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

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

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.

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

Received: 24 March 2013
Revised: 15 June 2013
Accepted manuscript online:

PACS:	94.05.Fg	(Solitons and solitary waves)
	87.10.Tf	(Molecular dynamics simulation)
	87.14.gk	(DNA)
	87.53.Ay	(Biophysical mechanisms of interaction)

Corresponding Authors: Mirabeau Saha, Timoléon C. Kofané
E-mail: sahamirabeau@yahoo.fr;tckofane@yahoo.com

Cite this article:

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

[1]	Davydov A 1981 Solitons in Molecular Systems (Dordrecht: Kluwer)
[2]	Englander S, Kallenbach N, Heeger A, Krumhansl J and Litwin A 1980 Proc. Natl. Acad. Sci. USA 77 7222
[3]	Kalosakas G, Rasmussen K O and Bishop A R 2004 Synth. Met. 141 93
[4]	Yakushevich L V 1994 Physica D 79 77
[5]	Yakushevich L V 2004 Nonlinear Physics of DNA (Berlin: Wiley-VCH)
[6]	Stryer L 1995 Biochemistry, 4-th edn. (New York: W. H. Freeman and Company)
[7]	Dauxios T 1991 Phys. Lett. A 159 390
[8]	Xia J F and Jia Y 2010 Chin. Phys. B 19 040506
[9]	Tabi C B, Mohamadou A and Kofané T C 2009 Chin. Phys. Lett. 26 68703
[10]	Zayed E M E and Arnous A H 2012 Chin. Phys. Lett. 29 080203
[11]	Cadoni M, Leo R De and Gaeta G 2007 Phys. Rev. E 75 021919
[12]	Baverstock K F and Cundall R B 1988 Nature 332 312
[13]	Salerno M 1991 Phys. Rev. A 44 5292
[14]	Qian J, Xie P, Xue X G and Wang P Y 2009 Chin. Phys. B 18 4852
[15]	Yan X L and Dong R X 2007 Chin. Phys. 16 2062
[16]	Gao J and Xue Z Y 2009 Chin. Phys. B 18 370
[17]	Peyrard M, Lopez S C and James G 2009 J. Biol. Phys. 35 73
[18]	M Salerno 1992 Phys. Lett. A 167 49
[19]	Han J J and Fu W J 2010 Chin. Phys. B 19 010205
[20]	Zhou Q and Chen Z Q 2010 Chin. Phys. B 19 090508
[21]	Gueron M, Kochoyan M and Leroy J J 1987 Nature 328 89
[22]	Daniel M and Vasumathi V 2007 Physica D 231 10
[23]	Fujimoto S and Yu Y X 2010 Chin. Phys. B 19 088701
[24]	Yan Y Y and Zhu P 2011 Chin. Phys. B 20 018701
[25]	Vasumathi V and Daniel M 2009 Phys. Rev. E 80 061904
[26]	Dandoloff R and Saxena A 1997 J. Phys.: Condens. Matter 9 L667
[27]	Homma S and Takeno S 1983 Prog. Theor. Phys. 70 308
[28]	Takeno S and Homma S 1984 Prog. Theor. Phys. 72 679
[29]	Zdravkovic S and Sataric M V 2001 Phys. Scr. 64 612
[30]	Zdravkovic S and Sataric M V 2003 Int. J. Mod. Phys. B 17 5911
[31]	Tabi C B, Mohamadou A and Kofane T C 2008 J. Phys.: Condens. Matter 20 415104
[32]	Zdravkovic S and Sataric M V 2007 Europhys. Lett. 78 38004
[33]	Tabi C B, Fouda H P E and Kofane T C 2011 J. Comput. Theor. Nanosci. 8 1
[34]	Woafo P, Kofané T C and Bokosah A S 1992 J. Phys.: Condens. Matter 4 3389
[35]	Tchawoua C, Kofané T C and Bokosah A S 1993 J. Phys. A: Math. Gen. 26 6477
[36]	Saha M and Kofané T C 2012 Chaos 22 013116
[37]	Rau D C and Parsegian V A 1992 Biophys. J. 61 246
[38]	Larsen P V, Christiansen P L, Bang O, Archilla J F R and Gaididei Yu B 2004 Phys. Rev. E 70 036609
