1.on finding clusters in undirected simple graphs: application to protein complex detection 2.dpclus...
TRANSCRIPT
1. On finding clusters in undirected simple graphs: application to protein complex detection
2. DPClus software tool
3. Introduction to DPClusO
4. Concept of BiClustering
5. Concept of DNA sequencing
Today’s lecture will cover the following topics
Outline
•Introduction
•Some basic concepts
•The proposed algorithm
•The DPClus software
•Results & Discussion
•Conclusions
On finding clusters in undirected simple graphs: application to protein complex detection
Introduction
•There is no universal definition of a cluster.
•But clustering is an important issue.•Consequently there are diverse definitions and various methods.•The major purpose of clustering is finding cohesive groups.
•Here, we are going to discuss a graph clustering algorithm.
Regarding a graph, a cluster is a subgraph whose nodes are densely connected with each other compared to their connections with other nodes in the graph.
This is a flexible definition of a cluster.
Intuitively, we can recognize two clusters in this arbitrary graph.
Introduction
But it is difficult to draw a big graph revealing its clusters.
An E. coli protein-protein interaction network---consisting of 3007 proteins and 11531 interactions (From Mori Lab NAIST, Japan)
Some algorithm is needed to detect locally dense regions……
Introduction
Md. Altaf-Ul-Amin, Yoko Shinbo, Kenji Mihara, Ken Kurokawa and Shigehiko Kanaya, “Development and implementation of an algorithm for detection of protein complexes in large interaction networks”, BMC Bioinformatics 7:207, April 2006.
Introduction
Some basic concepts
It is likely that two nodes belong to the same cluster have more common neighbors than two nodes that are not
It is likely that two nodes belong to the same cluster have more common neighbors than two nodes that are not
Some basic concepts
•The density d of a cluster is the ratio of the number of edges present in it and the maximum possible number of edges in it.
•It is easy to realize that d = |E|/|E|max = 2*|E|/|N|*(|N|-1).
•d is a real number ranging from 0 to 1.
Some basic concepts
Density of the total graph = 0.241
d=0.9
d=1.0
The density of the complexes are relatively higher
Some basic concepts
Considering density alone is not enough
Such situations can be tackled by keeping track of the periphery
Some basic concepts
•Both the graphs consist of 8 nodes and both are of density 0.5
•But one of them seems to be a single cluster while the other is divided into two clusters
a
b c
d
e
g f
h
a
b
cd
ef
g
h
Some basic concepts
The cluster property of any node n with respect to any cluster k of density dk and size Nk is defined as follows:
cpnk=|Enk|/(dk* |Nk|)
Here, |Enk| is the total number of edges between the node n and each of the nodes of cluster k.
a
b c
d
e
g f
h
a
b
cd
ef
g
h
Cluster property of node f 0.57
Cluster property of node f = 0.2
The proposed algorithm is a sequential constructive algorithm:
It initializes the complex/cluster by choosing a seed node.
It then repeatedly add other nodes on the basis of priority and some conditions.
The major methods of the algorithm
•Choosing a seed node.
•Selecting a priority node.
•Checking necessary conditions before adding a node to a complex.
The proposed Algorithm
Inputs to the algorithm are:
•The associated matrix of the network.
•A minimum threshold density for the generated clusters.
•A parameter to determine how we separate a complex from its periphery.
Output of the algorithm are :
Overlapping/non-overlapping complexes whose densities are more or equal to the given density.
The proposed Algorithm
-
The proposed AlgorithmInput an undirected simple graph G.
Set thresholds din and cpin
and initialize cluster ID k = 1.
Generate degrees of the nodes of G.Determine the highest highest node degree (Dh). Dk= 0
Start at highest weight nodeof G as the kth cluster.
dk > din
No
Yescpp(k-p) > cpin
Yes
No
Deduct the last added node from kth cluster.
No
End
All neighbors of kth cluster are checked?
No
Yes
Print kth cluster.G G – kth cluster
k k+1.
Yes
Input & Initialization
Generate weight of each node of G.
highest node weight= 0 YesNo
Start at highest degree nodeof G as the kth cluster.
Generate the neighbors of the kth cluster in G. and sort them according to priority.Add the highest prority neigbor (p) to the cluster.
Add the next priority neighbor (p) to kth cluster.
Termination check
Seed selection
Cluster formation
Output & update
Flowchart of the proposed Algorithm
0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 1 0 0 0 0 0 0 0 0
0 1 0 1 1 1 0 0 0 0 0 0 0 0
0 1 1 0 1 1 0 1 0 0 0 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0
0 1 1 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 1 0 0 0
0 0 0 1 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 0 0 1 1
0 0 0 0 0 0 0 0 1 0 1 0 1 1
0 0 0 0 0 0 1 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1 1 0 1 0 1
0 0 0 0 0 0 0 0 1 1 0 0 1 0
M =
Muv = 1 if there is an edge between nodes u and v and 0 otherwise.
