SOLITON EXCITATIONS IN AN (3+1) DIMENSIONAL Alpha-HELIX PROTEIN SYSTEM WITH QUADRAPOLE-QUADRAPOLE INTERACTIONS

Authors

  • R. Jeba Vijitha Reg.No.21213282132009, Research Scholar, Department of Physics, Women’s Christian College, Nagercoil 629 001,Tamilnadu, India
  • S. Beauno Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, Tamilnadu, India

DOI:

https://doi.org/10.29121/shodhkosh.v5.i6.2024.3464

Keywords:

Protein, Alpha Helix, Soliton

Abstract [English]

This paper aims to explore that the soliton solutions for the three-dimensional (3D) model Hamiltonian equation, specifically as it pertains to protein molecules. The considered equation has been thoroughly analyzed that, with every step of the calculations discussed in detail and the main results are clearly explained. Notably, eight distinct types of the soliton structures are identified and the surfaces corresponding to each solitons solution are graphically illustrated as described. The explicit forms of the eight soliton solutions are presented. Additionally, mathematical derivations and numerical graphs are provided to support and visualize the soliton solutions of the energy equation.

References

Zitnik, M., Nguyen, F., Wang, B., Leskovec, J., Goldenberg, A., & Hoffman, M. M. (2018). Machine learning for integrating data in biology and medicine: Principles, practice, and opportunities. Information Fusion, 50, 71–91. https://doi.org/10.1016/j.inffus.2018.09.012 DOI: https://doi.org/10.1016/j.inffus.2018.09.012

Salem, M. S. Z. (2018). Biological Networks: An Introductory Review. Journal of Proteomics and Genomics Research, 2(1), 41–111. https://doi.org/10.14302/issn.2326-0793.jpgr-18-2312 DOI: https://doi.org/10.14302/issn.2326-0793.jpgr-18-2312

Fowler, S., Roush, R., & Wise, J. (2023d). Concepts of biology.

Molecular biology of the cell. (2002d).

Prevention of intravascular catheter-related infections. (2021). Indian Journal of Continuing Nursing Education, 22(1), 104. https://doi.org/10.4103/2230-7354.320831 DOI: https://doi.org/10.4103/2230-7354.320831

Poulsen, N., & Kröger, N. (2004). Silica Morphogenesis by Alternative Processing of Silaffins in the Diatom Thalassiosira pseudonana. Journal of Biological Chemistry, 279(41), 42993–42999. https://doi.org/10.1074/jbc.m407734200 DOI: https://doi.org/10.1074/jbc.M407734200

Bhutani, S. P. (2019). Chemistry of Biomolecules, Second Edition. CRC Press. DOI: https://doi.org/10.1201/9780429266423

Prins, L. J., Reinhoudt, D. N., & Timmerman, P. (2001). Noncovalent synthesis using hydrogen bonding. Angewandte Chemie International Edition, 40(13), 2382–2426. https://doi.org/10.1002/1521-3773(20010702)40:13 DOI: https://doi.org/10.1002/1521-3773(20010702)40:13<2382::AID-ANIE2382>3.0.CO;2-G

Fox, A. J. S., Bedi, A., & Rodeo, S. A. (2009). The basic science of articular cartilage: structure, composition, and function. Sports Health a Multidisciplinary Approach, 1(6), 461–468. https://doi.org/10.1177/1941738109350438 DOI: https://doi.org/10.1177/1941738109350438

Bittencourt, J. (2015). The power of carbohydrates, proteins, and lipids: How to Make Wise Choices in Diet and Nutrition. CreateSpace.

Bhat, S. (2012). Biomaterials. Springer Science & Business Media.

Adamatzky, A. (2002). Collision-Based computing. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-1-4471-0129-1

Debnath, L. (1994). Nonlinear water waves. Academic Press.

Cline, D. (2018). Variational principles in Classical mechanics: 2nd Edition.

Barone, M., & Selleri, F. (2012). Frontiers of Fundamental Physics. Springer Science & Business Media.

