Equilibrium location for spherical DNA and toroidal cyclodextrin
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Cyclodextrin comprises a ring structure composed of glucose molecules with an ability to form complexes of certain substances within its central cavity. The compound can be utilised for various applications including food, textiles, cosmetics, pharmaceutics, and gene delivery. In gene transfer, the possibility of forming complexes depends upon the interaction energy between cyclodextrin and DNA molecules which here are modelled as a torus and a sphere, respectively. Our proposed model is derived using the continuum approximation together with the Lennard-Jones potential, and the total interaction energy is obtained by integrating over both the spherical and toroidal surfaces. The results suggest that the DNA prefers to be symmetrically situated about 1.2 Å above the centre of the cyclodextrin to minimise its energy. Furthermore, an optimal configuration can be determined for any given size of torus and sphere.
KeywordsCyclodextrin DNA Interaction energy Lennard-Jones potential Continuum approximation
Mathematics Subject Classification74G65 82B21 82C22
PS gratefully acknowledges the financial support from the Royal Golden Jubilee Ph.D. Scholarship of Thailand. DB is also grateful for the support of the Thailand Research Fund (RSA610018).
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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