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无标度性、小世界性、功能模块结构及度负关联性是大量生物网络共同的特征. 为了理解生物网络无标度性、小世界性和度负关联性的形成机制, 研究者已经提出了各种各样基于复制和变异的网络增长模型. 在本文中,我们从生物学的角度通过引入偏爱小复制原则及变异和非均匀的异源二聚作用构建了一个简单的蛋白质相互作用网络演化模型.数值模拟结果表明,该演化模型几乎可以再现现在实测结果所公认的蛋白质相互作用网络的性质：无标度性、小世界性、度负关联性和功能模块结构. 我们的演化模型对理解蛋白质相互作用网络演化过程中的可能机制提供了一定的帮助.
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关键词:
- 蛋白质相互作用网络 /
- 偏爱小 /
- 非均匀的异源二聚作用 /
- 功能模块结构
Scale-free connectivity, small-world pattern, hierarchical modularity and disassortative mixing are prominent features shared by most biological networks. Up to now, various network growth models invoking gene duplication and divergence have been proposed to understand the evolutionary mechanisms shaping the scale-free connectivity, small-world pattern and disassortative mixing . In this paper, we present an evolutionary model by introducing a rule of small preference duplication of a node and sequently divergence plus non-uniform heterodimerization meaning that the probability that an heterodimerization link is added between duplicated nodes is proportional to the number of common neighbors shared by these nodes based on biological background, showing that our model can almost display series of topological characteristics of real protein interaction networks, such as scale-free connectivity, small-world pattern, disassortativity of degree-degree correlation and hierarchical modularity. Our model may yield relevant insights into the evolutionary mechanism of protein interaction networks behind it.-
Keywords:
- protein interaction networks /
- small-preference duplication /
- non-uniform heterodimerization /
- hierarchical modularity
[1] Uetz P, Giot L, Cagney G, Mansfield T A, Judson R S, Knight J R, Lockshon D, Narayan V, Srinvasan M, Pochart P, Emili Q A, Li Y, Godwin B, Conover D, Kalbfleisch T, Vijayadamodar G, Yang M, Johnston M, Fields S, Rothberg J M 2000 Nature 403 623
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[5] Giot L, Bader J S, Brouwer C, Chaudhuri A, Kuang B, Li Y, Hao Y L, Ooi C E, Godwin B, Vitols E, Vijayadamodar G, Pochart P, Machineni H, Welsh M, Kong Y, Zerhusen B, Malcolm R, Varrone Z, Collis A, Minto M, Burgess S, Mcdaniel L, Stimpson E, Spriggs F, Williams J, Neurath K, Loime N, Agee M, Voss E, Furtak K, Renzulli R, Aanensen N, Carrolla S, Bickelhaupt E, Lazovatsky Y, Dasilva A, Zhong J, Stanyon C A, Finley R L, White K P, Braverman M, Jarvie T, Gold S, Leach M, Knight J, Shimkets R A, Mckenna M P, Chant J, Rothberg J M 2003 Science 302 1727
[6] Wanger A 2001 Mol. Biol. Evol. 18 1283
[7] Sole R V, Pastor-Satorras R, Smith E D, Kepler T 2002 Adv. Comp. Syst. 5 43
[8] Jeong H, Mason S P, Barabasi A L, Oltvai Z N 2001 Nature 411 41
[9] Ravasz E, Barabasi A L 2003 Phys. Rev. E 67 026112
[10] Williams R J, Martinez N D, Berlow E L, Dunne J A, Barabasi A L 2002 Science 297 1551
[11] Yook S H, Oltvai Z N, Barabasi A L 2004 Proteomics 4 929
[12] Hase T , Niimura Y, Kaminuma T, Tanaka H 2008 PloS One 3 e1667
[13] Maslov S, Sneppen K 2002 Science 296 910
[14] Vazquez A, Flammini A, Maritan A, Vespignani A 2003 Com- PlexUs 1 38
[15] Chung F, Lu L, Dewey T G, Galas D J 2003 J. Comput. Biol. 10 677
[16] Pastor-Satorras R, Smith E, Sole R V 2003 J. Theor. Biol. 222 199
[17] Ispolatov I, Krapivsky P L, Yuryev A 2005 Phys. Rev. E 71 061911
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[19] Dan Z, Liu Z R, Wang J Z 2007 Chin. Phys. Lett. 24 2766
[20] Xu C S, Liu Z R, Wang R Q 2010 Physica A 389 643
[21] Takemoto K, Oosawa C 2005 Phys. Rev. E 71 046116
[22] Takemoto K, Oosawa C 2007 Math. Bios. 208 454
[23] Kellis M, Patterson N, Endrizzi M, Birren B, Lander E S 2003 Nature 423 241
[24] Prachumwat A, Li W H 2006 Mol. Biol. Evol. 23 30
[25] Ohno S 1970 Evolution by Gene Duplication (New York: Springer-Verlag) pp100–110
