Properties of Biological Networks

Transcription

1 Properties of Biological Networks presented by: Ola Hamud June 12, 2013 Supervisor: Prof. Ron Pinter Based on: NETWORK BIOLOGY: UNDERSTANDING THE CELL S FUNCTIONAL ORGANIZATION By Albert-László Barabási & Zoltán N. Oltvai Nature Reviews Genetics, 2004 An Introduction to Systems Biology: Design Principles of Biological Circuits By Uri Alon

2 General background on biological research Introduction A key aim of post-genomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. We will understand how, and develop basic understanding of the properties of biological cellular networks.

3 Shifting point in biological research Reductionism individual cellular components and their functions. complex interactions between the cell s numerous constituents, such as proteins, DNA, RNA and small molecules. Network biology quantifiable tools of network theory offer unforeseen possibilities to understand the cell s internal organization and evolution, fundamentally altering our view of cell biology.

4 Shifting point in biological research net of networks Various types of interaction webs, or networks emerge from the sum of these interactions. None of these networks are independent, instead they form a network of networks that is responsible for the behavior of the cell. challenge figure out how to integrate, map out, model, and understand the topological & dynamical properties of cellular networks.

5 Universality Realization The behavior of most complex systems, from the cell to the Internet, emerges from the orchestrated activity of many components that interact with each other through pairwise interactions. internet Computer Chips society Research has shown that these networks are governed by a few universal laws. Do these same laws apply to biological networks?

6 Basic Network Nomenclature Degree (connectivity) - <k> Directed and undirected graph. High k is a hub. Average degree in undirected graph with L links and N nodes : <k> = 2L/N What is the degree of node A?

7 Basic Network Nomenclature Degree distribution P(k) P(k) is obtained by counting the number of nodes with k links and dividing by N. The degree distribution is used to classify networks, for example: peaked degree distribution The system has a characteristic degree and no hubs. power-law degree distribution few hubs hold together numerous small nodes.

8 Network Basic Network measures Nomenclature Shortest path and mean path length - < l > The shortest path between two nodes is the minimum number of links that must be traversed to travel from one node to the other. The mean path length <l> is the average of the shortest paths between all pairs of nodes. l BA = 1 l AB = 3

9 Network Basic Network measures Nomenclature Clustering Coefficient - <C> The clustering coefficient measures the tendency of nodes to form clusters. If a is connected to b and b is connected to c, then a is connected to c? C i = 2n i /k(k 1) where n i is the number of links connecting the k i neighbors of node i to each other, i.e. C i gives us the number of triangles that go through node i. <C> is the average clustering coefficient. It measures the overall tendency of nodes to form clusters. C(k) is the average clustering coefficient of all nodes with k links.

10 Network Basic Network measures Nomenclature Clustering Coefficient - <C> Example: n A = 1 C i = 2n i /k(k 1) C A = 2 1/5 (5 1) = 2/20 C F = C D = C E = C G = 0

11 Network Basic Network measures Nomenclature General diagnostics Depend on the size of the network : <k> average degree. <l> average length. <C> average clustering coefficient. Independent of the network s size : P(k) degree distribution C(k) average clustering coefficient function. capture a network s generic features, which allows them to be used to classify various networks.

12 Network Architectural measures features of cellular networks Network models Random nodes randomly connected with edges Scale-free lack of any typical node to compare the others Hierarchical similar to scale-free, but forms unique modules (clusters)

13 Network Architectural measures features of cellular networks Random Networks Paul Erdös and Alfréd Rényi, who in 1960 initiated the study of the mathematical properties of random networks. The Erdös Rényi (ER) model of a random network: starts with N nodes (a fixed number of nodes ). connects each pair of nodes with probability p. Results in a graph with approximately pn(n 1)/2 randomly placed links. P(k) follows a Poisson distribution - most nodes have a degree that is close to <k> C(k) is constant. The mean path length <l> ~ log N, which indicates that the network has the small world property (which we will discuss soon)

14 Network Architectural measures features of cellular networks Scale-Free Networks Their feature is the coexistence of nodes of widely different degree (scales), so they could be easily called scale-rich as well. Networks with a power-law degree distribution P k ~ k γ where γ is the degree exponent. For most networks 2 < γ < 3. The smaller γ is, the more important the role of hubs is. When γ > 3, scale-free features disappear and network behaves like a random one. Scale-free networks are characterized by a few hub nodes of high degree, and many nodes of low degree. C(k) is constant, like random networks. <l> ~ log log N, which means it has ultra-small-world property (which we will discuss soon).

15 Network Architectural measures features of cellular networks Hierarchical Networks A hierarchical architecture implies that sparsely connected nodes are part of highly clustered areas, with communication between the clusters being maintained by a few hubs. P(k) follows a power-law degree distribution. C(k) ~k 1, unlike random and scale- free networks.

