Solving Haplotype Assembly Problem Using Harmony Search

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1 Internatonal Journal of Computer Networks and Communcatons Securty VOL. 1, NO. 4, SEPTEMBER 013, Avalable onlne at: ISSN C N C S Solvng Haplotype Assembly Problem Usng Harmony Search Saman Poursah Nav 1, Ehsan Asgaran 1 Department of Computer Engneerng, Islamc Azad Unversty, Quchan Branch, Quchan, Iran Department of Computer Engneerng, Sharf Unversty of Technology, Tehran, Iran E-mal: 1 samanpoursah@gmal.com ABSTRACT Sngle Nucleotde Polymorphsms (SNPs), a sngle DNA base varyng from one ndvdual to another, are beleved to be the most frequent form responsble for genetc dfferences. Haplotypes have more nformaton for dsease-assocatng than ndvdual SNPs or genotypes; t s substantally more dffcult to determne haplotypes through eperments. Hence, computatonal methods that can reduce the cost of determnng haplotypes become attractve alternatves. MEC, as a standard model for haplotype reconstructon, s fed by fragments nput to nfer the best par of haplotypes wth mnmum errors needng correcton. It s proved that haplotype reconstructon n the MEC model s a NP-Hard problem. Thus, researchers desre reduced runnng tme and obtanng acceptable results. Heurstc algorthms and dfferent clusterng methods are employed to acheve these goals. In ths paper, Harmony Search (HS) s consdered a clusterng approach. Etensve computatonal eperments ndcate that the desgned HS algorthm acheves a hgher accuracy than the genetc algorthm (GA) or partcle swarm optmzaton (PSO) to the MEC model n most cases. Keywords: Clusterng, Bonformatcs, Evolutonary Optmzaton, Reconstructon Rate. 1 INTRODUCTION Avalablty of the complete genome sequence for human bengs makes t possble to nvestgate genetc dfferences and assocate genetc varatons wth comple dseases [1]. It s generally accepted that all human bengs share about 99% dentty at the DNA level, wth only some regons of dfferences n DNA sequences responsble for genetc dseases [4, 5]. Sngle Nucleotde Polymorphsms (SNPs), a sngle DNA base varyng from one ndvdual to another, are beleved to be the most frequent form responsble for genetc dfferences [16] and are found appromately every 1,000 base pars n the human genome. They are promsng tools for dsease assocaton studes. Every nucleotde n an SNP ste s called an allele. Almost all SNPs have two dfferent alleles, known here as 'A' and 'B'. The SNP sequence on each copy of a chromosome par n a dplod genome s called a haplotype, whch s a strng over {'A', 'B'}. SNP fragments are composed of gaps and errors. One queston arsng from ths dscusson s how the dstrbuton of gaps and errors n the nput data affects computatonal complety. Some models dscussed for haplotype reconstructon nclude Mnmum Error Correcton (MEC) [17], Longest Haplotype Reconstructon (LHR) [7], Mnmum Error Correcton wth Genotype Informaton (MEC/GI) [1], and Mnmum Conflct Indvdual Haplotypng (MCIH) [1]. Our research chose the standard MEC, a standard model for haplotype reconstructon that s fed by fragments as an nput to nfer the best par of haplotypes wth mnmum error correcton. For the MEC model, two dfferent procedures can be employed to resolve the problem: Frst, parttonng and clusterng methods can be desgned to dvde the SNP fragments nto two classes. In ths approach, each class corresponds to one haplotype. To nfer the haplotypes from each partton, another functon s desgned, descrbed later n ths paper. The second approach s based on nferrng haplotypes drectly from SNP fragments and smultaneously correctng the errors. It was proved that haplotype reconstructon n the

