microarray technology , monitoring mrna abundance of tens of thousands of genes simultaneously , provides an efficient tool to characterize a cell at the molecular level .
it has been applied to a variety of research areas , ranging from biomarker detection [ 1 , 2 ] to gene regulatory networks [ 35 ] and cancer classification [ 68 ] . when applied to cancer research ,
microarray technology typically measures gene expressions of cancer and normal tissues or different types of cancer .
one important area in microarray - based cancer research is to identify genes that are differentially expressed between cancerous and normal cells and to discover diagnostic and prognostic signatures in order to predict therapeutic responses . over the years
, many statistical methods for the identification of differentially expressed genes have been developed , and most of them focused on the expression analysis of individual genes [ 915 ] .
however , the simple list of individual differentially expressed genes can only tell us which genes are altered by biological differences between different cell types and/or states .
it can not explain the reasons for the significant alterations in gene expression levels and the effects of such changes on other genes ' activities .
it is well known that in a biological system genes interact with each other forming various biological pathways in order to carry out a multitude of biological processes . to better understand the roles of these differentially expressed genes and their interactions in a complex biological system ,
since the identification of biological pathways is significantly influenced by those differentially expressed genes from different datasets or different statistical methods [ 16 , 17 ] , we reason here that an integration of multiple cancer microarray datasets and identification of the most common pathways from these data would reveal key relationships between crucial genes in carcinogenesis .
our focus on the interactions and pathways of cancer - related genes is important since changes in gene relations and key pathways are more relevant to carcinogenesis than individual genes alone .  
li   observed differences of gene coexpression patterns in different cellular states and attributed these changes in gene coexpression patterns to some third set of influential genes .
lai et al .    proposed a similar method to identify differential gene - gene coexpression patterns in cells from normal state to cancerous state .
however , these methods often perform the analyses on one single microarray dataset and typically generate unreliable results ; the results from different microarray datasets and various statistical methods could hardly overlap using these methods [ 20 , 21 ] .
furthermore , these methods fail to grasp the common molecular changes in cells transitioning from a normal state to the cancerous state .
choi et al .   introduced a model to find differential gene coexpression patterns related to cancer by combining independent datasets for different cancers .
they used a model similar to the t - test , which only considered the mean and variance of two groups of samples .
it is well known that traditional t - test has two disadvantages for microarray data analysis : first , it assumes that the datasets under analysis have a normal distribution , which is usually violated in microarray datasets ; second , if the number of genes is large and the number of samples is small , some of the standard deviations will be extremely small , and therefore the test statistics will be very high , which may lead to a significant bias .
nonparametric statistical test methods , such as the k - s test , require fewer assumptions for the data and may be preferred , especially , when the number of samples is small . in this paper
, we propose a novel method to detect the differentially changed gene relations in cancer versus normal tissues .
these 36 datasets contain both normal and tumor samples , which can subsequently yield two pearson correlation coefficient vectors for every gene pair , one for normal samples and the other for tumor samples .
we then perform a bootstrapping k - s test to identify some differentially changed gene relations .
finally we verify our results with three key pathways related to cancer and demonstrate that our method can find some meaningful alterations of gene relations .
as shown in table 1 , these microarray datasets contain both normal and tumor samples across 21 different types of cancer , and their platforms come from one of the three platforms : gpl570 ( affymetrix genechip human genome u133 plus 2.0 array ) , gpl96 ( affymetrix genechip human genome u133 array set hg - u133a ) , and gpl91 ( affymetrix genechip human genome u95 version set hg - u95a ) .
we divided every dataset into two expression data matrices : one matrix includes all normal samples , and the other includes all tumor samples . to integrate multiple microarray datasets across different platforms , we mapped each probe in different platforms to a unique entrez gene i d or a unique unigene symbol . for genes with more than one probe in one platform , we chose the probe with the highest mean expression value .
these pathways are related to three common traits in most and perhaps all types of human cancer : self - sufficiency in growth signals , insensitivity to antigrowth signals , and evading programmed cell death ( apoptosis ) .
in fact , hanahan and weinberg have already identified some signaling pathways to demonstrate the capabilities cancer cells acquire during tumor development in .
we extended these signaling pathways to three relatively complete and larger cancer - associated pathways ( antigrowth signaling , apoptosis , and growth signaling pathways ) from the cell cycle pathway , the apoptosis pathway and the mapk pathway in kegg .
we used these three pathways ( i.e. , cell cycle , apoptosis , and mapk pathways ) as our seeds and the genes in these pathways as our seed genes .
next we constructed three gene networks corresponding to the three cancer - associated pathways from hprd ( human proteins reference database , http://www.hprd.org/ ) and transfac   based on seed genes and their interacting partners .
we downloaded the protein - protein interaction ( ppi ) data released by hprd on september 1 , 2007 .
this ppi dataset contains 37107 human binary protein - protein interactions whose supporting experiments are indicated as in vivo , in vitro , or yeast two - hybrid .
we also collected 1042 transcription factor - target gene relations on human species from transfac .
so our gene networks included seed genes , protein interaction partners , and transcription factors ( tfs ) of seed genes or target genes for which seed genes served as their tfs .  
we used the kolmogorov - smirnov test ( k - s test ) to determine whether the distributions of values in two datasets differed significantly .
the two - sample k - s test is the most useful for comparing two samples because it is nonparametric and distribution - free .
the null hypothesis for this test is that two datasets are drawn from the same distribution .
, xn   with some unknown distribution , we can define an empirical distribution function by 
					 ( 1)sn(x)={0,if  x < x(1),kn , if  x(k)x
< x(k+1)1,if  xx(n ) ,  for  k=1,2,  ,n-1 , 
  where x1 ,  , xn are ordered from the smallest to the largest value .
the kolmogorov - smirnov statistic for a given function s(x ) is 
					 ( 2)dn = max  x  |sn(x)-s(x)| . 
 

