Study On The Mechanical Properties Of DNA Nanotubes

For DNA nanotubes regarded as elements in DNA self-assembly technology,we investigate the initial packaging state,the elastic rigidity of DNA nanotubes,and the effects of salt concentration and temperature on their mechanical properties.Our methods,models and conclusions not only enrich the theoretical framework of soft mater mechanics,but also provide references and new ideas for the design of DNA nanostructures.The main works are as follows:(1)The torsional rigidity and bending rigidity of a DNA nanotube neglecting inter-chain interactions are studied.Under the condition of the hexagonal homogenous packaging,considering the statically indeterminate characteristic for the bending-torsional coupling problem of a single DNA bar,the bending-torsional coupling deformation in the magnetic tweezers torsional experiment of a DNA nanotube is predicted by combining the equilibrium equation,the deformation compatibility equation and the elastic constitutive equation,thereout an analytical model for predicting the torsional rigidity of the DNA nanotube is presented.The results show that with the increase of DNA bar number,the bending rigidity is greatly increased whereas the torsional rigidity is almost not changed,which rationally elucidates the relevant findings in the magnetic tweezers torsional experiment,and also provides a theoretical basis for clarifying the relevant disputes.(2)The effect of the repulsive inter-chain interactions on the initial packaging length,equivalent axial packaging force,the force-extension curve and tensile rigidity of a DNA nanotube are studied.Firstly,given the initial interchain spacing,the packaging length and axial packaging force of a DNA nanotube could be obtained by the principle of minimum potential energy.Secondly,after the initial pakaging state is determined,the deformation of the DNA nanotube under different external force is obtained by the principle of minimum potential energy,then its tensile rigidity is characterized.Finally,the effects of the inter-chain spacing,temperature and salt concentration on the packaging and tensile states of the DNA nanotube are studied.The results show that with the increase of the initial chain spacing,salt concentration or with the decrease of temperature,the packaging length decreases,so the tensile rigidity of the DNA nanotube is strengthened,and the effect of the initial chain spacing is the most robust.(3)The effect of the inter-chain repulsive interaction on the torsional rigidity and bending rigidity of a DNA nanotube are studied.Firstly,we use the method of quadratic integration to characterize the free-end deformation of a nanotube under the combination of the packaging force and the torque or bending moment,thereout an updated model for predicting the torsional rigidity and bending rigidity of the DNA nanotube considering the repulsive inter-chain interactions is developed.Secondly,the effect of the initial packaging force on torsional rigidity and bending rigidity of the DNA nanotube is discussed.The results show that the increasing repulsive inter-chain interaction enhances the torsional/bending rigidity of the nanotube,and the enhanced amplitude is the most prominent when the initial packaging inter-chain spacing is about 3 nm;and the effect of the repulsive inter-chain interaction on the torsional/bending rigidity is more significant than that of temperature and salt concentration.(4)The effect of Holliday junction on the torsional rigidity of a DNA nanotube is studied.Firstly,we attempt to simulate interconnect function of Holliday junction with discrete small cylinders,taking their deformation energy approximately equivalent to the shear deformation energy of thin rings in the torsional process.Thereout,the effect of junction influence on torsional rigidity of the DNA nanotube is studied by using the principle of virtual work.Secondly,the feasibility of the small cylinder model to simulate Holliday junction is verified by finite element method.The results show that the torsional rigidity of the DNA nanotube is improved with the increase of junction number;the number of junction density of 6-helical DNA nanotubes is 7 in the Kauert torsional experiment,namely,the number of Holliday junction is 42;changing the junction number is suggested to be a prior scheme due to the difficulty in changing the inter-chain spacing.