2 111 MEC model s an NP-Hard problem [1]. Thus, researches desre reduced runnng tme and obtanng acceptable results [18, 19]. A meta-heurstc algorthm, mmckng the mprovsaton process of musc players, has been recently developed and named Harmony Search (HS) [10, 14]. In ths paper, we propose an algorthm based on HS, for a haplotype reconstructon problem n a mnmum-errorcorrecton model. To demonstrate the effectveness and speed of HS, we have appled HS algorthms on a standard SNP fragments database and receved good results compared to GA and PSO. The evaluaton of the HS epermental results showed consderable mprovements and robustness. In the net secton, bologcal defntons such as SNP, SNP fragments, and haplotype are formulated. Net we ntroduce GA, PSO, and K- means as related works n the MEC model, two of these three approaches are consdered as supplemental methods for our soluton. In the net secton, the proposed approach s dscussed n detal. In ths secton, the HS algorthm (Harmony Search) and ts propertes, along wth functons of the algorthm, are dscussed for the MEC model. The fnal two sectons are Results and Dscusson regardng the dfferent data-sets and Concluson. FORMULATIONS AND PROBLEM DEFINITIONS Suppose there are m SNP fragments from a par of haplotypes. Each SNP fragment (here after "fragment") corresponds to one of the two target haplotypes. M=mj s defned as a matr of fragments, of whch each entry mj has a value A, B or - ( - s a mssng or skpped SNP ste, whch s called a "gap"). The rows and column of the matr Mn m demonstrate fragments and SNP stes, respectvely. The length of fragments ncludng ther gaps s the same as the two haplotypes, whch s equal to n. We use partton P(C1,C) (C1 and C are two classes) to formulate the problem. P s an eact algorthm or clusterng method that dvdes fragments nto C 1 and C (Fgure 1). Fg. 1. Classfyng SNP Fragments from M Each haplotype s reconstructed from the members of one of the classes wth votng functon. The functon s performed on all fragment columns of each class n to decde the values on the correspondng SNP ste of related haplotypes. The functon s so defned: (N A(M) (or N B(M)) denotng the number of A s (or 'B's) n j th column of matr M) j j A N A ( C ) N B ( C ) Vj B Otherwse 1, 0 j p n Class1: Class: Class: Class1: Class1: Class: Class1: Class: Class: Reconstructon rate (RR) s a smple, popular means to compare the results of desgned algorthms on estng datasets. RR, whch s based on Hammng dstance (HD), s the degree of smlarty between the orgnal haplotypes (h = (h 1, h)) and reconstructed ones (h' = (h' 1, h' )). The formula d(,y) s defned as the dfference of two alleles n one SNP ste. HD of two fragments HD(f, f j ) and RR(h,h') are formulated as: 1 ( mj mkj ) d ( hj, hkj ) 0 Otherwse HD( h, h ) d ( h, h ) k j kj j1 r HD( h, h ), j 1, j j n mn( r11 r, r1 r1) RR( h, h) 1 n

3 11 HD 1 and HD are consdered the two dstances obtaned from comparson of f and the two other fragments (f 1 and f ). 3 RELATED WORK 3.1 Genetc algorthm (GA) To resolve haplotype assembly, Wang and colleagues proposed a genetc algorthm to cluster the fragments []. The chromosomes are defned as bnary strng of length m (number of fragments). When Ch s equal to 0 (or 1), t means that the th fragment s consdered to be one of the frst (or the second) class members. Goodness and badness of ndvduals must be assgned based on number of error correctons requred. But there are no cluster s centers obtaned yet. There s a ftness functon recommended for evaluatng the ndvduals by Wang and colleagues that computes the dstance of all fragments wth ther class centers (the class centers n ths problem are computed by the votng functon method) []. Snce n some problems, there are lots of fragments, codng method used n the prevous approaches would not lead to sutable results [3]. Therefore Wu et al, proposed a new codng method [3] n whch each chromosome n the populaton represents a haplotype that contans only heterogenous SNPs. We can etract laplotyps pars from chromosomes, because each haplotype par consst of dfferent alleles on heterogenous SNPs. Fg.. GA chromosome and nferrng haplotypes from one parttonng 3. Partcle Swarm Optmzaton (PSO) The partcle swarm optmzaton (PSO) method s much lke GA. In ths method, frst a populaton of random solutons s generated and each of these solutons moves n the search space to get