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Biological Networks Feng Luo

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**Biological Networks Biological Systems Biological Networks**

Made of many non-identical elements interact each other with diverse ways. Biological Networks Biological networks as framework for the study of biological systems

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Why Study Networks? It is increasingly recognized that complex systems cannot be described in a reductionist view. Understanding the behavior of such systems starts with understanding the topology of the corresponding network. Topological information is fundamental in constructing realistic models for the function of the network. We saw the complexity and volume of data sets we are dealing with. It is impossible to analysis or manage their properties and underlying principles due to their complexity.

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**Shortest Path/Geodesic distance**

Graph Terminology Node Edge Directed/Undirected Degree Shortest Path/Geodesic distance Neighborhood Subgraph Complete Graph Clique Degree Distribution Hubs

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**Type of Biological Networks**

Protein interaction networks Gene regulatory networks Metabolism networks Gene co-expression networks Signal transduction networks Genetic interaction networks

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**P. Uetz, et al. Nature, 2000; Ito et al., PNAS, 2001; …**

Protein Interactions Y2H method to detect interaction Bait and Prey protein P. Uetz, et al. Nature, 2000; Ito et al., PNAS, 2001; …

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**Protein Interaction Network**

Nodes: proteins Links: physical interactions (Jeong et al., 2001)

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**Metabolic network (KEGG)**

Graph Node: Object e.g. Chemical compound Edge: Relation between objects e.g. Chemical reaction

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**Nodes: chemicals (substrates)**

Links: chem. reaction Metabolic Network

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Metabolic Network Nodes: chemicals (substrates) Links: chemistry reactions (Ravasz et al., 2002)

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**Gene Regulation Proteins are encoded by the DNA of the organism.**

Proteins regulate expression of other proteins by interacting with the DNA protein protein protein Inducer (external signal) DNA promoter region ACCGTTGCAT Coding region

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**Activators increase gene production**

X Y Activator X No transcription gene Y X binding site Y Y Y Y Sx X X* INCREASED TRANSCRIPTION X* Bound activator

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**Repressors decrease gene production**

Bound repressor X Y Sx X X* No transcription X* Bound repressor Y Y Unbound repressor Y Y X

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**Gene Regulatory Networks**

Nodes are proteins (or the genes that encode them) X Y

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**The gene regulatory network of E. coli**

Shen-Orr et. al. Nature Genetics 2002 shallow network, few long cascades. modular compact in-degree, scale free outdegree (promoter size limitation)

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**Gene regulatory networks**

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**CoExpression Network Revealed from Yeast Cell Cycle Data**

1. Protein fate 2. Amino acid synthesis 3. Galactose metabolism 4. Protein glycosylation and transport Cell wall organization 5. Amino acid metabolism 6. Mating 7. Glucogenesis 8. unknown 9. Cell cycle regulation Y’-cluster Histone 11. Cell differentiation 12. Protein synthesis 10. Stress response 13. Cell wall 14. Energy transport 15. Ribosomal biogenesis Ribosomal proteins Mitochondrion Protein degradation Yeast cell cycle microarray data (Spellman et al., 1998)

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**Signal transduction networks**

(BD BioScience) Elements inside same module often involved in same biological process. This separation can originate from spatial localization or from chemical specificity. Insulation allows the cell to carry out many diverse reactions without cross-talk that would harm the cell. Connectivity allows one function to influence another. Functional modules reflect the critical level of biological organization. A modular system can reuse existing, well-tested modules.

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**Properties of Biological Networks**

Scale Free Small world Hierarchical Modular Robust Motif

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**Scale-Free Network Degree of a node P(k) Scale-free network**

The number of adjacent nodes P(k) Degree distribution Frequency of nodes with degree k Scale-free network P(k) follows power law Different from random networks

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**Connect with probability p**

Erdös-Rényi model (1960) Connect with probability p p=1/6 N=10 k ~ 1.5 Pál Erdös ( ) Poisson distribution - Democratic - Random

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**SCALE-FREE NETWORKS (1) The number of nodes (N) is NOT fixed.**

Networks continuously expand by the addition of new nodes Examples: WWW : addition of new documents Citation : publication of new papers (2) The attachment is NOT uniform. A node is linked with higher probability to a node that already has a large number of links. Examples : WWW : new documents link to well known sites (CNN, YAHOO, NewYork Times, etc) Citation : well cited papers are more likely to be cited again

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**Scale-free model P(k) ~k-3**

(1) GROWTH : At every timestep we add a new node with m edges (connected to the nodes already present in the system). (2) PREFERENTIAL ATTACHMENT : The probability Π that a new node will be connected to node i depends on the connectivity ki of that node P(k) ~k-3 A.-L.Barabási & R. Albert, Science, 1999

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**Metabolic network Archaea Bacteria Eukaryotes**

Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 2000

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**Topology of the protein network**

H. Jeong, S.P. Mason, A.-L. Barabasi & Z.N. Oltvai, Nature, 2001

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Nature (2000)

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p53 network (mammals)

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**Local clustering Clustering: My friends will likely know each other!**

Networks are clustered [large C]

