Complex networks and simple models in biology

Journal of the Royal Society Interface

Volumn 2, Issue 5, 2005, Pages 419-430

  De Silva, Eric ^a   Stumpf, Michael P H ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Biological networks; Network models; Network sampling; Protein interactions; Systems biology

Indexed keywords

PROTEOME;

ANIMAL; BIOLOGICAL MODEL; CELL FUNCTION; COMPUTER SIMULATION; GENE EXPRESSION; HUMAN; METABOLISM; METHODOLOGY; PHYSIOLOGY; REVIEW; SIGNAL TRANSDUCTION; SYSTEMS BIOLOGY;

ANIMALS; CELL PHYSIOLOGY; COMPUTER SIMULATION; GENE EXPRESSION; HUMANS; MODELS, BIOLOGICAL; PROTEOME; SIGNAL TRANSDUCTION; SYSTEMS BIOLOGY;

EID: 33747150019     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2005.0067     Document Type: Review

References (100)

1. Abramowitz, M. & Stegun, I. 1974 Handbook of mathematical functions. New York: Dover.
2. Agrafioti, I., Swire, J., Abbott, I., Huntely, D., Butcher, S. & Stumpf, M. 2005 Comparative analysis of the Saccaromyces cerevisiae and Caenorhabditis elegans protein interaction networks. BMC Evol. Biol. 5, 23. (doi:10.1186/1471-2148-5-23.)
3. Aiello, W., Chung, F. & Lu, L. 2001 A random graph model for power law graphs. Exp. Math. 10, 53-66.
4. Akaike, H. 1983 Information measures and model selection. In Proc. 44th Session of the Int. Statistical Institute, pp. 277-291. Voorburg, The Netherlands: International Statistical Institute.
5. Albert, R. & Barabasi, A. 2002 Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97. (doi:10.1103/RevModPhys.74.47.)
6. Alm, E. & Arkin, A. P. 2003 Biological networks. Curr. Opin. Struct. Biol. 13, 193-202. (doi:10.1016/S0959-440X(03) 00031-9.)
7. Bader, J. S., Chaudhuri, A., Rothberg, J. M. & Chant, J. 2004 Gaining confidence in high-throughput protein interaction networks. Nat. Biotechnol. 22, 78-85. (doi:10.1038/nbt924.)
8. Barabasi, A. & Albert, R. 1999 Emergence of scaling in random networks. Science 286, 509-512. (doi:10.1126/science.286.5439.509.)
9. Barabasi, A. & Albert, R. 1999a Mean-field theory for scale-free random networks. Physica A 272, 173-187.
10. Barabasi, A., Albert, R. & Schiffer, P. 1999b The physics of sand castles: maximum angle of stability in wet and dry granular media. Physica A Stat. Mech. Appl. 266, 366-371.
11. Barabasi, A., Ravasz, E. & Vicsek, T. 2001 Deterministic scale-free networks. Physica A 299, 559-564.
12. Bender, E. & Canfield, E. 1978 The asymptotic number of labeled graphs with given degree sequence. J. Comb. Theory A 24, 296-307. (doi:10.1016/0097-3165(78)90059-6.)
13. Berg, J. & Lässig, M. 2002 Correlated random networks. Phys. Rev. Lett. 89, 228 701. (doi:10.1103/PhysRevLett.89.228701.)
14. Berg, J. & Lässig, M. 2004 Local graph alignment and motif search in biological networks. Proc. Natl Acad. Sci. USA 101, 14 689-14 694. (doi:10.1073/pnas.0305199101.)
15. Berg, J., Lassig, M. & Wagner, A. 2004 Structure and evolution of protein interaction networks: a statistical model for link dynamics and gene duplications. BMC Evol. Biol. 5, 51. (doi:10.1186/1471-2148-4-51.)
16. Bloom, J. & Adami, C. 2004 Evolutionary rate depends on number of protein-protein interactions independently of gene expression level: response. BMC Evol. Biol. 4, 14. (http://www.biomedcentral.com/1471-2148/4/14.)
17. Bollobás, B. 1998 Random graphs. New York: Academic Press.
18. Bollobás, B. & Riordan, O. 2003 Mathematical results on scale-free graphs. In Handbook of graphs and networks (ed. S. Bornholdt & H. Schuster), pp. 1-34. New York: Wiley-VCH.
19. Bu, D. et al. 2003 Topological structure analysis of the protein-protein interaction network in budding yeast. Nucleic Acids Res. 31, 2443-2450. (doi:10.1093/nar/gkg340.)
20. Burda, Z. & Krzywicki, A. 2004 Uncorrelated random networks. Phys. Rev. E 67, 046118. (doi:10.1103/PhysRevE.67.046118.)