optmzed. PSO has no evolutonary operators such as crossover and mutaton, but the partcles share ther nformaton of the vsted areas and the best solutons met. Qan and colleagues used ths method for haplotype reconstructon problem n a MEC model n whch the partcles are coded the same as the descrbed genetc algorthm [6]. More recent work n ths area presented n[]. Authors propose to remove those SNPs whch contan a hgh percentage of 1s (0s), gnorng gaps, e.g. those SNPs wth 90% of 1s (0s) wll be removed from SNP matr. For ths case, they nsert the most observed allele (1s or 0s) nto two constructed haplotypes at that poston and remove the correspondng column from the SNP matr. 3.3 Heurstc Methods A heurstc clusterng method has been publshed by Wang and colleagues. Frst, two fragments are selected as the prmtve centers. The other fragments are clustered accordng to ther HD and the specfed centers. In teratons, the centers are updated accordng to newly constructed clusters and votng functon. Therefore n the net teraton, the dstance between the new centers and all the fragments has to be computed for clusterng. Numercal results approve the effcency of ths method. In [4] PSO and k-means algorthms are combned n two ways. In the frst type, k-means s utlzed as an nteror functon of PSO method; t runs for every partcle of PSO at every teraton n order to acheve a better clusterng. In the second type, k-means s frst run and the obtaned results are taken as the global best n the frst generaton of PSO. The numercal results show that they have hgher accuracy than the orgnal PSO. Another heurstc method was proposed n [5]. In ths method two parttons are consdered, one of whch s empty at start and the other contans all the fragments. Ths method conssts of two major steps. Frst step s the transfer step n whch fragments are transferred from ther current partton to the other one, f the transfer has the best beneft among all other possble transfers. The beneft of a transfer s the dfference between the number of correctons requred before and after the transfer. After transferrng a fragment, t wll be remaned untl the end of the transfer step. The value of ths beneft s saved to be used at the net step. After all fragments are transferred, the rollback step starts. In ths phase, the mamum beneft obtaned among all the transfers are calculated usng saved beneft values and then all the transfers are roll backed untl reachng the pont wth the mamum beneft. These two steps are terated untl the total obtaned beneft gets closed to zero. In [6], supervsory neural networks are used by Xu et al. A smple two-layered network n whch n the nput layer the number of neurons equals to the number of SNPs and the output layer contans two neurons correspondng to the parttonng of

4 113 fragments. Xu parttons the fragments to three sets at the preprocessng step. The frst and the second sets contans the fragments whch are consonant wth the haplotypes obtaned from the current members of the partton and also have the mamum dstance from haplotypes from the other set. The other fragments are placed n the thrd set. At the learnng step, the frst and second sets are used for learnng the network and fnally the class of the members of the thrd set, are yelded from the network. 4 THE PROPOSED FRAMEWORK In ths paper, we ntroduce Harmony Search to solve a MEC model. Pre-processng s used to make compatble nput for the mentoned model. We stress the basc elements of ths algorthm, as follows. The Harmony Search (HS) algorthm was recently developed n an analogy wth a musc mprovsaton process whereby musc players mprovse the ptches of ther nstruments to obtan better harmony [11]. The steps n the Harmony Search procedure are as follows [11]: Step 1. Intalze the problem and algorthm parameters. Step. Intalze the harmony memory. Step 3. Improvse a new harmony. Step 4. Update the harmony memory. Step 5. Check the stoppng crteron. These steps are descrbed n the followng subsectons. 