Transferability and reproducibility in electron-density studies – bond-topological and atomic properties of tripeptides of the type L-alanyl-X-L-alanine

In the last decade three different data bank approaches have been developed that are intended to make electron-density examinations of large biologically important molecules possible. They rely on Bader's concept of transferability of submolecular fragments with retention of their electronic properties. Therefore, elaborate studies on the quantification of transferability in experiment and theory are still very important. Tripeptides of the type L-alanyl-X-L-alanine (X being any of the 20 naturally encoded amino acids) serve as a model case between amino acids and proteins. The two experimental electron-density determinations (L-alanyl-L-histidinyl-L-alanine and L-alanyl-L-phenylalanyl-L-alanine, highly resolved synchrotron X-ray diffraction data sets) performed in this study and theoretical calculations on all 20 different L-alanyl-X-L-alanine molecules contribute to a better estimation of transferability in the peptide case. As a measure of reproducibility and transferability, standard deviations from averaging over bond-topological and atomic properties of atoms or bonds that are considered equal in their chemical environments were calculated. This way, transferability and reproducibility indices were introduced. It can be shown that experimental transferability indices generally slightly exceed experimental reproducibility indices and that these larger deviations can be attributed to chemical effects such as changes in the geometry (bond lengths and angles), the polarization pattern and the neighboring sphere due to crystal packing. These effects can partly be separated from each other and quantified with the help of gas-phase calculations at optimized and experimental geometries. Thus, the degree of transferability can be quantified in very narrow limits taking into account experimental errors and chemical effects.