×

A minimal model of DNA dynamics in interaction with RNA-polymerase. (English) Zbl 1227.92021

Summary: We introduce a minimal mesoscopic model for the DNA/RNAP complex; this is obtained as an extension of the familiar L. V. Yakushevich [Physica D 79, No. 1, 77–86 (1994; Zbl 0815.92008)] model for DNA dynamics. We study in particular the existence and stability of topological solitary waves for our model, motivated by the literature on would-be solitonic excitations in DNA.

MSC:

92C40 Biochemistry, molecular biology
37N25 Dynamical systems in biology

Citations:

Zbl 0815.92008

References:

[1] Englander, S. W.; Kallenbach, N. R.; Heeger, A. J.; Krumhansl, J. A.; Litwin, A., Nature of the open state in long polynucleotide double helices: possibility of soliton excitations, PNAS USA, 77, 7222-7226 (1980)
[2] Peyrard, M.; Bishop, A. R., Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett., 62, 2755-2758 (1989)
[3] Peyrard, M.; Bishop, A. R.; Dauxois, Th., Dynamics and thermodynamics of a nonlinear model for DNA denaturation, Phys. Rev. E, 47, 684-697 (1993), Entropy-driven DNA denaturation, Phys. Rev. E 47 (1993) R44-R47.
[4] Peyrard, M.; Dauxois, Th., Physique des solitons, Editions du CNRS Paris 2004, (Physics of Solitons (2006), Cambridge Universuty Press: Cambridge Universuty Press Cambridge) · Zbl 1192.35002
[5] Peyrard, M., Melting the double helix, Nature Phys., 2, 13-14 (2006)
[6] Barbi, M.; Cocco, S.; Peyrard, M., Helicoidal model for DNA opening, Phys. Lett. A, 253, 358-369 (1999), Vector nonlinear Klein-Gordon lattices: general derivation of small amplitude envelope soliton solution, Phys. Lett. A 253 (1999) 161-167
[7] Barbi, M.; Cocco, S.; Peyrard, M.; Ruffo, S., A twist-opening model of DNA, J. Biol. Phys., 24, 97-114 (1999)
[8] Cocco, S.; Monasson, R., Statistical mechanics of torque induced denaturation of DNA, Phys. Rev. Lett., 83, 5178-5181 (1999)
[9] Cocco, S.; Monasson, R., Theoretical study of collective modes in DNA at ambient temperature, J. Chem. Phys., 112, 10017-10033 (2000)
[10] Peyrard, M., Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17, R1-R40 (2004) · Zbl 1092.82015
[11] Yakushevich, L. V., Nonlinear DNA dynamics: a new model, Phys. Lett. A, 136, 413-417 (1989)
[12] Yakushevich, L. V., Nonlinear Physics of DNA (2004), Wiley: Wiley Chichester, 1998 · Zbl 0913.92001
[13] Yakushevich, L. V., Nonlinear DNA dynamics: hierarchy of the models, Physica D, 79, 77-86 (1994) · Zbl 0815.92008
[14] Yakushevich, L. V., Is DNA a nonlinear dynamical system where solitary conformational waves are possible?, J. Biosci., 26, 305-313 (2001)
[15] Yakushevich, L. V.; Savin, A. V.; Manevitch, L. I., Nonlinear dynamics of topological solitons in DNA, Phys. Rev. E, 66, 016614 (2002)
[16] Kovaleva, N. A., Topological solitons in an inhomogeneous DNA molecule, Polymer Sci. A, 48, 3, 278-293 (2006)
[17] Gaeta, G.; Reiss, C.; Peyrard, M.; Dauxois, Th., Simple models of non-linear DNA dynamics, Riv. del Nuovo. Cimento., 17, 4, 1-48 (1994)
[18] D. Poland, H.A. Scheraga, Phase transitions in one dimension and the helix-coil transition in polyamino acids, J. Chem. Phys. 45 1456-1463; Occurrence of a phase transition in nucleic acid models, J. Chem. Phys. 45 (1966) 1464-1469; Kinetics of the helix-coil transition in polyamino acids, J. Chem. Phys. 45 (1966) 2071-2090.; D. Poland, H.A. Scheraga, Phase transitions in one dimension and the helix-coil transition in polyamino acids, J. Chem. Phys. 45 1456-1463; Occurrence of a phase transition in nucleic acid models, J. Chem. Phys. 45 (1966) 1464-1469; Kinetics of the helix-coil transition in polyamino acids, J. Chem. Phys. 45 (1966) 2071-2090.
