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Introduction

Affinity propagation (AP) is a relatively new clustering algorithm that was introduced by Frey and Dueck (1) to determine a so-called exemplar for clustered data, which is a sample that is most representative for the respective cluster. It works for any meaningful measure of similarity between data samples, but does not require a vector space structure and the exemplars are selected amongst the data samples observed and not computed as hypothetical averages of cluster samples (2). These advantages make AP clustering particularly suitable for applications in bioinformatics, which has been verified by previously published studies (3–5). For instance, Kiddle et al (3) successfully revealed transcriptional modules in Arabidopsis thaliana based on temporal clustering of gene expression data by AP.

Prior to controlling the quality of the partition of a known number of clusters with AP, Sakellariou et al (6) supplemented the Krzanowski and Lai (KL) index (7) to evaluate the optimum number of clusters, by retaining maxT function in order to rank the genes in microarray data. This combination offers a more meaningful way of investigating exemplars or informative genes for disease and the relative target treatment. However, genes typically work together with other genes in complex processes associated with tumors. A network-based approach is capable of extracting informative and notable genes dependent on biomolecular networks. For instance, a protein-protein interaction network, co-expression network and mutual information network (MIN) rather than individual genes (8,9).

Therefore, the present study combined multiple (m) AP-KL and MIN to investigate key genes in fibroids, which made the results, more reliable. mAP-KL was initially implemented to investigate clusters and exemplars in fibroid, and the support vector machines (SVMs) model was selected to evaluate the classification performance of mAP-KL. MIN for cluster genes was constructed based on the context likelihood of relatedness (CLR) algorithm, and topological analysis (degree, closeness, betweenness and transitivity) of exemplars was performed to investigate key genes in fibroid. Key genes may be potential biomarkers for further prognostic and therapeutic insights for fibroid.

Materials and methods

Microarray data

In the present study, the gene expression data for the fibroid (access number E-GEOD-64763) originated from the A-AFFY-37-Affymetrix GeneChip Human Genome U133A 2.0 [HG-U133A_2] Platform of the ArrayExpress database (ebi.ac.uk/arrayexpress/), and shared a set of 25 fibroid samples that had been compared to 29 normal controls. The total samples were divided into two sets according to a ratio of 3:2, and 32 were kept to build a balanced training set (16 fibroid and 16 normal samples). In total, 22 were used to construct a test set for the purpose of validating the classification models (9 fibroid and 13 normal samples). In E-GEOD-64763, a total of 22,277 probes were detected.

To further control the quality of data and eliminate batch effects caused by experimental parameters and other factors, all data underwent mean-centering (10), z-score (11), quantile (12) and cyclic loess (13) normalization across samples, and log2 transformation was subsequently performed on the normalized data. The preprocessed results are illustrated in Fig. 1 and a better association was identified between the density and intensity of genes following cyclic loess preprocessing compared with that of raw data and other methods. Therefore, the preprocessed training set and test set data underwent further analysis for fibroid.

Figure 1. Preprocessing for microarray data by mean centering, z-score, quantile and cyclic loess methods.

mAP-KL

A data-driven and classifier-independent hybrid feature selection method was implemented, mAP-KL, which included maxT multiple hypothesis testing (14), KL cluster quality index (7) and the AP clustering algorithm (1), in order to select a small subset of informative genes of fibroid. The hypothesis was that among the statistically significant genes there should be clusters of genes that share similar biological functions correlated with the disease investigated, thus, instead of keeping a number of the top ranked genes, it would be more appropriate to define and keep a number of gene cluster exemplars (6). Subsequently, the index of KL was applied to determine the number of clusters solely on the fibroid samples of the training test set. Finally, the AP clustering method was engaged to detect clusters and provide a list of the most informative genes of each cluster, the so-called exemplars.

MaxT hypothesis testing

In the present study, the maxT function, which computes permutation adjusted P-values for step-down multiple testing procedures (15), was employed to rank the genes of the training set and the top N genes were then reserved for further exploitation (16). The family-wise error rate was evaluated in order to correct P-values using the Wilcoxon rank sum statistic with permuted class labels. Furthermore, the maximum Wilcoxon statistic was recorded for 1,000 random permutations and the P-value for each gene was estimated as the proportion of the maximum permutation-based t-statistics that were greater than the observed value (17).

