Intracellular Networks

Transcription

1 C E N T R E 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 Intracellular Networks (2) Intracellular Network Behaviour Slides on: 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 1

2 Small-world networks A recent 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. Motifs 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. Regular and random networks Regular, small-world and random networks: Rewiring experiments (Watts and Strogatz, 1998) random regular regular complete 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 and networks 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 socalled '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. 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. 2

3 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): Small-world networks Part of the reason for the interest in the results of Watts and Strogatz is that smallworld 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 highvoltage 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 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 random WagnerA, Fell D (2001) The small world inside large metabolic networks. Proc. R. Soc. London Ser. B 268, 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. 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." 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 a few have a very large k, leading to a bell-shaped Poisson distribution: 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 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 -γ 3

4 Because of the P(k) ~ k -γ power law relationship, a log-log plot of P(k) versus k gives a straight line of slope -γ : Some networks, especially smallworld 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. Hierarchical networks C(k) ~ k 1 a straight line of slope l on a log log plot (see figure, part Cc). A hierarchical architecture implies that sparsely connected nodes are part of highly clustered areas, with communication between the different highly clustered neighbourhoods being maintained by a few hubs Hierarchical networks Iterative construction leading to a hierarchical network. Starting from a fully connected cluster of five nodes shown in (a) (note that the diagonal nodes are also connected links not visible), we create four identical replicas, connecting the peripheral nodes of each cluster to the central node of the original cluster, obtaining a network of N=25 nodes (b). In the next step, we create four replicas of the obtained cluster, and connect the peripheral nodes again, as shown in (c), to the central node of the original module, obtaining a N=125-node network. This process can be continued indefinitely. 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). Before discovering scale-free networks, Barabasi and his team had been doing work that modeled surfaces in terms of fractals, which are also scale-free. Their discoveries about networks have been found to have implications well beyond the Internet; the notion of scale-free networks has turned the study of a number of fields upside down. Scale-free networks have been used to explain behaviors as diverse as those of power grids, the stock market and cancerous cells, as well as the dispersal of sexually transmitted diseases. Put simply, the nodes of a scale-free network aren't randomly or evenly connected. 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. In contrast, random connectivity distributions the kinds of models used to study networks like the Internet before Barabasi and his team made their observation predicted that there would be no well-connected nodes, or that there would be so few that they would be statistically insignificant. Although not all nodes in that kind of 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. 4

5 The ramifications of this difference between the two types of networks are significant, but it's worth pointing out that both scale-free and randomly distributed networks can be what are called "small world" networks. That means it doesn't take many hops to get from one node to another the science behind the notion that there are only six degrees of separation between any two people in the world. So, in both scale-free and randomly distributed networks, with or without very connected nodes, it may not take many hops for a node to make a connection with another node. There's a good chance, though, that in a scale-free network, many transactions would be funneled through one of the well-connected hub nodes - one like Google s Web portal. Because of these differences, the two types of 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. Resists Random Failure Scale-free networks, on the other hand, may show almost no degradation as random nodes fail. With their very connected nodes, which are statistically unlikely to fail under random conditions, connectivity in the network is maintained. It takes quite a lot of random failure before the hubs are wiped out, and only then does the network stop working. (Of course, there's always the possibility that the very connected nodes would be the first to go.) In a targeted attack, in which failures aren't random but are the result of mischief, or worse, directed at hubs, the scale-free network fails catastrophically. Take out the very connected nodes, and the whole network stops functioning. In these days of concern about cyber attacks on the critical infrastructure, whether the nodes on the network in question are randomly distributed or are scale-free makes a big difference. 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. Scale Free Network Hubs, highly connected nodes, bring together different parts of the network Rubustness: Removing random nodes has little effect Low attack resistance: Removing a hub is lethal (PPI: centrality-lethality rule, see later). Random Network No hubs Low robustness Low attack resistance 5