The proposed Algorithm
1 0 1 1 0 1 0 0 0 0 0 0 0 0
0 4 2 2 3 2 1 1 0 0 0 0 0 0
1 2 4 3 2 3 1 1 0 0 0 0 0 0
1 2 3 5 2 3 1 0 1 0 0 0 0 0
0 3 2 2 3 2 1 1 0 0 0 0 0 0
1 2 3 3 2 5 0 1 0 0 1 0 0 0
0 1 1 1 1 0 2 0 0 1 0 0 0 0
0 1 1 0 1 1 0 2 0 1 0 0 1 1
0 0 0 1 0 0 0 0 4 2 1 1 2 2
0 0 0 0 0 0 1 1 2 4 0 1 2 2
0 0 0 0 0 1 0 0 1 0 2 0 1 1
0 0 0 0 0 0 0 0 1 1 0 1 0 1
0 0 0 0 0 0 0 1 2 2 1 0 4 2
0 0 0 0 0 0 0 1 2 2 1 1 2 3
M2 =
(M2)uv for uv represents the number of common neighbor of the nodes u and v.
The proposed Algorithm
1 0 1 1 0 1 0 0 0 0 0 0 0 0
0 4 2 2 3 2 1 1 0 0 0 0 0 0
1 2 4 3 2 3 1 1 0 0 0 0 0 0
1 2 3 5 2 3 1 0 1 0 0 0 0 0
0 3 2 2 3 2 1 1 0 0 0 0 0 0
1 2 3 3 2 5 0 1 0 0 1 0 0 0
0 1 1 1 1 0 2 0 0 1 0 0 0 0
0 1 1 0 1 1 0 2 0 1 0 0 1 1
0 0 0 1 0 0 0 0 4 2 1 1 2 2
0 0 0 0 0 0 1 1 2 4 0 1 2 2
0 0 0 0 0 1 0 0 1 0 2 0 1 1
0 0 0 0 0 0 0 0 1 1 0 1 0 1
0 0 0 0 0 0 0 1 2 2 1 0 4 2
0 0 0 0 0 0 0 1 2 2 1 1 2 3
M2 =
(M2)uv for uv represents the number of common neighbor of the nodes u and v.
The proposed Algorithm
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
The proposed Algorithm
The weights of edges are derived by squaring the associated matrix of the graph
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
106
10
6
0
6
6
0
0
6
0
06
The proposed Algorithm
The weights of nodes (sum of the weights of the connecting edges)
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P1 2 1
P3 3 1
P4 2 1
P5 3 1
The proposed Algorithm
Seed
Neighbors
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P3 3 1
P5 3 1
P1 2 1
P4 2 1
The proposed Algorithm
Neighbors
cp of P3 = 1
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P1 4 2
P4 4 2
P5 6 2
P7 0 1
d=1.0
Neighbors
The proposed Algorithm
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P5 6 2
P1 4 2
P4 4 2
P7 0 1
d=1.0
Neighbors
The proposed Algorithm
cp of P5 = 1
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P1 4 2
P4 4 2
P6 0 1
P7 0 1
d=1.0
Neighbors
The proposed Algorithm
cp of P1 = 1
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P0 0 1
P4 4 2
P6 0 1
P7 0 1
d=1.0
Neighbors
The proposed Algorithm
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
Sum of edge weights
# of edges
P4 4 2
P0 0 1
P6 0 1
P7 0 1
d=1.0
Neighbors
The proposed Algorithm
cp of P4 = 0.75
2
2
3
22
0
3
2
2
0 02
2
2
2
23
0
0
00
2
10
10 6
10
6
0
6
6
0
0
6
0
06
d=0.9
Neighbors
The proposed Algorithm
Sum of edge weights
# of edges
cp-value
P0 0 1 ~0.22
P6 0 1 ~0.22
P7 0 1 ~0.22
02
2
2
2
2
0
0
0
2
6
0
6
6
0
6
0
0
The proposed Algorithm
The remaining graph
Seed
02
2
2
2
2
0
0
0
2
6
0
6
6
0
6
0
0
d=1.0
The proposed Algorithm
02
2
2
2
2
0
0
0
2
6
0
6
6
0
6
0
0
d=1.0
The proposed Algorithm
02
2
2
2
2
0
0
0
2
6
0
6
6
0
6
0
0
d=1.0
The proposed Algorithm
The proposed Algorithm
The remaining graph
The proposed Algorithm
Clustering by the proposed algorithm
Results: Complexes in the E. coli PPI Network
The network of E. coli proteins consists of 363 interactions involving a total of 336 proteins
DIP:339N GroEL DIP:1081N PrnP
DIP:1025N CarB DIP:1026N CarA
DIP:539N MalG DIP:508N MalE
DIP:124N XerD DIP:726N XerC
DIP:367N PntB DIP:366N PntA
DIP:342N SbcC DIP:572N Gam
-------------- --------- -------------- ---------
-------------- --------- -------------- ---------
http://dip.mbi.ucla.edu/
components of RNA polymerase (RpoA, RpoB, RpoC, Rsd, RpoZ RpoD, RpoN, FliA)
Results: Complexes in the E. coli PPI Network
components of ATP synthetase (AtpA, AtpB, AtpE, AtpF, AtpG, AtpH, AtpL);
Results: Complexes in the E. coli PPI Network
Proteins involved in cell division (FtsQ, FtsI, FtsW, FtsN, FtsK and FtsL)
Results: Complexes in the E. coli PPI Network
components of DNA polymerase (DnaX, HolA, HolB, HolD, and HolC);
Results: Complexes in the E. coli PPI Network
We extract a set of 12487 unique binary interactions involving 4648 proteins by discarding self-interactions of the PPI data obtained from ftp://ftpmips.gsf.de/yeast/PPI/.