KL cluster quality index

Prior to clustering analysis with AP, KL as induced in the ClusterSim package version 0.45–1 (University of Economics, Wroclaw, Poland) was utilized to define the number of clusters, which in essence would be the number of representative genes. The KL was calculated by the following formula:

Of which ∅(k)=(k–1)2/PWk–1–k2/PWk

Where k was the number of clusters and Wk represented the within-cluster sum of squared errors. The clusters that met a threshold of gene numbers <50 were regarded as KL clusters.

AP clustering algorithm

An AP clustering method included in the APCluster package version 1.3.2 (Johannes Kepler University, Linz, Austria) identifies an exemplar for each cluster, which was most representative for this cluster. It regards each data point as a node in a network and recursively transmits real-valued messages along edges of the network until a good set of exemplars and corresponding clusters emerge (2). In this final step, n (n=k, the KL index) clusters were explored among the top N genes according to the pre-defined number, and a list of n exemplars was obtained (18). These were expected to form a classifier to discriminate between the normal and fibroid classes in a test set that was formulated through retaining only those n genes required to proceed with the classification.

Classification and evaluation

In the present study, SVM (19) with linear kernel (20) was applied to evaluate the performance of mAP-KL. Initially, a five-fold cross-validation was conducted on the training set to evaluate the potential classification strength of the models, and then its prediction was computed on a separate test set.

For the purpose of accessing the classification results, several measures were selected, which included the area under the receiver operating characteristics curve (AUC), the true negative rate (TNR), true positive rate (TPR) and the Matthews coefficient correlation classification (MCC). In detail, accuracy (ACC) was one of the most popular performance measures in machine learning classification; however, it did not take into account the nature of the incorrect predictions. Therefore, the AUC was used, as it had been introduced as a better measure for evaluating the predictive ability of machine learners compared with ACC (21). Additionally, TNR or specificity represented the ratio of correctly classified negatives to the actual number of negatives, as well as TPR or sensitivity, which was defined to be the ratio of positives correctly classified to the actual number of positives (22). Furthermore, MCC was a measure of the quality of binary classification and considered the true and false positive and negatives (23). The combination of those measures provided an adequate overview of the classification's performance.

MIN construction and topological analysis

MIN typically relied on the estimation of mutual information (MI) between all pairs of variables, and has previously attracted the attention of the bioinformatics community for the inference of very large networks (24,25). MIN construction for cluster related top N genes was comprised of three steps. The first step was the computation of the MI matrix (MIM), a square matrix whose i, j-th element was the mutual information between the random genes Xi and Xj, and q was a probability measure.

The second step was the computation of an edge score for each pair of nodes by the algorithm. The CLR algorithm was an extension of the relevance network approach (25) and the MI for each pair of genes was computed and a score related to the empirical distribution of the MI values was derived (26). In particular, instead of considering the information I (Xi; Xj) between genes Xi and Xj, it took into account the edge score:

Where zi=max(0,I(Xi;Xj–μi)σi)

Of which µi and σi represented the sample mean and standard deviation of the empirical distribution of the values I (Xi; Xj), respectively.

The final step was to input the genes and edge scores into the igraph software package (27) and to visualize the MIN.

In order to investigate the biological functions and significance of nodes in the MIN, the importance was characterized using indices of topological analysis [degree (28), closeness (29), betweenness (30) and transitivity (31)]. The degree quantifies the local topology of each gene by summing up the number of its adjacent genes. Closeness centrality was a measure of the average length of the shortest paths to access all other genes in the network. Betweenness centrality was a shortest paths enumeration-based metric in graphs for determining how the neighbors of a node were interconnected, and was considered the ratio of the node in the shortest path between two other nodes. Furthermore, transitivity, a measure for clustering coefficient, gave an indication of the clustering in the whole network.

Results

In the present study, the top 200 genes in the gene expression profile were reserved based on maxT multiple hypothesis testing for further exploitation, and the top 100 genes are listed in Table I. Following the AP-KL, an elaborate set of analytical clusters with SVM on the training set was executed, and validation was conducted on a separate test set in order to evaluate its performance across the gene expression data. Meanwhile, MIN for the top 200 genes was constructed and its topological properties were identified in order to investigate the roles and significance of cluster genes and exemplars obtained from mAP-KL in fibroid.

Table I. Top 100 genes based on maxT multiple hypothesis testing.

Table I.

