Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Nanotechnology has generated considerable interest for potential applications, and especially in medical nanodevices designed to transport individual molecules through cell membranes. Nanobiotechnology is a multidisciplinary research area which combines the studies of biology and nanotechnology. It is critical that researchers fully understand the underlying mechanisms of such devices, particularly, those used in biological and medical applications. This thesis aims to investigate three aspects of nanobiotechnology applications: firstly, transportation of water, covalent and non-covalent molecules through special channels called aquaporins, secondly, the use of carbon nanotubes as carriers for drug delivery, and finally, the application of fullerenes to inhibit the activity of HIV protease.

The molecular van der Waals interaction between two nanostructures is typically obtained by either summing over all the individual atomic interaction pairs in the discrete atom-atom formulation or by using a continuum approach. In this thesis, we adopt the continuum approach. For this approach, atoms are assumed to be uniformly distributed over the surface or the volume of each interacting molecule. This approach is suitable for symmetrical nanostructures, enabling analytical solutions which require less computational time in comparison to the discrete atom-atom formulation. A hybrid discrete-continuum formulation is also adopted in this thesis to model irregular shaped molecules interacting with symmetrical structures. The concept of discrete-continuum approach assumes that one of the interacting molecules is discretized while the other is continuous.

Scientists often look to nature for inspiration to enhance the electrical, chemical and physical properties of nanodevices. Aquaporin channels have generated a great deal of research interest because they achieve very high flow rates. Discovering how aquaporins accomplish this could lead to the development of better pore technology for water desalination, gas separation, medical and other applications. This understanding would also be beneficial for the design of nanoscaled materials which can pass through various types of aquaporins. Thus, a study of the interactions between molecular structures (water, ionic and non ionic molecules and gas molecules) and aquaporin channels is crucial, and an understanding of the mechanism of these interactions is necessary for creating new technology for transporting water and other molecules through cell membranes. The study of molecular interaction for various molecules with different kinds of aquaporins seeks to investigate the underlying processes and to offer a deeper understanding of the biological mechanism. In this thesis, specific problems are investigated, namely (i) the non-columbic interaction between aquaporin-Z (AqpZ) and aquaglyceroporin (GlpF)channels and a water molecule, (ii) ions and ion-water clusters interacting with GlpF and aquaporin-1 (AQP1) channels and (iii) the interaction of gases, such as ammonia, nitric oxide and carbon dioxide with the latter two kinds of aquaporins.

The discovery of carbon nanostructures, such as fullerenes, nanobuds and carbon nanotubes, has led to the development of various medical devices. These nanodevices posses huge potential for the development of new techniques for drug delivery systems across biological barriers. In particular, this thesis investigates the encapsulation of L-Histidine amino acid inside a single-walled carbon nanotube. Further, this thesis studies the effectiveness of combining fullerenes C60 with chemical compounds to increase the inhibition the activity of HIV protease. Here, we adopt the 6 - 12 Lennard-Jones potential to evaluate the interaction energy by performing the surface or volume integration over each molecule. The analytical expressions for these interactions so obtained here are often quite complicated. However, they are readily calculated by using computer packages, such as MAPLE and MATLAB.

In summary, this thesis undertakes mathematical modelling in nanobiotechnology to provide more natural and objective about the mechanism of the transportation of various molecules through cell membranes. The techniques could also be employed in other nanodevices for which to overcome biological energetic barriers would enhance their chemical and physical properties.