Modulating DNA Configuration By Interfacial Traction: An Elastic Rod Model To Characterize DNA Folding And Unfolding

Mechanics for a super-thin rod with the biological background of DNA supercoilingmacromolecules is an interdisciplinary area of classical mechanics and molecular biology. It is also oneof dynamics and elastic theory because elastic bodies are analyzed via the theory of dynamics. It is infrontiers of general mechanics (dynamics, vibration and control). This dissertation investigates thegeometric configuration of a constrained super-thin elastic rod. On the basic of continuum mechanicsconception and interfacial tension theory, the constrained super-thin elastic rod is used to stimulate theDNA molecular which is in intercellular solution. Then we obtain the definite expression of Kirchhoffformulua for super-thin elastic rod and the governing equation for the super-thin elastic rod’sdeformation. The last work in the dissertation is that we add the self-contact effect in the theory wehave already had. In this dissertation the geometrical constraint is used to avoid the self-contact andpenetration of the super-thin elastic rod. The dissertation consists of five parts shown below:1) The DNA molecular research history and DNA supercoiling structure are outlined. The methodsfor researching DNA molecular are detailed.2) The application background of elastic rod mechanics and DNA supercoiling structure areoutlined. The super-thin elastic rod research history and current developments are detailed. It shows theinterdisciplinary of elastical mechanics, molecular biology and elastic mechanics for this subject. Inthis dissertation, interactions of DNA with the intracellular solution can be characterized by interfacialtraction between the rod and the solution surrounding the rod. Add the interfacial tension theory to theKirchhoff equations for the thin elastic rod; we can obtain a system of equations, which is the controlequation for the thin elastic rod.3) According to the control equations, the computing procedure can be acquired, which can beused to write FORTRAN program for solving the system of differential equations. Then we can obtainthe equilibrium configuration of DNA, the configuration of which is a segment of circul helix, underthe action of interfacial traction by using the FORTRAN program. In order to investigate theconfiguration of the DNA segment changes with its interfacial energy factor and bending stiffness, weseparately compute the equilibrium configuration of DNA when it is in different solution.4) The self-contact effect is considered on the basis of control equations for the thin elastic rod andgeometric constraint is used to avoid self-contact.Then we can obtain three new equilibriumconfiguration of DNA segment under the same conditions of the above chapter. The change of DNAconfiguration with the self-contact effect can be acquired by comparing the equilibrium configuration of DNA when the self-cnontact is considered fore and after.5) Conclusions of the paper are given. Future research topics proposed. Those topics include thestructure of DNA molecular, the intermolecular repulsion, numerical simulation for general case and soon.