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Nonlinear lattice models for biopolymers: Dynamical coupling to a ionic cloud and application to actin filaments
1. | Institut de Mathématiques de Toulouse (UMR 5219), Département de Mathématiques, INSA-Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France |
2. | Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 38041 Grenoble Cedex 9, France |
3. | Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France |
References:
[1] |
T. E. Angelini, et al., Counterions between charged polymers exhibit liquid-like organization and dynamics, Proc. Natl. Acad Sci. USA, 103 (2006), 7962-7967.
doi: 10.1073/pnas.0601435103. |
[2] |
N. Ben Abdallah, F. Méhats and N. Vauchelet, A note on the long time behavior for the drift-diffusion-Poisson system, C. R. Acad. Sci. Paris Ser. I, 339 (2004), 683-688.
doi: 10.1016/j.crma.2004.09.025. |
[3] |
D. ben-Avraham and M. Tirion, Dynamic and elastic properties of F-actin: A normal mode analysis, Biophys. J., 68 (1995), 1231-1245.
doi: 10.1016/S0006-3495(95)80299-7. |
[4] |
L. A. Bulavin, S. N. Volkov, S. Yu. Kutuvy and S. M. Perepelytsya, Observation of the DNA ion-phosphate vibrations, Proceedings of National Academy of Science of Ukraine, 11 (2007), 69-73, arXiv:0805.0696v1. |
[5] |
M.-F. Carlier, Actin: Protein structure and filament dynamics, J. Biol. Chem., 266 (1991), 1-4. |
[6] |
P. L. Christiansen, A. V. Savin and A. V. Zolotaryuk, Soliton analysis in complex molecular systems: A zig-zag chain, Journal of Computational Physics, 134 (1997), 108-121.
doi: 10.1006/jcph.1997.5676. |
[7] |
J. Edler, R. Pfister, V. Pouthier, C. Falvo and P. Hamm, Direct observation of self-trapped vibrational states in $\alpha$-helices, Phys. Rev. Lett., 93 (2004), 106405.
doi: 10.1103/PhysRevLett.93.106405. |
[8] |
F. Fogolari, P. Zuccato, G. Esposito and P. Viglino, Biomolecular electrostatics with the linearized Poisson-Boltzmann equation, Biophys. J., 76 (1999), 1-16.
doi: 10.1016/S0006-3495(99)77173-0. |
[9] |
M. K Gilson, M. E. Davis, B. A. Luty and J. A. McCammon, Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation, J. Phys. Chem., 97 (1993), 3591-3600.
doi: 10.1021/j100116a025. |
[10] |
K. C. Holmes, et al., Atomic model of the actin filament, Nature, 347 (1990), 44-49.
doi: 10.1038/347044a0. |
[11] |
M. Karplus, Y. Q. Gao, J. Ma, A. van der Vaart and W. Yang, Protein structural transitions and their functional role, Phil. Trans. R. Soc. A, 363 (2005), 331-355.
doi: 10.1098/rsta.2004.1496. |
[12] |
H. Kojima, A.Ishijima and T.Yanagida, Direct measurements of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation, Proc. Natl. Acad. Sci. USA, 91 (1994), 12962-12966.
doi: 10.1073/pnas.91.26.12962. |
[13] |
A. Lader, H. Woodward, E. Lin and H. Cantiello, Modeling of ionic waves along actin filaments by discrete electrical transmission lines, METMBS'00 International Conference, (2000), 77-82. |
[14] |
E. Lin and H. Cantiello, A novel method to study the electrodynamic behavior of actin filaments. Evidence for cable-like properties of actin, Biophys. J., 65 (1993), 1371-1378.
doi: 10.1016/S0006-3495(93)81188-3. |
[15] |
X. Liu and H. Pollack, Mechanics of F-actin characterized with microfabricated cantilevers, Biophys. J., 83 (2002), 2705-2715.
doi: 10.1016/S0006-3495(02)75280-6. |
[16] |
T. Odijk, Stiff chains and filaments under tension, Macromolecules, 28 (1995), 7016-7018.
doi: 10.1021/ma00124a044. |
[17] |
A. Orlova and E. H. Egelman, F-actin retains a memory of angular order, Biophys. J., 78 (2000), 2180-2185.
doi: 10.1016/S0006-3495(00)76765-8. |
[18] |
S. M. Perepelytsya and S. N. Volkov, Counterion vibrations in the DNA low-frequency spectra, Eur. Phys. J. E., 24 (2007), 261-269.