dn will converge to 0 if the sample comes from distribution s(x ) . moreover , the cumulative distribution function of kolmogorov distribution is 
					 ( 3)k(x)=1 - 2i=1(-1)i-1e-2i2x2=2xi=1e-(2i-1)2  2/(8x2 ) . 
 
it is easy to prove that ndn = n  maxx|sn(x)-s(x)| will converge to the kolmogorov distribution .
therefore if ndn > k=pr(kk)=1- , the null hypothesis for the kolmogorov - smirnov test will be rejected at level . for the case of determining whether the distributions of two data vectors differ significantly , the kolmogorov - smirnov statistic is 
					 ( 4)dn , m = maxx|sn(x)-sm(x)| , 
  and the null hypothesis will be rejected at level  if 
					 ( 5)nmn+mdn , m > k. 
  the p - value from the k - s test can measure the confidence of the comparison results against the null hypothesis .
obviously , the smaller the p - value , the more confident we are of rejecting the null hypothesis .  
assume that we have n microarray datasets and a list of m genes , we denote the expression data matrix for normal samples as 
					 ( 6)nk=(x11kx12kx1pkx21kx22kx2pk .... xm1kxm2kxmpk )  k=1,  ,n , 
							 and the expression data matrix for tumor samples as 
				
					 ( 7)tl=(y11ly12ly1qly21ly22ly2ql .... ym1lym2lymql )  l=1,  ,n , 
  where p(k ) is   the number of normal samples in the kth dataset , and q(l ) is the number of tumor samples in the lth dataset .
for these two types of expression data matrices , each row represents one gene , and each column represents one sample .
the correlation coefficient for gene i   and gene   j from the kth normal sample can be calculated by 
					 ( 8)npcijk=a=1p(xiak - xik)(xjak - xjk)a=1p(xiak - xik)2a=1p(xjak - xjk)2 , 
  where xik is the average value of expression levels for gene i. the correlation coefficient for every gene pair from tumor samples can be calculated similarly .  
we use the bootstrapping k - s test to detect some gene relations with different pc ( pearson coefficient ) distributions .
the bootstrapping method generates n bootstrapping samples npc and tpc by repeatedly sampling with replacement from the original npcij and tpcij ( e.g. , step 4 ) , respectively .
it can give us an empirical distribution of p - value  , with which , we can estimate the probability that the distribution of two pc vectors are different . in our computational experiment , for a gene pair ,
if its value of pr( < 0.05 ) was larger than 0.8 , we considered it as a pair of genes with the correlation relation significantly different between normal and cancer cells .
for example , npc is an m  m matrix from normal samples in the first dataset , and npcij represents the correlation coefficient between gene 
 i ,   and gene j. compute n correlation coefficient matrices npc 
for example , npc is an m  m matrix from normal samples in the first dataset , and npcij represents the correlation coefficient between gene 
 i ,   and gene j. step 2compute n correlation coefficient matrices   tpc 
step 3for every gene pair ( gene i   and gene j ) , let 
						 ( 9)npcij=[npcij1npcij2npcij3npcijn],tpcij=[tpcij1tpcij2tpcij3  tpcijn ] , 
  for every gene pair ( gene i   and gene j ) , let 
						 ( 9)npcij=[npcij1npcij2npcij3npcijn],tpcij=[tpcij1tpcij2tpcij3  tpcijn ] , 
  step 4perform the following ( n is the number of samples we will generate using bootstrapping ) . 