[19] Kafri, Y.; Mukamel, D.; Peliti, L., Why is the DNA denaturation transition first order?, Phys. Rev. Lett., 85, 4988-4991 (2000)
[20] Lavery, R.; Lebrun, A.; Allemand, J.; Bensimon, D.; Croquette, V., Structure and mechanics of single biomolecules: experiment and simulation, J. Phys. C, 14, R383-R414 (2002)
[21] Ritort, F., Single-molecule experiments in biological physics: methods and applications, J. Phys. C, 18, R531-R583 (2006)
[22] Greenleaf, W.; Woodside, M.; Block, S., High-resolution, single-molecule measurements of biomolecular motion, Ann. Rev. Biophys. Mol. Struct., 36, 171-190 (2007)
[23] Calladine, C.; Drew, H.; Luisi, B.; Travers, A., Understanding DNA (2004), Academic Press: Academic Press London
[24] Saenger, W., Principles of Nucleic Acid Structure (1984), Springer: Springer Berlin
[25] Cadoni, M.; De Leo, R.; Gaeta, G., A composite model for DNA torsion dynamics, Phys. Rev. E, 75, 021919 (2007)
[26] Cadoni, M.; De Leo, R.; Demelio, S.; Gaeta, G., Nonlinear torsional dynamics of macromolecules: from DNA to polyethylene, Int. J. Non-Linear Mech., 43, 1094-1107 (2008) · Zbl 1203.35281
[27] De Leo, R.; Demelio, S., Numerical analysis of solitons profiles in a composite model for DNA torsion dynamics, Int. J. Non-Linear Mech., 43, 1029-1039 (2008) · Zbl 1203.35283
[28] Cadoni, M.; De Leo, R.; Demelio, S.; Gaeta, G., A non-homogeneous composite model for DNA torsion dynamics, J. Nonlinear Math. Phys, 17, 557-569 (2010) · Zbl 1242.92006
[29] Cadoni, M.; De Leo, R.; Demelio, S., Soliton propagation in homogeneous and inhomogeneous models for DNA torsion dynamics, J. Nonlinear Math. Phys., 18, 287-319 (2011) · Zbl 1362.35076
[30] Yakushevich, L., Nonlinear dynamics of DNA: velocity of the kinks activated in homogeneous polynucleotide chains, Int. J. Quantum Chem., 110, 270-275 (2010)
[31] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0762.35001
[32] A.C. Newell, Solitons in mathematics and physics, Society for Industrial and Applied Mathematics, Pennsylvania, 1985.; A.C. Newell, Solitons in mathematics and physics, Society for Industrial and Applied Mathematics, Pennsylvania, 1985. · Zbl 0565.35003
[33] Bullough, R. K.; Caudrey, P. J.; Gibbs, H. M., The double sine-Gordon equation: a physically applicable system of equations, (Bullough, R. K.; Caudrey, P. J., Solitons. Solitons, Topics in Current Physics, vol. 17 (1980), Springer: Springer Berlin) · Zbl 0404.35085
[34] Calogero, F.; Degasperis, A., Spectral Transform and Solitons (1982), North Holland: North Holland Amsterdam · Zbl 0501.35072
[35] Mann, E., Systematic perturbation theory for sine-Gordon solitons without use of inverse scattering methods, J. Phys. A: Math. Gen., 30, 1227-1241 (1997) · Zbl 1001.81514
[36] G. Derks, A. Doelman, C. Knight, H. Susanto, Analysis of pinned fluxons in a Josephon junction with a finite-length inhomogeneity, Eur. J. Appl. Math. (2011) in press (doi:10.1017/S0956792511000301http://arxiv.org/abs/1102.3417; G. Derks, A. Doelman, C. Knight, H. Susanto, Analysis of pinned fluxons in a Josephon junction with a finite-length inhomogeneity, Eur. J. Appl. Math. (2011) in press (doi:10.1017/S0956792511000301http://arxiv.org/abs/1102.3417 · Zbl 1245.82086
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.