Rigidity and flexibility of biological networks

Briefings in Functional Genomics

Volumn 11, Issue 6, 2012, Pages 443-456

  Gáspár, Merse E ^a   Csermely, Peter ^a  

^a SEMMELWEIS UNIVERSITY   (Hungary)

Author keywords

Cellular networks; Cytoskeleton; Functional flexibility; Protein structure; Structural combinatorial rigidity; Thermostability

Indexed keywords

ALLOSTERISM; ANALYSIS; ARTICLE; COMBINATORIAL RIGIDITY ANALYSIS; GENE REGULATORY NETWORK; NERVE CELL NETWORK; NETWORK ANALYSIS; PROTEIN ANALYSIS; PROTEIN FUNCTION; PROTEIN PROTEIN INTERACTION; PROTEIN STRUCTURE; RIGIDITY; STRUCTURAL RIGIDITY ANALYSIS; STRUCTURAL RIGIDITY THEORY; THEORY; THERMOSTABILITY;

ALGORITHMS; MODELS, BIOLOGICAL; MODELS, THEORETICAL; SIGNAL TRANSDUCTION;

EID: 84870328990     PISSN: 20412649     EISSN: 20412657     Source Type: Journal    
DOI: 10.1093/bfgp/els023     Document Type: Article

References (140)