Results: Complexes in the S. cerevisiae PPI Network
Results: Details of a Group of Predicted Complexes
Information on the complexes that are of size 6 of the set generated using din=0.7, cpin=0.50 and non-overlapping mode.
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1 5 10 15
17
13
14
14
12
12
11
9
8
8
8
8
8
7
7
7
7
6
6
6
6
6
6
6
6
6
6
6
28 0.71
0.72
1.00
0.83
0.71
0.94
0.71
0.98
0.72
0.93
0.72
0.71
0.71
0.71
0.95
0.76
0.71
0.71
0.80
0.80
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
CTF4,CTF8,CTF18,CTF19,CIN1,CIN2,CIN8,GIM3,GIM4,GIM5,MAD1,MAD2,MAD3,BUB1,BUB3,PAC2,PAC10,ARP6,BIK1,BIM1,CHL1,CSM3, DCC1,HTZ1,KAR3,SCC1-73,TUB3,YKE2
CHS3,CHS5,CHS7,BNI1,BNI4,RVS161,RVS167,ARC40,ARP2,BCK1,CLA4,FKS1,KRE1,SKT5,SLT2, SMI1,SWI4
TAF17,TAF25,TAF60,TAF61,TAF90,SPT3,SPT7,SPT8,SPT20,ADA2,GCN5,HFI1,NGG1,TRA1
LSM1,LSM2,LSM3,LSM4,LSM5,LSM6,LSM7,LSM8,DCP1,KEM1,MRNa,PAT1,SNRNa,U6
RAD27,RAD50,CDC45-1,ELG1,ESC2,HPR5,MMS4,MRC1,POL32,RRM3,SGS1,TOF1,TOP3
TRS20,TRS23,TRS31,TRS33,TRS65,TRS85,TRS120,TRS130,BET3,BET5,GSG1,KRE11
COG5,COG6,COG7,COG8,ARL1,ARL3,GOS1,GYP1,RIC1,SWF1,TLG2,YPT6
APC1,APC2,APC4,APC5,APC9,APC11,CDC16,CDC23,CDC26,CDC27,DOC1
CDC73,CTI6,DEP1,LEO1,SAP30,SET2,SIF2,SWR1,VPS71
CFT1,CFT2,FIP1,PAP1,PFS2,PTA1,YSH1,YTH1
MED2,MED4,MED7,MED8,PGD1,RPB3,SOH1,SRB4
BEM1,BEM2,BOI1,BOI2,CDC24,CDC42,MSB1,STE20
ARP1,ASE1,CLB4,JNM1,KAR9,KIP3,NIP100,PAC11
CDC4,CDC34,CDC53,CLN1,CLN2,CLN3,SIC1,SKP1
CDC3,CDC10,CDC11,CDC12,GIN4,SEP7,SHS1
CKA1,CKA2,CKB1,CKB2,CDC7-1,RHO3,TOP2
SNR3,SNR10,SNR11,SNR189,GAR1,NHP2,NOP10
SPC19,SPC24,NNF1,NUF2,SMC1,TID3,YDR295c
YGL161c,YGL198w,GCS1,YDR425w,YIP1,YPL095c
PRP5,PRP9,PRP11,PRP21,NOG2,YNR053c
NUP49,NUP57,APG17,NIC96,NSP1,SEC35
KTR3,LAS17,SLA1,YFR024c,YOR284w,YSC84
ECM31,GCD7,NIP29,TEM1,YJL199c,YPL070w
ERB1,HAS1,NIP7,NOP7,NUG1,SSF1
SEC2,SEC4,SEC10,SEC15,MYO2,SMY1
MYO3,MYO5,BBC1,BZZ1,UBP7,VRP1
DBF2,DBF20,CDC15,LTE1,MOB1,SPO12
HHF1,HHF2,HHT1,HHT2,SPT6,STH1
CBF1,CEP3,CHL4,CTF13,MCM21,MIF2
N d Function Class Gene Name
YIP1
GCS1
YGL161c
YPL095c
YGL198w
YDR425w
(a) (b)
3.9x10-17
9.0x10-13
1.7x10-11
1.1x10-6
3.7x10-4
3.4x10-11
4.0x10-6
2.1x10-10
1.9x10-5
4.8x10-7
3.4x10-5
3.1x10-9
4.5x10-7
6.8x10-7
3.5x10-6
5.4x10-3
1.3x10-4
3.5x10-6
9.5x10-4
1.3x10-7
6.3x10-10
1.0x10-4
4.8x10-1
2.3x10-3
2.4x10-5
1.0x10-4
1.2x10-3
1.8x10-5
2.3x10-5
Corrected P-value
We considered 15 functional classes: (1) Cell cycle and DNA processing, (2) Protein with binding function or cofactor requirement (structural or catalytic), (3) Protein fate (folding, modification, destination), (4) Biogenesis of cellular components, (5) Cellular transport, transport facilitation and transport routes, (6) Metabolism, (7) Interaction with the cellular environment, (8) Transcription, (9) Energy, (10) Cell rescue, defense and virulence, (11) Cell type differentiation, (12) Cellular communication/signal transduction mechanism, (13) Protein activity regulation, (14) Protein synthesis, and (15) Transposable elements, viral and plasmid proteins
1
01
k
i
C
N
iC
FN
i
F
P
Results: Hypergeometric distribution
N= Total number of proteins in the network
F= Number of proteins of a functional group in the network
C= Number of proteins in a cluster
k= Number of proteins of a functional group in a cluster
The p-value of a cluster implies the probability that the proteins of the cluster have been randomly selected
The lower the p-value the higher the statistical significance
3 green and 4 red balls
Put them in a box
Randomly choose any 3
P0(# of red ball is 0) = 35
