Network Analysis and Visualization of Staphylococcus aureus. by Russ Gibson

Transcription

1 Network Analysis and Visualization of Staphylococcus aureus by Russ Gibson

2 Network analysis Based on graph theory Probabilistic models (random graphs) developed by Erdős and Rényi in 1959 Theory and tools further developed by sociologists during latter 20 th century Last decade: Resurgence of research, more empirical studies, used to analyze: Social networks Biological networks Etc.

3 Review: some graph theory Graph mathematical structure used to model pairwise relations between objects from a certain collection Composed of: nodes - represent objects V(G) = {v 1, v 2,... v n } edges - represent relations, ( G) V( G) V( G) Graph drawing of the graph Used to model almost anything consisting of objects and relations

4 Graph types Graphs can be: Directed Undirected Weighted Unweighted

5 Gene regulatory networks DNA segments that interact with each other via RNA and protein products Experimental data is gene expression levels obtained from microarray Gene expression levels change in response to experimental conditions, as well as biochemical activity of other genes

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7 Modelling GRNs Nodes: genes & their corresponding transcription products Edges: molecular reactions through which products of one gene affect another

8 Network Analysis Several aspects of network structure have received attention in biological networks: 1. Degree 2. Characteristic path length 3. Clustering and modular structure

9 Degree Indegree Outdegree

10 Common degree distributions Poisson P( k, ) k e k! Power law P ( k) k

11 Path Length Average shortest path L 1 n( n 1) n i, j d( v i, v j ) d is min path between v i, v j Diameter Maximum d(v i, v j ) taken over all pairs of nodes

12 Clustering Clustering coefficient for directed graph Ratio of actual to potential edges between neighbors of v i Average clustering coefficient <C> gives network s overall tendency for nodes to form groups

13 Network models Random network Model by Erdős and Rényi Start with nodes, connect each pair with probability p Degree distribution is Poissonian Most links have degree close to <k> = 2L/N Very few links of higher degree (hub nodes) Clustering coeff distribution is flat, i.e. C(k) is independent of k Avg shortest path: L ~ log N Small world property Used to answer questions about graph theory

14 Scale free network Model by Barabasi & Albert Preferential node attachment to hub nodes Degree distribution follows Power Law Presence of hub nodes Biological systems show i k / i j k Clustering coeff distribution is flat Avg shortest path: L ~ log log N Ultra small-world property Models many real-world systems, including Internet, social, PPI/metabolic/transcriptomic biological networks j 2 3

15 Hierarchical network However, some biological systems do not have flat clustering coefficient distributions Nodes seem to cluster into modules, possibly subdivided into smaller modules We can tweak our scale-free model so that nodes cluster hierarchically, yielding C(k) ~ k -1

16 Network models - summary

17 So What is the Research? Staphylococcus aureus: golden staph Causes a wide variety of infections in humans SAMMD S. aureus Microarray Meta-Database Contains transcriptional profiles for many S. aureus experiments Hosted at:

18 Goals Analyze the S. aureus gene regulatory network Compute appropriate network metrics Characterize it according to current models Find regulatory elements related to sara and SA1233 genes Detect functional network modules to inform eventual simulation - ongoing Implement web visualization methods for researchers exploring SAMMD - ongoing

19 Network Analysis software NetworkX Programming library developed at Los Alamos for general network research Easily extensible, interoperable with other Python scientific packages (Numpy, Pyplot, etc.) Cytoscape Analysis & visualization platform

20 Method 1. Categorize SAMMD data into 4 growth phases: expo, lag, post, biofilm 2. Run SQL query on SAMMD to retrieve data for each phase, as well as for entire network 3. Construct network representation of each phase. Data structure is node adjacency dictionary. 4. Compute degree distribution, avg path length, and clustering coefficient distribution 5. For genes related to sara and SA1233, implement BFS using these as these as source nodes

21 Results Indegree distribution (all phases) y * k Correlation: Conclusion: Scale-free network, biological value for exponent

22 Results Outdegree distribution (all phases) y 1.304* k Correlation: Conclusion: unknown distribution, possible experimental sampling bias

23 Results Average Path Length (all phases) L = Diameter = 4 Conclusion: small-world property verified: L <= log N Hypothesized to be important small number of intermediate reactions necessary to transmit information

24 Results Clustering coefficient (all phases) Power law: y = * k Correlation: Conclusion: hierarchical network

25 Results BFS for sara and SA1233 Gene Neighbors found, hops=1 Neighbors found, hops=2 sara SA

26 Visualization Ongoing work with Mike Goldman to produce web visualization for SAMMD Using combination of Cytoscape and Javascript libraries to provide: Graphical network layouts that clarify network topology Mouseover and tabular display of single- and multiple-node metrics Publication-quality downloadable images

27 Detecting modules Module subsystem that performs a distinct, semi-autonomous function Clustering coefficient distribution for SAMD suggests modularity (hierarchical network) Clustering coeff is limited as a metric Only considers direct neighbors of the target node Neglects peripheral nodes connected to core gene clusters

28 Edge Betweenness Edge betweenness # of shortest paths passing through edge e for all pairs in G Insight: edges lying between modules have greater betweenness than edges within them. Girvan-Newman (G-N) algorithm stochastic algorithm for calculating edge-betweenness for a graph

29 dmonet Deterministic module detection algorithm, recently developed by R. Chang et al Definitions: Modularity - for a subgraph U, Indegree # of edges within U ind ( U) M U outd ( U) Outdegree - # of edges reaching outside of U U is a module if M U > 1 Complex module can be separated into >2 modules by re-application of dmonet Simple module not complex dmonet uses G-N, modified to be deterministic (dg-n)

30 dmonet algorithm 1. Use dg-n to recursively determine order of edge deletion, highest edge-betweenness first 2. List of edges sets created in reverse order of #1 3. Each edge set is classified is classified whether it connects mergeable or unmergeable subgraphs dmonet results correlate well with established module detection algorithms, but with greater sensitivity

31 Problems with dmonet Edge betweenness is valid metric for only for undirected graphs Solution 1. Only iterate over target nodes that are reachable from each source node Solution 2. Use a centrality metric, such as Closeness centrality Eigenvector centrality

32 Questions?