¹Institute of Mathematical Problems of Biology – the Branch of the Keldysh Institute of Applied Mathematics of the RAS, Pushchino,  Russia
²School of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia
³CICECO-Aveiro Institute of Materials, University of Aveiro, Aveiro, Portugal
⁴Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract. The structure and properties of diphenylalanine peptide nanotubes based on phenylalanine were investigated by various molecular modeling methods. The main approaches were semi-empirical quantum-chemical methods (PM3 and AM1), and molecular mechanical ones. Both the model structures and the structures extracted from their experimental crystallographic databases obtained by X-ray methods were examined. A comparison of optimized model structures and structures obtained by naturally-occurring self-assembly showed their important differences depending on D- and L-chirality. In both the cases, the effect of chirality on the results of self-assembly of diphenylalanine peptide nanotubes was established: peptide nanotubes based on the D-diphenylalanine (D-FF) has high condensation energy E₀ in transverse direction and forms thicker and shorter peptide nanotubes bundles, than that based on L-diphenylalanine (L-FF). A topological difference was established: model peptide nanotubes were optimized into structures consisting of rings, while naturally self-assembled peptide nanotubes consisted of helical coils. The latter were different for the original L-FF and D-FF. They formed helix structures in which the chirality sign changes as the level of the macromolecule hierarchy raises. Total energy of the optimal distances between two units are deeper for L-FF (–1.014 eV) then for D-FF (–0.607 eV) for ring models, while for helix coil are approximately the same and have for L-FF (–6.18 eV) and for D-FF (–6.22 eV) by PM3 method; for molecular mechanical methods energy changes are of the order of 2–3 eV for both the cases. A topological transition between a ring and a helix coil of peptide nanotube structures is discussed: self-assembled natural helix structures are more stable and favourable, they have lower energy in optimal configuration as compared with ring models by a value of the order of 1 eV for molecular mechanical methods and 5 eV for PM3 method.

Key words: diphenylalanine, peptide nanotube, molecular modeling, semi-empirical methods, DFT, ab initio methods, molecular mechanics, chirality, topology, self-assembly.