On The Relation Between The Continuous Media Mechanics Models On DNA Molecule Configurations

With the development and advancement of it, the biological science and technology became more and more important than before in 21st century. However, there are many biological function that can't be explained reasonably in present. These biological function have consanguineously relation with the configuration and elastic property of biopolymers. DNA is an important biopolymer. In recent years, the configurations and elastic property of DNA and other biopolymers have been one of the pop researching topics.DNA molecule and other biopolymers are simplified and investigated generally as material mathematical or physical models. The elastic property of DNA is characterized by the elastic rod and filament approximately when its length is almost equal to the bending persistence length. The centerline of elastic rod or elastic filament can be abstracted as space curves to deal with them by the knowledge of the theory of space curve and differential geometry. The theories which are discussed are based on it in this paper.To begin with,we introduce four continuous media mechanics models on DNA molecule confugurations: Helfrich elastic chiral filament model, uniform Kirchhoff elastic rod model, Kamien theory model and Wormlike Chain model. Then we research the Helfrich elastic chiral filament model and uniform Kirchhoff elastic rod model primarily. We gained the relation of two configuration equation in equilibrium: the closed configurations given by the centerline of uniform Kirchhoff rod in equilibrium is a subset of the closed equilibrium configurations given by the Helfrich elastic filament model at last.We correct a sign that is wrong in previous document about the configuration equation of Helfrich elastic filament theory and check the discussion on the unstable phenomenon of circle DNA molecule in this document. But we find which doesn't influence the conclusion.The original Helfrich theory has not the topological constraint. How will it change with the topological constraint? It is shown that the chiral module has important role on the stability of this configuration from the conclusion. The theory with topological constraint and without topological constraint draw the same conclusion except for it.In the end we investigate Kamien theory model and find that its expression of...