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. 2020 Feb 26;10(1):3439.
doi: 10.1038/s41598-020-60105-3.

A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

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Free PMC article

A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Mobin Marvi et al. Sci Rep. .
Free PMC article

Abstract

The DNA molecule is the most evolved and most complex molecule created by nature. The primary role of DNA in medicine is long-term storage of genetic information. Genetic modifying is one of the most critical challenges that scientists face. On the other hand, it is said that under the influence of acoustic, electromagnetic, and scalar waves, the genetic code of DNA can be read or rewritten. In this article, the most accurate and comprehensive dynamic model will be presented for DNA. Each of the two strands is modeled with an out of plane curved beam and then by doubling this two strands with springs, consider the hydrogen bond strength between this two strands. Beams are traditionally descriptions of mechanical engineering structural elements or building. However, any structure such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed similarly. Also, in this model, the mass of the nucleobases in the DNA structure, the effects of the fluid surrounding the DNA (nucleoplasm) and the effects of temperature changes are also considered. Finally, by deriving governing equations from Hamilton's principle method and solving these equations with the generalized differential quadrature method (GDQM), the frequency and mode shape of the DNA is obtained for the first time. In the end, validation of the obtained results from solving the governing equations of mathematical model compared to the obtained results from the COMSOL software is confirmed. By the help of these results, a conceptual idea for controlling cancer with using the DNA resonance frequency is presented. This idea will be presented to stop the cancerous cell's protein synthesis and modifying DNA sequence and genetic manipulation of the cell. On the other hand, by the presented DNA model and by obtaining DNA frequency, experimental studies of the effects of waves on DNA such as phantom effect or DNA teleportation can also be studied scientifically and precisely.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Schematic of PBD model (a) and its updates (b–d). These images have been drawn with Adobe Photoshop CC 2018.
Figure 2
Figure 2
A rod model that looks at DNA on a larger scale. This image has been designed with Adobe Photoshop CC 2018.
Figure 3
Figure 3
(a) Imagined shape for DNA © 2013 Nature Education Adapted from Pray, L. (2008) Discovery of DNA structure and function: Watson and Crick. Nature Education 1(1):100. All rights reserved. (b) The GMDM Mathematical model, which is presented in this paper for dynamics investigations of DNA. This image has been modeled with COMSOL Multiphysics 5.3a and edited with Adobe Photoshop CC 2018.
Figure 4
Figure 4
(a) DNA’s shape before reaching resonant frequency. (b) DNA’s shape after reaching resonant frequency. (c) Establishes a hydrogen bond between the nucleobases upper with nucleobases lower. (d) Removal of additional and remaining nucleotides with the help of restriction enzyme. (e) New DNA’s shape and disorganization in a sequence of DNA. These images have been modeled with COMSOL Multiphysics 5.3a and edited with Adobe Photoshop CC 2018.
Figure 5
Figure 5
An out of plane curved beam. This image has been modeled with CATIA V5 and edited with Adobe Photoshop CC 2018.
Figure 6
Figure 6
A small cut of a cross section of a beam. This image has been modeled with Adobe Photoshop CC 2018.
Figure 7
Figure 7
Model of DNA that has been designed with COMSOL Multiphysics 5.3a.
Figure 8
Figure 8
First 20 mode shape of DNA’s vibration (3D). These images have been modeled and simulated with COMSOL Multiphysics 5.3a and edited with Adobe Photoshop CC 2018.

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