1
3
7
3
3
0
4
P1(# of red ball is 1) = 35
12
3
7
2
3
1
4
P2(# of red ball is 2) = P3(# of red ball is 3) = 35
18
3
7
1
3
2
4
35
4
3
7
0
3
3
4
Notice that, P0 +P1+P2+P3=1
P-value & Hyper geometric distribution
P0(# of red ball is 0) = 35
1
3
7
3
3
0
4
P1(# of red ball is 1) = 35
12
3
7
2
3
1
4
P2(# of red ball is 2) = P3(# of red ball is 3) = 35
18
3
7
1
3
2
4
35
4
3
7
0
3
3
4
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 32
P-value & Hyper geometric distribution
P0(# of red ball is 0) = 35
1
3
7
3
3
0
4
P1(# of red ball is 1) = 35
12
3
7
2
3
1
4
P2(# of red ball is 2) = P3(# of red ball is 3) = 35
18
3
7
1
3
2
4
35
4
3
7
0
3
3
4
P(# of red ball ≤ 1)= P0 +P1
P(# of red ball ≥ 2)=1-(P0 +P1)
P(# of red ball ≥ k)=1-(P0 +P1+…+Pk-1)
1
01
k
i
C
N
iC
FN
i
F
P N=7, F=4, C=3
P-value & Hyper geometric distribution
Results: Details of a Group of Predicted Complexes
Information on the complexes that are of size 6 of the set generated using din=0.7, cpin=0.50 and non-overlapping mode.
Protein YDR425w of complex 19 is related to cellular transport and YIP1, YGL198w, YGL161c and GCS1 are related to vesicular transport. Hence, we predict the function-unknown protein YPL095c of this complex is a transport related protein most likely related to vesicular transport.
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1 5 10 15
17
13
14
14
12
12
11
9
8
8
8
8
8
7
7
7
7
6
6
6
6
6
6
6
6
6
6
6
28 0.71
0.72
1.00
0.83
0.71
0.94
0.71
0.98
0.72
0.93
0.72
0.71
0.71
0.71
0.95
0.76
0.71
0.71
0.80
0.80
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
CTF4,CTF8,CTF18,CTF19,CIN1,CIN2,CIN8,GIM3,GIM4,GIM5,MAD1,MAD2,MAD3,BUB1,BUB3,PAC2,PAC10,ARP6,BIK1,BIM1,CHL1,CSM3, DCC1,HTZ1,KAR3,SCC1-73,TUB3,YKE2
CHS3,CHS5,CHS7,BNI1,BNI4,RVS161,RVS167,ARC40,ARP2,BCK1,CLA4,FKS1,KRE1,SKT5,SLT2, SMI1,SWI4
TAF17,TAF25,TAF60,TAF61,TAF90,SPT3,SPT7,SPT8,SPT20,ADA2,GCN5,HFI1,NGG1,TRA1
LSM1,LSM2,LSM3,LSM4,LSM5,LSM6,LSM7,LSM8,DCP1,KEM1,MRNa,PAT1,SNRNa,U6
RAD27,RAD50,CDC45-1,ELG1,ESC2,HPR5,MMS4,MRC1,POL32,RRM3,SGS1,TOF1,TOP3
TRS20,TRS23,TRS31,TRS33,TRS65,TRS85,TRS120,TRS130,BET3,BET5,GSG1,KRE11
COG5,COG6,COG7,COG8,ARL1,ARL3,GOS1,GYP1,RIC1,SWF1,TLG2,YPT6
APC1,APC2,APC4,APC5,APC9,APC11,CDC16,CDC23,CDC26,CDC27,DOC1
CDC73,CTI6,DEP1,LEO1,SAP30,SET2,SIF2,SWR1,VPS71
CFT1,CFT2,FIP1,PAP1,PFS2,PTA1,YSH1,YTH1
MED2,MED4,MED7,MED8,PGD1,RPB3,SOH1,SRB4
BEM1,BEM2,BOI1,BOI2,CDC24,CDC42,MSB1,STE20
ARP1,ASE1,CLB4,JNM1,KAR9,KIP3,NIP100,PAC11
CDC4,CDC34,CDC53,CLN1,CLN2,CLN3,SIC1,SKP1
CDC3,CDC10,CDC11,CDC12,GIN4,SEP7,SHS1
CKA1,CKA2,CKB1,CKB2,CDC7-1,RHO3,TOP2
SNR3,SNR10,SNR11,SNR189,GAR1,NHP2,NOP10
SPC19,SPC24,NNF1,NUF2,SMC1,TID3,YDR295c
YGL161c,YGL198w,GCS1,YDR425w,YIP1,YPL095c
PRP5,PRP9,PRP11,PRP21,NOG2,YNR053c
NUP49,NUP57,APG17,NIC96,NSP1,SEC35
KTR3,LAS17,SLA1,YFR024c,YOR284w,YSC84
ECM31,GCD7,NIP29,TEM1,YJL199c,YPL070w
ERB1,HAS1,NIP7,NOP7,NUG1,SSF1
SEC2,SEC4,SEC10,SEC15,MYO2,SMY1
MYO3,MYO5,BBC1,BZZ1,UBP7,VRP1
DBF2,DBF20,CDC15,LTE1,MOB1,SPO12
HHF1,HHF2,HHT1,HHT2,SPT6,STH1
CBF1,CEP3,CHL4,CTF13,MCM21,MIF2
N d Function Class Gene Name
YIP1
GCS1
YGL161c
YPL095c
YGL198w
YDR425w
(a) (b)
3.9x10-17
9.0x10-13
1.7x10-11
1.1x10-6
3.7x10-4
3.4x10-11
4.0x10-6
2.1x10-10
1.9x10-5
4.8x10-7
3.4x10-5
3.1x10-9
4.5x10-7
6.8x10-7
3.5x10-6
5.4x10-3
1.3x10-4
3.5x10-6
9.5x10-4
1.3x10-7
6.3x10-10
1.0x10-4
4.8x10-1
2.3x10-3
2.4x10-5
1.0x10-4
1.2x10-3
1.8x10-5
2.3x10-5
Corrected P-value
Conclusions
•In this work, we present an algorithm to detect locally dense regions in undirected simple graphs.
