Introduction to Bioinformatics Lecture 20 Global network behaviour C E N T 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 E

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.)

TF Ribosomal proteins

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

A seminal paper, Collective dynamics of "small-world" networks, by Duncan J. Watts and Steven H. Strogatz, which appeared in Nature volume 393, pp (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. Small-world networks

Regular and random networks randomregularregular complete

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.

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.

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.

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):

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). Small-world networks

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. The graphs 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. Wagner A, Fell D (2001) The small world inside large metabolic networks. Proc. R. Soc. London Ser. B 268, random

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." Scale-free Networks Often small-world networks are also scale-free. In a scale-free network the characteristic clustering is maintained even as the networks themselves grow arbitrarily large.

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 - 

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.

Comparing Random and Scale-Free Distribution In 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).

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. 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) Scale-free Networks

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

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 s 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.

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) subtypes (paralogs) paralogs (black) have evolved to binding different partners (grey) but still share MARK3 as binding partner

…connect preferentially to a hub

Preferential attachment Hub protein characteristics: Multiple binding sites Promiscuous binding Non-specific binding

Network motifs Different Motifs in different processes Observation: more interconnected motifs are more conserved

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)

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

The “Matchmaker” 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)

dimer structure

network (hub?) promotion by binding and bringing together two different proteins

Janus-faced character of s Identified (co)-targets fall in opposing classes: they seem to both cause and work against cancer... Clear color: actin growth, pro- apoptotic, stimulation of transcription, nuclear import, neuron development. Hatched: opposing functions. 100% = 56 proteins (De Boer & Jimenez, unpubl. data.).

Targets of proteins implicated in tumor development. Arrows indicate positive effects while sticks represent inhibitory effects. Targets involved in primary apoptosis and cell cycle control are not shown due to space limitations.

Role of proteins in apoptosis proteins inhibit apoptosis through multiple mechanisms: sequestration and control of subcellular localization of phosphorylated and nonphosphorylated pro- and anti-apoptotic proteins. What is the role of the subtypes? Modularity?

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 subtypes (paralogs) Different subtypes display different binding modes, reflecting pronounced divergent evolution after duplication subtypes , ,  and 

How can we get the edges (connections) of the cellular networks? We can predict functions of genes or proteins so we know where they would fit in a metabolic network There are also techniques to predict whether two proteins interact, either functionally (e.g. they are involved in a two-step metabolic process) or directly physically (e.g. are together in a protein complex) Protein Interaction Prediction

The state of the art – it’s not complete Many genes are not annotated, and many more are partially or erroneously annotated. Given a genome which is partially annotated at best, how do we fill in the blanks? Of each sequenced genome, 20%-50% of the functions of proteins encoded by the genomes remains unknown! How then do we build a reasonably complete networks when the parts list is so incomplete? Protein Function Prediction

Protein interaction prediction through co-evolution FALSE NEGATIVES: need many organisms relies on known orthologous relationships FALSE POSITIVES Phylogenetic signals at the organsism level Functional interaction may not mean physical interaction

Phylogenetic profile analysis (recap) Function prediction of genes based on “guilt-by- association” – a non-homologous approach The phylogenetic profile of a protein is a string that encodes the presence or absence of the protein in every sequenced genome Because proteins that participate in a common structural complex or metabolic pathway are likely to co-evolve, the phylogenetic profiles of such proteins are often ``similar'‘ This means that such proteins have a good chance of being physically or metabolically connected

Phylogenetic profile analysis (Recap) Phylogenetic profile (against N genomes) –For each gene X in a target genome (e.g., E coli), build a phylogenetic profile as follows –If gene X has a homolog in genome #i, the ith bit of X’s phylogenetic profile is “1” otherwise it is “0”

Phylogenetic profile analysis (recap) Example – phylogenetic profiles based on 60 genomes orf1034: orf1036: orf1037: orf1038: orf1039: orf104: orf1040: orf1041: orf1042: orf1043: orf1044: orf1045: orf1046: orf1047: orf105: orf1054: Genes with similar phylogenetic profiles have related functions or functionally linked – D Eisenberg and colleagues (1999) By correlating the rows (open reading frames (ORF) or genes) you find out about joint presence or absence of genes: this is a signal for a functional connection gene genome

Phylogenetic profile analysis Evolution suppresses unnecessary proteins Once a member of an interaction is lost, the partner is likely to be lost as well

Phylogenetic profile analysis (recap) Phylogenetic profiles contain great amount of functional information Phlylogenetic profile analysis can be used to distinguish orthologous genes from paralogous genes Subcellular localization: 361 yeast nucleus-encoded mitochondrial proteins are identified at 50% accuracy with 58% coverage through phylogenetic profile analysis Functional complementarity: By examining inverse phylogenetic profiles, one can find functionally complementary genes that have evolved through one of several mechanisms of convergent evolution.