6 subtypes (paralogs) 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). connect preferentially to a hub Preferential attachment Hub protein characteristics: Multiple binding sites Promiscuous binding Non-specific binding connect preferentially to a hub Hub proteins in yeast Genome-wide studies show that deletion of a hub protein is more likely to be lethal than deletion of a non-hub protein, a phenomenon known as the centrality-lethality rule. [..] network analysis suggests that the centrality-lethality rule is unrelated to the network architecture, but is explained by the simple fact that hubs have large numbers of PPIs, therefore high probabilities of engaging in essential PPIs He X, Zhang J (2006) Why do hubs tend to be essential in protein networks? PLoS Genet 2(6):e88 Network motifs Network motifs Types of feed-forward loops Transcription regulation networks control the expression of genes. The transcription networks of well-studied microorganisms appear to be made up of a small set of recurring regulation patterns, called network motifs. The same network motifs have recently been found in diverse organisms from bacteria to humans, suggesting that they serve as basic building blocks of transcription networks. Uri Alon, Nature 8, ;

7 Network motifs Different Motifs in different processes More interconnected motifs are more conserved Network Dynamics Party hubs: always the same partners (same time and space) Date hubs: different partners in different conditions (different time and/or space) Difference is important for inter-process communication Network Dynamics Party hubs: always the same partners (same time and space) Multiple small binding surfaces Date hubs: different partners in different conditions (different time and/or space) A single (or perhaps a few) large (and less specific) binding surfaces s Date hubs: large binding surfaces / Party hubs: small binding surfaces Need to create new binding interfaces 7

8 A network example from Meta-genomics Ecogenomics soil ecosystems A virtual network where species are nodes and (groups of) chemical compounds are exchanged between the nodes Preferential attachment in biodegradation networks New degradable compounds are observed to attach preferentially to hubs close to (or in) the Central Metabolism Valencia and co-workers 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 8

9 network (hub?) promotion by binding and bringing together two different proteins Janus-faced character of s Identified (co)-targets fall in opposing classes. Clear color: actin growth, proapoptotic, 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? subtypes (paralogs) Different subtypes display different binding modes, reflecting pronounced divergent evolution after duplication 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 ζ,β,γ and η Phylogenetic profile analysis n Function prediction of genes based on guilt-byassociation a non-homologous approach n The phylogenetic profile of a protein is a string that encodes the presence or absence of the protein in every sequenced genome n 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'' 9

10 Phylogenetic profile analysis Phylogenetic profile analysis Evolution suppresses unnecessary proteins Once a member of an interaction is lost, the partner is likely to be lost as well n 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 i th bit of X s phylogenetic profile is 1, otherwise it is 0 gene Phylogenetic profile analysis n Example phylogenetic profiles based on 60 genomes genome orf1034: orf1036: orf1037: orf1038: orf1039: orf104: orf1040: orf1041: orf1042: orf1043: orf1044: orf1045: orf1046: orf1047: orf105: orf1054: 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 Genes with similar phylogenetic profiles have related functions or functionally linked D Eisenberg and colleagues (1999) Phylogenetic profile analysis n Phylogenetic profiles contain great amount of functional information n Phlylogenetic profile analysis can be used to distinguish orthologous genes from paralogous genes n Subcellular localization: 361 yeast nucleus-encoded mitochondrial proteins are identified at 50% accuracy with 58% coverage through phylogenetic profile analysis n 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 Rosetta stone n 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 A Though gene-fusion has low prediction coverage, it false-positive rate is low (high specificity) B C Two-domain protein Gene (domain) fusion example n Vertebrates have a multi-enzyme protein (GARs- AIRs-GARt) comprising the enzymes GAR synthetase (GARs), AIR synthetase (AIRs), and GAR transformylase (GARt). n In insects, the polypeptide appears as GARs- (AIRs) 2 -GARt. n In yeast, GARs-AIRs is encoded separately from GARt n In bacteria each domain is encoded separately (Henikoff et al., 1997). GAR: glycinamide ribonucleotide AIR: aminoimidazole ribonucleotide 10

11 Protein interaction prediction through coevolution Protein interaction database n There are numerous databases of protein-protein interactions n DIP is a popular protein-protein interaction database FALSE NEGATIVES: need many organisms relies on known orthologous relationships FALSE POSITIVES Phylogenetic signals at the organismal level Functional interaction may not mean physical interaction 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 Protein interaction database 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 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 ( 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. 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

