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Continuation and bifurcations of breathers in a finite discrete NLS equation
Breather-mediated energy transfer in proteins
1. | Centre de Biophysique Moleculaire (CBM-CNRS), University of Orleans, Rue Charles Sadron, 45071 Orleans, France |
2. | Laboratoire Biotechnologie, Biocatalyse et Biorégulation, UMR 6204 du CNRS, Faculté des Sciences et des Techniques, 2, rue de la Houssinière, 44322 Nantes Cedex 3, France |
References:
[1] |
F. Abdullaev, O. Bang and M. P. Sorensen (eds.), "Nonlinearity and Disorder: Theory and Applications,", vol. \textbf{45}, 45 (2001). Google Scholar |
[2] |
J. F. R. Archilla, Yu. B. Gaididei, P. L. Christiansen and J. Cuevas, Stationary and moving breathers in a simplified model of curved alpha-helix proteins,, Journal of Physics A: Mathematical and General, 35 (2002), 8885.
doi: 10.1088/0305-4470/35/42/301. |
[3] |
S. Aubry, Discrete breathers: Localization and transfer of energy in discrete hamiltonian nonlinear systems,, Physica D: Nonlinear Phenomena, 216 (2006), 1.
doi: 10.1016/j.physd.2005.12.020. |
[4] |
I. Bahar, A. R. Atilgan and B. Erman, Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential,, Fold. Des., 2 (1997), 173.
doi: 10.1016/S1359-0278(97)00024-2. |
[5] |
I. Bahar and Q. Cui (eds.), "Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems,", C&H/CRC Mathematical & Computational Biology Series, 9 (2005). Google Scholar |
[6] |
B. R. Brooks and M. Karplus, Harmonic dynamics of proteins: Normal modes and fluctuations in bovine pancreatic trypsin inhibitor,, Proc. Natl. Acad. Sci. USA, 80 (1983), 6571.
doi: 10.1073/pnas.80.21.6571. |
[7] |
V. M. Burlakov, S. A. Kiselev and V. N. Pyrkov, Computer-simulation of intrinsic localized modes in one-dimensional and 2-dimensional anharmonic lattices,, Physical Review B, 42 (1990), 4921.
doi: 10.1103/PhysRevB.42.4921. |
[8] |
F. Columbus (ed.), "Soft Condensed Matter. New Research,", Nova Science Publishers, (2005). Google Scholar |
[9] |
T. Dauxois, R. Khomeriki, F. Piazza and S. Ruffo, The anti-FPU problem,, Chaos, 15 (2005).
doi: 10.1063/1.1854273. |
[10] |
T. Dauxois, A. Litvak-Hinenzon, R. MacKay and A. Spanoudaki (eds.), "Energy Localisation and Transfer in Crystals, Biomolecules and Josephson Arrays,", Advanced Series in Nonlinear Dynamics, 22 (2004). Google Scholar |
[11] |
A. del Sol, C. J. Tsai, B. Y. Ma and R. Nussinov, The origin of allosteric functional modulation: Multiple pre-existing pathways,, Structure, 17 (2009), 1042.
doi: 10.1016/j.str.2009.06.008. |
[12] |
F. d'Ovidio, H. G. Bohr and P.-A. Lindgård, Solitons on H-bonds in proteins,, Journal of Physics: Condensed Matter, 15 (2003).
doi: 10.1088/0953-8984/15/18/304. |
[13] |
F. d'Ovidio, H. G. Bohr and P.-A. Lindgrd, Analytical tools for solitons and periodic waves corresponding to phonons on lennard-jones lattices in helical proteins,, Physical Review E, 71 (2005), 026606.
doi: 10.1103/PhysRevE.71.026606. |
[14] |
J. J. Falke, Enzymology: A moving story,, Science, 295 (2002), 1480.
doi: 10.1126/science.1069823. |
[15] |
S. Flach and G. Mutschke, Slow relaxation and phase-space properties of a conservative system with many degrees of freedom,, Physical Review E, 49 (1994), 5018.
