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Albany 2019: 20th Conversation - Abstracts

category image Albany 2019
Conversation 20
June 11-15 2019
Adenine Press (2019)

Modeling Physical Analogues of DNA

The creation of mechanical, electronic, and other physical analogues of living systems, including whole organisms, individual organs, cells, and even biological molecules, helps to deepen our knowledge of the nature of these systems. In this paper, we consider a possibility to create the mechanical and electronic analogs of the DNA molecule (Fig.1), as well as mathematical methods that allow to calculate the parameters of these analogues. The goal of this research is to find the coefficients of the transformation that relates the structural and dynamic parameters of DNA with similar parameters of the mechanical and electronic analogues of the molecule. The basis of the proposed approach is the ideas of Scott (Scott, 1969) and of Englander and co-authors (Englander, Kallenbach, Heeger, et al., 1980), supplemented by recently proposed mathematical model of the DNA torsion dynamics (Grinevich, Ryasik & Yakushevich, 2015). They allowed us to find (1) the transformation required, (2) the values of the parameters of the mechanical analogue (pendulums mass m, pendulums length r, stiffness of springs K, the distances between neighboring pendulums a),, (3) the values of the electronic circuit parameters (L, C, I0, d) and (4) the relationship between the parameters of the mechanical and electronic analogues and the parameters of DNA M, K b, R). The obtained results show that the creation of the mechanical and electronic analogues of the DNA molecule can be realized and used to study various dynamic regimes that occur in the molecule, in particular, the modes associated with the emergence and spread of the transcription bubbles that play an important role in the functioning of the DNA molecule.

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References
    A. C. Scott (1969) A nonlinear Klein-Gordon equation, Am. J. Phys. 37, 52-61.
    S. W. Englander, N. R. Kallenbach, A. J. Heeger, et al. (1980) Nature of the open state in long polynucleotide double helices: possibility of soliton excitations, Proc. Natl. Acad. Sci. USA 77, 7222 – 7226
    A. A. Grinevich, A. A. Ryasik & L. V. Yakushevich (2015) Trajectories of DNA bubles. Chaos, Solitons & Fractals 75, 62-75. .

Valentina N. Balashova1*,
Ludmila V Yakushevich2 and
Farit K. Zakiryanov1

1Bashkir State University
Ufa, 450076
Russian Federation
2Institute of Cell Biophysics RAS,
Pushchino, 142290,
Russian Federation

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