16 Network Architectural measures features of cellular networks Cellular Networks

17 Network Architectural measures features of cellular networks Cellular Networks Yeast protein interaction Network a few highly connected nodes -hubs hold the network together. The largest cluster, which contains ~78% of all proteins, is shown.

18 Network Architectural measures features of cellular networks Cellular networks are scale-free A key feature of scale-free networks is the presence of hubs First evidence seen in metabolic network Most metabolic substrates participate in only one or two reactions A few participate in dozens (hubs) More evidence in PPI network maps, transcription regulatory networks, and more.

19 The importance of the hubs Small-world effect Random networks have the small world property. Hubs allow for a smaller mean path length. The ultra-small-world effect scale-free networks are ultra small - their path length is much shorter than predicted by the small-world effect. Ultra-small-world effect was first documented for metabolism, where paths of only three to four reactions can link most pairs of metabolites. Everyone in the world knows everyone else through an average chain of relatively few people.

20 The importance of the hubs Assortativity Social networks are assortative Well connected people tend to know each other. Cellular networks are dissassortative Highly connected nodes don t link directly to each other. Hubs tend to link to nodes with small degree why do hubs avoid linking directly to each other? Remains unexplained

21 Network How did measures networks evolve this way? Evolutionary origin of scale-free networks Two fundamental processes have a key role in the development of real networks - Growth process - Preferential attachment Both are jointly responsible for the emergence of the scale-free property in complex networks

22 Network How did measures networks evolve this way? Growth Process new nodes join the system over an extended time period. Preferential attachment [New] nodes prefer to connect to more connected nodes. This node will therefore gain new links at a higher rate than its less connected peers and will turn into a hub. Growth and preferential attachment generate hubs through a rich-gets-richer mechanism.

23 Network How did measures networks evolve this way? Gene duplication [example] In protein interaction networks, scale-free topology see to have its origin in gene duplication. Part b shows a small protein interaction network (blue) and the genes that encode the proteins (green).

24 Network Motifes, modules measures and hierarchical networks Cellular function is modular Modularity: group of physically or functionally linked molecules (nodes) that work together to achieve a distinct function. Biology is full of examples of modularity High modularity is an inherent part of cellular networks Questions of interest: Is a given network modular? What are the modules in a network? What are their relationships in a given network?.

25 Motifes, modules and hierarchical networks High Clustering in Cellular Networks In a network representation, a module appears as a highly interconnected group of nodes Each module can be reduced to a set of triangles, and the clustering coefficient can be computed to quantify modularity. a high density of triangles is reflected by the clustering coefficient is the signature of a network s potential modularity. Random networks have much lower <C> values Metabolic, PPI, and protein domain networks have all exhibited high clustering

26 Network Motifes, modules measures and hierarchical networks Motifs are elementary units of cellular networks Examples of motifs: A Motif is a sub-graph which is over represented as compared to a randomized version of the same network. The directed triangle motif that is known as the feed-forward loop (FFL) emerges in both transcription-regulatory and neural networks.

27 Network Motifes, modules measures and hierarchical networks Motifs are elementary units of cellular networks The motifs and sub-graphs that occur in a given network are not independent of each other.

28 Network Motifes, modules measures and hierarchical networks Hierarchical modularity As the number of nodes increases, the number of modules increases exponentially The quantifiable signature of hierarchical modularity is the dependence of the clustering coefficient on the degree of a node, which follows C k ~ k 1 The coexistence of modularity (clusters) and scale-free topology (hubs) in many real systems leads to the assumption clusters combine in an iterative manner, generating a hierarchical network.

29 Network robustness Robustness of biological networks A key feature of many complex systems is their robustness, which refers to the system s ability to respond to changes in the external conditions or internal organization while maintaining relatively normal behavior. Complex systems, from the cell to the Internet, can be amazingly resilient against component failure. The distinct modules probably limit the effects of local changes in cellular networks. Robustness is inevitably accompanied by vulnerabilities we ll see how in a minute

30 Network robustness Topological robustness In random networks, if a random critical fraction of nodes is removed, the network breaks into tiny islands of nodes. In scale-free networks, even if 80% randomly selected nodes are removed, the rest still form a compact cluster with a path connecting any two nodes! The secret: statistics - only few hubs Trade-off: attack vulnerability - the removal of just a few key hubs kills the network. Shows a positive relationship between the degree of the node and its biological importance

31 Network robustness Functional and dynamical robustness Each node has a different biological function - the effect of a change is not depended on the node s degree only. Experimentally identified protein complexes tend to be composed of uniformly essential or nonessential molecules. Whereas some environmental and local important parameters must remain unchanged, others canvary widely.

32 Shifting point in biological research Concluding thoughts Network and systems biology are still in their infancy, but have come a long way Structure, topology, network usage, robustness, and function are all connected Will eventually have important implications for the study of disease and the practice of medicine

33 Thank you for your attention!