1. Barabaái AL, Albert R. Emergence of scaling in random networks. Science 1999;286:509-12.
2. Watts DJ, Strogatz SH. Collective dynamics of 'small--world' networks. Nature 1998;393:440-2.
3. Whitty A. Cooperativity and biological complexity. Nat Chem Biol 2008;4:435-9.
4. Csermely P. Weak Links: AUniversal Key forNetworkDiversity and Stability. Heidelberg: Springer-Verlag, 2006.
5. Bagler G, Sinha S. Network properties of protein structures. Physica A 2004;346:27-33.
6. Krishnan A, Zbilut JP, Tomita M, et al. Proteins as networks: usefulness of graph theory in protein science. Curr Protein Pept Sci 2008;9:28-38.
7. Sun W, He J. From isotropic to anisotropic side chain representations: comparison of three models for residue contact estimation. PLoSONE 2011;6:e19238.
8. Karlebach G, Shamir R. Modelling and analysis of gene regulatory networks. Nat RevMol Cell Biol 2008;9:770-80.
9. de Jong H. Modeling and simulation of genetic regulatory systems: a literature review. JComputBiol 2002;9:67-103.
10. Bachmaier C, Brandes U, Schreiber F. Biological Networks. In: Roberto T (ed). Handbook of Graph Drawing and Visualization. Boca Raton, FL: CRC Pressin press, 2012.
11. Zhu X, Gerstein M, Snyder M. Getting connected: analysis and principles of biological networks. Genes Dev 2007;21: 1010-24.
12. Almaas A, Kovaás B, Vicsek T, et al. Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature 2004;427:839-43.
13. Ronen M, Rosenberg R, Shraiman BI, et al. Assigning numbers to the arrows: parameterizing a gene regulation network by using accurate expression kinetics. Proc Natl Acad SciUSA 2002;99:10555-60.
14. Mason MJ, Fan G, Plath K, et al. Signed weighted gene co-expression network analysis of transcriptional regulation in murine embryonic stem cells. BMCGenomics 2009;10:327.
15. Maxwell JC. On reciprocal figures and diagrams of forces. PhilosMag 1864;4:250-61.
16. Ingber DE. The architecture of life. ScientificAm 1998;278: 48-57.
17. Liljenström H. Neural stability and flexibility: a computational approach. Neuropsychopharmacology 2003;28:S64-73.
18. Vakulenko SA, Radulescu O. Flexible and robust networks. J Bioinform Comp Bio 2012;10:1241011.
19. Servatius B, Servatius H. Generic and abstract rigidity. In: Thorpe MF, Duxbury PM (eds). Rigidity Theory and Applications. Heidelberg, Germany: Kluwer Academic Publishers, 2002.
20. Roth B, Whiteley W. Tensegrity frameworks. Trans Am Math Soc 1981;265:419-46.
21. Connelly R. Tensegrity structures: why are they stable?. In: Thorpe MF, Duxbury PM (eds) Rigidity Theory and Applications. Heidelberg, Germany: Kluwer Academic Publishers, 1999.
22. Connelly R. Questions, conjectures and remarks on global rigid tensegrities. Proceedings of Summer ResearchWorkshop on Volume Inequalities and Rigidity, Budapest, Hungary, 2009. www.math.cornell.edu/_connelly/09-Thoughts.pdf.
23. Katoh N, Tanigawa S. On the infinitesimal rigidity of bar-and-slider frameworks. Lecture Notes Comput Sci 2009; 5878:524-33.
24. Asimow L, Roth B. The rigidity of graphs. Trans AmMath Soc 1978;245:279-89.
25. Power S. Crystal frameworks, symmetry and affinely periodic flexes. http://arxiv.org/pdf/1103.1914v3.pdf (2011).
26. Borcea CS, Streinu I. Frameworks with crystallographic symmetry. http://arxiv.org/pdf/1110.4662v1.pdf (2011).
27. Clark P, Grant J, Monastra S, et al. Periodic rigidity of protein crystal structures. 2nd IEEE International Conference on Computational Advances in Bio andMedical Sciences, 2012. 1-6.
28. Owen JC, Power SC. Infinite bar-joint frameworks, crystals and operator theory. http://arxiv.org/abs/1009.3954 (2011).
29. Connelly R, Servatius H. Higher-order rigidity-what is the proper definition? Discrete Comput Geom 1994;11: 193-200.
30. White N. MatroidApplications. Cambridge University Press, 1992.
31. Jackson B, Jordán T. On the rank function of the 3-dimensional rigidity matroid. Technical reports: ISSN 1587-4451 2005.
