341: introduction to bioinformatics
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341: Introduction to Bioinformatics. Dr. Nataša Pržulj Department of Computing Imperial College London [email protected] Winter 2011. Topics. Introduction: biology Introduction: graph theory Network properties Network/node centralities Network motifs Network models - PowerPoint PPT PresentationTRANSCRIPT
341: Introduction to Bioinformatics
Dr. Nataša PržuljDepartment of ComputingImperial College [email protected]
Winter 2011
Topics
• Introduction: biology• Introduction: graph theory• Network properties
– Network/node centralities– Network motifs
• Network models• Network/node clustering• Network comparison/alignment• Software tools for network analysis• Interplay between topology and biology
Network Properties
1. Global Network Properties (Chapter 3 of the course textbook “Analysis of
Biological Networks” by Junker and Schreiber)
They give an overall view of a network:1) Degree distribution2) Clustering coefficient and spectrum3) Average diameter
1) Degree Distribution
G
Research debates…
• Degree correlation:– Pearson corr. coefficient between degrees of adjacent vertices– Average neighbor degree; then average over all nodes of
degree k• Structural robustness and attack tolerance:
– “Robust, yet fragile”• Scale-free degree distribution:
– Party vs. date hubs• J.D. Han et al., Nature, 430:88-93, 2004
– Bias in the data construction (sampling)?• M. Stumpf et al., PNAS, 102:4221-4224, 2005• J. Han et al., Nature Biotechnology, 23:839-844, 2005
• High degree nodes:– Essential genes
• H. Jeong at al., Nature 411, 2001. – Disease/cancer genes
• Jonsson and Bates, Bioinformatics, 22(18), 2006• Goh et al., PNAS, 104(21), 2007
• Cv – Clustering coefficient of node vCA= 1/1 = 1CB = 1/3 = 0.33CC = 0 CD = 2/10 = 0.2 …
• C = Avg. clust. coefficient of the whole network = avg {Cv over all nodes v of G}
• C(k) – Avg. clust. coefficient of all nodesof degree kE.g.: C(2) = (CA + CC)/2 = (1+0)/2 = 0.5
=> Clustering spectrum
E.g. (not for G)
2) Clustering Coefficient and Spectrum
G
Need to evaluate whether the value of C (or any other property) is statistically significant.
3) Average Diameter
G
u
v
E.g.(not for G)
• Distance between a pair of nodes u and v:
Du,v = min {length of all paths between u and v} = min {3,4,3,2} = 2 = dist(u,v)
• Average diameter of the whole network:
D = avg {Du,v for all pairs of nodes {u,v} in G}
• Spectrum of the shortest path lengths
Network Properties
• Global network properties might not be detailed enough to capture complex topological characteristics of large networks
Network Properties
2. Local Network Properties(Chapter 5 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber)
• They encompass larger number of constraints, thus reducing degrees of freedom in which networks being compared can vary
• How do we show that two networks are different?
• How do we show that they are the same?• How do we quantify the level of their similarity?
Network Properties
2. Local Network Properties(Chapter 5 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber)
1) Network motifs2) Graphlets:
2.1) Relative Graphlet Frequency Distance between 2 networks
2.2) Graphlet Degree Distribution Agreement between 2 networks
• Small subgraphs that are overrepresented in a network when compared to randomized networks
• Network motifs:– Reflect the underlying evolutionary processes that generated the network– Carry functional information– Define superfamilies of networks
- Zi is statistical significance of subgraph i, SPi is a vector of numbers in 0-1
• But:– Functionally important but not statistically significant patterns could be missed– The choice of the appropriate null model is crucial, especially across “families”
1) Network motifs (Uri Alon’s group, ’02-’04)
• Small subgraphs that are overrepresented in a network when compared to randomized networks
• Network motifs:– Reflect the underlying evolutionary processes that generated the network– Carry functional information– Define superfamilies of networks
- Zi is statistical significance of subgraph i, SPi is a vector of numbers in 0-1
• But:– Functionally important but not statistically significant patterns could be missed– The choice of the appropriate null model is crucial, especially across “families”– Random graphs with the same in- and out- degree distribution as data might not be
the best network null model
1) Network motifs (Uri Alon’s group, ’02-’04)
1) Network motifs (Uri Alon’s group, ’02-’04)
http://www.weizmann.ac.il/mcb/UriAlon/
Also, see Pajek, MAVisto, and FANMOD
N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
_____
Different from network motifs: Induced subgraphs Of any frequency
2) Graphlets (Przulj group, ’04-’10)
N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free
or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free
or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free
or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
2.1) Relative Graphlet Frequency (RGF) distance between networks G and H:
Generalize node degree
2.2) Graphlet Degree Distributions
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.
T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008.
Network structure vs. biological function & disease
Graphlet Degree (GD) vectors, or “node signatures”
Similarity measure between “node signature” vectors
T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008.
T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008.
Signature Similarity Measure between nodes u and v
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
40%SMD1
PMA1
YBR095C
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
90%*
SMD1
SMB1RPO26
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
*Statistically significant threshold at ~85%
Later we will see how to use this and other techniquesto link network structure with biological function
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.
Generalize Degree Distribution of a network
The degree distribution measures:• the number of nodes “touching” k edges for each value of k
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.
/ sqrt(2) ( to make it between 0 and 1)
This is called Graphlet Degree Distribution (GDD) Agreement between networks G and H.
Software that implements many of these networkproperties and compares networks with respect to them: GraphCrunchhttp://www.ics.uci.edu/~bio-nets/graphcrunch/
Network properties
3. Network/node centralities(Chapter 4 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber)
• Rank nodes according to their “topological importance”
3) Network/node centralities
1 2 3 4 5 6
7
8
9
10
If nodes are housing communities, where to build a hospital?
3) Network/node centralities
1 2 3 4 5 6
If nodes are housing communities, where to build a hospital?
Network properties
3. Network/node centralities
• Different centrality measures exist• Centrality values comparable inside a given
network only• Centrality values of two centrality measures
incomparable even within the same network• Some centrality measures can be applied to
connected networks only
3) Network/node centralities
• Degree centrality• Closeness centrality• Eccentricity centrality• Betweenness centrality
• Other centrality measures exist, e.g.:– Eigenvector centrality– Subgraph centrality– …
• Software tools: Visone (social nets) and CentiBiN (biological nets)
3) Network/node centralities
• Degree centrality:– Nodes with high degrees have high centrality
Cd(v)=deg(v)
• Closeness centrality:– Nodes with short paths to all other nodes have
high centrality
3) Network/node centralities
• Essentricity centrality:– Nodes with short paths to any other node have
high centrality
• Betweenness centrality:– Nodes (or edges) that occur in many of the
shortest paths have high centrality
Topics
• Introduction: biology• Introduction: graph theory• Network properties
– Network/node centralities– Network motifs
• Network models• Network/node clustering• Network comparison/alignment• Software tools for network analysis• Interplay between topology and biology