Prediction of protein-protein interactions (recap) Rosetta stone method Gene fusion is the an effective method for prediction of protein-protein interactions –If proteins A and B are homologous to two domains of a protein C, A and B are predicted to have interaction Though gene-fusion has low prediction coverage, it false-positive rate is low (high specificity) A B C

Gene (domain) fusion example Vertebrates have a multi-enzyme protein (GARs- AIRs-GARt) comprising the enzymes GAR synthetase (GARs), AIR synthetase (AIRs), and GAR transformylase (GARt). In insects, the polypeptide appears as GARs- (AIRs) 2 -GARt. In yeast, GARs-AIRs is encoded separately from GARt In bacteria each domain is encoded separately (Henikoff et al., 1997). GAR: glycinamide ribonucleotide AIR: aminoimidazole ribonucleotide

Protein interaction database (recap) There are numerous databases of protein-protein interactions DIP is a popular protein-protein interaction database The DIP database catalogs experimentally determined interactions between proteins. It combines information from a variety of sources to create a single, consistent set of protein-protein interactions.

Protein interaction databases (Recap) BIND - Biomolecular Interaction Network Database DIP - Database of Interacting Proteins PIM – Hybrigenics PathCalling Yeast Interaction Database MINT - a Molecular Interactions Database GRID - The General Repository for Interaction Datasets InterPreTS - protein interaction prediction through tertiary structure STRING - predicted functional associations among genes/proteins Mammalian protein-protein interaction database (PPI) InterDom - database of putative interacting protein domains FusionDB - database of bacterial and archaeal gene fusion events IntAct Project The Human Protein Interaction Database (HPID) ADVICE - Automated Detection and Validation of Interaction by Co-evolution InterWeaver - protein interaction reports with online evidence PathBLAST - alignment of protein interaction networks ClusPro - a fully automated algorithm for protein-protein docking HPRD - Human Protein Reference Database

Protein interaction database (recap)

Network of protein interactions and predicted functional links involving silencing information regulator (SIR) proteins. Filled circles represent proteins of known function; open circles represent proteins of unknown function, represented only by their Saccharomyces genome sequence numbers ( Solid lines show experimentally determined interactions, as summarized in the Database of Interacting Proteins 19 ( mbi.ucla.edu). Dashed lines show functional links predicted by the Rosetta Stone method 12. Dotted lines show functional links predicted by phylogenetic profiles 16. Some predicted links are omitted for clarity. Recap

Network of predicted functional linkages involving the yeast prion protein 20 Sup35. The dashed line shows the only experimentally determined interaction. The other functional links were calculated from genome and expression data 11 by a combination of methods, including phylogenetic profiles, Rosetta stone linkages and mRNA expression. Linkages predicted by more than one method, and hence particularly reliable, are shown by heavy lines. Adapted from ref. 11. Recap

STRING - predicted functional associations among genes/proteins STRING is a database of predicted functional associations among genes/proteins. Genes of similar function tend to be maintained in close neighborhood, tend to be present or absent together, i.e. to have the same phylogenetic occurrence, and can sometimes be found fused into a single gene encoding a combined polypeptide. STRING integrates this information from as many genomes as possible to predict functional links between proteins. Berend Snel en Martijn Huynen (RUN) and the group of Peer Bork (EMBL, Heidelberg) Recap

STRING - predicted functional associations among genes/proteins STRING is a database of known and predicted protein- protein interactions. The interactions include direct (physical) and indirect (functional) associations; they are derived from four sources: 1.Genomic Context (Synteny) 2.High-throughput Experiments 3.(Conserved) Co-expression 4.Previous Knowledge STRING quantitatively integrates interaction data from these sources for a large number of organisms, and transfers information between these organisms where applicable. The database currently contains proteins in 179 species Recap

STRING - predicted functional associations among genes/proteins Conserved Neighborhood This view shows runs of genes that occur repeatedly in close neighborhood in (prokaryotic) genomes. Genes located together in a run are linked with a black line (maximum allowed intergenic distance is 300 bp). Note that if there are multiple runs for a given species, these are separated by white space. If there are other genes in the run that are below the current score threshold, they are drawn as small white triangles. Gene fusion occurences are also drawn, but only if they are present in a run. Recap

STRING - predicted functional associations among genes/proteins Genes clustered in a genomic region are likely to interact co-ordinated expression co-ordinated gene gains/losses Recap

Understand regular, random, small-world and scale-free networks –Know and understand observations on path length, clustering coefficients, etc. Know and understand interaction prediction using phylogenetic co-evolution, phylogenetic profiling, Rosetta stone methods and the STRING server Comparing and overlaying various networks (e.g. regulation, signalling, metabolic, PPI) and studying evolutionary conservation at these network levels is one of the current grand challenges, and will be crucially important for a systems–based approach to (intra)cellular behaviour. Wrapping up