32. Laman G. On graphs and rigidity of plane skeletal structures. J EngMath 1970;4:331-40.
33. Tay TS, Whiteley W. Recent advances in the generic rigidity of structures. StructTopol 1984;9:31-8.
34. Jacobs DJ. Generic rigidity in three-dimensional bondbending networks. J Phys A:Math Gen 1998;31:6653-68.
35. Edmonds J. Minimum partition of a matroid into independent subsets. JResNat Bur Standards B 1965;69:67-72.
36. Gabow HN, Westermann HH. Forests, frames and games: algorithms for matroid sums and applications. 20th Annual ACMSymposium on theTheory of Computing,1988. 407-21.
37. Jacobs D, Hendrickson B. An algorithm for twodimensional rigidity percolation: the pebble game. JComputPhys 1997;137:346-65.
38. Jacobs DJ, Rader AJ, Kuhn LA, et al. Protein flexibility predictions using graph theory. Proteins 2001;44:150-65.
39. Fontana A, Filippis V, Laureto PP. Rigidity of thermophilic enzymes. Progr Biotechnol 1998;15:277-94.
40. Huber R. Flexibility and rigidity of proteins and protein- pigment complexes. AngewChemInt EdEngl 1998;27:79-88.
41. Rader AJ, Brown SM. Correlating allostery with rigidity. Mol Biosyst 2011;7:464-71.
42. Huang SW, Hwang JK. On the structural characteristic of the protein active sites and their relation to thermal fluctuations. In: Yang NS (ed). Systems and Computational BiologyçMolecular and Cellular Experimental Systems. InTech, 2011.
43. Fox N, Jagodzinski F, Li Y, et al. KINARI-Web: a server for protein rigidity analysis. Nucleic Acids Res 2011;39: W177-83.
44. Chubynsky MV, Hespenheide BM, Jacobs DJ, et al. Constraint theory applied to proteins. Nanotechnol Res J 2008;2:61-72.
45. Fulle S, Gohlke H. Analyzing the flexibility of RNA structures by constraint counting. BiophysJ 2008;94:4202-19.
46. Fulle S, Gohlke H. Statics of the ribosomal exit tunnel: implications for co-translational peptide folding, elongation regulation, and antibiotics binding. J Mol Biol 2009;387: 502-17.
47. Fulle S, Gohlke H. Constraint counting on RNA and ribosomal structures: linking flexibility and function. JCheminform 2011;3:O11.
48. Thomas S, Tang X, Tapia L, et al. Simulating protein motions with rigidity analysis. JComput Biol 2007;14:839-55.
49. Lei M, Zavodszky MI, Kuhn LA, et al. Sampling protein conformations and pathways. J Comput Chem 2004;25: 1133-48.
50. Wells S, Menor S, Hespenheide B, et al. Constrained geometric simulation of diffusive motion in proteins. Phys Biol 2005;2:S127-36.
51. David CC, Jacobs DJ. Characterizing protein motions from structure. JMolGraphModel 2011;31:41-56.
52. Jimenez-Roldan JE, Freedman RB, Römer RA, etal. Rapid simulation of protein motion: merging flexibility, rigidity and normal mode analyses. Phys Biol 2012;9:016008.
53. Wells SA, Jimenez-Roldan JE, Römer RA. Comparative analysis of rigidity across protein families. Phys Biol 2009;6: 046005.
54. González LC, Wang H, Livesay DR, et al. Calculating ensemble averaged descriptions of protein rigidity without sampling. PLoSONE 2012;7:e29176.
55. Andrusier N, Mashiach E, Nussinov R, et al. Principles of flexible protein-protein docking. Proteins 2008;73:271-89.
56. Pandurangan AP, Topf M. Finding rigid bodies in protein structures: application to flexible fitting into cryoEM maps. J StructBiol 2012;177:520-31.
57. Potestio R, Pontiggia F, Micheletti C. Coarse-grained description of protein internal dynamics: an optimal strategy for decomposing proteins in rigid subunits. Biophys J 2009; 96:4993-5002.
58. Trueblood KN, Burgi HB, Burzlaff H, et al. Atomic displacement parameters nomenclature. Acta CvstalogrA 1996; 52:770-81.
59. Bhalla J, Storchan GB, MacCarthy CM, et al. Local flexibility in molecular function paradigm. MolCellProteomics 2006; 5:1212-23.
60. Schneider TR. What can we learn from anisotropic temperature factors? Proceedings of the CCP4 Study Weekend. Daresbury, UK: SERC Darsbury Laboratory, 1996.