doi: 10.1103/PhysRevE.49.5018. |
[16] |
S. Flach and C. R. Willis, Discrete breathers,, Physics Reports, 295 (1998), 181.
doi: 10.1016/S0370-1573(97)00068-9. |
[17] |
S. Flach and A. V. Gorbach, Discrete breathers - advances in theory and applications,, Physics Reports, 467 (2008), 1.
doi: 10.1016/j.physrep.2008.05.002. |
[18] |
S. Hayward, A. Kitao and N. Go, Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis,, Proteins, 23 (1995), 177.
doi: 10.1002/prot.340230207. |
[19] |
K. A. Henzler-Wildman, M. Lei, V. Thai, S. Jordan Kerns, M. Karplus and D. Kern, A hierarchy of timescales in protein dynamics is linked to enzyme catalysis,, Nature, 450 (2007), 913.
doi: 10.1038/nature06407. |
[20] |
K. Hinsen, Analysis of domain motions by approximate normal mode calculations,, Proteins, 33 (1998), 417.
doi: 10.1002/(SICI)1097-0134(19981115)33:3<417::AID-PROT10>3.0.CO;2-8. |
[21] |
B. Juanico, Y.-H. Sanejouand, F. Piazza and P. De Los Rios, Discrete breathers in nonlinear network models of proteins,, Phys. Rev. Lett., 99 (2007).
doi: 10.1103/PhysRevLett.99.238104. |
[22] |
G. Kopidakis, S. Aubry and G. P. Tsironis, Targeted energy transfer through discrete breathers in nonlinear systems,, Phys. Rev. Lett., 87 (2001).
doi: 10.1103/PhysRevLett.87.165501. |
[23] |
D. M. Leitner, Anharmonic decay of vibrational states in helical peptides, coils, and one-dimensional glasses,, Journal of Physical Chemistry A, 106 (2002), 10870.
doi: 10.1021/jp0206119. |
[24] |
D. M. Leitner, Vibrational energy transfer in helices,, Phys. Rev. Lett., 87 (2001).
doi: 10.1103/PhysRevLett.87.188102. |
[25] |
M. Levitt, C. Sander and P. S. Stern, Normal-mode dynamics of a protein: Bovine pancreatic trypsin inhibitor,, Int. J. Quant. Chem., 10 (1983), 181. Google Scholar |
[26] |
R. M. Levy, D. Perahia and M. Karplus, Molecular dynamics of an alpha-helical polypeptide: Temperature dependance and deviation from harmonic behavior,, Proc. Natl. Acad. Sci. USA, 79 (1982), 1346.
doi: 10.1073/pnas.79.4.1346. |
[27] |
K. Moritsugu, O. Miyashita and A. Kidera, Vibrational energy transfer in a protein molecule,, Physical Review Letters, 85 (2000), 3970.
doi: 10.1103/PhysRevLett.85.3970. |
[28] |
T. Noguti and N. Go, Collective variable description of small-amplitude conformational fluctuations in a globular protein,, Nature, 296 (1982), 776.
doi: 10.1038/296776a0. |
[29] |
M. Peyrard, "Nonlinear Excitations in Biomolecules,", Springer, (1995). Google Scholar |
[30] |
M. Peyrard, The pathway to energy localization in nonlinear lattices,, Physica D: Nonlinear Phenomena, 119 (1998), 184.
doi: 10.1016/S0167-2789(98)00079-7. |
[31] |
F. Piazza and Y.-H. Sanejouand, Discrete breathers in protein structures,, Phys. Biol, 5 (2008).
doi: 10.1088/1478-3975/5/2/026001. |
[32] |
F. Piazza and Y.-H. Sanejouand, Long-range energy transfer in proteins,, Physical Biology, 6 (2009).
doi: 10.1088/1478-3975/6/4/046014. |
[33] |
K. O. Rasmussen, D. Cai, A. R. Bishop and N. Gronbech-Jensen, Localization in a nonlinear disordered system,, Europhysics Letters, 47 (1999), 421.