Top 100 genes based on maxT multiple hypothesis testing.

Number	Gene
1	IGSF3
2	NAV2
3	KIF5C
4	CAPN6
5	FMO4
6	BAX
7	EPB41L2
8	KCNS3
9	COL4A1
10	SYBU
11	GPSM2
12	ABLIM3
13	CAMKMT
14	POPDC2
15	MAP4K4
16	CALCOCO2
17	TIMM44
18	NPDC1
19	HEPH
20	ANXA1
21	COL4A2
22	KCNN1
23	PIK3R1
24	COPS8
25	BCAN
26	ITM2C
27	C9orf3
28	DCHS1
29	ADGRL1
30	ALDH2
31	PHYHIP
32	FAM63B
33	CYR61
34	LGALS3
35	BCAN
36	SNCG
37	PLAT
38	UST
39	VAMP2
40	SAV1
41	COL9A2
42	RPL38
43	GATA2
44	TEX10
45	IRF2
46	CBX8
47	MST1
48	PRR5L
49	PXDN
50	PRKD1
51	PEX7
52	TMEM246
53	EGFR
54	HTATIP2
55	PDGFC
56	PCBP2
57	SULT1A1
58	GCN1L1
59	COL5A2
60	COPS8
61	FBXL7
62	LMBRD1
63	DPT
64	PCNA
65	ADGRE5
66	PARVB
67	SULT1A2
68	ACAN
69	KLF4
70	PHLDA3
71	BMP7
72	SERPINF1
73	ADD3
74	VPS13D
75	MST1
76	USP3
77	SERINC5
78	LRP5
79	FAM46A
80	PA2G4
81	AIM1
82	TIA1
83	SYT11
84	MAPK10
85	IGFBP6
86	KLF4
87	FAM131B
88	C1R
89	FSD1
90	CADM1
91	SYT11
92	ADIRF
93	R3HCC1
94	SMC6
95	PIK3R1
96	ARRB1
97	SLC48A1
98	TNFRSF10B
99	DYRK2
100	MYO7A

Clusters and exemplars

By performing the AP clustering algorithm in conjunction with KL cluster quality for the top 200 genes, the quantity of clusters with <50 genes was 9, whose gene compositions are displayed in Table II. In addition, the gene compositions of different clusters were varied, and amongst them cluster 5 contained the highest number of genes (33 genes), whereas, only 12 genes were present in cluster 2. Furthermore, for each cluster, an exemplar was detected on the basis of the AP clustering method, which may be important in the progress of fibroid. From cluster 1 to 9, their exemplars were CALCOCO2, COL4A2, COPS8, SNCG, PA2G4, C17orf70, MARK3, BTNL3 and TBC1D13, respectively.

Table II. Clusters identified by the mAP-KL method for fibroids.

Table II.

Clusters identified by the mAP-KL method for fibroids.

Cluster	No. of genes	Genes
1	31	NAV2, CALCOCO2, NPDC1, PLAT, RPL38, COPS8, LMBRD1, PCNA, SERPINF1, SERINC5, KLF4, C1R, ADIRF, R3HCC1, FNBP1L, RTN3, YARS, ABLIM1, IVNS1ABP, TRPS1, ADD3, C1S, IFT20, UBE2L6, SMARCA2, LOXL2, SUCLG2, RPL38, BCAM, H1FX, MAFB
2	12	COL4A1, COL4A2, PDGFC, COL5A2, FN1, COL3A1, PALLD, SOX4, CST3, CD74, SPARC, FN1
3	21	HEPH, ANXA1, PIK3R1, COPS8, ITM2C, C9orf3, DCHS1, ALDH2, CYR61, LGALS3, PXDN, FBXL7, ADGRE5, PIK3R1, FYN, SMS, ENAH, SPCS3, SLC24A3, GNG11, CYR61
4	18	SNCG, HTATIP2, DPT, SULT1A2, KLF4, AIM1, ARRB1, SLC48A1, NPR1, TPSAB1, HFE, RAC2, RPS11, TOE1, SLC7A6, TESC, VRK3, SERPINB1
5	33	KIF5C, CAPN6, EPB41L2, MAP4K4, ADGRL1, VAMP2, SAV1, TEX10, IRF2, PRKD1, GCN1, PHLDA3, ADD3, USP3, FAM46A, PA2G4, TIA1, SYT11, MAPK10, IGFBP6, SMC6, TNFRSF10B, DYRK2, LRP12, NUDT3, TFAP2C, INPP1, ABCC1, ECI2, FLOT2, PPARD, GPSM2, TFPI
6	13	BAX, GPSM2, TIMM44, UST, COL9A2, LRP5, CADM1, FAAP100, AEN, TTC27, GSTM5, KNOP1, C1QL1
7	20	IGSF3, KCNS3, POPDC2, GATA2, PCBP2, SULT1A1, FAM131B, SYT11, NRN1, ENOX2, NUDT11, TDRD7, MTCL1, ALDH1A1, RARRES3, MARK3, ST3GAL2, ST3GAL1, SLC46A3
8	22	FMO4, ABLIM3, CAMKMT, KCNN1, FAM63B, BCAN, CBX8, PRR5L, PARVB, ACAN, BMP7, VPS13D, FSD1, MYO7A, CDK18, TMEM59L, FLT3LG, NPR1, PLCE1, BTNL3, POLG, CSPP1
9	18	SYBU, BCAN, RTP4, PHYHIP, MST1, PEX7, TMEM246, EGFR, MST1, PTK2B, TBC1D13, RALGDS, SP140L, ZMYND8, CCDC22, CLCN7, PIDD1, NKX3-1,

