Continuous Approximation for Interaction Energy Transfer of DNA through Lipid Bilayers

Abstract

In this study the interaction energies for single-stranded DNA and double-stranded DNA molecules with a lipid bilayer are investigated. The 6-12 Lennard-Jones potential and continuous approximation are used to derive analytical expressions for these interaction energies. Assuming that there is a circular gap in the lipid bilayer, we determine the relationship of the molecular interaction energy, including the circular gap radius and the perpendicular distance of the single-stranded DNA and double-stranded DNA molecules from the gap. For both single-stranded and double-stranded DNA molecules, the relationship between the minimum energy location and the hole radius b is calculated; in the case of the double-stranded DNA molecule, we assume that the helical phase angle ϕ is equal to π. By minimizing the total interaction energies, the results demonstrate that the single-stranded DNA and double-stranded DNA molecules move through a lipid bilayer when the gap radius b> 10 Å and b> 13.8 Å, respectively. The results present in this project can be leveraged to understand the interactions between cell-penetrating peptides and biomembranes, which may improve gene and drug delivery.