[26] Evlampiev K, Isambert H 2008 Proc. Natl. Acad. Sci. USA 105 9863
[27] Watts D J, Strogatz S H 1998 Nature 393 440
[28] Zhou Y B, Cai S M, Wang W X, Zhou P L 2009 Physica A 388 999
[29] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[30] Costa L F, Rodrigues F A, Vieso G T, Boas P R V 2007 Adv. Phys. 56 167
[31] Farid N, Christensen K 2006 New J. Phys. 8 212
[32] Li L, Huang Y, Xia X, Sun Z 2006 Mol Biol Evol. 23 12
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[1] Uetz P, Giot L, Cagney G, Mansfield T A, Judson R S, Knight J R, Lockshon D, Narayan V, Srinvasan M, Pochart P, Emili Q A, Li Y, Godwin B, Conover D, Kalbfleisch T, Vijayadamodar G, Yang M, Johnston M, Fields S, Rothberg J M 2000 Nature 403 623
[2] Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y 2001 Proc. Natl. Acad. Sci. USA 98 4569
[3] Guldener U, Munsterkotter M, Oesterheld M, Pagel P, Ruepp A, Mewes H W, Stumpflen V 2006 Nucleic Acids Res. 34 436
[4] Li S, Armstrong C M, Bertin N, Ge H, Milstein S, Boxem M, Vidalain P O, Han J J, Chesneau A, Xu L, Tewari M, Wong S L, Zhang L V, Berriz G F, Jacotot L, Vaglio P, Reboul J, Kishikawa T, Li Q, Gabel H W, Elewa A, Baumgartner B, Rose D J, Yu H, Bosak S, Sequerra R, Fraser A, Mango S, Saxton W M, Strome S, Heuvel S, Piano F, Vandenhaute J, Sardet C, Gerstein M, Stamm L, Cunsalus K, Harper J W, Cusick M E, Roth F P, Hill D E, Vidal M 2004 Science 303 540
[5] Giot L, Bader J S, Brouwer C, Chaudhuri A, Kuang B, Li Y, Hao Y L, Ooi C E, Godwin B, Vitols E, Vijayadamodar G, Pochart P, Machineni H, Welsh M, Kong Y, Zerhusen B, Malcolm R, Varrone Z, Collis A, Minto M, Burgess S, Mcdaniel L, Stimpson E, Spriggs F, Williams J, Neurath K, Loime N, Agee M, Voss E, Furtak K, Renzulli R, Aanensen N, Carrolla S, Bickelhaupt E, Lazovatsky Y, Dasilva A, Zhong J, Stanyon C A, Finley R L, White K P, Braverman M, Jarvie T, Gold S, Leach M, Knight J, Shimkets R A, Mckenna M P, Chant J, Rothberg J M 2003 Science 302 1727
[6] Wanger A 2001 Mol. Biol. Evol. 18 1283
[7] Sole R V, Pastor-Satorras R, Smith E D, Kepler T 2002 Adv. Comp. Syst. 5 43
[8] Jeong H, Mason S P, Barabasi A L, Oltvai Z N 2001 Nature 411 41
[9] Ravasz E, Barabasi A L 2003 Phys. Rev. E 67 026112
[10] Williams R J, Martinez N D, Berlow E L, Dunne J A, Barabasi A L 2002 Science 297 1551
[11] Yook S H, Oltvai Z N, Barabasi A L 2004 Proteomics 4 929
[12] Hase T , Niimura Y, Kaminuma T, Tanaka H 2008 PloS One 3 e1667
[13] Maslov S, Sneppen K 2002 Science 296 910
[14] Vazquez A, Flammini A, Maritan A, Vespignani A 2003 Com- PlexUs 1 38
[15] Chung F, Lu L, Dewey T G, Galas D J 2003 J. Comput. Biol. 10 677
[16] Pastor-Satorras R, Smith E, Sole R V 2003 J. Theor. Biol. 222 199
[17] Ispolatov I, Krapivsky P L, Yuryev A 2005 Phys. Rev. E 71 061911
[18] Ispolatov I, Krapivsky P L, Yuryev A 2005 New J. Phys. 7 145
[19] Dan Z, Liu Z R, Wang J Z 2007 Chin. Phys. Lett. 24 2766
[20] Xu C S, Liu Z R, Wang R Q 2010 Physica A 389 643
[21] Takemoto K, Oosawa C 2005 Phys. Rev. E 71 046116
[22] Takemoto K, Oosawa C 2007 Math. Bios. 208 454
[23] Kellis M, Patterson N, Endrizzi M, Birren B, Lander E S 2003 Nature 423 241
[24] Prachumwat A, Li W H 2006 Mol. Biol. Evol. 23 30
[25] Ohno S 1970 Evolution by Gene Duplication (New York: Springer-Verlag) pp100–110
[26] Evlampiev K, Isambert H 2008 Proc. Natl. Acad. Sci. USA 105 9863
[27] Watts D J, Strogatz S H 1998 Nature 393 440
[28] Zhou Y B, Cai S M, Wang W X, Zhou P L 2009 Physica A 388 999
[29] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[30] Costa L F, Rodrigues F A, Vieso G T, Boas P R V 2007 Adv. Phys. 56 167
[31] Farid N, Christensen K 2006 New J. Phys. 8 212
[32] Li L, Huang Y, Xia X, Sun Z 2006 Mol Biol Evol. 23 12
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