for 
 k = 1 to n 
 do   generate bootstrap samples npc   and   tpc   from   npcij   and   tpcij , respectively . 

k 
  = 
 p - value of k - s test on   npc   and   tpc.end-foroutput pr( < 0.05 ) =  (  < 0.05)/n .
perform the following ( n is the number of samples we will generate using bootstrapping ) . 

do   generate bootstrap samples npc   and   tpc   from   npcij   and   tpcij , respectively . 

k 
  = 
 p - value of k - s test on   npc   and   tpc . output pr( <
in this section , we applied the bootstrapping k - s test method to analyze three cancer related pathways .  
cancer cells have the ability to evade these antiproliferation signals . in the antigrowth signaling pathway , transforming growth factor beta ( tgf ) initiates this pathway by binding to two tgf receptors , tgfbr1 and tgfbr2 .
the smad family proteins then transduce antigrowth signals to the cell cycle inhibitors p21 , p16 , p27 , and p15 , which can inhibit the action of cyclin - cdk complex .
the cyclin - cdk complex can phosphorylate rb and make rb dissociate from the e2f / rb complex to liberate e2f to activate the cell cycle procession from g1 to s phase ( figure 1(a ) ) .  
we found 689 unique genes related to these 19 genes from transfac and hprd . among these 708 genes , there were 4215 paired gene interactions , among which the correlation relations of 47 gene pairs were identified as significantly changed between normal and cancer cells .
among these 47 relations , we detected a cluster around smad family proteins which contained 15 relations with different distributions between normal samples and tumor samples ( figure 1(b ) ) .
most of them came from large - scale protein - protein interaction experiments without the associated molecular function .
for example , ( smad1arl4d ) , ( rhod  smad2 ) , and ( wee1smad3 ) in , ( papola  smad2 ) , ( snrp70smad5 ) , ( gpnmb  smad4 ) , ( psmd11smad3 ) , and ( smad9mbd1 ) in , and ( ewsr1smad4 ) in , all of them were detected based on large - scale protein - protein interaction experiments without annotation of molecular function .
our results indicate that although their associated functions and internal mechanisms are still unclear , these gene pairs are related to the tgf-smad signaling pathway , and the relation between the two genes in each pair is significantly different in cancer and normal cells .   additionally , we identified some differentially changed relations with known molecular functions as follows : magi2 ( a.k.a .
arip1)smad3 . magi2 ( arip1 ) can interact with smad3 , and overexpression of arip1 can significantly suppress smad3-induced transcriptional activity .
we validated this from the boxplot for magi2 ( arip1)smad3 ( figure 2(a ) ) . in normal samples ,
magi2 ( arip1 ) and smad3 showed a high positive correlation , while they had a high negative correlation in tumor samples .
although the experiment type of the interaction between ewsr1 and smad4 is yeast two - hybrid , mutations in ewsr1 are known to cause ewing sarcoma and other members of the ewing family of tumors . from the boxplot for ewsr1smad4
, we found that the third quartile is the densest part of the whole distribution for both normal and tumor samples .
the third quartile for normal samples showed a positive correlation whereas that for tumor samples showed a negative correlation ( figure 2(b ) ) .
therefore , we suspect that ewsr1 can suppress the activity of smad4 in tumor samples .
trap1 has been shown to bind to tgf receptors and play a role in tgf signaling pathway .
mutant trap1 can prevent the formation of the smad2smad4 complex to inhibit the tgf signaling pathway . in the boxplot for trap1tgfbr2 ( figure 2(c ) ) , the densest quartile for tumor samples showed a high negative correlation .
tnf , fasl , trail , and other genes can initiate apoptosis by binding to their receptors such as tnfr1 , fas , and trail - r .
mitochondria can help transduce the apoptosis signals by releasing cytochrome c ( cytc ) , a potent catalyst of apoptosis .
there are two different bcl-2 family members : proapoptotic members ( bid , bad ) and antiapoptotic members ( bcl-2 , bcl - xl ) , which activate and inhibit , respectively , the release of cytc .
finally , two key caspases ( casp8 and casp9 ) activate other downstream caspases that perform the cascading events of cell death ( figure 3(a ) ) .   in our results
, we detected 33 relations with different distributions in the apoptosis pathway , and some are supported by existing experimental evidence .
examples include ( figure 3(b ) ) the following :   puma  bcl - xl ( bcl2l1 ) .
puma can interact with bcl - xl and meanwhile puma can also neutralize and antagonize all the bcl-2-like proteins . from the boxplot for puma  bcl - xl , we can find that bcl - xl , and puma showed a higher negative correlation in normal samples than in tumor samples ( figure 4(a ) ) .