61. Schomaker V, Trueblood KN. On the rigid-body motion of molecules in crystals. Acta Cryst 1968;B24:63-76.
62. Kuriyan J, Weis WI. Rigid protein motion as a model for crystallographic temperature factors. Proc Natl Acad Sci USA 1991;88:2773-7.
63. Eastman P, Pellegrini M, Doniach S. Protein flexibility in solution and in crystals. JChemPhys 1999;110:10141.
64. Smith D, Radivojac P, Obradovic Z, et al. Improved amino acid flexibility parameters. Protein Sci 2003;12:1060-72.
65. Livesay DR, Dallakyanb S, Wood GG, et al. A flexible approach for understanding protein stability. FEBS Lett 2004; 576:468-76.
66. Rose GD, Gierasch LM, Smith JA. Turns in peptides and proteins. Adv Protein Chem 1985;37:1-109.
67. Halle B. Flexibility and packing in proteins. Proc Natl Acad SciUSA 2002;99:1274-9.
68. Ragone R, Facchiano F, Facchiano A, et al. Flexibility plot of proteins. Protein Eng 1989;2:497-504.
69. Huang SW, Shih CH, Lin CP, et al. Prediction of NMR order parameters in proteins using weighted protein contact-number model. TheorChemAcc 2008;121:197-200.
70. Yuan Z, Zhao J, Wang ZX. Flexibility analysis of enzyme active sites by crystallographic temperature factors. Protein Eng 2003;16:109-14.
71. Richarz R, Nagayama K, Wüthrich K. Carbon-13 nuclear magnetic resonance relaxation studies of internal mobility of the polypeptide chain in basic pancreatic trypsin inhibitor and a selectively reduced analog. Biochemistry 1980;19: 5189-96.
72. Zaccai G. How soft is a protein? A protein dynamics force constant measured by neutron scattering. Science 2000;288: 1604-7.
73. Atilgan AR, Durell SR, Jernigan RL, et al. Anisotropy of fluctuation dynamics of proteins with an elastic network model. BiophysJ 2001;80:505-15.
74. Ming D, Brüschweiler R. Reorientational contactweighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation. BiophysJ 2006;90:3382-8.
75. Linding R, Jensen LJ, Diella F, et al. Protein disorder prediction: implications for structural proteomics. Structure 2003;11:1453-9.
76. Kundu S, Melton JS, Sorensen DC, et al. Dynamics of proteins in crystals: comparison of experiment with simple models. BiophysJ 2002;83:723-32.
77. Leherte L, Vercauteren DP. Collective motions of rigid fragments in protein structures from smoothed electron density distributions. JComputChem 2008;29:1472-89.
78. Eyal E, Chennubhotla C, Yang LW, et al. Anisotropic fluctuations of amino acids in protein structures: insights from X-ray crystallography and elastic network models. Bioinformatics 2007;23:i175-84.
79. Diamond R. On the use of normal modes in thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor. Acta CrystallogrA 1990; 46:425-35.
80. Sacquin-Mora S, Lavery R. Investigating the local flexibility of functional residues in hemoproteins. Biophys J 2006;80: 2706-17.
81. Najmanovich R, Kuttner J, Sobolev V, et al. Side-chain flexibility in proteins upon ligand biding. Proteins 2000;39: 261-8.
82. Ruvinsky AM, Kirys T, Tuzikov AV, et al. Structure fluctuations and conformational changes in protein binding. J Bioinf CompBio 2012;10:1241002.
83. Yang LW, Bahar I. Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes. Structure 2005;13:893-904.
84. Csermely P. Creative elements: network-based predictions of active centres in proteins, cellular and social networks. Trends Biochem Sci 2008;33:569-76.
85. Csermely P, Palotai R, Nussinov R. Induced fit, conformational selection and independent dynamic segments: an extended view of binding events. Trends Biochem Sci 2010; 35:539-46.
86. Piazza F, Sanejouand YH. Discrete breathers in protein structures. Phys Biol 2008;5:026001.
87. Piazza F, Sanejouand YH. Long-range energy transfer in proteins. Phys Biol 2009;6:046014.
