. This study ultimately aims to provide a foundation for a framework on building polypeptide PES from individual amino acid PESs.

Finding a relationship on how a three-dimensional protein folds from its linear amino acid chain gets more complex with increasing chain length, so working on a smaller peptide conformational problem can provide initial ideas on what are the main molecular forces and how these influence the folding process. Following the study of conformations of amino acid units entering the proteins to understand the secondary structure of small peptides, this paper proposes mathematical models for the several two-rotor cross-sections of the five-dimensional N-acetyl-glycyl-glycine-N′-methylamide potential energy hypersurface (PEHS). These cross-sections are extracted along the first glycine subunit, with its coordinates fixed at the five energy minima of the glycine diamide. The resulting mathematical models yield an average RMSE of 1.36 kJ mol−1 and an average R2 of 0.9923 with respect to energy values obtained from DFT calculations. The minima geometries obtained from these models are also in good agreement with DFT-optimized energy minima conformers. An important aspect of this study also tackles the relationship between the PEHS of the glycyl-glycine diamide and its glycine subunits. It has been observed that there are deviations up to 28.35 kJ mol−1 and 29.52 kJ mol−1 between the PEHS cross-sections along γL and γD conformations, respectively, in the first glycine subunit. This may suggest that there are significant backbone–backbone intermolecular forces acting on the dipeptide. The abovementioned findings can help in developing more complex mathematical models for polypeptide folding from amino acid subunits.