An effective model of DNA like helicoidal structure: with length fluctuation nonlinearity

One of the natural helicoidal nanostructure, which thermomechanical features are studied carefully with the help of different mechanical models, is a DNA cell / molecule. Our study proves that the experimentally determined nonlinear fluctuations of the molecular length of DNA can be better understood by modeling the molecule as a helicoidal pretwisted nanostrip sensor with nonlinear function. The calculations presented here are in good agreement with the experimental data within 10%. Other used by many researchers mechanical models such as an elastic rod, wormlike chain (WLC), accordion bellows, or an elastic core wrapped with rigid wires do not show the possible variance nonlinearity of thermomechanical DNA molecular length fluctuations. We have found that the nonlinear variance of the length fluctuations is an intrinsic property of the micro-nano-sensors with helicoidal shape. This model allows us to estimate the persistence length and twist-stretch coupling of a DNA molecule as well. It also shows the molecule's overwinding possibility at initial stretching with correct numerical representation