1. Network Analysis of Protein-Protein Interactions
Xiaohua Tony Hu
College of Information Science & Technology
Drexel University
Philadelphia, PA 19104
(O)
(F)

2. Outline Introduction Research Goals Topological Analysis
The algorithm - CommBuilder
Experimental Results
Conclusions & Discussion
Q&A
September 22, 2018

3. Introduction Biological Networks
Protein-Protein Interaction (PPI) Networks
Network Community Structure
Community Detection
Network Growing
September 22, 2018

4. protein-protein interactions Bio-chemical reactions
Biological Networks
GENOME
PROTEOME
protein-protein interactions
Citrate Cycle
METABOLISM
Bio-chemical reactions
September 22, 2018

5. Biological Networks Modeling biological systems Genetic networks
Gene association and expression
Protein networks
Protein structure and interactions
Metabolic pathways
Challenging
Non-trivial and irregular
Incomplete and noisy
September 22, 2018

6. Related Work
The “small world” model was first proposed by Watts and Strogatz, referring to the small average distance between any two vertices in the network.
Barabasi and Albert discovered a highly heterogeneous PPI network with scale-free connectivity properties in yeast., PPI networks of S. cerevisiae, H. pylori, C.elegans, and D. melanogaster [11-13]. Thus, the scale-free network model has been well accepted.
In PPI networks, not only the degree distribution exhibits power-law dependence, other topological properties have also been shown scale-free topology such as clustering coefficient. Yook and colleagues observe that the clustering coefficient of S. cerevisiae follows a power-law.
However, not all research agrees on the power-law behavior in all PPI networks. Thomas and colleagues find that the connectivity distribution in a human PPI network does not follow power law. They argue that current belief of power law distribution may reflect a behavior of a sampled subgraph. From a slightly different angle,
Colizza and colleagues also evaluate three PPI networks constructed from yeast data sets. Although they observe that the connectivity distribution follows power law, only one of the three networks exhibits approximate power law behavior for the clustering coefficient. Soffer and Vazquez find that the power law dependence of the clustering coefficient is to some extent caused by the degree correlations of the networks, with high degree vertices preferentially connecting with low degree vertices.
September 22, 2018

7. PPI Networks – Why?
Proteins are executors of genetic program and rarely act alone
Functional assignments of uncharacterized proteins
Targets of new drugs
September 22, 2018

8. PPI Networks - Properties
PPI network models
Scale-free (Barabasi & Albert, 1999)
Geometric random (Przulj et al, 2004)
Tolerant to random errors but fragile against the removal of the most connected nodes (hubs)
Modularity and community structure
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9. PPI Networks - Models A.-L. B. and Z.N. Oltvai, Nat. Rev. Gen.(2004)
September 22, 2018

10. Yeast PPI Network Nodes: proteins Edges : physical Interactions
H. Jeong et al, Nature 411, (2001).
September 22, 2018

11. PPI Networks - Topology
H. Jeong et al., Nature 411, (2001)
September 22, 2018

12. PPI Networks - Topology
Origin of scale-free
gene duplication
Preferential attachment
Vazquez et al. 2003; Sole et al. 2001; Bhan et al
September 22, 2018

13. Network Community Structure
Gathering of vertices into groups such that the connections within groups are denser than between groups (Girvan & Newman, 2002)
An important property of PPI networks
Delineation of functional groups/processes
Transfer of information
September 22, 2018

14. Community Detection The GN algorithm (Girvan & Newman, 2002)
Based on betweenness
High computational cost
Well adopted
Metabolic networks (Holme et al, 2003)
Functional units
Gene networks (Wilkinson & Huberman, 2004)
Related genes
September 22, 2018

15. Network Growing Genetic regulatory networks (Hashimoto et al, 2004)
Based on probabilistic Boolean networks
Web (Flake et al, 2002)
Based on the self-organization of the network structure and a maximum flow method
September 22, 2018

