Dihedral Angle Calculations To Elucidate the Folding of Peptides through Its Main Mechanical Forces

Abstract

This study reports a general method to calculate dihedral angles (φ and ψ) of a given amino acid sequence, focusing on potential energy and torque moment concepts. By defining these physical measures in relation to the chemical interactions that occur on each single amino acid residue within a peptide, the folding process is analysed as the result of main mechanical forces (MMF) exerted in the specific amino acid chain of interest. As a proof of concept, Leu-enkephalin was initially used as a model peptide to carry out the theoretical study. Our data show agreement between calculated Leu-enkephalin backbone dihedral angles and the corresponding experimentally determined x-ray values. Hence, we used calcitonin to validate our MMF-based method on a larger peptide, i.e. 32 amino acid residues forming an α-helix. Through a similar approach (although simplified with regards to electrostatic interactions), the calculations for calcitonin also demonstrate a good agreement with experimental values. This study offers new opportunities to analyse a peptides' amino acid sequences and help in the prediction of how they must fold, assisting the development of new computational techniques in the field.

Polypeptides Folding: Rules for the Calculation of the Backbone Dihedral Angles φ starting from the Amino Acid Sequence

“…This study is focused on the chemical interactions developed amongst the side chains of the residues and these were considered to be the informations required to fold the polypeptide. The survey shows a good agreement between the calculated and the experimentally determined values, thus the method presented, combined to the previous [6] , reveals to be an efficient approach to predict at least the backbone dihedral angles φ starting from the amino acid sequence.…”

“…The chemical interactions among the side chains of the amino acid residues were supposed to be the informations required to fold the polypeptide: these allow the development of mechanical forces which induce the twistings necessary to fold the polypeptide. This approach, already reported in literature [6] and deepen in this study, showed that it is possible to calculate the backbone dihedral angles φ starting from the amino acid are wrong. The method thus, aims to be a useful tool to investigate partially the structure of a polypeptide chain (since concerns only φ), predicting it starting from the amino acid sequence.…”

“…For the polar residues, the hydrophobic interactions may occur up to a distance of 12 Å, whereas for the apolar residues, the threshold distances for the hydrophobic interactions are listed in table 2. for the chemical interactions to occur. Twisting constants have been reported to be fundamental for the determination of the folding factors [6] and the latter to be, in turn, a fundamental physical measure for the calculation of dihedral angles. Anyway, in the previous study, the definition of the twisting constants was described as the main limit of the whole work [6] .…”

“…Twisting constants have been reported to be fundamental for the determination of the folding factors [6] and the latter to be, in turn, a fundamental physical measure for the calculation of dihedral angles. Anyway, in the previous study, the definition of the twisting constants was described as the main limit of the whole work [6] . At this purpose, this work has been realized with the aim to define univocally the twisting constants in order to allow, in the end, the precise calculation of the backbone dihedral angles, specifically the backbone dihedral angles φ.…”

“…Anyway, concerning the calculations, the latter study showed some limits on the definition of the degrees of freedom [6] (now twisting constant) so that, this problem was further investigated in order to enunciate rules to define univocally the twisting constants and the threshold distances for the chemical interactions to occur. In this context, the present study realized on the DNA binding domain of the γ δ resolvase (PDB code: 1res) [7] , aims to establish rules that allow to predict and calculate the backbone dihedral angles φ, so that, combined with the previous study [6] , could furnish a theoretical method to predict the structure of peptides and proteins starting from the amino acid sequence. This study is focused on the chemical interactions developed amongst the side chains of the residues and these were considered to be the informations required to fold the polypeptide.…”