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Carbon nanotubes play a significant role in facilitating and controlling the transportation of drugs and bio-molecules through their internal and external surfaces. Carbon nanotubes are also selective nano-devices because of their outstanding properties and huge potential use in many bio-medical and drug delivery applications. The proposed model aims to investigate the encapsulation of Alanine molecule inside a single-walled carbon nanotube, and to determine the minimum energy which is arising from the Alanine interacting with single-walled carbon nanotubes with variant radii r. We consider two possible structures as models of Alanine molecule which are a spherical shell as a continuum configuration and discrete configuration modelled as comprising three components: the linear molecule, cylindrical group, and CH3 molecule as a sphere, all interacting with infinite cylindrical single-walled carbon nanotube. The adsorption of Alanine amino acid and magnitude of total energy for each orientation calculated based on the nanotube radius r and the orientation angle $$\phi$$ which the amino acid makes with central axis of the cylindrical nanotube. Our results indicate that the Alanine molecule encapsulated inside the nanotubes of radius greater than 3.75 A, which are in excellent agreement with recent findings.

Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C $$_{60}$$ antiviral compounds and the HIV. In particular, this paper predicts the energy and force arising from the interaction between HIV active region and the antiviral molecule which is attached to the external surface of a fullerene C $$_{60}$$ . These interactions are calculated based on the structure of the antiviral molecules. Our results show that the binding of fullerene C $$_{60}$$ to the antiviral molecules increases the efficiency of the compound to prohibit the activity of HIV.

Aquaporin (AQP) is a family of membrane proteins that enable water and small individual molecules to permeate cell membranes. Examples of these protein channels are aquaglyceroporin and aquaporin-1 (AQP1). Here, we investigate the permeability of carbon dioxide $$(\hbox {CO}_2)$$ through both aquglyceroporin and AQP1 channels and explain their selectivity mechanisms. We provide a mathematical model which determines the molecular interaction potential between carbon dioxide molecule and an AQP channel. We evaluate this interaction using two approaches, namely discrete-continuum and completed discrete approaches. Both calculations agree well and our results indicate the acceptance of $$(\hbox {CO}_2)$$ molecule into these channels which is in good agreement with other recent studies.

Aquaporin is a family of small membrane-proteins that are capable of transporting nano-sized materials. In the present paper, we investigate the structure of these channels and provide information about the mechanism of individual molecules being encapsulated into aquaglyceroporin (GlpF) and aquaporin-1 (AQP1) channels by calculating the potential energy. In particular, we presents a mathematical model to determine the total potential energy for the interaction of the ammonia and nitric oxide molecules and different aquaporin channels which we assume to have a symmetrical cylindrical structure. We propose to describe these interactions in two steps. Firstly, we model the nitrogen atom as a discrete point and secondly, we model the three hydrogen atoms on the surface of a sphere of a certain radius. Then, we find the total potential energy by summing these interactions. Next, by considering the nitric oxide molecule as two discrete atoms uniformly distributed interacting with GlpF and AQP1 channels then gathering all pairs of interaction to determine the potential energy. Our results show that the ammonia and nitric oxide molecules can be encapsulated into both GlpF and AQP1 channels Refereed/Peer-reviewed