16. Graph Theory
Modeling real-world phenomena, e.g. World Wide Web, electronic circuits, collaborations between scientists, co-citations, biological networks, etc.
A mathematical formalism
Global properties: e.g. diameter, clustering, degree distribution
Local properties: vertex density, motif and graphlet
September 22, 2018

17. Graph Theory - Models Random Model Small-world Model
The probability of an edge between two nodes is distributed randomly.
Erdos & Renyi
Small-world Model
Small diameters and large clustering coefficients
Watts & Strogatz
September 22, 2018

18. Graph Theory - Models Scale-free Model Random Geometric Model
Degree distribution follows a power law of the form P(k) ~ k−γ.
Robustness and fragility
Preferential attachment (graph evolution)
A-L Barabasi
Random Geometric Model
Nodes randomly distributed in a geometric space (Przulj, et al)
September 22, 2018

19. Research Goals
To analyze the topological properties of protein-protein interaction networks
Different organisms
Different experimental systems
Different confidence levels
September 22, 2018

20. Research Goals What is the community to which a given protein belongs?
Desirable and computationally more feasible to study a community containing a few proteins of interest
September 22, 2018

21. Topological Analysis Method Protein-Protein Interaction Networks
Constructed from different data sets
Statistical analysis of topological properties
SPSS
September 22, 2018

22. Topological Analysis Data Sets DIP – Database of Interacting Proteins
Species-specific PPI data sets:
D. melanogaster (fly), S. cerevisiae (yeast), E. coli, C. elegans (worm), H. pylori, H. sapiens (human), M. musculus (mouse)
BIND – Biomolecular Interaction Network Database
Fly PPI with assigned confidence scores (Giot, 2003)
GRID – General Repository for Interaction Datasets
Yeast and fly PPI (including experiment systems used to obtain the data)
September 22, 2018

23. Topological Analysis The experimental systems-specific set includes
(1) fly and yeast PPI networks, downloaded from the General Repository for Interactions Datasets (GRID). From fly data set, we constructed three PPI networks, representing interactions detected by one of the following experimental systems: Enhancement (Fly-E), Suppression (Fly-S), and Two Hybrid (Fly-TH). From yeast data set, we constructed PPI networks representing three experimental systems: Affinity Precipitation (Yeast-AP), Synthetic Lethality (Yeast-SL), and Two Hybrid (Yeast-TH).
(2) We also constructed a network representing the entire set of protein interactions (Fly and Yeast). The confidence levels-specific set contains fly data set downloaded from the Biomolecular Interaction Network Database (BIND). We constructed three networks: one with confidence >= 0.5 (Fly50), one with confidence >= 0.3 (Fly30), and the third containing all interactions (Fly00).
September 22, 2018

24. Topological Analysis Definitions Graph G(V, E) V: vertex set
Vertex (or Node)
Degree: number of edges
connected to the vertex.
G(V, E)
V: vertex set
E: edge set
|V|, |E|: sizes V1
e.g.
|V| = 4
|E| = 6
Edge
September 22, 2018

25. Topological Analysis P(k) ~ k-γ Degree distribution P(k)
the probability of a vertex has degree of k.
power law:
P(k) ~ k-γ
Diameter (length)
the shortest path from one vertex to another
September 22, 2018

26. Topological Analysis Clustering coefficient (C) Vertex Density (D)
Ci = 2ei / (ki*(ki – 1))
ei : # of edges between neighbors of vertex i
ki : # of neighboring vertices of i
i not included in both
Vertex Density (D)
Same as C but includes i
September 22, 2018