4.1 Step1: Intalze the problem and algorthm parameters. In Step 1, the optmzaton problem s specfed as follows: In the lght of the goal of the MEC model, the goodness and badness of an ndvdual s dependent on the number of error correctons. Hence, we desgn the followng objectve functon: mn. E( P{,,..., }) Maf sb to mn. 1 m ( 1,,..., m),. : 0,1 Where m s length of SNP fragment, n s number of SNP fragments, s th SNP of current SNP fragment, P{ 1,,, m } s a parttonng of { 1,,, m }, and E(P{ 1,,, m }) s the correspondng error correcton n comparson wth ther own center, (.e., the dstance between center and each fragment). Harmony memory (HM) s a memory locaton where all the soluton vectors (sets of decson varables) are stored. HM s smlar to the genetc pool n GA [13]. Here, harmony memory consderng rate (HMCR) and ptch adjustng rate (PAR) are parameters used to mprove the soluton vector. Both are defned n Step. 4. Step: Intalze the harmony memory In Step, the HM matr s flled as follows: The frst half of harmony memory s generated randomly, and the rest of the harmony vector s produced by combnng two fragments. For the second half, two dfferent fragments are chosen from the lst of fragments (random selecton). These two fragments are consdered as the centers of two classes. Then, the rest of the fragments are separated n two classes accordng to the hammng dstance between the mentoned centers and the fragments: h[ center ] 0 1 h[ center ] 1 0 HD ( M[ ], M[ Center 1]) HD ( M[ ], M[ Center ]) h[ ] 1 Otherwse Where h[] as one harmony_vector[], HD as hammng dstance, M[] as th fragments and also center 1 and center both as ndees of two fragments m 1 m 1... m 1 m HM M M M M M HMS 1 HMS 1 HMS 1 HMS m 1 m HMS HMS HMS HMS 1... m 1 m j {0,1}, 1,,..., m, j 1,,..., HMS For constructon of the hypothess space, we use a bnary strng of {0, 1} to epress a classfcaton of SNP fragments (a feasble soluton to the MEC model). The HMS s a number of soluton vectors n HM, the length of the hypothess space (m) s number of SNP fragments, and the value 0 or 1 on th ste denotes th fragment s class-membershp. For eample, f there are eght SNP fragments, a bnary strng of { } denotes a partton: 1,4,5,6 are n a class and (left),3,7,8 n another class. Thus, all bnary strngs wth the length of m consttute the hypothess space.,

5 114 Fg. 3. Harmony Search Approach 4.3 Step 3. Improvse a new harmony A new harmony vector, ( 1,,..., m ) s generated based on three rules: (1) memory consderaton, () ptch adjustment and (3) random selecton. Generatng a new harmony s called mprovsaton [10]. In the memory consderaton, the value of the frst decson varable ( ) for the new vector s chosen from any of the values n the specfed HM range ( 1 HMS 1 1 ). Values of the other decson (,..., m ) are chosen n the same varables manner. The HMCR, whch vares between 0 and 1, s the rate of choosng one value from the hstorcal values stored n the HM, whle (1 HMCR) s the rate of randomly selectng one value from the possble range of values. 1 HMS {,,..., } wthprobablty HMCR, X wthprobablty (1 HMCR ). For eample, a HMCR of 0.85(0.9) ndcates that the HS algorthm wll choose the decson varable value from hstorcally stored values n the HM wth 90% probablty or from the entre possble range wth a (100 90) % probablty. Every component obtaned by the memory consderaton s eamned to determne whether t should be ptch-adjusted. Ths operaton uses the PAR parameter, whch s the rate of ptch adjustment as follows: Yes No wthprobablty PAR, wthprobablty (1 PAR ). The value of (1 PAR) sets the rate of dong nothng. If the ptch adjustment decson for s YES, s replaced as follows: rand()* Where rand() s a random number between 0 and 1. In Step 3, HM consderaton, ptch adjustment or random selecton are appled to each varable of the new harmony vector n turn. 4.4 Step 4. Update harmony memory If the new harmony vector, s better than the worst harmony n the HM, judged n terms of the objectve functon value, the new harmony s ncluded n the HM and the estng worst harmony s ecluded from the HM.