21. Burda, Z., Correia, J. D. & Krzywicki, A. 2001 Statistical ensemble of scale-free random graphs. Phys. Rev. E 64, 046118. (doi:10.1103/PhysRevE.64. 046118.)
22. Burnham, K. & Anderson, D. 1998 Model selection and multimodel inference. Berlin: Springer.
23. Chen, Y. 2003 Computational analyses of high-throughput protein-protein interaction data. Curr. Protein Pept. Sci. 4, 159-181. (doi:10.2174/ 1389203033487225.)
24. Chung, F. 1997 Spectral graph theory. Regional Conference Series in Mathematics, vol. 91. Providence, RI: American Mathematical Society.
25. Cox, D. & Hinkley, D. 1974 Theoretical statistics. London: Chapman & Hall/CRC.
26. Davison, A. 2003 Statistical models. Cambridge: Cambridge University Press.
27. Dorogovtsev, S. & Mendes, J. 2003 Evolution of networks. Oxford: Oxford University Press.
28. Dorogovtsev, S., Mendes, J. & Samukhin, A. 2000 Structure of growing networks with preferential linking. Phys. Rev. Lett. 85, 4633. (doi:10.1103/PhysRevLett.85.4633.)
29. Dorogovtsev, S., Mendes, J. & Samukhin, A. 2002 Multifractal properties of growing networks. Europhys. Lett. 57, 334-338. (doi:10.1209/epl/i2002-00465-1.)
30. Efron, B. & Tibshirani, R. 1998 An introduction to the bootstrap. New York: Chapman & Hall/CRC.
31. Erdös, P. & Rényi, A. 1959 On random graphs i. Pubclicationes Mathematicae Debrecen 5, 290-297.
32. Erdös, P. & Rényi, A. 1960 On the evolution of random graphs. Magyar Tud. Akad. Math. Kutató Int. Közl 5, 17-61.
33. Evangelisti, A. & Wagner, A. 2004 Molecular evolution in the yeast transcriptional regulation network. J. Exp. Zool. B Mol. Dev. Evol. 302B, 392-411. (doi:10.1002/jez.b.20027.)
34. Evans, T. 2004 Complex networks. Contemp. Phys. 45, 455-474. (doi:10.1080/00107510412331283531.)
35. Farkas, I., Derenyi, I., Barabasi, A. & Vicsek, T. 2001 Spectra of 'real-world' graphs: beyond the semicircle law. Phys. Rev. E 64, 026704.
36. Felsenstein, J. 2003 Inferring phytogenies. Sunderland, MA: Sinauer Associates.
37. Fraser, H. & Hirsh, A. 2004 Evolutionary rate depends on number of protein-protein interactions independently of gene expression level. BMC Evol. Biol. 4, 13. (http://www. biomedcentral.com/1471-2148/4/13.)
38. Fraser, H. B., Hirsh, A. E., Steinmetz, L. M. & Scharfe, C. 2002 Evolutionary rate in the protein interaction network. Science 296, 750-752. (doi:10.1126/science.1068696.)
39. Fraser, H., Wall, D. & Hirsh, A. 2003 A simple dependence between protein evolution rate and the number of protein protein interactions. BMC Evol. Biol. 3, 11. (http://www. biomedcentral.com/1471-2148/3/11.)
40. Gilbert, E. 1959 Random graphs. Ann. Math. Stat. 30, 1141-1144.
41. Goh, K.-I., Oh, E., Jeong, H., Kahng, B. & Kim, D. 2002 Classification of scale-free networks. Proc. Natl Acad. Sci. USA 99, 12 583-12 588. (doi:10.1073/pnas.202301299.)
42. Janson, S., Lucaz, T. & Rucinski, A. 1999 Random graphs. New York: Wiley.
43. Jensen, H. F. 1998 Self-organized criticality. Cambridge: Cambridge University Press.
44. Jordan, I. K., Wolf, Y. I. & Koonin, E. V. 2003 No simple dependence between protein evolution rate and the number of protein-protein interactions: only the most prolific interactors tend to evolve slowly. BMC Evol. Biol. 3, 1. (doi:10.1186/1471-2148-3-1.)
45. Kamp, C. & Christensen, K. 2003 Spectral analysis of protein-protein interactions in Drosophila melanogaster. Available at http://arxiv.org/abs/q- bio.MN/0405021.
46. Kashtan, N., Itzkovitz, S., Milo, R. & Alon, U. 2004 Topological generalizations of network motifs. Phys. Rev. E 70, 031909. (doi:10.1103/ PhysRevE.70.031909.)
47. Kelley, B., Sharan, R., Karp, R., Sittler, T., Root, D., Stockwell, B. & Ideker, T. 2003 Conserved pathways within bacteria and yeast as revealed by global protein network alignment. Proc. Natl Acad. Sci. USA 100, 11 394-11 399. (doi:10.1073/pnas.1534710100.)
