Discrete breathers in protein structures
Open accessAbstract
Recently, using a numerical surface cooling approach, we have shown that highly energetic discrete breathers (DBs) can form in the stiffest parts of nonlinear network models of large protein structures. In the present study, using an analytical approach, we extend our previous results to low-energy discrete breathers as well as to smaller proteins. We confirm and further scrutinize the striking site selectiveness of energy localization in the presence of spatial disorder. In particular, we find that, as a sheer consequence of disorder, a non-zero energy gap for exciting a DB at a given site either exists or not. Remarkably, in the former case, the gaps arise as a result of the impossibility of exciting small-amplitude modes in the first place. In contrast, in the latter case, a small subset of linear edge modes acts as accumulation points, whereby DBs can be continued to arbitrary small energies, while unavoidably approaching one of such normal modes. In particular, the case of the edge mode seems peculiar, its dispersion relation being simple and little system dependent. Concerning the structure-dynamics relationship, we find that the regions of protein structures where DBs form easily (zero or small gaps) are unfailingly the most highly connected ones, also characterized by weak local clustering. Remarkably, a systematic analysis on a large database of enzyme structures reveals that amino-acid residues involved in catalysis tend to be located in such regions. This finding reinforces the idea that localized modes of nonlinear origin may play an important biological role, e.g., by providing a ready channel for energy storage and/or contributing to lower energy barriers of chemical reactions.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Propagation of conformational change at certain locations can cause large-amplitude fluctuations of linked domains.
“The propagation of conformational change at certain locations228–230 can lead to large amplitude fluctuations of the linked domains.231”
From Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell (2016) · cites this paper as [229]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Hansen, J. P., McDonald, I. R., & Henderson, D. J. (1976) · Cited by 7,897 · see citing works
Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis
Tirion, M. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.1905 · Cited by 1,617 · see citing works
Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential
Bahar, İ., Atılgan, A. R., & Erman, B. (1997) · Folding and Design · doi:10.1016/s1359-0278(97)00024-2 · Cited by 1,377 · see citing works
Flach, S., & Willis, C. R. (1998) · Physics Reports · doi:10.1016/s0370-1573(97)00068-9 · Cited by 1,233 · see citing works
Conformational change of proteins arising from normal mode calculations
Tama, F., & Sanejouand, Y. (2001) · Protein Engineering Design and Selection · doi:10.1093/protein/14.1.1 · Cited by 895 · see citing works
Self-citationAnalysis of domain motions by approximate normal mode calculations
Hinsen, K. (1998) · Proteins Structure Function and Bioinformatics · doi:10.1002/(sici)1097-0134(19981115)33:3 · Cited by 703 · see citing works
Jones, R. (2002) · European Journal of Physics · doi:10.1088/0143-0807/23/6/703 · Cited by 667 · see citing works
Scott, A. C. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90093-f · Cited by 658 · see citing works
Porter, C. T. (2003) · Nucleic Acids Research · doi:10.1093/nar/gkh028 · Cited by 605 · see citing works
Merchant, K. A., Best, R. B., Louis, J. M., Gopich, I. V., & Eaton, W. A. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0607097104 · Cited by 350 · see citing works
Brooks, B., & Karplus, M. (1985) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.82.15.4995 · Cited by 344 · see citing works
SYMMETRY, FORM, AND SHAPE: Guiding Principles for Robustness in Macromolecular Machines
Tama, F., & Brooks, C. L. (2006) · Annual Review of Biophysics and Biomolecular Structure · doi:10.1146/annurev.biophys.35.040405.102010 · Cited by 266 · see citing works
Krebs, W. G., Alexandrov, V., Wilson, C. A., Echols, N., Yu, H., & Gerstein, M. (2002) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.10168 · Cited by 256 · see citing works
Targeted Energy Transfer through Discrete Breathers in Nonlinear Systems
Kopidakis, G., Aubry, S., & Tsironis, G. P. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.165501 · Cited by 252 · see citing works
Delarue, M. H., & Sanejouand, Y. (2002) · Journal of Molecular Biology · doi:10.1016/s0022-2836(02)00562-4 · Cited by 246 · see citing works
Self-citationLong-Lived Amide I Vibrational Modes in Myoglobin
Xie, A., van der Meer, L., Hoff, W. D., & Austin, R. H. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.5435 · Cited by 208 · see citing works
Energy Thresholds for Discrete Breathers in One-, Two-, and Three-Dimensional Lattices
Flach, S., Kladko, K., & MacKay, R. S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.1207 · Cited by 190 · see citing works