doi: 10.1209/epl/i1999-00405-1. |
[34] |
J. Ross, Energy transfer from adenosine triphosphate,, The Journal of Physical Chemistry B, 110 (2006), 6987.
doi: 10.1021/jp0556862. |
[35] |
M. Rueda, P. Chacon and M. Orozco, Thorough validation of protein normal mode analysis: A comparative study with essential dynamics,, Structure, 15 (2007), 565.
doi: 10.1016/j.str.2007.03.013. |
[36] |
B. Rumpf, Growth and erosion of a discrete breather interacting with rayleigh-jeans distributed phonons,, EPL, 78 (2007).
doi: 10.1209/0295-5075/78/26001. |
[37] |
S. Sacquin-Mora, E. Laforet and R. Lavery, Locating the active sites of enzymes using mechanical properties,, Proteins, 67 (2007), 350.
doi: 10.1002/prot.21353. |
[38] |
D. E. Sagnella, J. E. Straub and D. Thirumalai, Time scales and pathways for kinetic energy relaxation in solvated proteins: Application to carbonmonoxy myoglobin,, J. Chem. Phys., 113 (2000), 7702.
doi: 10.1063/1.1313554. |
[39] |
K. W. Sandusky, J. B. Page and K. E. Schmidt, Stability and motion of intrinsic localized modes in nonlinear periodic lattices,, Physical Review B, 46 (1992), 6161.
doi: 10.1103/PhysRevB.46.6161. |
[40] |
M. Sato and A. Sievers, Experimental and numerical exploration of intrinsic localized modes in an atomic lattice,, Journal of Biological Physics, 35 (2009), 57.
doi: 10.1007/s10867-009-9135-2. |
[41] |
A. Scott, Davydov's soliton,, Physics Reports, 217 (1992), 1.
doi: 10.1016/0370-1573(92)90093-F. |
[42] |
E. Segré (ed.), "Collected Papers of Enrico Fermi,", University of Chicago Press, (1965). Google Scholar |
[43] |
F. Tama and Y. H. Sanejouand, Conformational change of proteins arising from normal mode calculations,, Protein Engineering Design and Selection, 14 (2001), 1.
doi: 10.1093/protein/14.1.1. |
[44] |
M. M. Tirion, Large amplitude elastic motions in proteins from a single-parameter, atomic analysis,, Physical Review Letters, 77 (1996), 1905.
doi: 10.1103/PhysRevLett.77.1905. |
[45] |
C. J. Tsai, A. del Sol and R. Nussinov, Allostery: Absence of a change in shape does not imply that allostery is not at play,, Journal of Molecular Biology, 378 (2008), 1.
doi: 10.1016/j.jmb.2008.02.034. |
[46] |
C. J. Tsai, A. Del Sol and R. Nussinov, Protein allostery, signal transmission and dynamics: A classification scheme of allosteric mechanisms,, Molecular Biosystems, 5 (2009), 207.
doi: 10.1039/b819720b. |
[47] |
P. C. Whitford, J. N. Onuchic and P. G. Wolynes, Energy landscape along an enzymatic reaction trajectory: Hinges or cracks?,, HFSP Journal, 2 (2008), 61.
doi: 10.2976/1.2894846. |
[48] |
S. Woutersen and P. Hamm, Nonlinear two-dimensional vibrational spectroscopy of peptides,, Journal of Physics: Condensed Matter, 14 (2002).
doi: 10.1088/0953-8984/14/39/202. |
[49] |
A. Xie, A. F. G. van der Meer and R. H. Austin, Excited-state lifetimes of far-infrared collective modes in proteins,, Physical Review Letters, 88 (2001).
doi: 10.1103/PhysRevLett.88.018102. |
[50] |
A. Xie, L. van der Meer, W. Hoff and R. H. Austin, Long-lived amide i vibrational modes in myoglobin,, Physical Review Letters, 84 (2000), 5435.
doi: 10.1103/PhysRevLett.84.5435. |
[51] |
L. W. Yang and I. Bahar, Coupling between catalytic site and collective dynamics: A requirement for mechanochemical activity of enzymes,, Structure, 13 (2005), 893.
