1 Structure, Function and Evolution of Metabolic Networks (II) Jing Zhao College of Pharmacy, Second Military Medical University Shanghai Center for Bioinformation and Technology Spring school on multiscale methods and modeling in biophysics and system biology, Shanghai, China

2 I. Global structure of metabolic networks: bow-tie topology II. Hierarchical modularity of nested bow-ties in metabolic networks III. Modular Co-evolution of metabolic networks Outline

3 I.Global structure of metabolic networks: bow-tie topology Zhao J, Tao L, Yu H, Luo J-H, Cao ZW, Li Y: Bow-tie topological features of metabolic networks and the functional significance. Chinese Science Bulletin 2007, 52:

4 Csete M, Doyle J: Bow ties, metabolism and disease. Trends in Biotechnology 2004, 22: Biological viewpoint of metabolic system: bow-tie From the standard biochemical point of view, the metabolic system is organized as a bow-tie

5 Biological viewpoint of metabolic system: bow-tie The three essential pathways – TCA (tricarboxylic acid) cycle, pentose phosphate pathways and glycolysis pathways that produce the 12 precursors

6 E.coli metabolic network Topological viewpoint of metabolic networks: bow tie

7 Ma H-W, Zeng A-P: The connectivity structure, giant strong component and centrality of metabolic networks. Bioinformatics 2003, 19: Topological viewpoint of metabolic networks: bow tie

8 Bow-tie structure in the coarse-grained graph of the E.coli metabolic network Zhao J, Yu H, Luo J, Cao Z, Li Y: Complex networks theory for analyzing metabolic networks. Chinese Science Bulletin 2006, 51(13): Zhao J, Tao L, Yu H, Luo J-H, Cao ZW, Li Y: Bow-tie topological features of metabolic networks and the functional significance. Chinese Science Bulletin 2007, 52: Topological viewpoint of metabolic networks: bow tie Robust yet frangile

9 reciprocity of the whole network: mean: standard deviation: reciprocity in GSC: mean: standard deviation: Reciprocity of the GSC

10 Main cores of the GSC Two main cores of the GSC, and the two metabolites (triangle nodes) directly connecting them. Red nodes participate in carbohydrate metabolism while green nodes include in amino acid metabolism. Six precursors (box nodes) are included in the main cores.

11 II. Hierarchical modularity of nested bow- ties in metabolic networks Zhao J, Yu H, Luo J, Cao Z, Li Y: Hierarchical modularity of nested bow-ties in metabolic networks. BMC Bioinformatics 2006:7:386.

12 Life’s complex Pyramid Oltvai, Z.N., Barabási, A.-L., Life’s Complexity Pyramid, SCIENCE, 2002, 298: Biological viewpoint of biological systems: hierarchical organization

13 Topological viewpoint of metabolic networks: hierarchical modularity Ravasz E, Somera A L, Mongru D A, Oltvai Z N, Barabasi A L, Hierarchical organization of modularity in metabolic networks, Science,2002,297:

14 1.Remove all the linear branches of the GSC part and get the Core. 2. Decompose the Core of the GSC by Ward’s clustering based on the following: dissimilarity index : get its hierarchical clustering tree. 3. Cut the hierarchical clustering tree into m clusters so that the value of modularity metric is the largest 4. Expand the clusters of the Core to the whole metabolic network by the “majority rule” Decomposition algorithm

15 Illustration of the algorithm Bow tie structure of Aeropyrum pernix (ape) network.

16 Illustration of the algorithm GSC part of the ape network

17 Illustration of the algorithm Core of the GSC part for the ape network, obtained by removing all the linear branches of GSC.

18 Illustration of the algorithm Hierarchical tree for the Core of the GSC of ape network The hierarchical tree is cut into 4 sub-trees

19 Illustration of the algorithm Decomposition of the Core for the GSC of ape. The nodes included in the biggest strongly connected component of each cluster are shown in red colour.

20 Illustration of the algorithm Decomposition of the ape metabolic network by expanding the clustering of the Core. Triangles correspond to the nodes of the Core.

21 Topological feature: bow-tie modules Decomposition of the E.coli metabolic network

22 The connections among the GSC parts of the twelve bow-tie like modules. Topological feature: hierarchically nested bow-tie organization

23 Cartographic representation of the metabolic network for E.coli.. Topology vs. functionality: functional clustering of bow-tie modules

24 Case 1: most modules are dominated by one major category of metabolisms Topology vs. functionality: Are bow-tie modules also functional modules?

25 Topology vs. functionality: Are bow-tie modules also functional modules? Case 2 : Some modules are mixtures of pieces of several conventional biochemical pathways.