Hinge‐bending motion in citrate synthase arising from normal mode calculations
Marques, O., & Sanejouand, Y. (1995) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340230410 · Cited by 188 · see citing works
Self-citationDiscrete Breathers: Localization and transfer of energy in discrete Hamiltonian nonlinear systems
Aubry, S. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2005.12.020 · Cited by 185 · see citing works
Stability and motion of intrinsic localized modes in nonlinear periodic lattices
Sandusky, K. W., Page, J. B., & Schmidt, K. E. (1992) · Physical review. B, Condensed matter · doi:10.1103/physrevb.46.6161 · Cited by 181 · see citing works
Vibrational Energy Transfer and Heat Conduction in a Protein
Xin, Y., & Leitner, D. M. (2003) · The Journal of Physical Chemistry B · doi:10.1021/jp026462b · Cited by 172 · see citing works
Nonlinear two-dimensional vibrational spectroscopy of peptides
Woutersen, S., & Hamm, P. M. (2002) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/14/39/202 · Cited by 159 · see citing works
Hayward, S., Kitao, A., & Gō, N. (1995) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340230207 · Cited by 155 · see citing works
Thorough Validation of Protein Normal Mode Analysis: A Comparative Study with Essential Dynamics
Rueda, M., Chacón, P., & Orozco, M. (2007) · Structure · doi:10.1016/j.str.2007.03.013 · Cited by 154 · see citing works
Nonlinear Excitations in Biomolecules
Peyrard, M. (1995) · Springer eBooks · doi:10.1007/978-3-662-08994-1 · Cited by 154 · see citing works
Burlakov, V. M., Киселев, С. А., & Pyrkov, V. N. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.42.4921 · Cited by 145 · see citing works
The Role of Shape in Determining Molecular Motions
Lu, M., & Ma, J. (2005) · Biophysical Journal · doi:10.1529/biophysj.105.065904 · Cited by 136 · see citing works
Levy, R. M., Perahia, D. G. S., & Karplus, M. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.4.1346 · Cited by 129 · see citing works
Nonlinear dynamics of topological solitons in DNA
Yakushevich, L. V., Savin, A. V., & Manevitch, L. I. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.66.016614 · Cited by 121 · see citing works
Excited-State Lifetimes of Far-Infrared Collective Modes in Proteins
Xie, A., van der Meer, A. F. G., & Austin, R. H. (2001) · Physical Review Letters · doi:10.1103/physrevlett.88.018102 · Cited by 113 · see citing works
Protein Structural Variation in Computational Models and Crystallographic Data
Kondrashov, D. A., Wynsberghe, A. W. V., Bannen, R. M., Cui, Q., & Phillips, G. N. (2007) · Structure · doi:10.1016/j.str.2006.12.006 · Cited by 104 · see citing works
Sagnella, D. E., Straub, J. E., & Thirumalai, D. (2000) · The Journal of Chemical Physics · doi:10.1063/1.1313554 · Cited by 103 · see citing works
Pérahia, D., & Mouawad, L. (1995) · Computers & Chemistry · doi:10.1016/0097-8485(95)00011-g · Cited by 101 · see citing works
Variational proof for hard Discrete breathers in some classes of Hamiltonian dynamical systems
Aubry, S., Kopidakis, G., & Kadelburg, V. (2001) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2001.1.271 · Cited by 100 · see citing works
The pathway to energy localization in nonlinear lattices
Peyrard, M. (1998) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00079-7 · Cited by 98 · see citing works
Locating the active sites of enzymes using mechanical properties
Sacquin‐Mora, S., Laforet, É., & Lavery, R. (2007) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21353 · Cited by 97 · see citing works
Functional Modes of Proteins Are among the Most Robust
Nicolay, S., & Sanejouand, Y. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.078104 · Cited by 96 · see citing works
Self-citationIntraband discrete breathers in disordered nonlinear systems. I. Delocalization
Kopidakis, G., & Aubry, S. (1999) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(99)00027-5 · Cited by 94 · see citing works
Discrete Breathers in Nonlinear Network Models of Proteins
Juanico, B., Sanejouand, Y., Piazza, F., & Rios, P. D. L. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.238104 · Cited by 92 · see citing works
Self-citationDavson, H. (1961) · BMJ · doi:10.1136/bmj.2.5247.291 · Cited by 85 · see citing works
Vibrational Energy Transfer in Helices
Leitner, D. M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.188102 · Cited by 76 · see citing works
Intraband discrete breathers in disordered nonlinear systems. II. Localization
Kopidakis, G., & Aubry, S. (2000) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(99)00220-1 · Cited by 69 · see citing works
Falke, J. J. (2002) · Science · doi:10.1126/science.1069823 · Cited by 66 · see citing works
Micheletti, C., Lattanzi, G., & Maritan, A. (2002) · Journal of Molecular Biology · doi:10.1016/s0022-2836(02)00710-6 · Cited by 64 · see citing works
Existence of breathers on FPU lattices
James, G. (2001) · Comptes Rendus de l Académie des Sciences - Series I - Mathematics · doi:10.1016/s0764-4442(01)01894-8 · Cited by 62 · see citing works
Vibrational Energy Transfer in Helices