48. Krzywicki, A. 2001 Defining statistical ensembles of random graphs. Available at http://arxiv.org/abs/cond-mat/0110574.
49. Lappe, M. & Holm, L. 2004 Unraveling protein interaction networks with nearoptimal efficiency. Nat. Biotechnol. 22, 98-103. (doi:10.1038/nbt921.)
50. Li, S. et al. 2004 A map of the interactome network of the metazoan C. elegans. Science 303, 540-543. (doi:10.1126/science.1091403.)
51. Li, W.-H. 1997 Molecular evolution. Sunderland, MA: Sinauer Associates.
52. Ma, H. & Zeng, P. 2003 Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics 19, 270-277. (doi:10.1093/bioinformatics/19.2.270.)
53. Maslov, S. & Sneppen, K. 2002 Specificity and stability in topology of protein networks. Science 296, 910-913. (doi:10.1126/science.1065103.)
54. Maslov, S., Sneppen, K. & Alon, U. 2003 Correlation profiles and motifs in complex networks Handbook of graphs and networks. New York: Wiley-VCH.
55. Mazurie, A., Bottani, S. & Vergassola, M. 2005 An evolutionary and functional assessment of regulatory network motifs. Genome Biol. 6, R35. (doi:10.1186/gb-2005-6-4-r35.)
56. Middendorf, M., Ziv, E., Adams, C., Horn, J., Koytcheff, R., Levovitz, C., Woods, G., Chen, L. & Wiggins, C. 2004 Discriminative topological features reveal biological network mechanisms. BMC Bioinform. 5, 181. (doi:10.1186/1471-2105-5-181.)
57. Middendorf, M., Etay, Z. & Wiggins, C. 2005 Inferring network mechanisms: the Drosophila melanogaster protein interaction network. Proc. Natl Acad. Sci. USA 102, 3192-3197. (doi:10.1073/pnas.0409515102.)
58. Milgram, S. 1967 The small world problem. Psychol. Today 2, 60-67.
59. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D. & Alon, U. 2002 Network motifs: simple building blocks of complex networks. Science 298, 824-827. (doi:10.1126/science.298.5594.824.)
60. Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S., Ayzenshtat, I., Sheffer, M. & Alon, U. 2004 Superfamilies of evolved and designed networks. Science 303, 1538-1542. (doi:10.1126/science.1089167.)
61. Molloy, M. & Reed, B. 1995 A critical point for random graphs with a given degree distribution. Random Struct. Algor. 6, 161-179.
62. Moreira, A., Andrade, J. & Amaral, L. 2002 Extremum statistics in scale-free network models. Phys. Rev. Lett. 89, 268703. (doi:10.1103/ PhysRevLett.89.268703.)
63. Newman, M. 2000 Models of the small world. J. Stat. Phys. 101, 819-841. (doi:10.1023/A:1026485807148.)
64. Newman, M. 2001 Clustering and preferential attachment in growing networks. Phys. Rev. E 64, 025102.
65. Newman, M. 2003a The structure and function of complex networks. SIAM Rev. 45, 167-256.
66. Newman, M. 2003b Properties of highly clustered networks. Phys. Rev. E 68, 026121.
67. Newman, M. 2003c Random graphs as models of networks. In Handbook of graphs and networks (ed. S. Bornholdt & H. Schuster), pp. 35-68. New York: Wiley-VCH.
68. Newman, M. & Watts, D. 1999 Scaling and percolation in the small-world network model. Phys. Rev. E 60, 7332-7342. (doi:10.1103/PhysRevE.60. 7332.)
69. Newman, M., Moore, C. & Watts, D. 2000 Mean-field solution of the small-world network model. Phys. Rev. Lett. 84, 3201-3204. (doi:10.1103/ PhysRevLett.84.3201.)
70. Newman, M., Strogatz, S. & Watts, D. 2001 Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118. (doi:10.1103/PhysRevE.64. 026118.)
71. Pal, C., Papp, B. & Hurst, L. 2001 Highly expressed genes in yeast evolve slowly. Genetics 158, 927-931.
72. Penrose, M. 2003 Random geometric graphs. Oxford: Oxford University Press.
73. Przulj, N., Corneil, D. G. & Jurisica, I. 2004 Modeling interactome: scale-free or geometric? Bioinformatics. (doi10.1093/bioinformatics/bth436.)
74. Qin, H., Lu, H. H. S., Wu, W. B. & Li, W.-H. 2003 Evolution of the yeast protein interaction network. Proc. Natl Acad. Sci. USA 100, 12 820-12 824. (doi:10.1073/pnas.2235584100.)