27. Table 1 Protein interaction networks of different organisms.
PROTEINS
INTERACTIONS
COMPONENTS
GIANT COM
D. Melanogaster
7441
22636 52
7330 (98.5%)
S. cerevisiae (Core)
2614
6379 66
2445 (93.5%)
E. coli
1640
6658
200
1396 (85.1%)
C. elegans
2629
3970 99
2386 (90.8%)
H. pylori
702
1359 9
686 (97.7%)
H. sapiens
1059
1318
119
563 (53.2%)
M. musculus
327
274 79
49 (15.0%)
Table 1 shows the small sizes of giant components for H. sapiens and especially for M. musculus, meaning that we have
a fairly large number of unconnected small subgraphs in these two networks. As one can expect, the size of the giant component decreases in higher confidence networks while the number of unconnected subgraphs increases.
September 22, 2018

28. Table 2
Protein interaction networks of D. melanogaster – different confidence.
NETWORK
CONFIDENCE
PROTEINS
INTERACTIONS
COMPONENTS
GIANT COMPONENT
Fly00
> 0
7064
21111 68
6929 (98.1%)
Fly30
>= 0.3
6382
9157
213
5881 (92.1%)
Fly50
>= 0.5
4689
4877
590
3068 (65.4%)
Across species, all networks exhibit small values of average degree and diameters, even though the absolute values differ significantly. Except for C. elegans, PPI networks for all other species have larger average clustering coefficient comparing to the corresponding random clustering coefficient, indicating a non-random and hierarchical structure within these networks.
September 22, 2018

29. Protein interaction networks of S. cerevisiae: with confidence.
Table 3
Protein interaction networks of S. cerevisiae: with confidence.
NETWORK
PROTEINS
INTERACTIONS
COMPONENTS
GIANT COMPONENT
YeastCore
2614
6379 66
2445 (93.5%)
Yeast00
4770
15199 41
4687 (98.3%)
September 22, 2018

30. Table 4
Protein interaction networks of D. melanogaster: different experimental systems
NETWORK
EXP SYSTEMS
PROTEINS
INTERACTIONS
COMPONENTS
GIANT COMPONENT
Fly
Combined
7938
25827 72
7793 (98.2%)
Fly-E
Enhancement
1054
1819 56
902 (85.6%)
Fly-S
Suppression
1121
2247 44
1020 (91.0%)
Fly-TH
Two Hybrid
5614
17544 12
5591 (99.6%)
September 22, 2018

31. Affinity Precipitation
Table 5
Protein interaction networks of S. cerevisiae: different experimental systems
NETWORK
EXP SYSTEMS
PROTEINS
INTERACTIONS
COMPONENTS
GIANT COMPONENT
Yeast
Combined
4918
18119 48
4824 (98.1%)
Yeast-AP
Affinity Precipitation
2388
7405 39
2292 (96.0%)
Yeast-SL
Synthetic Lethality
1468
4773 44
1343 (91.5%)
Yeast-TH
Two Hybrid
3937
6358
138
3632(92.3%)
September 22, 2018

32. NETWORK Kmax <k> <l> <D> <C> <Crand>
Table 6
Topology of protein interaction networks.
NETWORK
Kmax
<k>
<l>
<D>
<C>
<Crand>
D. melanogaster
178
6.08
4.39
0.5840
0.0159
0.0097
S. cerevisiae (Core)
111
4.88
5.00
0.6949
0.2990
0.0103
E. coli
152
8.12
3.73
0.8092
0.5889
0.1168
C. elegans
187
3.02
4.81
0.7889
0.0490
0.0462
H. pylori 54
3.87
4.14
0.6624
0.0255
0.0403
H. sapiens 33
2.49
6.80
0.7983
0.1658
0.0098
M. musculus 12
1.68
3.57
0.8670
0.1011
0.0062
September 22, 2018

33. NETWORK Kmax <k> <l> <D> <C>
Table 6 (conti.) Topology of protein interaction networks.
NETWORK
Kmax
<k>
<l>
<D>
<C>
<Crand>
S. cerevisiae
283
6.37
4.18
0.6001
0.0928
0.0196
S. cerevisiae (Core)
111
4.88
5.00
0.6949
0.2990
0.0103
Fly00
178
5.98
4.45
0.5939
0.0281
0.0095
Fly30 59
2.87
7.06
0.7227
0.0518
0.0015
Fly50 42
2.08
9.42
0.8010
0.0793
0.0008
September 22, 2018

