Introduction to Bioinformatics

1. C E N T E R F O R I N T E G R A T I V E B I O I N F O R M A T I C S V U Introduction to Bioinformatics Lecture 20 Global network behaviour

2. Networks "The thousands of components of a living cell are dynamically interconnected, so that the cell’s functional properties are ultimately encoded into a complex intracellular web [network] of molecular interactions." "This is perhaps most evident with cellular metabolism, a fully connected biochemical network in which hundreds of metabolic substrates are densely integrated through biochemical reactions." (Ravasz E, et al.)

4. TF Ribosomal proteins

13. (4- 1/(4(4-1)/2) =1/6 How linked up are the direct neighbours of a node considered?

15. Small-world networks A seminal paper, Collective dynamics of "small-world" networks, by Duncan J. Watts and Steven H. Strogatz, which appeared in Nature volume 393, pp. 440-442 (4 June 1998), has attracted considerable attention. One can consider two extremes of networks: The first are regular networks, where "nearby" nodes have large numbers of interconnections, but "distant" nodes have few. The second are random networks, where the nodes are connected at random. Regular networks are highly clustered, i.e., there is a high density of connections between nearby nodes, but have long path lengths, i.e., to go from one distant node to another one must pass through many intermediate nodes. Random networks are highly un-clustered but have short path lengths. This is because the randomness makes it less likely that nearby nodes will have lots of connections, but introduces more links that connect one part of the network to another.

16. Regular and random networks random regular regular complete

17. Making a small world A small-world network can be generated from a regular one by randomly disconnecting a few points and randomly reconnecting them elsewhere. Another way to think of a small world network is that some so-called 'shortcut' links are added to a regular network as shown here: The added links are shortcuts because they allow travel from node (a) to node (b), to occur in only 3 steps, instead of 5 without the shortcuts.

18. Regular, small-world and random networks:Rewiring experiments (Watts and Strogatz, 1998) p is the probability that a randomly chosen connection will be randomly redirected elsewhere (i.e.,p=0 means nothing is changed, leaving the network regular; p=1 means every connection is changed and randomly reconnected, yielding complete randomness). For example, for p = .01, (so that only 1% of the edges in the graph have been randomly changed), the "clustering coefficient" is over 95% of what it would be for a regular graph, but the "characteristic path length" is less than 20% of what it would be for a regular graph.

19. Small-world networks • Network characterisation: • L = characteristic path length • C = clustering coefficient • A small-world network is much more highly clustered than an equally sparse random graph (C >> Crandom), and its characteristic path length L is close to the theoretical minimum shown by a random graph (L ~ Lrandom). • The reason a graph can have small L despite being highly clustered is that a few nodes connecting distant clusters are sufficient to lower L. • Because C changes little as small-worldliness develops, it follows that small-worldliness is a global graph property that cannot be found by studying local graph properties.

20. Small-world networks A network or order (0<p<1 as in earlier slides) can be characterized by the average shortest length L(p) between any two points, and a clustering coefficient C(p) that measures the cliquishness of a typical neighbourhood (a local property). These can be calculated from mathematical simulations and yield the following behavior (Watts and Strogatz):

22. Small-world networks Part of the reason for the interest in the results of Watts and Strogatz is that small-world networks seem to be good models for a wide variety of physical situations. They showed that the power grid for the western U.S. (nodes are power stations, and there is an edge joining two nodes if the power stations are joined by high-voltage transmission lines), the neural network of a nematode worm (nodes are neurons and there is an edge joining two nodes if the neurons are joined by a synapse or gap junction), and the Internet Movie Database (nodes are actors and there is an edge joining two nodes if the actors have appeared in the same movie) all have the characteristics (high clustering coefficient but low characteristic path length) of small-world networks. Intuitively, one can see why small-world networks might provide a good model for a number of situations. For example, people tend to form tight clusters of friends and colleagues (a regular network), but then one person might move from New York to Los Angeles, say, introducing a random edge. The results of Watts and Strogatz then provide an explanation for the empirically observed phenomenon that there often seem to be surprisingly short connections between unrelated people (e.g., you meet a complete stranger on an airplane and soon discover that your sister's best friend went to college with his boss's wife).

23. Small world example: metabolism. • Wagner and Fell (2001) modeled the known reactions of 287 substrates that represent the central routes of energy metabolism and small-molecule building block synthesis in E. coli. This included metabolic sub-pathways such as: • glycolysis • pentose phosphate and Entner-Doudoro pathways • glycogen metabolism • acetate production • glyoxalate and anaplerotic reactions • tricarboxylic acid cycle • oxidative phosphorylation • amino acid and polyamine biosynthesis • nucleotide and nucleoside biosynthesis • folate synthesis and 1-carbon metabolism • glycerol 3-phosphate and membrane lipids • riboflavin • coenzyme A • NAD(P) • porphyrins, haem and sirohaem • lipopolysaccharides and murein • pyrophosphate metabolism • transport reactions • glycerol 3-phosphateproduction • isoprenoid biosynthesis and quinone biosynthesis • These sub-pathways form a network because some compounds are part of more than one pathway and because most of them include common components such as ATP and NADP. • Thegraphs on the left show that considering either reactants or substrates, the clustering coefficient C>>Crandom, and the length coefficient L is near that of Lrandom, characteristics of a small world system. random Wagner A, Fell D (2001) The small world inside large metabolic networks. Proc. R. Soc. London Ser. B 268, 1803-1810.