75. Ronen, M., Rosenberg, R., Shraiman, B. & Alon, U. 2002 Assigning numbers to the arrows: parameterizing a gene regulation network by using accurate expression kinetics. Proc. Natl Acad. Sci. USA 99, 10 555-10 560. (doi:10. 1073/pnas.152046799.)
76. Sharan, R., Suthram, S., Kelley, R., McCuine, S., Uetz, P., Sittler, T., Karp, R. & Ideker, T. 2005 Conserved patterns of protein interactions in multiple species. Proc. Natl Acad. Sci. USA 102, 1974-1979. (doi:10.1073/pnas. 0409522102.)
77. Shen-Orr, S., Milo, R., Mangan, S. & Alon, U. 2002 Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet. 31, 64-68. (doi:10.1038/ng881.)
78. Silvey, S. 1975 Statistical inference. London: Chapman & Hall.
79. Sonnhammer, E. & Koonin, E. 2002 Orthology, paralogy and proposed classification for paralog subtypes. Trends Genet. 18, 619-620. (doi:10.1016/S0168-9525(02)02793-2.)
80. Sornette, D. 2003 Critical phenomena in natural sciences. Berlin: Springer.
81. Stauffer, D. & Aharony, A. 1992 Introduction to percolation theory, 2nd edn. London: Taylor and Francis.
82. Strimmer, K. & Rambaut, A. 2002 Inferring confidence sets of possibly misspecified gene trees. Proc. R. Soc. B 269, 127-142. (doi:10.1098/rspb.2001. 1872.)
83. Stumpf, M. & Ingram, P. 2005 Probability models for degree distributions of protein interaction networks. Europhys. Lett. 71, 152-158. (doi:10.1209/epl/i2004-10531-8.)
84. Stumpf, M. & Wiuf, C. In press. Sampling properties of random graphs: the degree distribution, Phys. Rev. E. (http://arxiv.org/abs/cond-mat/0507345.)
85. Stumpf, M., Wiuf, C. & May, R. 2005 Subnets of scale-free networks are not scalefree: the sampling properties of networks. Proc. Natl Acad. Sci. USA 102, 4221-4224. (doi:10.1073/pnas.0501179102.)
86. Stumpf, M., Ingram, P., Nouvel, I. & Wiuf, C. In press. Statistical model selection methods applied to biological networks. Trans. Comput. Syst. Biol. (http://arXiv.org/abs/q-bio/0506013.)
87. Tong, A. H. Y. 2004 Global mapping of the yeast genetic interaction network. Science 303, 808-813. (doi:10.1126/science.1091317.)
88. Travers, J. & Milgram, S. 1969 An experimental study of the small world problem. Sociometry 32, 425-443.
89. Uetz, P. et al. 2000 A comprehensive analysis of protein-protein interaction networks in Saccharomyces cerevisiae. Nature 403, 623-627. (doi:10.1038/35001009.)
90. Valiente, G. 2002 Algorithms on trees and graphs. Berlin: Springer.
91. Wagner, A. 2001 The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Mol. Biol. Evol. 18, 1283-1292.
92. Wagner, A. 2003 How the global structure of protein interaction networks evolves. Proc. R. Soc. B 270, 457-466. (doi:10.1098/rspb.2002.2269.)
93. Watts, D. 1999 Small worlds. Princeton: Princeton University Press.
94. Watts, D. & Strogatz, S. 1998 Collective dynamics of small-world networks. Nature 393, 440-442. (doi:10.1038/30918.)
95. Williams, E. & Hurst, L. 2000 The proteins of linked genes evolve at similar rates. Nature 407, 900-903. (doi:10.1038/35038066.)
96. Wolf, Y., Karev, G. & Koonin, E. 2002 Scale-free networks in biology: new insights into the fundamentals of evolution? Bioessays 24, 105-109. (doi:10.1002/bies.10059.)
97. Wuchty, S. & Almaas, E. 2005 Evolutionary cores of domain co-occurrence networks. BMC Evol. Biol. 5, 24. (doi:10.1186/1471-2148-5-24.)
98. Wuchty, S. & Stadler, P. F. 2003 Centers of complex networks. J. Theor. Biol. 223, 45-53. (doi:10.1016/S0022-5193(03)00071-7.)
99. Yook, S.-H., Oltvai, Z. N. & Barabsi, A.-L. 2004 Functional and topological characterization of protein interaction networks. Proteomics 4, 928-942. (doi:10.1002/pmic.200300636.)
100. Zhou, H. 2002 Scaling exponents and clustering coefficients of a growing random network. Phys. Rev. E 66, 016125.