active forms of akt can phosphorylate bad in vivo and in vitro to prevent it from promoting cell death . in the boxplot for akt1bad , the first quartile , the densest quartile for normal samples , showed a higher positive correlation than the second quartile , the densest for tumor samples ( figure 4(b ) ) .
krt18 may inactivate tradd to prevent interactions between tradd and the activated tnfr1 and thus affect tnf-induced apoptosis . in the boxplot for krt18tradd
the interaction between the death domain of tnf receptor-1 ( tnfr1 ) and tradd can trigger distinct signaling pathways leading to apoptosis .
tradd also interacts strongly with another death domain protein ; rip and rip plays an important role in the tnf signaling cascades leading to apoptosis . in the boxplot for tnfr1ripk1 , tnfr1 and ripk1
inhibitor of apoptosis ( iap ) suppresses the activities of caspases and inhibits different apoptotic pathways .
iap and casp9 showed a high negative correlation in tumor samples ( figure 4(f ) ) . among the eight differential gene relations in figure 3(b ) ,
three of them were in the seed pathway : trail - r  fadd , iap  casp9 , and akt  bad , which demonstrates the effectiveness of the proposed method .
egf , tgf , and pdgf are activated and then bind to their receptors to transduce the growth signals .
the activated growth factor receptors can in turn activate the sos - ras_raf_mapk cascade . in the growth signal pathway ( figure 5 ) ,
. we could find 68 relations with different distributions in the growth signal pathway , and we discuss three relations as follows : rassf2kras .
although different forms of ras are frequently thought of as oncogenes , they also have the ability to produce antigrowth effects such as cell cycle arrest , differentiation , and apoptosis .
moreover , rassf2 can inhibit the growth of tumor cells , and the activated k - ras can enhance this ability .  
this might be why rassf2 and ras showed a high positive correlation in normal samples in the boxplot ( figure 6(a ) ) .
as expected , maz and myc demonstrated a higher positive correlation in tumor samples ( figure 6(b ) ) .
activated epidermal growth factor receptors ( egfrs ) can both physically and functionally interact with plscr1 . in turn
, plscr1 can interact with shc and thus accelerate the activation of src kinase through the egf receptor , while src can initiate some activating pathway for the oncogene jun . in the boxplot for plscr1egfr , the densest quartile for normal samples showed a low negative correlation , whereas the densest quartile for tumor samples showed a low positive correlation ( figure 6(c ) ) .
after several decades of cancer research , some details of the underlying mechanisms of cancer at the gene level are still unclear . in this paper , we propose an integrative method based on the bootstrapping k - s test to evaluate a large number of microarray datasets generated from 21 different types of cancer in order to identify gene pairs that have different relationships in normal versus cancer tissues .
the significant alteration of gene relations can greatly extend our understanding of the molecular mechanisms of human cancer . in our method , we obviate the disadvantage of the traditional t - test , which only considers the mean and variance of samples and fails in the analysis of microarray data with small numbers of samples . instead of the t - test , we propose the use of the bootstrapping k - s test method to detect gene pairs with different distributions of pearson correlation coefficient values in normal and tumor samples .
the experimental results demonstrated that our method could find meaningful alterations in gene relations and opened a potential door for further cancer research .
 previous applications of microarray technology for cancer research have mostly focused on identifying genes that are differentially expressed between a particular cancer and normal cells . in a biological system , genes perform different molecular functions and regulate various biological processes via interactions with other genes thus forming a variety of complex networks . 
 therefore , it is critical to understand the relationship ( e.g. , interactions ) between genes across different types of cancer in order to gain insights into the molecular mechanisms of cancer . 
 here we propose an integrative method based on the bootstrapping kolmogorov - smirnov test and a large set of microarray data produced with various types of cancer to discover common molecular changes in cells from normal state to cancerous state . 
 we evaluate our method using three key pathways related to cancer and demonstrate that it is capable of finding meaningful alterations in gene relations . 