34. Topology of protein interaction networks.
Table 6 (conti.)
Topology of protein interaction networks.
NETWORK
Kmax
<k>
<l>
<D>
<C>
<Crand>
Fly
178
6.51
4.39
0.6005
0.0675
0.0104
Fly-E
110
3.45
4.44
0.8085
0.3441
0.0725
Fly-S
124
4.01
4.30
0.7875
0.3459
0.0735
Fly-TH
144
6.25
4.23
0.5870
0.0093
0.0123
Yeast
288
7.37
4.12
0.6000
0.1538
0.0240
Yeast-AP 69
6.20
4.43
0.6638
0.2646
0.0163
Yeast-SL
157
6.50
3.84
0.7150
0.2324
0.1600
Yeast-TH
3.23
4.96
0.7362
0.0869
0.0368
September 22, 2018

35. Observations:Average Topological Properties of the PPI Networks
Across species, all networks exhibit small values of average degree and diameters, even though the absolute values differ significantly. Except for C. elegans, PPI networks for all other species have larger average clustering coefficient comparing to the corresponding random clustering coefficient, indicating a non-random and hierarchical structure within these networks.
Networks with higher confidence have larger diameters, larger average clustering coefficient, and a smakker average degree. They shift further away from random structure.
September 22, 2018

36. Figure 1 Degree Distribution P(k): PPI of Different Organisms
September 22, 2018

37. Figure 2 Degree Distribution P(k) of yeast: with Confidence.
September 22, 2018

38. Figure 3 Degree Distribution P(k) of Fly: with Confidence.
September 22, 2018

39. Figure 4 Degree Distribution P(k): Methodology Difference.
September 22, 2018

40. Observations: Degree Distribution P(k)
The log-log plot clearly demonstrates the power law dependence of P(k) on degree k. For our analysis, we select to use directly the raw data, instead of following [4] with exponential cutoff. Without exponential cutoff, our regression analysis yields power law exponent γ between 1.31 and 2.76, in fairly good agreement with previously reported results.
Using SPSS software package, we create a scatter plot of residues by fit values for the power law model. The result, shown clearly indicates a pattern in the data that is not captured by the model. This means that the power law is a model that has excellent fit statistics, but poor residuals, an indication of its inadequacy.
September 22, 2018

41. Figure 5 Average clustering coefficient C(k): Different Organisms.
September 22, 2018

42. Figure 6 Average clustering coefficient C(k): with Confidence.
September 22, 2018

43. Figure 7 Average clustering coefficient C(k): Methodology Difference.
September 22, 2018

44. Observations: The Average Clustering Coefficient
indicate that while E. coli and S. cerevisiae PPI networks show somewhat weak power law distribution, networks of other species do not follow a power law. Different experimental systems and different confidence levels do not seem to change this non-scale-free behavior.
September 22, 2018

45. Figure 8 Average vertex density D(k): Different Organisms
September 22, 2018

46. Figure 9 Average vertex density D(k): with Confidence.
September 22, 2018

47. Figure 10 Average vertex density D(k): Methodology Difference.
September 22, 2018

48. Observations: The Average Vertex Density
All networks display consistent power law behavior for the vertex density spectrum
September 22, 2018

49. Topological Analysis Exponents Degree Distribution: P(k) ~ k-γ
Clustering Coeffient:
C(k) ~ k-α
Vertex Density:
D(k) ~ k-β
September 22, 2018