doi: 10.1140/epje/i2007-10236-x. |
[19] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[20] |
M. Peyrard, S. Cuesta-López and G. James, Nonlinear analysis of the dynamics of DNA breathing, Journal of Biological Physics, 35 (2009), 73-89.
doi: 10.1007/s10867-009-9127-2. |
[21] |
S. Portet, C. Hogue, J. A. Tuszyński and J. M. Dixon, Elastic vibrations in seamless microtubules, European Biophysics Journal, 34 (2005), 912-920.
doi: 10.1007/s00249-005-0461-4. |
[22] |
A. Priel, A. J. Ramos, J. A. Tuszyński and H. F. Cantiello, A biopolymer transistor: Electrical amplification by microtubules, Biophys. J., 90 (2006), 4639-4643.
doi: 10.1529/biophysj.105.078915. |
[23] |
A. Priel and J. A. Tuszyński, A nonlinear cable-like model of amplified ionic wave propagation along microtubules, EPL, 83 (2008), 68004. |
[24] |
M. Salerno and Y. S. Kivshar, DNA promoters and nonlinear dynamics, Phys. Lett. A, 193 (1994), 263-266.
doi: 10.1016/0375-9601(94)90594-0. |
[25] |
A. V. Savin, L. I. Manevich, P. L. Christiansen and A. V. Zolotaryuk, Nonlinear dynamics of zigzag molecular chains, Physics-Uspekhi, 42 (1999), 245-260.
doi: 10.1070/PU1999v042n03ABEH000539. |
[26] |
J. A. Tuszyński, S. Portet, J. M. Dixon, C. Luxford and H. F. Cantiello, Ionic wave propagation along actin filaments, Biophys. J., 86 (2004), 1890-1903. |
[27] |
L. V. Yakushevich, A. V. Savin and L. I. Manevitch, Nonlinear dynamics of topological solitons in DNA, Phys. Rev. E, 66 (2002), 016614.
doi: 10.1103/PhysRevE.66.016614. |
[28] |
A. V. Zolotaryuk, P. L. Christiansen and A. V.Savin, Two-dimensional dynamics of a free molecular chain with a secondary structure, Phys. Rev. E, 54 (1996), 3881-3894.
doi: 10.1103/PhysRevE.54.3881. |
show all references
References:
[1] |
T. E. Angelini, et al., Counterions between charged polymers exhibit liquid-like organization and dynamics, Proc. Natl. Acad Sci. USA, 103 (2006), 7962-7967.
doi: 10.1073/pnas.0601435103. |
[2] |
N. Ben Abdallah, F. Méhats and N. Vauchelet, A note on the long time behavior for the drift-diffusion-Poisson system, C. R. Acad. Sci. Paris Ser. I, 339 (2004), 683-688.
doi: 10.1016/j.crma.2004.09.025. |
[3] |
D. ben-Avraham and M. Tirion, Dynamic and elastic properties of F-actin: A normal mode analysis, Biophys. J., 68 (1995), 1231-1245.
doi: 10.1016/S0006-3495(95)80299-7. |
[4] |
L. A. Bulavin, S. N. Volkov, S. Yu. Kutuvy and S. M. Perepelytsya, Observation of the DNA ion-phosphate vibrations, Proceedings of National Academy of Science of Ukraine, 11 (2007), 69-73, arXiv:0805.0696v1. |
[5] |
M.-F. Carlier, Actin: Protein structure and filament dynamics, J. Biol. Chem., 266 (1991), 1-4. |
[6] |
P. L. Christiansen, A. V. Savin and A. V. Zolotaryuk, Soliton analysis in complex molecular systems: A zig-zag chain, Journal of Computational Physics, 134 (1997), 108-121.
doi: 10.1006/jcph.1997.5676. |
[7] |
J. Edler, R. Pfister, V. Pouthier, C. Falvo and P. Hamm, Direct observation of self-trapped vibrational states in $\alpha$-helices, Phys. Rev. Lett., 93 (2004), 106405.
doi: 10.1103/PhysRevLett.93.106405. |
[8] |
F. Fogolari, P. Zuccato, G. Esposito and P. Viglino, Biomolecular electrostatics with the linearized Poisson-Boltzmann equation, Biophys. J., 76 (1999), 1-16.
