Topology and Elastic Theory of DNA Molecule

Subhamoy Singha Roy

doi:doi:10.11648/j.sjams.20221001.12

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Topology and Elastic Theory of DNA Molecule

Subhamoy Singha Roy

Published in Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 1)

Received: 11 January 2022 Accepted: 27 January 2022 Published: 15 March 2022

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Abstract

We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 1)
DOI	10.11648/j.sjams.20221001.12
Page(s)	10-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

DNA Molecule, Linking Number, Elastic Forces, Gauge Fields

References

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[2]	Boles, T. C., White, J. H. & Cozzarelli, N. R. (1990). Structure of plectonemically supercoiled DNA. J. Mol. Biol. 21, 3931. doi: 10.1016/S0022-2836(05)80272-4.
[3]	Bednar, J., Furrer, P., Stasrak, A., Dubochet, J., Engelman, C. H. & Bates, A. D. (1994). J. Mol. Biol.235825.
[4]	Goswami, G. & Bandyopadhyay, P. (1995). Spin system, gauge theory, and renormalization group equation. J. Math. Phys. 34 749. doi: https://doi.org/10.1063/1.530218.
[5]	Bandyopadhyay, P. (2010) The geometric phase and the spin-statistics relation. Proc. Roy. Soc (Londan) A. 466, 2917. https://doi.org/10.1098/rspa.2010.0042.
[6]	Calugareanu, I. (1961). Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants. Czechoslovak Math. Czechoslovak Mathematical Journal, Vol. 11 (1961), No. 4, 588–625. https://doi.org/10.21136/CMJ.1961.100486.
[7]	White, J. H. (1969). Self-Linking and the Gauss Integral in Higher Dimensions. Am. J. Math. 91, 693. URL: http://links.jstor.org/sici?sici=0002-9327%28196907%2991%3A3%3C693%3ASATGII%3E2.0.CO%3B2-V.
[8]	Fuller, F. B. (1978). Decomposition of the linking number of a closed ribbon: A problem from molecular biology Proc. Natl. Acad. Sci (USA) 75, 3557, https://doi.org/10.1073/pnas.75.8.3557.
[9]	Swigon, D. (2009). In Mathematics of DNA Structure, Function and Interactions (eds. C. J. Benham. et. al) (Springer Science Business Media).
[10]	Stone, M. & Goldbart, P. (2009), Mathematics for Physics (Pimander Casaubon, Londan).
[11]	Polyakov, A. M. (1988). Fermi-Bose transmutations induced by gauge fields. Mod. Physics Letters A. 3, 325. https://doi.org/10.1142/S0217732388000398.
[12]	Bandyopadhyay, A., Chatterjee, P. & Bandyopadhyay, P. (1986). Quantum Gravity Effect in Torsion Driven Inflation and CP violation. Gen. Rel. Grav18, 1293.
[13]	Nelson, P. (1999). Transport of torsional stress in DNA. Proc. Natl. Acad. Sci (USA) 96, 14342. https://doi.org/10.1073/pnas.96.25.14342.
[14]	Roy, A. & Bandyopadhyay, P. (1989). Topological aspects of a fermion and the chiral anomaly. J. Math. Phys. 30, 2366. https://doi.org/10.1063/1.528566.
[15]	Roy, S. Singha. (2017). DNA Molecule as a Spin System and the Symmetric Top Model. Theoretical Physics, 2, Number 3, 141.
[16]	Roy, S. Singha. & Bandyopadhyay, P. (2018). Quantum perspective on the localized strand separation and cyclization of DNA double helix. Phys. Lett. A 382, 1973. https://doi.org/10.1016/j.physleta.2018.04.048.

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Subhamoy Singha Roy. (2022). Topology and Elastic Theory of DNA Molecule. Science Journal of Applied Mathematics and Statistics, 10(1), 10-14. https://doi.org/10.11648/j.sjams.20221001.12

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Subhamoy Singha Roy. Topology and Elastic Theory of DNA Molecule. Sci. J. Appl. Math. Stat. 2022, 10(1), 10-14. doi: 10.11648/j.sjams.20221001.12

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AMA Style

Subhamoy Singha Roy. Topology and Elastic Theory of DNA Molecule. Sci J Appl Math Stat. 2022;10(1):10-14. doi: 10.11648/j.sjams.20221001.12

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@article{10.11648/j.sjams.20221001.12,
  author = {Subhamoy Singha Roy},
  title = {Topology and Elastic Theory of DNA Molecule},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {1},
  pages = {10-14},
  doi = {10.11648/j.sjams.20221001.12},
  url = {https://doi.org/10.11648/j.sjams.20221001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221001.12},
  abstract = {We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.},
 year = {2022}
}

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TY  - JOUR
T1  - Topology and Elastic Theory of DNA Molecule
AU  - Subhamoy Singha Roy
Y1  - 2022/03/15
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221001.12
DO  - 10.11648/j.sjams.20221001.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221001.12
AB  - We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.
VL  - 10
IS  - 1
ER  -

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Author Information

Subhamoy Singha Roy

Department of Physics, JIS College of Engineering, West Bengal University of Technology, Kalyani, India

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APA Style

Subhamoy Singha Roy. (2022). Topology and Elastic Theory of DNA Molecule. Science Journal of Applied Mathematics and Statistics, 10(1), 10-14. https://doi.org/10.11648/j.sjams.20221001.12

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ACS Style

Subhamoy Singha Roy. Topology and Elastic Theory of DNA Molecule. Sci. J. Appl. Math. Stat. 2022, 10(1), 10-14. doi: 10.11648/j.sjams.20221001.12

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AMA Style

Subhamoy Singha Roy. Topology and Elastic Theory of DNA Molecule. Sci J Appl Math Stat. 2022;10(1):10-14. doi: 10.11648/j.sjams.20221001.12

Copy | Download

@article{10.11648/j.sjams.20221001.12,
  author = {Subhamoy Singha Roy},
  title = {Topology and Elastic Theory of DNA Molecule},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {1},
  pages = {10-14},
  doi = {10.11648/j.sjams.20221001.12},
  url = {https://doi.org/10.11648/j.sjams.20221001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221001.12},
  abstract = {We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Topology and Elastic Theory of DNA Molecule
AU  - Subhamoy Singha Roy
Y1  - 2022/03/15
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221001.12
DO  - 10.11648/j.sjams.20221001.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221001.12
AB  - We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.
VL  - 10
IS  - 1
ER  -

Copy | Download