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We examine the van der Waals interactions between water molecules with both water channels, aquaporin-Z and glycerol channel GlpF. Here we model these problems using classical applied mathematics and obtain the potential energy for a water molecule interacting with the channels which we assume in both cases to have a flaired right cylindrical geometry. We propose a continuous model where all the atoms comprising the channels are assumed to be uniformly distributed within their volume. We model a water molecule as comprising two parts: firstly as a single point representing the location of the oxygen atom, and a spherical shell over which we assume a uniform distribution of the two hydrogen atoms. Our results indicate the spontaneous acceptance of water molecules into these channels. Refereed/Peer-reviewed

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

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 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.These interactions are calculated based on the structure of the antiviral molecules. Our results show that the binding of fullerene C to the antiviral molecules increases the efficiency of the compound to prohibit the activity of HIV. Refereed/Peer-reviewed