Transcription’s bubble under the influence of long-range interactions and helicoidal coupling

doi:10.1088/1674-1056/22/12/129402

摘要/Abstract

摘要： The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase (RNAP) binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schrödinger (NLS) equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.

关键词: DNA, helicoidal coupling, RNA-polymerase, spin model, Riemann zeta function, power-law long-range interaction, breather-like soliton

Abstract: The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase (RNAP) binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schrödinger (NLS) equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.

Key words: DNA, helicoidal coupling, RNA-polymerase, spin model, Riemann zeta function, power-law long-range interaction, breather-like soliton

中图分类号: (Solitons and solitary waves)

94.05.Fg

87.10.Tf (Molecular dynamics simulation) 87.14.gk (DNA) 87.53.Ay (Biophysical mechanisms of interaction)

Mirabeau Saha, Timoléon C. Kofané. Transcription’s bubble under the influence of long-range interactions and helicoidal coupling[J]. 中国物理B, 2013, 22(12): 129402-129402.

Mirabeau Saha, Timoléon C. Kofané. Transcription’s bubble under the influence of long-range interactions and helicoidal coupling[J]. Chin. Phys. B, 2013, 22(12): 129402-129402.

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