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 OJBIPHY  Vol.10 No.3 , July 2020
Mechanics of Twisted DNA Molecule Adsorbed on a Biological Membrane
Abstract: DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. The study of DNA molecule achieved in vitro while submitting the DNA to all chemicals agent capabilities to destabilize links hydrogen, such as pH, temperature. In fact, the DNA enveloped in the membrane cellular, so it is legitimate to study the influence of membrane undulations. In this work, we try to show that the fluctuations of the membrane can be considerate as a physics agent is also capable to destabilize links hydrogen. In this investigation, we assume that each pair base formed an angle an with the membrane’s surface. We have proposed a theoretical model, and we have established a relationship between the angle formed by the pair base θeq and an angle formed by the membrane and each pair base. We assume that DNA and biomembrane interact via a realistic potential of Morse type. To this end, use is made of a generalized model that extends that introduced by M. Peyrard and A. R. Bishop in the past modified by M. Zoli. This generalized model is based on the resolution of a Schrödinger-like equation. The exact resolution gives the expression of the ground state, and the associated eigenvalue (energy) that equals the free energy, in the thermodynamic limit. First, we compute the denaturation temperature of DNA strands critical temperature. Second, we deduce all critical properties that mainly depend on the parameters of the model, and we quantify the effects of the membrane undulations. These undulations renormalize all physical quantities, such as harmonic stacking, melting temperature, eigenfunctions, eigenvalues and regular part of specific heat.
Cite this paper: El Kinani, R. , Kaidi, H. and Barka, N. (2020) Mechanics of Twisted DNA Molecule Adsorbed on a Biological Membrane. Open Journal of Biophysics, 10, 129-149. doi: 10.4236/ojbiphy.2020.103011.
References

[1]   Watson, J.D. and Crick, F.H.C. (1953) Molecular Structure of Nucleic Acids. Nature, 171, 737-738.
https://doi.org/10.1038/171737a0

[2]   Saenger, W. (1984) Defining Terms for the Nucleic Acids. In: Principles of Nucleic Acid Structure, Springer, New York, 9-28.
https://doi.org/10.1007/978-1-4612-5190-3_2

[3]   Asakura, S. and Oosawa, F. (1954) On Interaction between Two Bodies Immersed in a Solution of Macromolecules. The Journal of Chemical Physics, 22, 1255-1256.
https://doi.org/10.1063/1.1740347

[4]   Zimmerman, S.B. and Minton, A.P. (1993) Macromolecular Crowding: Biochemical, Biophysical, and Physiological Consequences. Annual Review of Biophysics and Biomolecular Structure, 22, 27-65.
https://doi.org/10.1146/annurev.bb.22.060193.000331

[5]   Westheimer, F.H. (1987) Why Nature Chose Phosphates. Science, 235, 1173-1178.
https://doi.org/10.1126/science.2434996

[6]   Odijk, T. (2004) Statics and Dynamics of Condensed DNA within Phages and Globules. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 362, 1497-1517.
https://doi.org/10.1098/rsta.2004.1385

[7]   Squires, T.M. and Quake, S.R. (2005) Microfluidics: Fluid Physics at the Nanoliter Scale. Reviews of Modern Physics, 77, 977.
https://doi.org/10.1103/RevModPhys.77.977

[8]   Douarche, C., Cortès, R., Roser, S.J., Sikorav, J.L. and Braslau, A. (2008) DNA Adsorption at Liquid/Solid Interfaces. The Journal of Physical Chemistry B, 112, 13676-13679.
https://doi.org/10.1021/jp807759d

[9]   Buyukdagli, S. and Blossey, R. (2016) Correlation-Induced DNA Adsorption on Like-Charged Membranes. Physical Review E, 94, 042502.
https://doi.org/10.1103/PhysRevE.94.042502

[10]   Macedo, D.X., Guedes, I. and Albuquerque, E.L. (2014) Thermal Properties of a DNA Denaturation with Solvent Interaction. Physica A: Statistical Mechanics and its Applications, 404, 234-241.
https://doi.org/10.1016/j.physa.2014.02.029

[11]   Zoli, M. (2011) Thermodynamics of Twisted DNA with Solvent Interaction. The Journal of Chemical Physics, 135, 09B606.
https://doi.org/10.1063/1.3631564

[12]   Englander, S.W., Kallenbach, N.R., Heeger, A.J., Krumhansl, J.A. and Litwin, S. (1980) Nature of the Open State in Long Polynucleotide Double Helices: Possibility of Soliton Excitations. Proceedings of the National Academy of Sciences of the United States of America, 77, 7222-7226.
https://doi.org/10.1073/pnas.77.12.7222

[13]   Hwa, T., Marinari, E., Sneppen, K. and Tang, L.-H. (2003) Localization of Denaturation Bubbles in Random DNA Sequences. Proceedings of the National Academy of Sciences the United States of America, 100, 4411-4416.
https://doi.org/10.1073/pnas.0736291100