doi: 10.1016/j.str.2005.03.015. |
[52] |
X. Yu and D. M. Leitner, Vibrational energy transfer and heat conduction in a protein,, Journal of Physical Chemistry B, 107 (2003), 1698.
doi: 10.1021/jp026462b. |
show all references
References:
[1] |
F. Abdullaev, O. Bang and M. P. Sorensen (eds.), "Nonlinearity and Disorder: Theory and Applications,", vol. \textbf{45}, 45 (2001). Google Scholar |
[2] |
J. F. R. Archilla, Yu. B. Gaididei, P. L. Christiansen and J. Cuevas, Stationary and moving breathers in a simplified model of curved alpha-helix proteins,, Journal of Physics A: Mathematical and General, 35 (2002), 8885.
doi: 10.1088/0305-4470/35/42/301. |
[3] |
S. Aubry, Discrete breathers: Localization and transfer of energy in discrete hamiltonian nonlinear systems,, Physica D: Nonlinear Phenomena, 216 (2006), 1.
doi: 10.1016/j.physd.2005.12.020. |
[4] |
I. Bahar, A. R. Atilgan and B. Erman, Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential,, Fold. Des., 2 (1997), 173.
doi: 10.1016/S1359-0278(97)00024-2. |
[5] |
I. Bahar and Q. Cui (eds.), "Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems,", C&H/CRC Mathematical & Computational Biology Series, 9 (2005). Google Scholar |
[6] |
B. R. Brooks and M. Karplus, Harmonic dynamics of proteins: Normal modes and fluctuations in bovine pancreatic trypsin inhibitor,, Proc. Natl. Acad. Sci. USA, 80 (1983), 6571.
doi: 10.1073/pnas.80.21.6571. |
[7] |
V. M. Burlakov, S. A. Kiselev and V. N. Pyrkov, Computer-simulation of intrinsic localized modes in one-dimensional and 2-dimensional anharmonic lattices,, Physical Review B, 42 (1990), 4921.
doi: 10.1103/PhysRevB.42.4921. |
[8] |
F. Columbus (ed.), "Soft Condensed Matter. New Research,", Nova Science Publishers, (2005). Google Scholar |
[9] |
T. Dauxois, R. Khomeriki, F. Piazza and S. Ruffo, The anti-FPU problem,, Chaos, 15 (2005).
doi: 10.1063/1.1854273. |
[10] |
T. Dauxois, A. Litvak-Hinenzon, R. MacKay and A. Spanoudaki (eds.), "Energy Localisation and Transfer in Crystals, Biomolecules and Josephson Arrays,", Advanced Series in Nonlinear Dynamics, 22 (2004). Google Scholar |
[11] |
A. del Sol, C. J. Tsai, B. Y. Ma and R. Nussinov, The origin of allosteric functional modulation: Multiple pre-existing pathways,, Structure, 17 (2009), 1042.
doi: 10.1016/j.str.2009.06.008. |
[12] |
F. d'Ovidio, H. G. Bohr and P.-A. Lindgård, Solitons on H-bonds in proteins,, Journal of Physics: Condensed Matter, 15 (2003).
doi: 10.1088/0953-8984/15/18/304. |
[13] |
F. d'Ovidio, H. G. Bohr and P.-A. Lindgrd, Analytical tools for solitons and periodic waves corresponding to phonons on lennard-jones lattices in helical proteins,, Physical Review E, 71 (2005), 026606.
doi: 10.1103/PhysRevE.71.026606. |
[14] |
J. J. Falke, Enzymology: A moving story,, Science, 295 (2002), 1480.
doi: 10.1126/science.1069823. |
[15] |
S. Flach and G. Mutschke, Slow relaxation and phase-space properties of a conservative system with many degrees of freedom,, Physical Review E, 49 (1994), 5018.
