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![Page 1: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/1.jpg)
Algorithms for Biological Networks
Prof. Tijana MilenkovićComputer Science and Engineering
University of Notre Dame [email protected]
Fall 2010
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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
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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
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1) Degree Distribution
G
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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
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• 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.
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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
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Network Properties
• Global network properties might not be detailed enough to capture complex topological characteristics of large networks
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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?
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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
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• 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)
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• 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)
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1) Network motifs (Uri Alon’s group, ’02-’04)
http://www.weizmann.ac.il/mcb/UriAlon/
Also, see Pajek, MAVisto, and FANMOD
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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)
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N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free
or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
![Page 18: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/18.jpg)
N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free
or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.
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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:
![Page 20: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/20.jpg)
Generalize node degree
2.2) Graphlet Degree Distributions
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N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.
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N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.
![Page 23: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/23.jpg)
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”
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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.
![Page 25: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/25.jpg)
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
![Page 26: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/26.jpg)
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
![Page 27: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/27.jpg)
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).
![Page 28: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/28.jpg)
T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).
![Page 29: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/29.jpg)
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%
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Later we will see how to use this and other techniquesto link network structure with biological function
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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
![Page 32: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/32.jpg)
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.
![Page 33: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/33.jpg)
N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.
![Page 34: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/34.jpg)
/ sqrt(2) ( to make it between 0 and 1)
This is called Graphlet Degree Distribution (GDD) Agreement between networks G and H.
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Software that implements many of these networkproperties and compares networks with respect to them: GraphCrunchhttp://www.ics.uci.edu/~bio-nets/graphcrunch/
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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”
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3) Network/node centralities
1 2 3 4 5 6
7
8
9
10
If nodes are housing communities, where to build a hospital?
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3) Network/node centralities
1 2 3 4 5 6
If nodes are housing communities, where to build a hospital?
![Page 39: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/39.jpg)
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
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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)
![Page 41: Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1e5503460f94c3504a/html5/thumbnails/41.jpg)
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
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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
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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