88. Gombos L, Kardos J, Patthy A, etal. Probing conformational plasticity of the activation domain of trypsin: the role of glycine hinges. Biochemistry 2008;47:1675-84.
89. Gráf L. Structural basis of serine protease action: the fourth dimension. In: Zwilling R (ed). Natural Sciences and Human Thought. Heidelberg: Springer, 1995:139-48.
90. Fischer E. Einfluss der Configuration auf die Wirkung der Enzyme. BerDtsch Chem Ges 1894;27:2984-93.
91. Koshland DE. Application of a theory of enzyme specificity to protein synthesis. ProcNatlAcadSciUSA 1958;44:98-104.
92. Straub FB, Szabolcsi G. O dinamicseszkij aszpektah sztukturu ?fermentov. (On the dynamic aspects of protein structure). In: Braunstein AE (ed). Molecular Biology, Problems and Perspectives. Moscow: Izdat. Nauka, 1964:182-7.
93. Závodszky P, Abaturov LV, Varshavsky YM. Structure of glyceraldehyde-3-phosphate dehydrogenase and its alteration by coenzyme binding. Acta Biochim Biophys Acad Sci Hung 1966;1:389-403.
94. Tsai CJ, Kumar S, Ma B, et al. Folding funnels, binding funnels, and protein function. Protein Sci 1999;8: 1181-90.
95. Laskowski RA, Gerick F, Thornton JM. The structural basis of allosteric regulation in proteins. FEBS Lett 2009;583: 1692-8.
96. Zhuravlev PI, Papoian GA. Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework. QRev Biophys 2010;43:295-332.
97. Szilágyi A, Závodszky P. Structural differencies between mesophilic, moderately thermophilic and extremely thermophilic protein subunits: results of a comprehensive survey. Structure 2000;8:493-504.
98. Radestock S, Gohlke H. Protein rigidity and thermophilic adaptation. Proteins 2011;79:1089-108.
99. Vijayabaskar MS, Vishveshwara S. Comparative analysis of thermophilic and mesophilic proteins using protein energy networks. BMC Bioinformatics 2010;11:S49
100. Adamcsek B, Palla G, Farkas IJ, et al. CFinder: locating cliques and overlapping modules in biological networks. Bioinformatics 2006;22:1021-3.
101. Kanan N, Vishveshwara S. Aromatic clusters: a determinant of thermal stability of thermophilic proteins. Protein Eng 2000;13:753-61.
102. Gromiha MM, Suresh MX. Discrimination of mesophilic and thermophilic proteins using machine learning algorithms. Proteins 2008;70:1274-9.
103. Ha BY, Thirumalai D. Semiflexible chains under tension. JChemPhys 1997;106:4243-7.
104. Blundell JR, Terentjev EM. Forces and extensions in semiflexible and rigid polymer chains and filaments. J Phys A: MathTheor 2007;40:10951.
105. Trachtenberg S, Hammel I. Determining the persistence length of biopolymers and rod-like macromolecular assemblies from electron microscope images and deriving some of their mechanical properties. In: Vilas AM, Díaz J (eds). Microscopy: Science, Technology, Applications and Education. Bajadoz, Spain: Formatex Research Center, 2010.
106. Kellermayer MS, Smith SB, Granzier HL, et al. Foldingunfolding transitions in single titin molecules characterized with laser tweezers. Science 1997;276:1112-6.
107. Blundell JR, Terentjev EM. Affine model of stress stiffening in semiflexible filament networks. http://arxiv.org/pdf/ 0808.4088v1.pdf (2008).
108. Gutjahr P, Lipowsky R, Kierfeld J. Persistence length of semiflexible polymers and bending rigidity renormalization. Europhys Lett 2006;76:994-1000.
109. Hasnain IA, Donald AM. Microrheological characterization of anisotropic materials. Phys Rev E 2006;73:031901.
110. MacRaild CA, Stewart CR, Mok YF, et al. Non-fibrillar components of amyloid deposits mediate the self-association and tangling of amyloid fibrils. J Biol Chem 2004;279: 21038-45.
111. Mahler A, Reches M, Rechter M, et al. Rigid, selfassembled hydrogel composed of a modified aromatic dipeptide. AdvMater 2006;18:1365-70.
112. MacKintosh FC. Polymer-based models of cytoskeletal networks. In: Mofrad MRK, Kamm RD (eds). Cytoskeletal Mechanics. Cambridge, UK: Cambridge University Press, 2006.