26 Topology vs. functionality: Are bow-tie modules also functional modules? Case 3 : A standard textbook pathway can break into several modules.

27 Topology vs. functionality: e Bow-tie topology of functional modules 1.Chemical modules: 75 organisms(Eukaryote: 8; Bacteria: 56; Archaea: 11) carbohydrate metabolism: bow-tie lipid metabolism: not bow-tie amino acid metabolism: not bow-tie 2. Spatial modules: yeast cytosol: bow-tie mitochondrion: bow-tie peroxisome: not bow-tie

28 Significance of nested bow-tie organization Bow-tie modules may act as another kind of building block of metabolic networks Nested bow-tie organization contributes to system robustness

29 III. Modular Co-evolution of metabolic networks Topological modules and their functions Phylogenetic profiles of enzymes within modules Evolutionary ages of modules Evolutionary rates of enzyme genes in modules Comparison the metabolic network with its random counterparts Conclusion Zhao J, Ding G-H, Tao L, Yu H, Yu Z-H, Luo J-H, Cao Z-W, Li Y-X: Modular co-evolution of metabolic networks. BMC Bioinformatics 2007, 8:311.

30 Core-periphery organization of modules Table 1 Topological modules and their functions Homo Sapiens metabolic network

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32 Phylogenetic profiles of enzymes within modules 115 genomes -> 54 taxa

33 Spearman’s rank correlation is r= , P-value is Phylogenetic profiles of enzymes within modules

34 A module is regarded as an evolutionary module, if it satisfies all of the following three criteria: (1) Average JC of the module is bigger than (2) The fraction of enzyme pairs with JC>0.66 in the module is significantly bigger than We set the cutoff to 0.1. (3) The P-value is smaller than 0.05.

35 Hypergeometric distribution and P-value

36 Meaning of p-value:

37 Totally 12 of the 25 modules (module 7,3,25,9,16,4,6,22,12,15,19,21) were found to be evolutionary modules, most of which are periphery modules. Phylogenetic profiles of enzymes within modules

38 Evolutionary ages of enzymes: 1)Prokaryota: E. coli group (12 organisms) 2)Protists: Plasmodium falciparum, Trypanosoma brucei, Entamoeba histolytica 3) Fungi: Saccharomyces cerevisiae; Schizosaccharomyces pombe 4) Nematodes: Caenorhabditis elegans 5) Arthropods: Drosophila melanogaster 6) Mammalian: Mus musculus; Rattus norvegicus; Canis familiaris 7) Human: H. sapiens Evolutionary ages of modules

39 Evolutionary age of a module: The biggest value of the evolutionary age of enzymes included in this module, which satisfies all of the two criteria: (1) More than 1/3 enzymes of this module belong to the evolutionary age; (2) The corresponding P-value is smaller than 0.05.

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41 Table 2 Evolutionary ages of modules

42 Spearman’s rank correlation is r= , P-value= Evolutionary rates of enzyme genes in modules Extracted from HomoloGene database

43 1.Partition all the arcs of the original network into directed arcs and bi-directed arcs. 2. Reshuffle the bi-directed arcs: A↔ B, C↔ D => A↔ C, B ↔ D 3. Reshuffle the directed arcs: A→ B, C →D => A→D, C → B Features kept: Degree sequence Total number of bi- directed and directed arcs connectivity Compare the metabolic network with its random counterparts (1) topological null model

44 Z-score=19 Compare the metabolic network with its random counterparts

45 (2) biological null model Compare the metabolic network with its random counterparts

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47 Conclusions From Topology: metabolic networks exhibit highly modular core-periphery organization pattern. From Function: The core modules perform housekeeping functions, the periphery modules accomplish relatively specific functions. From Evolution: The core modules are more evolutionarily conserved, the periphery modules appear later in evolution history. => The core-periphery modularity organization reflects the functional and evolutionary requirement of metabolic system.

48 Scheme of Network Biology: 1.Construct a network 2.Study the topology of the network 3.Investigate the functional, evolutionary meaning of the topology, or the relation with other biological significance

49 Yi-Xue Li: Chinese Academy of Sciences, SCBIT Zhi-Wei Cao: Tongji University, SCBIT Jian-Hua Luo: Shanghai Jiao Tong University Lin Tao: SCBIT Guo-Hui Ding: Chinese Academy of Sciences Hong Yu: SCBIT Zhong-Hao Yu: Shanghai Jiao Tong University Petter Holme: Umea University, Sweden Acknowledgement:

50 Thanks!