50. Statistical analysis of the protein interaction networks.
Table 7
Statistical analysis of the protein interaction networks.
NETWORKS
γ (R2)
α (R2)
β (R2)
D. melanogaster
1.945 (0.923)
3.050 (0.311)
0.836 (0.989)
E. coli
1.355 (0.882)
0.562 (0.656)
0.536 (0.756)
C. elegans
1.599 (0.839)
0.625 (0.362)
0.833 (0.976)
H. pylori
1.651 (0.899)
0.495 (0.373)
0.826 (0.985)
H. sapiens
2.025 (0.931)
0.657 (0.190)*
0.626 (0.699)
M. musculus
2.360 (0.931)
0.598 (0.431)*
0.689 (0.965)
S. cerevisiae (Core)
1.977 (0.911)
0.893 (0.721)
0.759 (0.867)
* P > 0.05
September 22, 2018

51. Statistical analysis of the protein interaction networks. NETWORKS
Table 7 (conti.)
Statistical analysis of the protein interaction networks.
NETWORKS
γ (R2)
α (R2)
β (R2)
Fly00
1.980 (0.930)
0.382 (0.194)
0.789 (0.913)
Fly30
2.540 (0.931)
0.698 (0.265)
0.780 (0.918)
Fly50
2.763 (0.915)
0.791 (0.375)*
0.783 (0.920)
S. cerevisiae (Core)
1.977 (0.911)
0.893 (0.721)
0.759 (0.867)
S. cerevisiae
1.792 (0.883)
1.106 (0.525)
0.894 (0.872)
* P > 0.05
September 22, 2018

52. Statistical analysis of the protein interaction networks. NETWORKS
Table 7 (conti.)
Statistical analysis of the protein interaction networks.
NETWORKS
γ (R2)
α (R2)
β (R2)
Fly
1.947 (0.934)
0.555 (0.334)
0.758 (0.865)
Fly-E
1.518 (0.858)
1.020 (0.539)
0.769 (0.886)
Fly-S
1.527 (0.936)
0.879 (0.513)
0.747 (0.893)
Fly-TH
1.912 (0.923) ND
0.783 (0.867)
Yeast
1.761 (0.919)
0.752 (0.326)
0.728 (0.698)
Yeast-AP
1.819 (0.904)
0.635 (0.301)
0.619 (0.664)
Yeast-SL
1.311 (0.830)
0.650 (0.342)
0.674 (0.734)
Yeast-TH
1.614 (0.843)
1.453 (0.664)
0.947 (0.918)
*P > ND: Not Determined
September 22, 2018

53. Residues vs fit values for P(k)~k-γ.
September 22, 2018

54. Discussion
Our results confirmed that PPI networks have small diameters and small average degrees. All networks we evaluated display power law degree distribution. However, further statistical analysis indicates an inadequacy of such model in capturing certain features in the data.
Most of the networks we evaluated also reveal a larger clustering coefficient, indicating non-random structure of these networks. However, the values of the clustering coefficient vary significantly across different species. This may result from the incompleteness and noise of the data, indicated by the significant differences in the clustering coefficient between networks with different confidence levels. In addition, networks from different experimental systems differ significantly in the clustering coefficient. The spectrum of the average clustering coefficient over degree k fails to exhibit scale free behavior in most of the networks evaluated.
we did not observe the power law distribution of C(k) over degree k, but the power law behavior appears when we modify the C(k) to D(k). We expect this information will be helpful because we have already seen the application of vertex density in [23].
September 22, 2018

55. Conclusions & Discussion
PPI networks have small diameters and small average degrees.
Most of the PPI networks display power law degree distribution. However, further statistical analysis indicates inadequacy of the power-law model.
Most networks have a larger clustering coefficient, indicating the non-random structure of the networks.
September 22, 2018

56. Conclusions & Discussion
Networks from different experimental systems differed significantly in the values of the clustering coefficient.
The average clustering coefficient over degree k fails to exhibit the power law behavior in most of the networks.
The vertex density distribution follows a power law for all the networks studied.
September 22, 2018