•The algorithm can be used to detect protein complexes in large protein-protein interaction networks or co-expressed gene clusters based on microarray data.
•It can also be used for protein/gene function prediction by way of finding complexes/clusters in networks consisting of function known and function unknown proteins.
•Also, DPClus can be applied to other networks where finding cohesive groups is an agenda.
The DPClus software is available at http://kanaya.naist.jp/DPClus/
Md. Altaf-Ul-Amin, Hisashi Tsuji, Ken Kurokawa, Hiroko Asahi, Yoko Shinbo, Shigehiko Kanaya, “DPClus: A Density-periphery Based Graph Clustering Software Mainly Focused on Detection of Protein Complexes in Interaction Networks”, Journal of Computer Aided Chemistry , Vol.7, 150-156, 2006.
2. The DPClus Software
The DPClus software is available at http://kanaya.naist.jp/DPClus/
The DPClus software has been developed based on the proposed algorithm.
The main window of DPClus
The DPClus Software
AtpB AtpAAtpG AtpEAtpA AtpHAtpB AtpHAtpG AtpHAtpE AtpH
The input file format
0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0
List of edgesCorresponding network
Adjacency matrix
The DPClus Software
Adjacency list
AtpA AtpB, AtpH AtpB AtpA , AtpH AtpH AtpB, AtpA, AtpG, AtpE AtpG AtpH, AtpEAtpE AtpG
ClusterLength of cluster 1 is: 8RpoARpoBRpoCRsdRpoZRpoDRpoNFliAClusterLength of cluster 2 is: 8AtpHAtpGAtpBAtpAAtpFAtpLAtpEAtpB(A)ClusterLength of cluster 3 is: 5----------------------------------------------------------------------------
Output file format
The DPClus Software
Click!
Intra cluster edges are green and inter cluster edges are red
Nodes have been arranged by dragging
The DPClus Software
Click
Click
Click
Hierarchical graph of the clusters
The DPClus Software
Clustering of microarray data
Sample microarray data
To apply DPCcus, we need to convert this data to a network
The DPClus Software
Experiment ID
Genes
m
kjjk
m
kiik
m
kjjkiik
ij
xxxx
xxxxR
1
2
1
2
1
)()(
))((
Gene-Gene correlation
Select highly correlated gene pairs
Edges of a Network
At3g10060At3g54150At3g10060At3g63140At3g10060At5g07020-------------- --------------------------- -------------
The DPClus Software
# of experiments 626 Threshold correlation 0.95cp value 0.5density value 0.9Minimum cluster size 3
The DPClus Software
Ribosomal proteinclusters
Electron transport clusters
Photosynthesis clusters
The DPClus Software
Partitioning a PPI Network into Overlapping Modules Constrained by High-Density and Periphery Tracking Md. Altaf-Ul-Amin, Masayoshi Wada and Shigehiko KanayaVolume 2012 (2012), Article ID 726429, ISRN Biomathematics
The DPClusO Algorithm
DPClusO has been developed with similar concepts like DPClus but DPClusO is more general and advantageous.
•each node goes to at least one cluster •no two clusters are completely the same •density of each cluster is more than or equal to user given density• clusters are constrained by periphery if that exists
Major differences with DPClus
•each node goes to at least one cluster as big as possible
•Memory efficient
•Faster computation
C D A B E F G H I K L MQ R S T ON J P
C D A B E F G Q R S T O L K I H M J G I N J M H E F O M N P N J
Clustering by DPClus Clustering by DPClusO
Example showing difference in clustering by DPClus and DPClusO
In both cases clustering was done using din = 0.6 and cpin = 0.5
Evaluation of DPClusO
Measures used for Evaluation
Overlapping score: How two clusters match with each other
How a set of predicted clusters match with a set of known clusters
How rich a cluster is with similar function proteins
Plot of the number of clusters generated by DPClusO with respect to maximum overlapping. OVmax=0 means all modules are completely non-overlapping. For other points OVmax indicates the maximum overlapping score between any two modules.
