On the dynamics of inhomogeneous short-range DNA interactions at a defect
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On the dynamics of inhomogeneous short-range DNA interactions at a defect M. Tantawy1,a , H. I. Abdel-Gawad2 1 Department of Basic Science, Faculty of Engineering, October 6 University, 6th of October City, Egypt 2 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Received: 17 February 2020 / Accepted: 18 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract DNA defect is due to any change that introduces a deviation from the usual double helical structure. At this state, the study of the motion of DNA molecules requires novel dynamical models. Recently, a few works in the nonlinear dynamics of DNA at a defect, or the level of bases, have been carried out. We suggest a model which describes the links between the different bases of DNA, by accounting for nth site of bases (or space) dependent and the inverse width and the rigidity of the backbone. Short-range interactions at microscopic scale are considered. We mention that the inter-chain interactions as well as the long-chain interactions may introduce a big change of a comprehensive mapping of DNA. The structural properties depend on the velocity of connected base-pairs pbs. Resonance frequency between pbs like damped oscillatory waves propagation has been predicted . Here, the model presented is based on the in-homogeneity of the medium, due to defect, and non-homogeneity of the localization of bases in the opening motion of DNA. Exact solutions of the model equation are obtained by using the extended unified method. Numerical evaluations of these solutions are carried out. It is found that when the inverse width and the rigidity of the backbone are very high, the motion is not like a wave, while for too small or moderate values, wave motion holds. These results found in this work consolidate those found in the literature as the solutions found here are exact.
1 Introduction Many arguments in the favor of the DNA molecules structure are known [1], and different theoretical models have been suggested to describe the nonlinear dynamics of the complex structure of DNA [2–13]. All these models are successfully used for the interpretation of the homogeneous structure (both stacking and hydrogen H-bonding) of DNA. In the last years, the defect has been defined as a deviation of double-helical confirmation from its normal configuration. This may be argued to the changes which include structural distortions that interfere with replication error and transcription. This may arise from both normal metabolic activities and environmental factors such as radiation. The study at a defect was considered premiere to investigate the occurrence of the thermal inhomogeneous structure of DNA. For example, it had been shown that the DNA may contain the rogue base difluorotoluene (F) in place of a thymine (T) base, which has been obtained in [14]. This is done by adding noise and
a e-mail: [email protected] (corresponding author)
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