doi: 10.1016/S0006-3495(99)77173-0. |
[9] |
M. K Gilson, M. E. Davis, B. A. Luty and J. A. McCammon, Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation, J. Phys. Chem., 97 (1993), 3591-3600.
doi: 10.1021/j100116a025. |
[10] |
K. C. Holmes, et al., Atomic model of the actin filament, Nature, 347 (1990), 44-49.
doi: 10.1038/347044a0. |
[11] |
M. Karplus, Y. Q. Gao, J. Ma, A. van der Vaart and W. Yang, Protein structural transitions and their functional role, Phil. Trans. R. Soc. A, 363 (2005), 331-355.
doi: 10.1098/rsta.2004.1496. |
[12] |
H. Kojima, A.Ishijima and T.Yanagida, Direct measurements of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation, Proc. Natl. Acad. Sci. USA, 91 (1994), 12962-12966.
doi: 10.1073/pnas.91.26.12962. |
[13] |
A. Lader, H. Woodward, E. Lin and H. Cantiello, Modeling of ionic waves along actin filaments by discrete electrical transmission lines, METMBS'00 International Conference, (2000), 77-82. |
[14] |
E. Lin and H. Cantiello, A novel method to study the electrodynamic behavior of actin filaments. Evidence for cable-like properties of actin, Biophys. J., 65 (1993), 1371-1378.
doi: 10.1016/S0006-3495(93)81188-3. |
[15] |
X. Liu and H. Pollack, Mechanics of F-actin characterized with microfabricated cantilevers, Biophys. J., 83 (2002), 2705-2715.
doi: 10.1016/S0006-3495(02)75280-6. |
[16] |
T. Odijk, Stiff chains and filaments under tension, Macromolecules, 28 (1995), 7016-7018.
doi: 10.1021/ma00124a044. |
[17] |
A. Orlova and E. H. Egelman, F-actin retains a memory of angular order, Biophys. J., 78 (2000), 2180-2185.
doi: 10.1016/S0006-3495(00)76765-8. |
[18] |
S. M. Perepelytsya and S. N. Volkov, Counterion vibrations in the DNA low-frequency spectra, Eur. Phys. J. E., 24 (2007), 261-269.
doi: 10.1140/epje/i2007-10236-x. |
[19] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[20] |
M. Peyrard, S. Cuesta-López and G. James, Nonlinear analysis of the dynamics of DNA breathing, Journal of Biological Physics, 35 (2009), 73-89.
doi: 10.1007/s10867-009-9127-2. |
[21] |
S. Portet, C. Hogue, J. A. Tuszyński and J. M. Dixon, Elastic vibrations in seamless microtubules, European Biophysics Journal, 34 (2005), 912-920.
doi: 10.1007/s00249-005-0461-4. |
[22] |
A. Priel, A. J. Ramos, J. A. Tuszyński and H. F. Cantiello, A biopolymer transistor: Electrical amplification by microtubules, Biophys. J., 90 (2006), 4639-4643.
doi: 10.1529/biophysj.105.078915. |
[23] |
A. Priel and J. A. Tuszyński, A nonlinear cable-like model of amplified ionic wave propagation along microtubules, EPL, 83 (2008), 68004. |
[24] |
M. Salerno and Y. S. Kivshar, DNA promoters and nonlinear dynamics, Phys. Lett. A, 193 (1994), 263-266.
doi: 10.1016/0375-9601(94)90594-0. |
[25] |
A. V. Savin, L. I. Manevich, P. L. Christiansen and A. V. Zolotaryuk, Nonlinear dynamics of zigzag molecular chains, Physics-Uspekhi, 42 (1999), 245-260.
doi: 10.1070/PU1999v042n03ABEH000539. |
[26] |
J. A. Tuszyński, S. Portet, J. M. Dixon, C. Luxford and H. F. Cantiello, Ionic wave propagation along actin filaments, Biophys. J., 86 (2004), 1890-1903. |
[27] |
L. V. Yakushevich, A. V. Savin and L. I. Manevitch, Nonlinear dynamics of topological solitons in DNA, Phys. Rev. E, 66 (2002), 016614.
doi: 10.1103/PhysRevE.66.016614. |
[28] |
A. V. Zolotaryuk, P. L. Christiansen and A. V.Savin, Two-dimensional dynamics of a free molecular chain with a secondary structure, Phys. Rev. E, 54 (1996), 3881-3894.
doi: 10.1103/PhysRevE.54.3881. |
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