Evaluation by the SVM model

The test set consisted of the 9 exemplars. SVM with linear kernel was used to possess the performance of mAP-KL. This method achieved the highest classification scores (AUC=1.00, TNR=1.00, TPR=1.00 and MCC=1.00); therefore, it was concluded that the classification results were almost ideal during the SVM evaluation, and inferred that the mAP-KL methodology that combined ranking-filtering and cluster analysis was feasible and suitable for identifying exemplars of fibroid.

Topological analysis of MIN

The ideal evaluation of the classification for the mAP-KL method gave more confidence to the significance of 9 exemplars in fibroid, whereas those were also expected to form a classifier or module that is distinct between the normal controls and fibroid patients. Therefore, an MIN was constructed for the top 200 genes associated with cluster genes. A total of 178 genes were mapped to the MIN and 820 interactions were observed (Fig. 2). The topological properties of the 9 exemplars in the MIN are shown in Table III. The results for exemplars were inconsistent due to different methods, except for SNCG and COL4A2. Notably, the degree, closeness, betweenness and transitivity of SNCG were the highest among exemplars with 127, 263.29, 3.89 and 1122, separately. The second highest results were observed in COL4A2 with a degree, closeness, betweenness and transitivity of 110, 237.21, 3.71 and 1,075, respectively. Therefore, the two exemplars were more important for fibroid, thus we mined their connections from the MIN. The two genes were able to interact with each other and build a small module (Fig. 3) with 149 genes and 222 interactions. Furthermore, a MIN with 174 nodes and 1,002 interactions for the top 200 ranked genes in the microarray data was demonstrated in Fig. 4.

Figure 2. Mutual information network for clusters related the top 200 genes of fibroid. There were 174 nodes and 820 edges, where nodes represented genes, and edges were the interactions between two genes. The yellow nodes, CALCOCO2, COL4A2, COPS8, SNCG, PA2G4, C17orf70, MARK3, BTNL3 and TBC1D13, stood for exemplars of nine clusters identified via the multiple affinity propogation-Krzanowski and Lai method.

Figure 3. Sub-network for key genes (SNCG and COL4A2) extracted from the mutual information network, in which a total of 149 nodes and 222 edges were mapped. Nodes represented genes, and edges were the interactions between two genes. The yellow nodes were key genes of fibroid.

Figure 4. MIN for the top 200 ranked genes in the microarray data. There were 174 nodes and 1,002 interactions, where nodes represented genes, and edges were the interactions between two genes. The pink nodes were hub genes with top 5% degree distribution of the MIN. MIN, mutual information network.

Table III. Topological properties of exemplars in mutual information network.

Table III.

Topological properties of exemplars in mutual information network.