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**Clustering Coefficient**

The density of the network surrounding node I, characterized as the number of triangles through I. Related to network modularity k: neighbors of I nI: edges between node I’s neighbors The center node has 8 (grey) neighbors There are 4 edges between the neighbors C = 4 /((8*(8-1)) /2)= 4/28 = 1/7

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**Shortest-Path between nodes**

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**Shortest-Path between nodes**

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Small-world Network Every node can be reached from every other by a small number of hops or steps High clustering coefficient and low mean-shortest path length Random graphs don’t necessarily have high clustering coefficients Social networks, the Internet, and biological networks all exhibit small-world network characteristics

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**Modularity in Cellular Networks**

Hypothesis: Biological function are carried by discrete functional modules. Hartwell, L.-H., Hopfield, J. J., Leibler, S., & Murray, A. W., Nature, 1999. Traditional view of modularity:

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**Modular vs. Scale-free Topology**

(b)

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**How do we know that metabolic networks are modular?**

clustering coefficient is the same across metabolic networks in different species with the same substrate corresponding randomized scale free network: C(N) ~ N-0.75 (simulation, no analytical result) bacteria archaea (extreme-environment single cell organisms) eukaryotes (plants, animals, fungi, protists) scale free network of the same size

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**Real Networks Have a Hierarchical Topology**

What does it mean? Many highly connected small clusters combine into few larger but less connected clusters even larger and even less connected clusters The degree of clustering follows:

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**2. Clustering coefficient 3. Clustering coefficient scales**

Properties of hierarchical networks 1. Scale-free 2. Clustering coefficient independent of N 3. Clustering coefficient scales

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**Hierarchy in biological systems**

Metabolic networks Protein networks

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**Can we identify the modules?**

topological overlap J(i,j): # of nodes both i and j link to; +1 if there is a direct (i,j) link

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**Modules in the E. coli metabolism**

E. Ravasz et al., Science, 2002

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**Fraction of removed nodes, f**

Robustness Complex systems maintain their basic functions even under errors and failures (cell mutations; Internet router breakdowns) fc 1 Fraction of removed nodes, f S node failure

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**Robustness of scale-free networks**

3 : fc=1 (R. Cohen et. al., PRL, 2000) Failures Topological error tolerance 1 fc Attacks R. Albert et.al. Nature, 2000 S f 1

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**Attack Tolerance Max Cluster Size Path Length**

Max Cluster size changes accoeding to removing nodes Random network is vulnerable for random attacks, power law net is not. Random attack vs targeted atack

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**- lethality and topological position -**

Yeast protein network - lethality and topological position - Highly connected proteins are more essential (lethal)... H. Jeong, S.P. Mason, A.-L. Barabasi &Z.N. Oltvai, Nature, 2001

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Network Motifs

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Network motifs Comparable to electronic circuit types (i.e., logic gates) The notion of motif, widely used for sequence analysis, is generalizable to the level of networks. Network Motifs are defined as recurring patterns of interconnections found within networks at frequencies much higher than those found in randomized networks.

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**Random vs designed/evolved features**

Large networks may contain information about design principles and/or evolution of the complex system Which features are there for a reason? Design principles (e.g. feed-forward loops) Constraints (e.g. the all nodes on the Internet must be connected to each other) Evolution, growth dynamics (e.g. network growth is mainly due to gene duplication) All proteins are probably interconnected thru at least one part of the DNA – protein – metabolite network

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Network motifs Uri Alon et al : “Network Motifs: Simple building Blocks of Complex Networks”; Science, 2002. Different networks were found to have different motif abundances. The motifs reflect the underlying processes that generate each type of network.

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**Motifs in the network motif to be found graph**

motif matches in the target graph

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**Detecting network motifs**

There are three main tasks in detecting network motifs: (1) Generating an ensemble of proper random networks (2) Counting the subgraphs in the real network and in random networks (3) Search for graphs that appear disproportionately in one list vs. the other

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**All 3-node connected subgraphs**

13 different isomorphic types of 3-node connected subgraph There are: node subgraphs, 9,364 5-node subgraphs, etc…… In order to detect network motifs, one needs to count the number of appearances of all types of n-node subgraphs in the network as well as in an ensemble of randomized networks. There are many isomorphic types of subgraphs with a given number of nodes

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Motifs detected Two significant motifs appearing numerous times in non-homologous gene systems that perform diverse biological functions

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**S. Wuchty, Z. Oltvai & A.-L. Barabasi, Nature Genetics, 2003**

Motifs II S. Wuchty, Z. Oltvai & A.-L. Barabasi, Nature Genetics, 2003

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**Probabilistic algorithm for subgraph sampling**

The problem : Exhaustive subgraph enumeration complexity scales as # of subgraphs Exponential in subgraph size Infeasible for large networks with hubs Solution : An efficient sampling algorithm

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**Probabilistic algorithm for subgraph sampling**

Instead of examining absolute subgraph counts we define subgraph concentration : Sampling algorithm :

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**Different probabilities of sampling different subgraphs**

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**Weight of each sample corrects for its**

sampling probability P=0.14 W=7 P=0.33 W=3 4 5 1 2 3 6 7

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**Rapid convergence to real concentration**

Kashtan et. al. Bioinformatics 2004

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**Runtime almost independent of network size**

Kashtan et. al. Bioinformatics 2004

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