Modelling Lennard-Jones Interactions Between Two Peptide Rings

In recent years, peptide nanotubes have been studied extensively due to their unique structure and their potential applications in many diverse fields such as biology, chemistry, material science and medicine. Here, we determine the Lennard-Jones interactions between peptide rings through simple applied mathematical modelling as a first step towards fully understanding the formation of the complex structure of peptide nanotubes. In this paper we study the interaction potential between a pair of cyclo[(-D-Ala-L-Ala)₄–] and a pair of cyclo[(Gly-D-Ala)₄] which are the simplest possible units comprising a peptide nanotube. We assume the continuum approximation that the atoms maybe smeared uniformly over the peptide ring providing an average atomic density and the Lennard Jones potential to obtain the interaction energy between two peptide rings. Our results show that the two peptide rings reach equilibrium when the perpendicular distance between the centre of the two rings is 4.45–5.38 Å, and the minimum energy is 14.86–23.65 kcal/mol occuring when the second ring tilts at an angle 0.2443–0.3316 radian from the first ring. These results are in agreement with several recent molecular dynamics studies.