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A model of nonlinear DNA-protein interaction system with Cornell potential and its stability
Abstract
The purpose of this study was to determine the model of a interaction system between the DNA with protein. The interaction system consisted of a molecule of protein bound with a single chain of DNA. The interaction between DNA chain, especially adenine and thymine, and DNA-protein bound to glutamine and adenine. The forms of these bonds are adapted from the hydrogen bonds. The Cornell potential was used to describe both of the interactions. We proposed the Hamiltonian equation to describe the general model of interaction. Interaction system is divided into three parts. The interaction model is satisfied when a protein molecule triggers pulses on a DNA chain. An initial shift in position of protein xm should trigger the shift in position of DNA ym, or alter the state. However, an initial shift in DNA, yn, should not alter the state of a rest protein (i.e. xm = 0), otherwise, the protein would not steadily bind. We also investigated the stability of the model from the DNA-protein interaction with Lyapunov function. The stability of system can be determined when we obtained the equilibrium point.
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Castro, L. B., & De Castro, A. S. (2013). Missing solution in a Cornell potential. Annals of Physics, 338, 278-282.
Di Garbo, A. (2016). Anharmonic longitudinal motion of bases and dynamics of nonlinear excitation in DNA. Biophysical chemistry, 208, 76-83.
Dwiputra, D., Hidayat, W., Khairani, R., & Zen, F. P. (2016). Nonlinear Model of the Specificity of DNA-Protein Interactions and Its Stability. In Journal of Physics: Conference Series (Vol. 739, No. 1, p. 012030). IOP Publishing.
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, Proc. Natl. Acad. Sci. (USA) (777) :7222–7226.
Hamzavi, M., & Rajabi, A. A. (2013). Scalar–vector–pseudoscalar Cornell potential for a spin-1/2 particle under spin and pseudospin symmetries: 1+ 1 dimensions. Annals of Physics, 334, 316-320.
Hogan, M., Dattagupta, N., & Crothers, D. M. (1979). Transmission of allosteric effects in DNA. Nature, 278(5704), 521-524.
Peyrard, M., & Bishop, A. R. (1989). Statistical mechanics of a nonlinear model for DNA denaturation. Physical review letters, 62(23), 2755.
Ptashne, M. (1986). Gene regulation by proteins acting nearby and at a distance. Nature, 322, 697-701.
Rink, B.W. and Tuwankotta, J. M. (2000). Stability in Hamiltonian Systems (Universiteit Utrecht. Department of Mathematics).
Satarić, M. V., & Tuszyński, J. A. (2002). Impact of regulatory proteins on the nonlinear dynamics of DNA. Physical Review E, 65(5), 051901.
Sulaiman, A., Zen, F. P., Alatas, H., & Handoko, L. T. (2012). Dynamics of DNA breathing in the Peyrard–Bishop model with damping and external force. Physica D: Nonlinear Phenomena, 241(19), 1640-1647.
Sulaiman, A., Zen, F. P., Alatas, H., & Handoko, L. T. (2012). The thermal denaturation of the Peyrard–Bishop model with an external potential. Physica Scripta, 86(1), 015802.
Tom, M. (2011). DNA Protein Interactions: Principles and Protocols (Methods in Molecular Biology) 2nd Edition, USA : Humana Press.
Wang, J. C., & Giaever, G. N. (1988). Action at a distance along a DNA. Science, 240(4850), 300-305.
Watson, J. D., & Crick, F. H. C. (1953). Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid. Nature, 171(4356), 737–738. doi:10.1038/171737a0
Watson, J.D. (1976). Molecular Biology of the Gene. California: W. A. Benjamin, Menlo Park.
Yakushevich, L. V. (1989). Nonlinear DNA dynamics: A new model. Physics Letters A, 136(7-8), 413–417. doi:10.1016/0375-9601(89)90425-8
Yakushevich, L.V. (1998). Nonlinear Physics of DNA. Wiley Series in Nonlinear Science, Chichester : John Wiley.
Yuwono, T. ( 2005). Biologi Molekuler. Jakarta : Erlangga.
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