Three model shapes of Doxorubicin for liposome encapsulation.

Targeted drug delivery provides a possible method for the transfer of drug molecules into cancer cells. Liposomes together with a drug, such as Doxorubicin (DOX) inside the liposomes, can be formed as a nano-capsule. In this study, we are interested in finding a favorable size of liposome and an appropriate shape of DOX cluster: sphere, cylinder or ellipsoid. Using mathematical modeling, the interaction energy of the system is obtained from the Lennard-Jones potential and the continuum assumption which assumes that discrete atomic structure can be replaced by an average atomic density spread over a surface. The numerical results show that the spherical shape gives the lowest energy at the equilibrium configuration amongst the three shapes. In the case of equivalent surface areas, the spherical shape gives the energy lower than -4,000 kJ/mol at the equilibrium while the energies for the other cases do not come close to this level. Further in the case of a liposome of 50 nm in radius, the sphere of radius 49.726 nm, equivalent to 31,072 nm(2) surface area, gives the minimum energy at -6,642 kJ/mol. However, an equivalent cylindrical shape is not possible due to geometric constraints. The lowest minimum energy for the ellipsoid occurs for equal major and minor axes, namely for the spherical case. The results presented here are a first step in the design and implementation of a drug molecule for a targeted drug delivery system.