Mathematical model for drug molecules encapsulated in lipid nanotube

Lipid nanotube is considered as a nanocontainer for drug and gene delivery. It is important to understand a basic idea of the encapsulation process. In this paper, we use the Lennard-Jones potential function and the continuous approximation to explain the energy behaviour of three hollow shapes of Doxorubicin (DOX) clusters that are a sphere, a cylinder, and an ellipsoid interacting with the lipid nanotube. On assuming that the surface areas of the three structures are equal, we can find the minimum size of the lipid nanotube that encapsulates DOX inside by determining the suction energy. Moreover, we find that a long cylindrical drug provides the largest suction energy among other structures studied here due to the perfect fit between the cylindrical drug and the cylindrical tube. This investigation is the first step to develop the design of nanocapsule for medical application.