24. Scale-free Networks Using a Web crawler, physicist Albert-Laszlo Barabasi and his colleagues at the University of Notre Dame in Indiana in 1998 mapped the connectedness of the Web. They were surprised to find that the structure of the Web didn't conform to the then-accepted model of random connectivity. Instead, their experiment yielded a connectivity map that they christened "scale-free." • Often small-world networks are also scale-free. • Ina scale-free network the characteristic clustering is maintained even as the networks themselves grow arbitrarily large.

25. Scale-free Networks • In any real network some nodes are more highly connected than others. • P(k) is the proportion of nodes that have k-links. • For large, random graphs only a few nodes have a very small k and only very few have a very large k, leading to a bell-shaped Poisson distribution: Scale-free networks fall off more slowly and are more highly skewed than random ones due to the combination of small-world local highly connected neighborhoods and more 'shortcuts' than would be expected by chance. Scale-free networks are governed by a power law of the form: P(k) ~ k-

26. Scale-free Networks Because of the P(k) ~ k-power law relationship, a log-log plot of P(k) versus k gives a straight line of slope - :  Some networks, especially small-world networks of modest size do not follow a power law, but are exponential. This point can be significant when trying to understand the rules that underlie the network.

29. Comparing Random and Scale-Free DistributionIn the random network (right), the five nodes with the most links (in red) are connected to only 27% of all nodes (green). In the scale-free network (left), the five most connected nodes (red), often called hubs, are connected to 60% of all nodes (green).

30. Scale-free Networks • Barabasi and his team first studied the internet and discovered scale-free network behaviour • Since then, this has been observed for example for power grids, stock market, cancerous cells, and sexually transmitted diseases • From random network models, the idea was that large networks would hardly have any well-connected nodes. Although not all nodes in a random network would be connected to the same degree, most would have a number of connections hovering around a small, average value. Also, as a randomly distributed network grows, the relative number of very connected nodes decreases.

31. Scale-free Networks • Scale-free networks include many "very connected" nodes, hubs of connectivity that shape the way the network operates. The ratio of very connected nodes to the number of nodes in the rest of the network remains constant as the network changes in size. • Because of these differences, random and scale-free networks behave differently as they break down. The connectedness of a randomly distributed network decays steadily as nodes fail, slowly breaking into smaller, separate domains that are unable to communicate. • Scale-free networks are more robust, but in a special way • Scale-free networks can have small-world characteristics, as can randomly connected networks (but see the earlier experiment for small-world networks)

32. Scale Free Network •Hubs, highly connected nodes, bring together different parts of the network • Rubustness: Removing random nodes have little effect • Low attack resistance: Removing a hub is lethal. Random Network • No hubs • Low robustness • Low attack resistance

33. Scale-free Networks Epidemiologists are also pondering the significance of scale-free connectivity. Until now, it has been accepted that stopping sexually transmitted diseases requires reaching or immunizing a large proportion of the population; most contacts will be safe, and the disease will no longer spread. But if societies of people include the very connected individuals of scale-free networks—individuals who have sex lives that are quantitatively different from those of their peers—then health offensives will fail unless they target these individuals. These individuals will propagate the disease no matter how many of their more subdued neighbors are immunized. Now consider the following: Geographic connectivity of Internet nodes is scale-free, the number of links on Web pages is scale-free, Web users belong to interest groups that are connected in a scale-free way, and e-mails propagate in a scale-free way. Barabasi's model of the Internet tells us that stopping a computer virus from spreading requires that we focus on protecting the hubs.

36. 14-3-3 subtypes (paralogs) 14-3-3 paralogs (black) have evolved to binding different partners (grey) but still share MARK3 as binding partner Schematic representation of co-immunoprecipitation studies performed with anti- MARK (microtubule affinity-regulating kinase) antibodies. The strength of the interactions is indicated by the thickness of the arrows (after (2) .

37. …connect preferentially to a hub

38. Preferential attachment • Hub protein characteristics: • Multiple binding sites • Promiscuous binding • Non-specific binding …connect preferentially to a hub

40. Network motifs • Different Motifs indifferent processes • • Observation: more interconnectedmotifs are moreconserved

46. Robustness of the biodegradation network against perturbations is tested here by removing 200 edges randomly (simulating each time that the enzyme catalysing the reaction step has mutated) (A) For each connection lost (red line), 1.6 compounds lose their pathway to the Central Metabolism (CM). (B) However, the increase in the average pathway length to the CM for the remaining compounds is small The biodegradation network appears to be less tolerant to perturbations than metabolic networks (Jeong et al., 2000)

47. Preferential attachment in biodegradation networks New degradable compounds are observed to attach prefentially to hubs close to (or in) the Central Metabolism

48. The “Matchmaker” 14-3-3 family • Massively interacting protein family (the PPI champions) by means of various binding modes • Involved in many essential cell processes • Occurs throughout kingdom of life • Various numbers of isoforms in different organisms (7 in human)

49. 14-3-3 dimer structure

50. 14-3-3 network (hub?) promotion by binding and bringing together two different proteins