doi: 10.1103/PhysRevE.49.5018. |
[16] |
S. Flach and C. R. Willis, Discrete breathers,, Physics Reports, 295 (1998), 181.
doi: 10.1016/S0370-1573(97)00068-9. |
[17] |
S. Flach and A. V. Gorbach, Discrete breathers - advances in theory and applications,, Physics Reports, 467 (2008), 1.
doi: 10.1016/j.physrep.2008.05.002. |
[18] |
S. Hayward, A. Kitao and N. Go, Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis,, Proteins, 23 (1995), 177.
doi: 10.1002/prot.340230207. |
[19] |
K. A. Henzler-Wildman, M. Lei, V. Thai, S. Jordan Kerns, M. Karplus and D. Kern, A hierarchy of timescales in protein dynamics is linked to enzyme catalysis,, Nature, 450 (2007), 913.
doi: 10.1038/nature06407. |
[20] |
K. Hinsen, Analysis of domain motions by approximate normal mode calculations,, Proteins, 33 (1998), 417.
doi: 10.1002/(SICI)1097-0134(19981115)33:3<417::AID-PROT10>3.0.CO;2-8. |
[21] |
B. Juanico, Y.-H. Sanejouand, F. Piazza and P. De Los Rios, Discrete breathers in nonlinear network models of proteins,, Phys. Rev. Lett., 99 (2007).
doi: 10.1103/PhysRevLett.99.238104. |
[22] |
G. Kopidakis, S. Aubry and G. P. Tsironis, Targeted energy transfer through discrete breathers in nonlinear systems,, Phys. Rev. Lett., 87 (2001).
doi: 10.1103/PhysRevLett.87.165501. |
[23] |
D. M. Leitner, Anharmonic decay of vibrational states in helical peptides, coils, and one-dimensional glasses,, Journal of Physical Chemistry A, 106 (2002), 10870.
doi: 10.1021/jp0206119. |
[24] |
D. M. Leitner, Vibrational energy transfer in helices,, Phys. Rev. Lett., 87 (2001).
doi: 10.1103/PhysRevLett.87.188102. |
[25] |
M. Levitt, C. Sander and P. S. Stern, Normal-mode dynamics of a protein: Bovine pancreatic trypsin inhibitor,, Int. J. Quant. Chem., 10 (1983), 181. Google Scholar |
[26] |
R. M. Levy, D. Perahia and M. Karplus, Molecular dynamics of an alpha-helical polypeptide: Temperature dependance and deviation from harmonic behavior,, Proc. Natl. Acad. Sci. USA, 79 (1982), 1346.
doi: 10.1073/pnas.79.4.1346. |
[27] |
K. Moritsugu, O. Miyashita and A. Kidera, Vibrational energy transfer in a protein molecule,, Physical Review Letters, 85 (2000), 3970.
doi: 10.1103/PhysRevLett.85.3970. |
[28] |
T. Noguti and N. Go, Collective variable description of small-amplitude conformational fluctuations in a globular protein,, Nature, 296 (1982), 776.
doi: 10.1038/296776a0. |
[29] |
M. Peyrard, "Nonlinear Excitations in Biomolecules,", Springer, (1995). Google Scholar |
[30] |
M. Peyrard, The pathway to energy localization in nonlinear lattices,, Physica D: Nonlinear Phenomena, 119 (1998), 184.
doi: 10.1016/S0167-2789(98)00079-7. |
[31] |
F. Piazza and Y.-H. Sanejouand, Discrete breathers in protein structures,, Phys. Biol, 5 (2008).
doi: 10.1088/1478-3975/5/2/026001. |
[32] |
F. Piazza and Y.-H. Sanejouand, Long-range energy transfer in proteins,, Physical Biology, 6 (2009).
doi: 10.1088/1478-3975/6/4/046014. |
[33] |
K. O. Rasmussen, D. Cai, A. R. Bishop and N. Gronbech-Jensen, Localization in a nonlinear disordered system,, Europhysics Letters, 47 (1999), 421.
doi: 10.1209/epl/i1999-00405-1. |
[34] |
J. Ross, Energy transfer from adenosine triphosphate,, The Journal of Physical Chemistry B, 110 (2006), 6987.
doi: 10.1021/jp0556862. |
[35] |
M. Rueda, P. Chacon and M. Orozco, Thorough validation of protein normal mode analysis: A comparative study with essential dynamics,, Structure, 15 (2007), 565.