[39]	Mingaleev S F, Gaididei Y B and Mertens F G 1998 Phys. Rev. E 58 3833
[40]	Daniel M and Beula J 2008 Phys. Rev. B 77 144416
[41]	Zdravković S, Tuszyński J A and Satarić M V 2005 J. Comput. Theor. Nanosci. 2 263
[42]	Zdravković S 2005 Finely Dispersed Particles: Micro-, Nano-, and Atto Engineering, 130 Surfactant Science Series, eds. Spasic A M and Hsu J P (Dekker/CRC Press/Taylor & Francis Group) p. 779
[43]	Satarić M V, Matsson L and Tuszyński J A 2006 Phys. Rev. E 74 051902
[44]	Saha M and Kofané T C 2012 Int. J. Mod. Phys. B 26 1250101
[45]	Peyrard M and Bishop A R 1989 Phys. Rev. Lett. 62 2755
[46]	Dauxois T, Peyrard M and Bishop A R 1993 Phys. Rev. E 47 684
[47]	Fujita H, Imamura A and Nagata C 1974 J. Theor. Biol. 45 411
[48]	Zdravkovic S and Sataric M V 2006 Phys. Rev. E 73 021905
[49]	Zdravkovic S and Sataric M V 2008 Phys. Rev. E 77 031906
[50]	Lawrence A F, Daniel J C Mc, Chang D B and Birge R R 1987 Biophys. J. 51 785
[51]	http://www.peptideguide.com/peptide-bond.html
[52]	Daniel M and Kavitha L 2002 Phys. Lett. A 295 121
[53]	Holstein T and Primakoff H 1940 Phys. Rev. 58 1098
[54]	Nguenang J P and Kofané T C 1997 Phys. Scr. 55 367
[55]	Nguenang J P and Kofané T C 2000 Physica D 147 311
[56]	Glauber R J 1963 Phys. Rev. 131 2766
[57]	Rasmussen K Ø, Christiansen P L, Johansson M, Gaididei Yu B and Mingaleev S F 1998 Physica D 113 134
[58]	Peyrard M and Bishop A R 1989 Phys. Rev. Lett. 62 2755
[59]	Scott A C, Chu F Y F and McLaughlin D W 1973 Proc. IEEE 61 1443
[60]	Hasegawa A 1975 Plasma Instabilities and Nonlinear Effects (Berlin: Springer)
[61]	Zdravkovic S and Sataric M V 2008 Phys. Lett. A 373 126
[62]	Takeno S 2005 Phys. Lett. A 339 352
[63]	Wang J C, Jacobsen J H and Saucier J M 1977 Nucleic Acids Res. 4 1225
[64]	Hsieh T S and Wang J C 1978 Nucleic Acids Res. 5 3337
[65]	Melnikova A, Beabealashvilli R and Mirzabekov A D 1978 Eur. J. Biochem. 84 301
[66]	Siebenlist U 1979 Nature 279 651
[67]	Brunhuber C, Mertens F G and Gaididei Y 2007 Eur. Phys. J. B 57 57
[68]	Ishimori Y 1982 Prog. Theor. Phys. 68 402
[69]	Kodama Y and Ablowitz M J 1981 Stud. Appl. Math. 64 225
[70]	Beula J and Daniel M 2010 Physica D 239 397
[71]	Jurnak F A and McPherson A 1985 Structure of Biological Macromolecule and Assemblies (New York: John Wiley and Sons Inc.) 2 p. 172
[72]	Krusmhansl J A, Wysin G M, Alexander D M, Garcia A, Lomdahl P S and Layne S P 1985 Structure and Motion: Menbrane, Nucleic Acids and Proteins, eds. Sarma M H and Sarma R H (New York: Academic Press) p. 407
[73]	Banerjee A and Sobell H M 1983 J. Biomol. Struct. Dyn. 1 253
[74]	Choi C H, Kalosakas G, Rasmussen K φ, Hiromura M, Bishop A R and Usheva A 2004 Nucleic Acids Res. 32 1584
[75]	Ares S and Kalosakas G 2007 Nano. Lett. 7 2
[76]	Visinescu A and Grecu D 2004 Proc. Inst. Math. NAS Ukraine 50, Part 3, p. 1502

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

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