DPClusO generated clusters are not too overlapping
64
0
100
200
300
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500
0 0.5 1 0 0.5 1
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0 0.5 1 0 0.5 1
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DPClusO
Coach
Core
DPClusO/3
Coach/3
Core/3
# o
f m
atc
he
d c
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OV
(a) Union (b) Krogan
(d) Gavin(c) DIP
(e) MIPS
Plots showing how many and to what extent the known protein complexes (all complexes and size 3 or more complexes shown separately) of yeast matched with modules predicted by DPClusO, COACH and CORE corresponding to five different datasets.
DPClusO detected more known protein complexes
65
Variation of F-measure with maximum overlapping score (used as a filtering parameter) for modules of size 3 or more generated by DPClusO, COACH and CORE. The marked horizontal lines indicate F-measures for three algorithms in case of no filtering.
By adding simple filtering DPClusO achieved the best F-measure
0
500OriginalAddRemoveRearrange
0.0 0.5 1.00.0 0.5 1.0
0.0 0.5 1.00.0 0.5 1.00
500
(a) for 5% changes (b) for 5% changes (S3)
(c) for 10% changes (d) for 10% changes (S3)
OV
# of
mat
ched
clu
ster
s
Verifying robustness of DPClusO by comparing generated modules from real and randomly altered PPI networks in the context of matching with known complexes. (a) & (b) In case of addition, removal and rearrangement of 5% edges in the context of all and size 3 or more known complexes respectively. (c) & (d) In case of addition, removal and rearrangement of 10% edges in the context of all and size 3 or more known complexes respectively.
DPClusO is a robust algorithm
67
Comparison between the distributions of the high density modules and randomly selected protein groups with respect to –log(p-value) in the contexts of three types of gene ontology terms: (a), (b) biological process(BP), (c), (d) cellular cpmpartment (CC), (e), (f) molecular function(MF).
DPClusO detected modules are rich with similar function proteins
0
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1 150120906030 1 150120906030
1 150120906030 1 150120906030
1 150120906030 1 150120906030
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(a)BP (b) BP(random)
(c)CC (d) CC(random)
(e) MF (f) MF(random)
-log(p-value)#
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rs
Comparison between the distributions of the star and star like modules and randomly selected protein groups with respect to –log(p-value) in the contexts of three types of gene ontology terms: (a), (b) biological process(BP), (c), (d) cellular cpmpartment (CC), (e), (f) molecular function(MF).
Also as a consequence of DPClusO clustering it was learnt that a PPI network is a combination of mainly high density and star-like modules.
DPClusO is a network clustering algorithm
Easily we can convert multivariate data into networks and apply DPClusO for clustering
DPClusO is freely available at:http://kanaya.naist.jp/DPClusO
Given a nxp data matrix X, where n is the number of objects (e.g. genes) and p is the number of conditions (e.g. array), a bicluster is defined as a submatrix XIJ of X within which a subset of objects I express similar behavior across the subset of conditions J.
A nxp data matrix X can be easily converted to a bipartite graph by considering a threshold or so.
Finding bicluster (densely connected regions) in a bipartite graph is a similar problem.
Definition of a bicluster
A Graph G=(V,E) is bipartite if its vertex set V can be partitioned into two subsets V1, V2 such that each edge of E has one end vertex in V1 and another in V2.
V1
V2
Biclusters are densely connected regions in a bipartite graph
C d A a G g I f K k
D c A b G h I g L i
D d B a H e I h L j
E c B b H f J f L k
E d C a H g J g M l
F c C b H h K h M m
F d D a I e G f N l
G d D b K i C c N m
K j
Gene expression data can be represented as bipartite graphs
gene/cond. cond0 cond1 cond2 cond3 cond4
YAL005C 2.85 3.34 0 0 0
YAL012W 0.21 0.03 0.18 -0.27 -0.32
YAL014C -0.03 -0.07 0.28 0.32 -0.27
YAL015C -0.25 0.58 0.77 0.28 0.32
YAL016W 0.11 0.04 0.75 0.82 0.21
YAL017W 0.24 0.31 0.95 0.12 0.18
YAL021C -0.3 0.22 0.02 -0.64 0.06
gene/cond. cond0 cond1 cond2 cond3 cond4
YAL005C 1 1 0 0 0
YAL012W 0 0 0 0 0
YAL014C 0 0 0 0 0
YAL015C 0 0 0 0 0
YAL016W 0 0 0 1 0
YAL017W 0 0 1 0 0
YAL021C 0 0 0 0 0
By transforming highest 5% values to 1
Before transforming, the data can be normalized
Biclusters in gene expression data represents transcription modules/co-expressed gene groups
•Tanay,A. et al. (2002) Discovering statistically significant biclusters in gene expression data. Bioinformatics, 18 (Suppl. 1), S136–S144.
•Ihmels,J. et al. (2002) Revealing modular organization in the yeast transcriptional network. Nat. Genet., 31, 370–377.