Yalçiner, A. C., Pelinovsky, E. N., Okal, E., & Synolakis, C. E. (2003). Submarine landslides and tsunamis. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-94-010-0205-9

Fogel, M. B., Trullinger, S. E., Bishop, A. R., & Krumhansl, J. A. (1977). Dynamics of sine-Gordon solitons in the presence of perturbations. Physical Review. B, Solid State, 15(3), 1578–1592. https://doi.org/10.1103/physrevb.15.1578 DOI: https://doi.org/10.1103/PhysRevB.15.1578

Mandelstam, S. (1975). Soliton operators for the quantized sine-Gordon equation. Physical Review. D. Particles, Fields, Gravitation, and Cosmology/Physical Review. D. Particles and Fields, 11(10), 3026–3030. https://doi.org/10.1103/physrevd.11.3026 DOI: https://doi.org/10.1103/PhysRevD.11.3026

Cuevas-Maraver, J., Kevrekidis, P., & Williams, F. (2014). The sine-Gordon Model and its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics. Springer. DOI: https://doi.org/10.1007/978-3-319-06722-3

Davydov A S and Kisluka N I 1973 Phys. Stat. Sol. b 59 465.

Davydov A S and Kisluka N I 1976 Sov. Phys. JETP 44 571.

Davydov A S 1979 Phys. Scripta 20 387. DOI: https://doi.org/10.1088/0031-8949/20/3-4/013

Davydov A S 1980 Sov. Phys. JETP 51 397.

A. S Davydov, J. Theor. Bio. 66 (1977) 376. DOI: https://doi.org/10.1063/1.433647

Haken, H. (2012). Synergetics: A Workshop Proceedings of the International Workshop on Synergetics at Schloss Elmau, Bavaria, May 2–7, 1977. Springer Science & Business Media.

Evans, C. R., Finn, L. S., & Hobill, D. W. (1989). Frontiers in numerical relativity. Cambridge University Press.

Huang, K. (2008). Quantum Field Theory: From Operators to Path Integrals. John Wiley & Sons.

Waldrop, M. M. (2019d). Complexity: The Emerging Science at the Edge of Order and Chaos. Open Road Media.

Butcher, P. N., & Cotter, D. (1990). The elements of nonlinear optics. Cambridge University Press DOI: https://doi.org/10.1017/CBO9781139167994

Landa, P. (2013c). Nonlinear oscillations and waves in dynamical systems. Springer Science & Business Media.

Chen, F. F. (2013c). Introduction to plasma physics and controlled fusion: Volume 1: Plasma Physics. Springer Science & Business Media.

Chen, F. F. (2013b). Introduction to plasma physics and controlled fusion: Volume 1: Plasma Physics. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-3-319-22309-4_11

Ibach, H. (2006). Physics of surfaces and interfaces. Springer Science & Business Media.

Trillo, S. (2001). Spatial solitons. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-3-540-44582-1

Shadrivov, I. V., Lapine, M., & Kivshar, Y. S. (2014). Nonlinear, tunable and active metamaterials. Springer. DOI: https://doi.org/10.1007/978-3-319-08386-5

Grant, I. P. (2007). Relativistic quantum theory of atoms and molecules: Theory and Computation. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-0-387-35069-1

Zangwill, A. (1988). Physics at surfaces. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511622564

Enns, R., & McGuire, G. (2013c). Nonlinear Physics with Maple for Scientists and Engineers. Springer Science & Business Media.

Trefethen, L. N. (2000). Spectral methods in MATLAB. SIAM. DOI: https://doi.org/10.1137/1.9780898719598

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Published

2024-06-30

How to Cite

Vijitha, R. J., & Beauno, S. (2024). SOLITON EXCITATIONS IN AN (3+1) DIMENSIONAL Alpha-HELIX PROTEIN SYSTEM WITH QUADRAPOLE-QUADRAPOLE INTERACTIONS. ShodhKosh: Journal of Visual and Performing Arts, 5(6), 2890–2902. https://doi.org/10.29121/shodhkosh.v5.i6.2024.3464