NETWORKS – THE UNIVERSAL LANGUAGE OF COMPLEX WORLD

1. NETWORKS – THE UNIVERSAL LANGUAGE OF COMPLEX WORLD Danail Bonchev

2. The Emerging New Paradigm of Science • The Reductionist Paradigm: The properties of the whole can be derived from the nature and properties of its elements. • The cracks on the solid building – cooperative effects,emergent events, self-organizing • Complexity: Relations, not size! 1 + 1 > 2 • The new Paradigm: Describe objects as a whole, as relational systems. • Dynamic Evolutionary Networks - The Universal Language to Describe Complex Systems in Nature and Technology

3. Social Networks

4. The Space-Time Network Space-time network (quantum gravity theory) Spin-network Markopoulou, Smolin, 1997

5. The Yeast Proteome H. Jeong, S. P. Mason, A.-L. Barabasi, Z. N. Oltvai, Nature (2001) 411, 41.

6. Food Webs

7. The Metabolic Network of E coli

8. Ai1 Mag1 Msh2 Mph1 Rfa1 Yku70 Rvb2 Rad23 Ufd2 DNADamage Response Network 76 proteins 5 complexes 5 components Swi4 Rtc4 Rad52 (Data: Y. Ho et al. (2002), Nature 415, 180-183) Ptc2 Asf1 Smc3 Rad53 Psc2 Ptc3 Rad59 Cdc5 Mgm101 Anc1 Rad28 Ntg1 Hpr5 Rad9 Rfc2 Cdc16 Rad24 Mgt1 Rfa2 Rfc3 Smc4 RFC Dun1 Xrs2 Rad50 Mre11 MRX Rfc5 Msi1 Ubc13 Rnr2 Rad10 Mms2 Rad18 Rfc4 Sml1 Rad1 Rpo21 PRR Rsp5 Rfc1 Rad4 Rnr3 Ddc1 Rad14 Rnq1 Cce1 Elc1 Rad7 Rad16 Mec3 Lif1 Ctf4 Rnr1 Lcd1 Dnl4 Rad17 NER Rad26 Tib3 PCNAL Rad3 Bcy1 Ccl1 Met18 Rvb1 Kin28

9. Cell Cycle Cell Polarity & Structure 7 Number of protein complexes 13 111 8 61 25 40 Number of proteins Transcription/DNA Maintenance/Chromatin Structure 77 19 15 Number of shared proteins 14 11 7 30 16 27 22 Intermediate and Energy Metabolism 187 55 740 43 221 94 33 73 83 37 103 65 11 Signaling Membrane Biogenesis & Turnover 13 20 125 20 147 53 35 321 19 41 299 49 596 75 97 Protein Synthesis and Turnover 28 692 33 419 RNA Metabolism 260 24 172 75 12 160 Protein RNA / Transport The YeastProteome Functional Organization 1400 proteins, 232 complexes, nine functional groups of complexes (Data A.-M. Gavin et al. (2002) Nature 415,141-147) Topological descriptors: V=9, E=36, C=28, Conn=100%, <d>=1, ai=di=8, <ai(multi)>=562, W=36, SC2=252, OC1=576, OC2=6048, Icomp(func)=0.626, Icomp(loc)=0.729, Ivd(multi)=0.766

10. V + C = E + K C = E - V + 1 Networks As Graphs • Every system composed of interacting elements can be represented by • a network of nodes (vertices, points) connected by links (edges, lines). • The specificity of network nodes and links can be quantitatively • characterized by weights. • Networks can be undirected or directed, depending on whether the • interaction between two neighboring nodes proceeds in both directions • or in only one of them, respectively. • Networks can be connected (presented by a single component) or disconnected • (presented by several disjoint components). • Networks having no cycles are termed trees. The more cycles the • network has, the more complex it is.

11. X Y Z Three chain: food webs X Y Z Feed-forward loop: protein, neuron, electronic X Three-node feedback loop: electronic Y Z X Y By-fan: protein, neuron, electronic Z W X Fully connected triad: World Wide Web Y Z How To Characterize a Network? • Qualitatively – Motifs, Patterns, Modules,… (R. Milo et al., Science, 298, 2002, 824-827

12. Modularity Topological Modules in E coli Metabolism Topological Overlap Matrix Pyrimidine Metabolism E. Ravasz et al., Nature 297(2002)1551

13. V = 4 E = 3 1 1 • Adjacency Matrix 1 2 3 3 1 4 1 2 3 4 ai 1 2 3 4 • 0 0 1 0 1 • 0 0 1 0 1 • 1 1 0 1 3 • 0 0 1 0 1 A = Vertex degrees Networks: Quantitative Characterization Connectivity • Adjacency relation, aij • aij = 1 (neighbors) • aij = 0 (otherwise) • Vertex degree, ai = Σj aij • Total adjacency, A = Σi ai ; A = 2E • Average Vertex Degree, <ai> = A/V