113. Levine AJ, Head DA, MacKintosh FC. The deformation field in semiflexible networks. J Phys Condens Matter 2004; 16:S2079.
114. Das M, MacKintosh FC, Levine AJ. Effective medium theory of semiflexible filamentous networks. Phys Rev Lett 2007;99:038101.
115. Gilden J, Krummel MF. Control of cortial rigidity by the cytoskeleton: emerging roles for septins. Cytoskeleton 2010; 67:477-86.
116. Ingber DE. Tensegrity-based mechanosensing from macro to micro. Prog BiophysMol Biol 2008;97:163-79.
117. Wang S, Wolynes PG. Tensegrity and motor-driven effective interactions in a model cytoskeleton. JChemPhys 2012; 136:145102.
118. Luo Y, Xu X, Lele T, et al. A multi-modular tensegrity model of an actin stress fiber. J Biomech 2008;41: 2379-87.
119. Huang S, Ernberg I, Kauffman S. Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. SeminCellDev Biol 2009;7:869-76.
120. Felli N, Cianetti L, Pelosi E, et al. Hematopoietic differentiation: a coordinated dynamical process towards attractor stable states. BMCSyst Biol 2010;4:85.
121. Mihalik A, Csermely P. Heat shock partially dissociates the overlapping modules of the yeast protein-protein interaction network. PLoSComput Biol 2011;7:e1002187.
122. Csermely P, Sandhu KS, Hazai E, et al. Disordered proteins and network disorder in network representations of protein structure, dynamics and function. Hypotheses and a comprehensive review. Curr Prot Pept Sci 2012;13: 19-33.
123. Kovács IA, Palotai R, Szalay MS, et al. Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics. PLoSONE 2010;5:e12528.
124. Szalay-Beko00 M, Palotai R, Szappanos B, et al. ModuLand plug-in for cytoscape: determination of hierarchical layers of overlapping network modules and community centrality. Bioinformatics 2012;28:2202-04.
125. Price ND, Reed JL, Papin JA, et al. Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices. BiophysJ 2003;84:794-804.
126. Papin JA, Price ND, Edwards JS, et al. The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J Theor Biol 2002;215:67-82.
127. Price ND, Papin JA, Palsson B? Determination of redundancy and systems properties of Helicobacterpylori's metabolic network using genome-scale extreme pathway analysis. Genome Res 2002;12:760-9.
128. Bateson P, Barker D, Clutton-Brock T, et al. Developmental plasticity and human health. Nature 2004;430:419-21.
129. Stephanopoulos G, Vallino JJ. Network rigidity and metabolic engineering in metabolite overproduction. Science 1991;252:1675-81.
130. Wagner A. Robustness against mutations in genetic networks of yeast. Nat Genet 2000;24:355-61.
131. Bhalla US, Iyengar R. Emergent properties of networks of biological signaling pathways. Science 1999;283:381-7.
132. Bergman A, Siegal ML. Evolutionary capacitance as a general feature of complex gene networks. Nature 2003;424:549-52.
133. Swinderen B, Greenspan RJ. Flexibility in a gene network affecting a simple behavior in Drosophila melanogaster. Genetics 2005;169:2151-63.
134. Gustafsson M, Hömquist M, Björkegren J, et al. Genomewide system analysis reveals stable yet flexible network dynamics in yeast. IETSyst Biol 2009;3:219-28.
135. Gustafsson M, Hömquist M. Stability and flexibility from a system analysis of gene regulatory networks based on ordinary differential equations. Open BioinformaJ 2011;5: 26-33.
136. Klowankar KM, Ren Q, Samal A, et al. Learning and structure of neuronal networks. Pramana 2011;77:817-26.
137. Schwab DJ, Bruinsma RF, Feldman JL, Levine AJ. Rhythmogenic neuronal networks, emergent leaders, and k-cores. Phys Rev E 2010;82:051911.
138. Badre D, Wagner AD. Computational and neurobiological mechanism underlying cognitive flexibility. Proc Natl Acad SciUSA 2006;103:7186-91.
139. Monsell S. Task switching. Trends Cogn Sci 2003;7:134-40.
140. Bassett DS, Wymbs NF, Porter MA, et al. Dynamic reconfiguration of human brain networks during learning. ProcNatl Acad SciUSA 2011;108:7641-6.