•Ben-Dor,A., Chor,B., Karp,R. and Yakhini,Z. (2002) Discovering local structure in gene expression data: the order-preserving sub-matrix problem. In Proceedings of the 6th Annual International Conference on Computational Biology, ACM Press, New York, NY, USA, pp. 49–57.
•Cheng,Y. and Church,G. (2000) Biclustering of expression data. Proc. Int. Conf. Intell. Syst. Mol. Biol. pp. 93–103.
•Murali,T.M. and Kasif,S. (2003) Extracting conserved gene expression motifs from gene expression data. Pac. Symp. Biocomput., 8, 77–88.
We propose a biclustering method incorporating DPClus
G/E a b c d e f g h i j k l m
A 1 1 0 0 0 0 0 0 0 0 0 0 0
B 1 1 0 0 0 0 0 0 0 0 0 0 0
C 1 1 1 1 0 0 0 0 0 0 0 0 0
D 1 1 1 1 0 0 0 0 0 0 0 0 0
E 0 0 1 1 0 0 0 0 0 0 0 0 0
F 0 0 1 1 0 0 0 0 0 0 0 0 0
G 0 0 0 1 1 1 1 0 0 0 0 0 0
H 0 0 0 0 1 1 1 1 0 0 0 0 0
I 0 0 0 0 1 1 1 1 0 0 0 0 0
J 0 0 0 0 1 1 0 0 0 0 0 0 0
K 0 0 0 0 0 0 0 1 1 1 1 0 0
L 0 0 0 0 0 0 0 0 1 1 1 0 0
M 0 0 0 0 0 0 0 0 0 0 0 1 1
N 0 0 0 0 0 0 0 0 0 0 0 1 1
An example bipartite graph and its corresponding matrix
1||
0
)()(C
jkjBGijBGik MMCN (for ik)
BiClus:Biclustering method incorporating DPClus
Concerning each row i (i=0 to |G|-1) of MCN, we calculate thresholdi=avgi+(maxi- avgi) Gmargin and set (MSG)ik =(MSG)ki=1if (MCN)ik thresholdi and thresholdi is not an indeterminate number (for k=0 to |G|-1).Here, avgi = SUMi/ni where ni is the number of non-zero entries in row i of MCN
and maxi is the maximum value of the entries in row i of MCN
Gmargin is a user defined value 1.
A B C D E F G H I J K L M N
A 0 2 2 2 0 0 0 0 0 0 0 0 0 0
B 2 0 2 2 0 0 0 0 0 0 0 0 0 0
C 2 2 0 4 2 2 1 0 0 0 0 0 0 0
D 2 2 4 0 2 2 1 0 0 0 0 0 0 0
E 0 0 2 2 0 2 1 0 0 0 0 0 0 0
F 0 0 2 2 2 0 1 0 0 0 0 0 0 0
G 0 0 1 1 1 1 0 3 3 2 0 0 0 0
H 0 0 0 0 0 0 3 0 4 2 1 0 0 0
I 0 0 0 0 0 0 3 4 0 2 1 0 0 0
J 0 0 0 0 0 0 2 2 2 0 0 0 0 0
K 0 0 0 0 0 0 0 1 1 0 0 3 0 0
L 0 0 0 0 0 0 0 0 0 0 3 0 0 0
M 0 0 0 0 0 0 0 0 0 0 0 0 0 2
N 0 0 0 0 0 0 0 0 0 0 0 0 2 0
Common neighbor matrix of the bipartite graph
A B C D E F G H I J K L M N
A 0 1 1 1 0 0 0 0 0 0 0 0 0 0
B 1 0 1 1 0 0 0 0 0 0 0 0 0 0
C 1 1 0 1 1 1 0 0 0 0 0 0 0 0
D 1 1 1 0 1 1 0 0 0 0 0 0 0 0
E 0 0 1 1 0 1 1 0 0 0 0 0 0 0
F 0 0 1 1 1 0 0 0 0 0 0 0 0 0
G 0 0 0 0 1 0 0 1 1 1 0 0 0 0
H 0 0 0 0 0 0 1 0 1 1 0 0 0 0
I 0 0 0 0 0 0 1 1 0 1 0 0 0 0
J 0 0 0 0 0 0 1 1 1 0 0 0 0 0
K 0 0 0 0 0 0 0 0 0 0 0 1 0 0
L 0 0 0 0 0 0 0 0 0 0 1 0 0 0
M 0 0 0 0 0 0 0 0 0 0 0 0 0 1
N 0 0 0 0 0 0 0 0 0 0 0 0 1 0
BiClus:Biclustering method incorporating DPClus
This matrix represents a simple graph
BiClus:Biclustering method incorporating DPClus
Simple graph derived from the common neighbor matrix.
We can use DPClus to find clusters in the simple graph.