[14]   Dauxois, T., Peyrard, M. and Bishop, A.R. (1993) Dynamics and Thermodynamics of a Nonlinear Model for DNA Denaturation. Physical Review E, 47, 684.
https://doi.org/10.1103/PhysRevE.47.684

[15]   Peyrard, M. (2004) Nonlinear Dynamics and Statistical Physics of DNA. Nonlinearity, 17, R1.
https://doi.org/10.1088/0951-7715/17/2/R01

[16]   Helfrich, W. (1973) Elastic Properties of Lipid Bilayers: Theory and Possible Experiments. Zeitschrift für Naturforschung C, 28, 693-703.
https://doi.org/10.1515/znc-1973-11-1209

[17]   Ben-Shaul, A. and Gelbart, W.M. (1994) Statistical Thermodynamics of Amphiphile Self-Assembly: Structure and Phase Transitions in Micellar Solutions. In: Micelles, Membranes, Microemulsions, and Monolayers, Springer, New York, 1-104.
https://doi.org/10.1007/978-1-4613-8389-5_1

[18]   Barbi, M., Lepri, S., Peyrard, M. and Theodorakopoulos, N. (2003) Thermal Denaturation of a Helicoidal DNA Model. Physical Review E, 68, 061909.
https://doi.org/10.1103/PhysRevE.68.061909

[19]   Lide, D.R. (1995) CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data. CRC Press, Boca Raton.

[20]   Sung, W. and Oh, E. (1996) Membrane Fluctuation and Polymer Adsorption. Journal de Physique II, 6, 1195-1206.
https://doi.org/10.1051/jp2:1996124

[21]   Gradshteyn, I.S. and Ryzhik, I.M. (2014) Table of Integrals, Series, and Products. Academic Press, Cambridge.

[22]   Scalapino, D.J., Sears, M. and Ferrell, R.A. (1972) Statistical Mechanics of One-Dimensional Ginzburg-Landau Fields. Physical Review B, 6, 3409.
https://doi.org/10.1103/PhysRevB.6.3409

[23]   Krumhansl, J.A. and Schrieffer, J.R. (1975) Dynamics and Statistical Mechanics of a One-Dimensional Model Hamiltonian for Structural Phase Transitions. Physical Review B, 11, 3535.
https://doi.org/10.1103/PhysRevB.11.3535

[24]   Bishop, A.R., Krumhansl, J.A. and Trullinger, S.E. (1980) Solitons in Condensed Matter: A Paradigm. Physica D: Nonlinear Phenomena, 1, 1-44.
https://doi.org/10.1016/0167-2789(80)90003-2

[25]   Morse, P.M. (1929) Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels. Physical Review, 34, 57.
https://doi.org/10.1103/PhysRev.34.57

[26]   Nelson, D.R., Piran, T. and Weinberg, S. (Eds.) (2004) Statistical Mechanics of Membranes and Surfaces. 2nd Edition, World Scientific, Singapore.
https://doi.org/10.1142/5473

[27]   Kriegel, F., Matek, C., Drsata, T., Kulenkampff, K., Tschirpke, S., Zacharias, M. and Lipfert, J. (2018) The Temperature Dependence of the Helical Twist of DNA. Nucleic Acids Research, 46, 7998-8009.
https://doi.org/10.1093/nar/gky599

[28]   Benhamou, M., El Kinani, R. and Kaidi, H. (2013) Rigorous Study of the Unbinding Transition of Biomembranes and Strings from Morse Potentials. Conference Papers in Science, 2013, Article ID: 320718.
https://doi.org/10.1155/2013/320718

[29]   Todica, M., Stefan, T., Simon, S., Balasz, I. and Daraban, L. (2014) UV-Vis and XRD Investigation of Graphite-Doped Poly (Acrylic) Acid Membranes. Turkish Journal of Physics, 38, 261-267.
https://doi.org/10.3906/fiz-1305-16

[30]   Smith, S.B., Finzi, L. and Bustamante, C. (1992) Direct Mechanical Measurements of the Elasticity of Single DNA Molecules by Using Magnetic Beads. Science, 258, 1122-1126.
https://doi.org/10.1126/science.1439819

[31]   Smith, S.B., Cui, Y. and Bustamante, C. (1996) Overstretching B-DNA: The Elastic Response of Individual Double-Stranded and Single-Stranded DNA Molecules. Science, 271, 795-799.
https://doi.org/10.1126/science.271.5250.795

[32]   Cluzel, P., Lebrun, A., Heller, C., Lavery, R., Viovy, J.L., Chatenay, D. and Caron, F. (1996) DNA: An Extensible Molecule. Science, 271, 792-794.
https://doi.org/10.1126/science.271.5250.792

 
 
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