Exemplar	Degree	Closeness	Betweenness	Transitivity
CALCOCO2	104	174.81	3.54	1022
COL4A2	110	237.21	3.71	1075
COPS8	88	147.27	3.29	657
SNCG	127	263.29	3.89	1122
PA2G4	91	152.57	1.83	35
C17orf70	85	155.03	0.50	0
MARK3	93	149.75	3.05	44
BTNL3	87	131.67	3.01	0
TBC1D13	90	158.98	3.55	897

Discussion

Fibroid, also known as uterine leiomyoma or uterine fibroid, is begin smooth muscle neoplasm of the uterus and the most widespread gynecological problem amongst women (32). Important symptoms of fibroid include abnormal uterine bleeding, heavy or painful menstrual periods, abdominal discomfort or bloating, painful defecation, back ache, urinary frequency or retention, and in some cases, infertility (33). Although surgical staging and nomograms may help predict the clinical outcome, the five-year survival rate for uterus-confined disease remains <50% (34). Therefore, understanding the molecular biology and investigating potential biomarkers of fibroid may provide further prognostic and therapeutic insights.

In the present study, nine exemplars were investigated for clusters, which were obtained from the top 200 genes via the mAP-KL method, including CALCOCO2, COL4A2, COPS8, SNCG and PA2G4. Subsequently, the SVM model was used to assess the performance of the mAP-KL method to classify normal controls and fibroid patients, and the results demonstrated that there was a good classification, which indicated the feasibility of the mAP-KL method to identify exemplars in fibroid. In order to further explore the biological significance of exemplars, the topological analysis (degree, closeness, betweenness and transitivity) for MIN constructed by the CLR algorithm were conducted and two key genes, SNCG and COL4A2, were obtained resulting from their better topological properties compared with the other seven genes.

Constructing the MIN for the cluster related top 200 genes and building a network for them allowed for the determination of the activities of the genes in the network. Fig. 4 shows the MIN for the 200 top ranked genes in the microarray data, but four types of topological properties had no intersections and it may be inferred that this network was not as strict as the cluster MIN. In general, the degree was a familiar index, thus genes with a quantile of the top 5% degree distributions were defined as hub genes. Therefore, 8 hub genes were obtained in total, which included RARRES3, RPL38, ADD3, C1R, KLF4, SULT1A1, SNCG and C1S. In addition, there were great differences between exemplars and hub genes, except for one common gene, SNCG.

SNCG is a member of the synuclein neuronal protein family along with SNCA and SNCB, and is highly tissue-specific. In addition, it is expressed at presynaptic terminals in the brain and the peripheral nervous system (35). It promotes migration, invasion and metastasis of tumor cells (36), which have proven that expression of SNCG protein is elevated in the advanced stages of various types of cancers, including ovarian (37), lung, liver (38), esophagus (39), colon (38) and in particular, breast (40,41). For example, Singh and Jia (41) revealed that SNCG protein expression was correlated with pathological factors, including lymph node metastasis, tumor size and stage, and follow-up revealed that the survival rate of patients with SNCG-positive protein expression were significantly lower than the patients with negative expression for 438 cases with breast cancer. Furthermore, it had been demonstrated that overexpression of SNCG was a predictor for aggressive tumor behavior and adverse outcome in patients with endometrial cancer (42), and was a prognostic tool and therapeutic target in uterine serous carcinoma (43). However, there is currently no published research reporting the association between SNCG and fibroids, although it correlated with other uterine-associated cancers as described above. To the best of our knowledge the present study proposed for the first time that SNCG acts as a key role in fibroid.

COL4A2 was the other key gene for fibroids, which was implicated in extracellular matrix formation and encoded for collagen α, which is one of the main components of the endothelial basement membrane (44). Previous research reported that COL4A2 was overexpressed in fibroid, and that it displayed an anti-angiogenic gene expression profile in fibroids when compared with adjacent normal myometrium. These observations may explain the reduced microvascular density observed in fibroids relative to the myometrium (45) and was in accordance with the reduced microvessel density based on anti-von Willebrand factor immunostaining that was observed in fibroid with respect to normal myometrium (46). Additionally, Gilden et al (47) suggested that protein expression of COL4A2, versican and fibromodulin was increased in untreated leiomyoma cells compared with untreated patient-matched myometrial cells. Therefore, COL4A2 was differentially expressed between normal controls and fibroids.

In conclusion, nine exemplars were identified based on the mAP-KL method, and two key genes (SNCG and COL4A2) were investigated according to a topological analysis of MIN. These genes may be potential biomarkers for the detection and therapy of fibroids. Furthermore, the present study may give an insight for future studies associated with fibroid.

References