Applied Nanoscience

, Volume 8, Issue 3, pp 537–544 | Cite as

Equilibrium location for spherical DNA and toroidal cyclodextrin

  • Pakhapoom SarapatEmail author
  • Duangkamon Baowan
  • James M. Hill
Original Article


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.


Cyclodextrin DNA Interaction energy Lennard-Jones potential Continuum approximation 

Mathematics Subject Classification

74G65 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).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMahidol UniversityBangkokThailand
  2. 2.Centre of Excellence in Mathematics, CHEBangkokThailand
  3. 3.School of Information Technology and Mathematical SciencesUniversity of South AustraliaMawson LakesAustralia

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