Leitner, D. M. (2001) · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · doi:10.17877/de290r-4312 · Cited by 62 · see citing works
Field, M. J. (2007) · Cambridge University Press eBooks · doi:10.1017/cbo9780511619076.010 · Cited by 58 · see citing works
Energy transport in α-helical protein models: One-strand versus three-strand systems
Hennig, D. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.65.174302 · Cited by 50 · see citing works
Energy Localisation and Transfer
Dauxois, T., Litvak-Hinenzon, A., MacKay, R. S., et al. (2004) · Advanced series in nonlinear dynamics · doi:10.1142/5458 · Cited by 49 · see citing works
Nonlinearity and Disorder: Theory and Applications
(2001) · Springer eBooks · doi:10.1007/978-94-010-0542-5 · Cited by 41 · see citing works
Kosevich, Y. A., Manevitch, L. I., & Savin, A. V. (2008) · Physical Review E · doi:10.1103/physreve.77.046603 · Cited by 40 · see citing works
Cooling nonlinear lattices toward energy localization
Piazza, F., Lepri, S., & Livi, R. (2003) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1535770 · Cited by 38 · see citing works
Self-citationGrowth and erosion of a discrete breather interacting with Rayleigh-Jeans distributed phonons
Rumpf, B. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/78/26001 · Cited by 36 · see citing works
Discrete breathers in a polyethylene chain
Savin, A. V., & Manevitch, L. I. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.67.144302 · Cited by 36 · see citing works
Slow relaxation and phase space properties of a conservative system with many degrees of freedom
Flach, S., & Mutschke, G. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.49.5018 · Cited by 36 · see citing works
Localization in a nonlinear disordered system
Rasmussen, K. Ø., Cai, D., Bishop, A. R., et al. (1999) · Europhysics Letters (EPL) · doi:10.1209/epl/i1999-00405-1 · Cited by 28 · see citing works
Anharmonic Decay of Vibrational States in Helical Peptides, Coils, and One-Dimensional Glasses
Leitner, D. M. (2002) · The Journal of Physical Chemistry A · doi:10.1021/jp0206119 · Cited by 25 · see citing works
Stationary and moving breathers in a simplified model of curved alpha--helix proteins
Archilla, J. F. R., Gaididei, Y. B., Christiansen, P. L., et al. (2002) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/35/42/301 · Cited by 19 · see citing works
Dimension dependent energy thresholds for discrete breathers
Kästner, M. (2004) · Nonlinearity · doi:10.1088/0951-7715/17/5/018 · Cited by 18 · see citing works
Stationary and moving breathers in a simplified model of curved alpha--helix proteins
Archilla, J. F. R., Gaididei, Y. B., Christiansen, P. L., et al. (2002) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 17 · see citing works
Solitons on H bonds in proteins
Ovidio, F. D., Bohr, H. G., & rd, P.-A. L. (2003) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/15/18/304 · Cited by 13 · see citing works
Torchia, D. A., & Ishima, R. (2003) · Pure and Applied Chemistry · doi:10.1351/pac200375101371 · Cited by 9 · see citing works
d’Ovidio, F., Bohr, H. G., & Lindgård, P.-A. (2005) · Physical Review E · doi:10.1103/physreve.71.026606 · Cited by 8 · see citing works
Moving electron–vibron breathers in random protein models
Hennig, D. (2002) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(02)00568-x · Cited by 5 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Csermely, P., Palotai, R., & Nussinov, R. (2010) · Trends in Biochemical Sciences · doi:10.1016/j.tibs.2010.04.009 · Cited by 821 · see citing works
Wei, G., Xi, W., Nussinov, R., & Ma, B. (2016) · Chemical Reviews · doi:10.1021/acs.chemrev.5b00562 · Cited by 436 · see citing works
Dynamic Allostery: Linkers Are Not Merely Flexible
Ma, B., Tsai, C.-J., Haliloğlu, T., & Nussinov, R. (2011) · Structure · doi:10.1016/j.str.2011.06.002 · Cited by 222 · see citing works
Long-range energy transfer in proteins
Piazza, F., & Sanejouand, Y.-H. (2009) · Physical Biology · doi:10.1088/1478-3975/6/4/046014 · Cited by 58 · see citing works
Self-citation
- Authors
- Piazza, F., & Sanejouand, Y.-H.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Biology
- Publisher
- IOP Publishing
- Published
- 2008-05-01
- Volume
- 5
- Issue
- 2
- Pages
- 026001
- ISSN
- 1478-3967 (ISSN-L)
- 1478-3975
- OpenAlex
- W2065371880
- Cited by
- 75
- References
- 64
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 1 · 2022: 2 · 2021: 2 · 2020: 3 · 2019: 4 · 2018: 2 · 2017: 3 · 2016: 8 · 2015: 3 · 2014: 11 · 2013: 8 · 2012: 6
- FWCI
- 2.60
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Biology (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- Florence Research (University of Florence) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Keywords
- discrete breathers, protein structure, energy localization, spatial disorder, nonlinear network model, edge states, site selectivity, protein connectivity, local clustering, enzyme catalytic residues, structure-dynamics relationship
- MeSH terms
- Computer Simulation, Protein Conformation, Proteins, Thermodynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