BiClus:Biclustering method incorporating DPClus
Clustering by DPClus
BiClus:Biclustering method incorporating DPClus
Clustering by DPClus
BiClus:Biclustering method incorporating DPClus
Finally determined biclusters
Evaluation of BiClus
-Using Synthetic data-Using real data
Synthetic data
Artificially embedded biclusters with noise
Evaluation of BiClus
Synthetic data
Artificially embedded biclusters with overlap
Evaluation of BiClus
||
||max
||
1),(
21
21
),(),(
121
*
111222 GG
GG
MMMS
MCGMCG
G
Let M1, M2 be two sets of biclusters. The gene match score of M1 with respect to M2 is given by the function
Evaluation of BiClus
A systematic comparison and evaluation of biclustering methodsfor gene expression dataAmela Prelic´, Stefan Bleuler, Philip Zimmermann, Anja Wille, Peter Bu¨ hlmann, Wilhelm Gruissem, Lars Hennig, Lothar Thiele and Eckart Zitzle
BIOINFORMATICS, Vol. 22 no. 9 2006, pages 1122–1129
effect of relevance of BCs
0
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0.4
0.6
0.8
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noise level
avg
mat
chin
g sc
ore
SAMBA
BiClus
Evaluation of BiClus
Synthetic data
Artificially embedded biclusters with noise
Evaluation of BiClus
regulatory complexity: relevance of BCs
0
0.2
0.4
0.6
0.8
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0 1 2 3 4 5 6 7 8 9
overlap degree
avg
mat
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ore
SAMBA
BiClus
Synthetic data
Artificially embedded biclusters with overlap
Gasch,A.P. et al. (2000) Genomic expression programs in the response of yeast cells to environmental changes. Mol. Biol. Cell, 11, 4241–4257.
Gene expression data collected from the above work
Gene expression data can be represented as bipartite graphs
gene/cond. cond0 cond1 cond2 cond3 cond4
YAL005C 2.85 3.34 0 0 0
YAL012W 0.21 0.03 0.18 -0.27 -0.32
YAL014C -0.03 -0.07 0.28 0.32 -0.27
YAL015C -0.25 0.58 0.77 0.28 0.32
YAL016W 0.11 0.04 0.75 0.82 0.21
YAL017W 0.24 0.31 0.95 0.12 0.18
YAL021C -0.3 0.22 0.02 -0.64 0.06
gene/cond. cond0 cond1 cond2 cond3 cond4
YAL005C 1 1 0 0 0
YAL012W 0 0 0 0 0
YAL014C 0 0 0 0 0
YAL015C 0 0 0 0 0
YAL016W 0 0 0 1 0
YAL017W 0 0 1 0 0
YAL021C 0 0 0 0 0
By transforming highest 5% values to 1
Before transforming, the data can be normalized
Biclusters in gene expression data represents transcription modules
0.001 0.010.0030.002
Evaluation of BiClus
Real gene expression data of yeast
P-values represents statistical significance of functional richness of the modules
P-Values calculated using FuncAssociate: The Gene Set Functionator from http://llama.med.harvard.edu/cgi/func/funcassociate
Application of network concepts in DNA sequencing
Sequencing by hybridization (SBH)
Input: A spectrum S representing all l-mers from an unknown string s
Output: The string s such that spectrum (s,l) = S.
Given an unknown DNA sequence, an array provides information about all strings of length l that the sequence contains
s=TATGGTGC
S(s,l)={TAT, ATG, TGG, GGT, GTG, TGC}
S(s,l)={GTG, ATG, TGG, TAT, GGT, TGC}
Orderly placed
Randomly placed
Input: A spectrum S representing all l-mers from an unknown string s
Output: The string s such that spectrum (s,l) = S.
The reduction of the SBH problem to an Eulerian path problem is to construct a graph whose edges correspond to l-mers from spectrum(s,l) and then to find a path in this graph visiting every edge exactly once.
Sequencing by hybridization (SBH)
The reduction of the SBH problem to an Eulerian path problem is to construct a graph whose nodes correspond to (l-1)-mers and edges correspond to l-mers from spectrum(s,l) and then to find a path in this graph visiting every edge exactly once.
S(s,l)={GTG, ATG, TGG, TAT, GGT, TGC}
(l-1)-mers: GT, TG, AT, TG, TG, GG, TA, AT, GG, GT, TG, GC
(l-1)-mers(redundancy removed): GT, TG, AT, GG, TA, GC
GT
AT GG
TA
GC
TG
s=TATGGTGC
Sequencing by hybridization (SBH)
A path in a graph visiting every edge exactly once is called Eulerian (pronounced Oilerian) path
A connected graph has an Eulerian path, if and only if it contains at most two semibalanced nodes and all other nodes are balanced.
Balanced node, indegree=outdegree
Semibalanced node |indegree-outdegree|=1
GT
AT GG
TA
GC
TG
Semibalanced
Sequencing by hybridization (SBH)
S(s,l)={ATG, TGG, TGC, GTG, GGC, GCA, GCG, CGT}
(l-1)-mers:AT, TG, TG, GG, TG, GC, GT, TG, GG, GC, GC, CA, GC, CG, CG, GT
(l-1)-mers(redundancy removed):AT, TG, GG, GC, GT, CA, CG
GGAT
GC
TG
GT CA
CG
ATGGCGTGCA
Sequencing by hybridization (SBH)
Another example
S(s,l)={ATG, TGG, TGC, GTG, GGC, GCA, GCG, CGT}
(l-1)-mers:AT, TG, TG, GG, TG, GC, GT, TG, GG, GC, GC, CA, GC, CG, CG, GT
(l-1)-mers(redundancy removed):AT, TG, GG, GC, GT, CA, CG
GGAT
GC
TG
GT CA
CG
ATGCGTGGCA
Sequencing by hybridization (SBH)