Continuous Approximation for Interaction Energy Transfer of DNA through Lipid Bilayers

Mansoor H Alshehri

doi:10.1155/2018/7017416

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.

Highlights

Nanomaterials have promised an unexpected growth in research and applications in many different areas, due to their nanoscales size, unique features, and distinct properties
We investigate the energy behavior of the molecular interaction energy of a lipid bilayer and a DNA molecule, by determining the penetration behavior of the ssDNA and dsDNA molecules through an assumed circular gap of radius b in the bilayer
As a part of the experiment, the interaction energies for the ssDNA and dsDNA molecules and the lipid bilayer are calculated and for the dsDNA we assume that the helical phase angle φ is equal to π

Summary

Introduction

Nanomaterials have promised an unexpected growth in research and applications in many different areas, due to their nanoscales size, unique features, and distinct properties. Maingi et al use molecular dynamics (MD) simulations to investigate the interactions of a simple DNA nanopore with a lipid bilayer They demonstrate the close packing of lipids around the stably inserted DNA pore and its cation selectivity [10]. He et al determined the interaction mechanism between polyarginine peptides and asymmetric membranes by performing a coarse-grained molecular dynamics (CGMD) simulation. Khalid et al utilize (CGMD) simulation to investigate the transfer potential of the DNA through a DPPC/DMTAP bilayer They find a high energy barrier to DNA insertion into the bilayer hydrophobic core of the bilayer [13]. Using continuous approximation and the Lennard-Jones potential function, the molecular interaction energies between ssDNA and dsDNA molecules and the dipalmitoylphosphatidylcholine bilayer (DPPC) are calculated.

Modelling Approach

Mathematical Derivation

Numerical Results and Discussions

Conclusion