14. d13 = d14= d23 = 1 d12 = Distance, dij > 0 4 d24 = d34 = 2 1 2 3 Distance degree, di = Σ dij Total distance, D = Σ di (The Wiener number, W= D/2) Distance matrix di 1 2 3 4 Distance degrees D = 16 5 1 2 3 4 • 0 1 1 1 3 • 1 0 1 2 4 • 1 1 0 2 4 • 1 2 2 0 5 D = 3 4 4 Graph Distances Average distance (graph radius), <d> = D/N(N-1) <d> = 1.33 Maximal graph distance (graph diameter), di = 2 Maximal vertex distance (vertex eccentricity), e1 = 1, e2 = e3 = e4 = 2

15. Criterion 1: 1 and 2(e = 2) Criterion 2: a1 = 8, a2 = 9 Other Criteria 2 1 Network Centrality: Graph Center • Classical definition: The graph center is the vertex(es) having the lowest eccentricity • Hierarchical definition: If several vertices have the same eccentricity ei, the center is the vertex having the lowest vertex distance degree di. The network vertices might thus be characterized by their centrality, i.e., according to their distance to the central vertex(es).

16. 1 2 3 4 5 6 7 10 8 9 Exercise: Comparative Topology of Graphs • Prepare input files for 10 graphs having the same number of vertices • Number arbitrarily each of the vertices in the graph. • Open a Notepad file. Write the vertex-vertex connectivity in pairs with a space between the vertex numbers; • one pair on each line. Example: 1 2 • 2 3 • ….. • Save the file in your work directory. • Due the same for the remaining 9 graphs. • Go to Programs Grafman. Select “Open File”, then, from ‘Options select Undirected from Nodes. OK. RUN.

17. Exercise: Comparative Topology of Graphs • The output window appears. The first line might look like: 5 8 1.60 0.32 0.40 40 8.00 1.60 2.00 5 is the number of vertices; 8 – the total adjacency; 1.60 is the average vertex degree; Neglect the fourth number (0.32); 0.40 (or 40%) is the graph connectedness; 40 is the total distance; 8.00 is the average vertex distance degree; neglect the penultimate term (1.60); 2.00 is the the average distance (the graph radius). • Collect all output data for the 10 graphs in a Table with 7 rows and 10 columns. • Reorder the Table according to connectedness values (starting from the highest one), and at the same connectedness – according to the increasing values of graph radius).

18. Home Assignment +Instructions How To Access Watson / The Grafman Software • Each student will open a temporary account on the Watson computer. The accounts are free and numbered demo#: • demo0, demo1, demo2,…,demo12. Use the SSH Secure Shell on your PC with your specific demo# and password • “abcd1234”. • The GRAFMAN software can be accessed by the command “ /usr/local/bin/grafman.pl interaction_file output_dir “ • [interaction_file_type] Write after a space the complete name of the input file to be used and after another space the • name of the directory where the output file will appear. Example: • home/dpuiu/MY_SOFTWARE/GRAFMAN/DIP.ECOLI.FULL/Ecoli20041003.txt home/dpuiu/MY_SOFTWARE/ • GRAFMAN/DIP.ECOLI.FULL/. • You have to use the following 5 subdirectories and files of GRAFMAN: • /DIP.CELEGANS.FULL/Celeg20041003.txt • /DIP.DMELANOGASTER.FULL/Dmela20041003.txt • /DIP.ECOLI.FULL/Ecoli20041003.txt • /DIP.HPYLORI.FULL/Dpylo20041003.txt • /DIP.SCEREVISIAE.FULL/Scere20041003.txt • 4. After pressing ENTER you will get some summarized results: • total number of vertices ; total number of edges ; total adjacency ; average vertex degree ; network connectedness; • information index for vertex degree distribution ; total distance; average distance degree; average distance. Put these • numbers in the first column of a comparable table of five organisms, which you have to build: • C. elegans, D. Melanogaster, E. coli, H. pylori, and S. cerevisiae. • Neglect the additional .out files which appear for each of the species in your account directory /home/demo#. • End your Home Assignment by ordering the five organisms, according to their topological parameters: • a) (decreasing) the average vertex degree; b) (decreasing) connectedness; c) (increasing) average distance.

19. Useful References: U. Alon, Biological Networks: The Tinkerer as an Engineer. Science 301, 1866-1867, 2003. D. Bray, Molecular Networks: The Top-Down View. Science 301, 1864-1865, 2003. Useful Software: Cytoscape – available in this Lab PathBlast (www.pathblast.org) Pajek (http://vlado.fmf.uni-lj.si/pub/networks/pajek/) PathWay Assist (ariadnegenomics.com)