12 STRING - predicted functional associations among genes/proteins n STRING is a database of predicted functional associations among genes/proteins. n 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. n 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) STRING - predicted functional associations among genes/proteins STRING is a database of known and predicted proteinprotein 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 STRING - predicted functional associations among genes/proteins Conserved Neighborhood STRING - predicted functional associations among genes/proteins Gene clusters in a genomic region are likely to interact co-ordinated expression 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. co-ordinated gene gains/losses Functional inference at systems level Functional inference at systems level n Function prediction of individual genes could be made in the context of biological pathways/networks n KEGG is database of biological pathways and networks n Example phob is predicted to be a transcription regulator and it regulates all the genes in the pho-regulon (a group of coregulated operons); and within this regulon, gene A is interacting with gene B, etc. phob 12

13 Functional inference at systems level Functional inference at systems level Consequence of evolution n Notion of comparative analysis (Darwin) n What you know about one species might be transferable to another, for example from mouse to human n Provides a framework to do multi-level large-scale analysis of the genomics data plethora Functional inference at systems level n By doing homologous search, one can map a known biological pathway in one organism to another one; hence predict gene functions in the context of biological pathways/networks n Mapping networks of multiple organisms and looking at the evolutionary conservation allows the delineation of modules and essential parts of the networks Network Evolution The citric-acid cycle Human Yeast This pathway diagram shows a comparison of pathways in (left) Homo sapiens (human) and (right) Saccharomyces cerevisiae (baker s yeast). Changes in controlling enzymes (square boxes in red) and the pathway itself have occurred (yeast has one altered ( overtaking ) path in the graph) 13

14 The citric-acid cycle The citric-acid cycle M. A. Huynen, T. Dandekar and P. Bork ``Variation and evolution of the citric acid cycle: a genomic approach'' Trends Microbiol, 7, (1999) Fig. 1. (a) A graphical representation of the reactions of the citric-acid cycle (CAC), including the connections with pyruvate and phosphoenolpyruvate, and the glyoxylate shunt. When there are two enzymes that are not homologous to each other but that catalyse the same reaction (nonhomologous gene displacement), one is marked with a solid line and the other with a dashed line. The oxidative direction is clockwise. The enzymes with their EC numbers are as follows: 1, citrate synthase ( ); 2, aconitase ( ); 3, isocitrate dehydrogenase ( ); 4, 2-ketoglutarate dehydrogenase (solid line; and ) and 2- ketoglutarate ferredoxin oxidoreductase (dashed line; ); 5, succinyl- CoA synthetase (solid line; ) or succinyl-coa acetoacetate-coa transferase (dashed line; ); 6, succinate dehydrogenase or fumarate reductase ( ); 7, fumarase ( ) class I (dashed line) and class II (solid line); 8, bacterial-type malate dehydrogenase (solid line) or archaeal-type malate dehydrogenase (dashed line) ( ); 9, isocitrate lyase ( ); 10, malate synthase ( ); 11, phosphoenolpyruvate carboxykinase ( ) or phosphoenolpyruvate carboxylase ( ); 12, malic enzyme ( or ); 13, pyruvate carboxylase or oxaloacetate decarboxylase ( ); 14, pyruvate dehydrogenase (solid line; and ) and pyruvate ferredoxin oxidoreductase (dashed line; ). b) Individual species might not have a complete CAC. This diagram shows the genes for the CAC for each unicellular species for which a genome sequence has been published, together with the phylogeny of the species. The distance-based phylogeny was constructed using the fraction of genes shared between genomes as a similarity criterion. The major kingdoms of life are indicated in red (Archaea), blue (Bacteria) and yellow (Eukarya). Question marks represent reactions for which there is biochemical evidence in the species itself or in a related species but for which no genes could be found. Genes that lie in a single operon are shown in the same color. Genes were assumed to be located in a single operon when they were transcribed in the same direction and the stretches of non-coding DNA separating them were less than 50 nucleotides in length. M. A. Huynen, T. Dandekar and P. Bork ``Variation and evolution of the citric acid cycle: a genomic approach'' Trends Microbiol, 7, (1999) Wrapping up n Prim s algorithm for MST and derived clustering protocol n Regular, random, small-world and scale-free networks n Evolution of topology and dynamics of biological networks, e.g. duplication, preferential attachment, party/date hub proteins,.. n We have seen a number of ways to infer a putative function for a protein sequence (e.g. guilt by association): PPI prediction is a special case and you should know the related methods n Phylogenetic signal to predict PPI (co-evolution) n To gain confidence, it is important to combine as many different prediction protocols as possible (the STRING server is an example of this) n Comparing and overlaying various networks (e.g. regulation, signalling, metabolic, PPI) and studying 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. 14