6 Step 5. Check stoppng crteron If the stoppng crteron (mamum number of mprovsatons) s satsfed, computaton s termnated. Otherwse, Steps 3 and 4 are repeated. 5 RESULTS AND DISCUSSION There are some smulaton and real bologcal datasets avalable for haplotype reconstructon problems. In ths paper, Daly, ACE, SIM0, and SIM50 were chosen. Our approaches were mplemented usng Vsual C#.Net 4.0 and eecuted on all the datasets. All datasets have 1 dfferent gap and error rates (Error Rate = 0.1, 0., 0.3 and 0.4 and Gap Rate = 0.5, 0.50 and 0.75). 5.1 Smulaton Datasets (SIM0 and SIM50) These two datasets are generated accordng to the smlarty of the result haplotypes (or the percentage of heterozygous ste n genotype). There s no smlarty between the two obtaned haplotypes n SIM0 datasets. Therefore, all postons are consdered as heterozygous stes. In ths dataset there are 30 test cases of 0 fragments wth 50 SNP ste lengths. 5. Daly and ACE Datasets Daly dataset ncludes 383 dfferent test cases for each error rate (153 for all error rates). Each test case conssts of 40 fragments of 53 SNP stes. The epermental results of new (HS) and prevous (Kmeans, GA and PSO) approaches for the MEC model are shown n Fgure 4(a-c). These dagrams are the reconstructon rate comparsons of K- means, GA, UWNN(PSO), and GKM(HS) approaches n Daly datasets. ACE (Angotensn Convertng Enzyme) as real dataset, ncludes 4 dfferent test cases for each error rate. (a) g = 0.5 (b) g = 0.5 (c) g = 0.75 Fg. 4. Comparson the results dfferent clusterng approaches for MEC model on Daly dataset To show the performance of our algorthm n Daly dataset, the reconstructon rates subtracton of our method and K-means, GA and PSO n MEC model s presented (Fgure 5). The X-as and Y- as of ths chart present dfferent error and gap rates and reconstructon rate subtracton consecutvely.

7 116 Fg. 5. Reconstructon rate subtracton (Improvement of HS from K-means, GA and PSO) on Daly dataset In Table1, the results of runnng the approaches above on four data sets are shown. It s obvous that the proposed method provdes better reconstructon rato than other methods. Table1: Reconstructon Rate on Daly, ACE, SIM0 and SIM50 Datasets for dfferent gap and error rate (MEC model) 6 CONCLUSIONS Haplotypes play a very mportant role n several areas of genetcs, e.g. dsease assocaton studes and populaton hstory studes. However, t s substantally more dffcult to determne haplotypes. MEC s a popular model and s used wdely n haplotype reconstructon process. In ths paper, we use Harmony Search (HS) to solve the haplotype reconstructon problem n the MEC model (whch s proved to be NP-Hard problem). HS was used to cluster data of our problem. In ths approach, HS was used to cover almost all soluton space and mprove the accuracy of the solutons. The results of the Harmony Search (HS) mplementaton were obtaned from dfferent real and smulaton datasets (Daly, ACE, SIM0, and SIM50) and compared wth GA, K-means and PSO. It was proved by eperences that the proposed methods outperform all prevous related works. The smulaton mplemented by Network Smulaton (NS) [14], to smulate moble ad hoc network crcumference. We accomplsh the random waypont moton model for our smulaton, n whch the node starts at accdental poston, wats for the pause tme, and then goes to another accdental poston wth the 0 m/s to the mamum smulaton speed. The sze of each packet s 51 bytes and a forwardng rate of 3 packets per sec [15]. The smulaton parameters are shown n Table 1. 7 REFERENCES [1] X. Zhang, R. Wang, L. Wu, W. Zhang, Mnmum conflct ndvdual Haplotypng from SNP fragments and related Genotype, Bonformatcs Oford Journal 006,

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