Eur. Phys. J. Plus (2022) 137: 793
https://doi.org/10.1140/epjp/s13360-022-03021-x

Regular Article

Encapsulation of immobilized lysozyme enzyme inside various types of nanotubes: a continuum study

Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran

^a f.sadeghi@uma.ac.ir

Received: 27 May 2021
Accepted: 28 June 2022
Published online: 9 July 2022

Abstract

The outstanding physiochemical properties of nanotubes make them very promising candidates as enzyme immobilized carriers. In this paper, the mechanics of lysozyme enzyme inside various types of nanotubes such as carbon (C), silicon (Si), silicon carbide (SiC), boron nitride (BN) and titania (TiO₂) nanotubes is studied. To this end, the continuum approximation along with the 6–12 Lennard–Jones (LJ) potential function is adopted to mathematically model the van der Waals (vdW) interactions between lysozyme and nanotubes of different materials. First, the interaction energy of an offset lysozyme inside an infinite nanotube is determined to predict its preferred position with reference to the cross section of nanotube. Thereafter, assuming that the center of lysozyme is located on the axis of a semi-infinite nanotube, explicit analytical expressions are presented to evaluate the vdW potential energy and interaction force of the concentric configuration. These expressions are then employed to obtain the acceptance and suction energies which are the two critical factors in enzyme delivery and storage. An acceptance condition is also introduced which examines whether the lysozyme at rest can pass through the nanotube or not. For each type of nanotube, the critical radius of nanotube which minimizes the interaction energy is determined. Moreover, some special radii of nanotube, namely suction, acceptance, ultimate and optimal radii, which relate to encapsulation process are calculated for different nanotube materials. The numerical results demonstrate that the type of nanotube material has a negligible effect on the values of the introduced radii. The distributions of vdW potential energy and interaction force along with suction and acceptance energies are also presented by varying the radius and type of nanotube. Comparing the effectiveness of different nanotubes, it is revealed that TiO₂ nanotube is the most favorable candidate for lysozyme delivery and storage.