doi: 10.1016/j.str.2007.03.013. |
[36] |
B. Rumpf, Growth and erosion of a discrete breather interacting with rayleigh-jeans distributed phonons,, EPL, 78 (2007).
doi: 10.1209/0295-5075/78/26001. |
[37] |
S. Sacquin-Mora, E. Laforet and R. Lavery, Locating the active sites of enzymes using mechanical properties,, Proteins, 67 (2007), 350.
doi: 10.1002/prot.21353. |
[38] |
D. E. Sagnella, J. E. Straub and D. Thirumalai, Time scales and pathways for kinetic energy relaxation in solvated proteins: Application to carbonmonoxy myoglobin,, J. Chem. Phys., 113 (2000), 7702.
doi: 10.1063/1.1313554. |
[39] |
K. W. Sandusky, J. B. Page and K. E. Schmidt, Stability and motion of intrinsic localized modes in nonlinear periodic lattices,, Physical Review B, 46 (1992), 6161.
doi: 10.1103/PhysRevB.46.6161. |
[40] |
M. Sato and A. Sievers, Experimental and numerical exploration of intrinsic localized modes in an atomic lattice,, Journal of Biological Physics, 35 (2009), 57.
doi: 10.1007/s10867-009-9135-2. |
[41] |
A. Scott, Davydov's soliton,, Physics Reports, 217 (1992), 1.
doi: 10.1016/0370-1573(92)90093-F. |
[42] |
E. Segré (ed.), "Collected Papers of Enrico Fermi,", University of Chicago Press, (1965). Google Scholar |
[43] |
F. Tama and Y. H. Sanejouand, Conformational change of proteins arising from normal mode calculations,, Protein Engineering Design and Selection, 14 (2001), 1.
doi: 10.1093/protein/14.1.1. |
[44] |
M. M. Tirion, Large amplitude elastic motions in proteins from a single-parameter, atomic analysis,, Physical Review Letters, 77 (1996), 1905.
doi: 10.1103/PhysRevLett.77.1905. |
[45] |
C. J. Tsai, A. del Sol and R. Nussinov, Allostery: Absence of a change in shape does not imply that allostery is not at play,, Journal of Molecular Biology, 378 (2008), 1.
doi: 10.1016/j.jmb.2008.02.034. |
[46] |
C. J. Tsai, A. Del Sol and R. Nussinov, Protein allostery, signal transmission and dynamics: A classification scheme of allosteric mechanisms,, Molecular Biosystems, 5 (2009), 207.
doi: 10.1039/b819720b. |
[47] |
P. C. Whitford, J. N. Onuchic and P. G. Wolynes, Energy landscape along an enzymatic reaction trajectory: Hinges or cracks?,, HFSP Journal, 2 (2008), 61.
doi: 10.2976/1.2894846. |
[48] |
S. Woutersen and P. Hamm, Nonlinear two-dimensional vibrational spectroscopy of peptides,, Journal of Physics: Condensed Matter, 14 (2002).
doi: 10.1088/0953-8984/14/39/202. |
[49] |
A. Xie, A. F. G. van der Meer and R. H. Austin, Excited-state lifetimes of far-infrared collective modes in proteins,, Physical Review Letters, 88 (2001).
doi: 10.1103/PhysRevLett.88.018102. |
[50] |
A. Xie, L. van der Meer, W. Hoff and R. H. Austin, Long-lived amide i vibrational modes in myoglobin,, Physical Review Letters, 84 (2000), 5435.
doi: 10.1103/PhysRevLett.84.5435. |
[51] |
L. W. Yang and I. Bahar, Coupling between catalytic site and collective dynamics: A requirement for mechanochemical activity of enzymes,, Structure, 13 (2005), 893.
doi: 10.1016/j.str.2005.03.015. |
[52] |
X. Yu and D. M. Leitner, Vibrational energy transfer and heat conduction in a protein,, Journal of Physical Chemistry B, 107 (2003), 1698.
doi: 10.1021/jp026462b. |
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