Simple models of non-linearDNA dynamics

Abstract

7. Introduction. Stucture and properties of DNA. 21. Structure of DNA. 22. Degrees of freedom of the base pairs. 23. Degrees of freedom of the sugar-phosphate backbone. 24. Forces acting on the double helix. 25. Opening of the double helix. 2'6. Conformational defects in the double helix and their propagauon: early proposals for solitons in I)NA. Introduction of simple models for DNA dynamics. 31. Classical models of DNA. 32. Non-linear models of DNA dynamics. 33. Common features of DNA models. Planar models of DNA dynamics. 41. A model of DNA torsion dynamics. 42. The continuum limit of planar Yakushevich model. 43. Solitons in planar Yakushevich model. 44. A model of DNA vibration dynamics. 45. The continuum lirnit of planar Peyrard-Bishop model. Helicoidal models of DNA dynamics. 51. Helical geometry and helicoidal DNA models. 52. Introduction of helicoidal mrms in the Peyrard-Bishop model. 53. Dispersion relations for the helicoidal Peyrard-Bishop model. 54. Non dispersive waves and breather modes in the helicoidal Peyrard Bishop model. 55. Introduction of helicoidal terms in the Yakushevich model. 56. Solitons in the helicoidal Yakushevich model. 57. Exact solution for the helicoidal (1, 0) soliton. 5'8. Numerical results for solitons in the helicoidal Yakushevich model. Thermodynamics of the PB model. 61. Statistical mechanics of the PB model. 62. Numerical simulations at constrained temperature. 6'3. An improved model for denaturation. Conclusions and discussion.