Accelerating Motif Finding Problem using Grid Computing with Enhanced Brute Force

Transcription

1 Acceerating Motif Finding Probem using Grid Computing with Enhanced Brute Force HM Faheem, PhD Associate Professor, Computer Systems Dept, Facuty of Computer and Information Sciences, Ain Shams University, Cairo, Egypt Abstract Motif finding probem is a major task to understand the mechanisms of gene expression reguation Motif is generay defined as a recurring pattern in the sequence of nuceotides or amino acids In the DNA sequence, it is usuay a short segment that occurs frequenty, but not required to be an exact copy for each occurrence This property of motif makes motif mining very difficut In fact, motif finding probem is proven to be NP- Compete Many agorithms fai to sove the we-known chaenge probem of finding a motif of ength 15 and has at most 4 mutations (15, 4) due to the huge runtime needed Others fai to distinguish the motif from background sequences Brute Force is one of the exact agorithms that never fai to find the motif, but it suffers from an intractabe running time In this paper, we present a nove approach to acceerate the motif finding probem using grid computing As grid computing makes avaiabe owcost high-performance computing (HPC) infrastructures, the best candidates for using such infrastructures are appications that require high computationa power, arge storage capacity, or fast and high-throughput networking The nature of motif finding probem is considered one of the perfect scenarios for grid computing We depoyed an enhanced version of the Brute Force; skip-brute Force running on EUMEDGRID infrastructure (Co- Funded project by the European Commission in the framework of FP6, with the aim of supporting the deveopment of a Grid e- Infrastructure in the Mediterranean Area and promoting the porting of computationay intensive appications on the Grid patform) The idea behind our skip Brute Force agorithm is that it skips a the iterations that wi not ead to a correct soution The message passing programming paradigm is depoyed since it assumes a partitioned address space and supports expicit paraeization Our experimenta resuts showed boosting in the performance without sacrificing the exactness of the Brute Force Keywords- Motif findin; DNA sequence anaysis; Grid Computing I Introduction Understanding the mechanisms that reguate gene expression is a major chaenge in bioogy Motif finding probem is considered an important task in this chaenge Addressing the compexity nature of the probem together with being very data intensive has encouraged introducing grid computing to the probem Grid computing is very powerfu in such computationay intensive tasks Many Agorithms are introduced to sove this probem They can be categorized into pattern-based and profie-based agorithms [1-3] Pattern-based agorithms incude PROJECTION [4,5], MULTIPROFILER [6], and MITRA [3] Profie-based agorithms incuding CONSENSUS [7], MEME [2] and Gibbs samping [5], try to find the starting positions of the occurrences of the motif in each sequence Athough these agorithms show good performance, they sti can fai to identify a the possibe motifs in the sequences They aso show poor performance when trying to sove the chaenge probem presented by Pvzner and Sze [8] Some of them fai due to oca search; others which are based on statistica measures fai to separate the motif from the background sequences We can aso categorize Motif finding agorithms due to the soution they provide Some agorithms provide exact soution others provide approximate one Brute Force agorithm is an exact agorithm It never misses a motif, as it aways searches in a the possibe ocations What makes Brute Force an impossibe soution is the intractabiity of its running time It increases exponentiay with the size of the required motif This makes the Brute Force unsuitabe for ong motifs Many approaches can be appied to speed up the running time of any agorithm using hardware; exampes incude chip mutiprocessors, graphics processing units (GPUs), (FPGAs), and specia hardware soutions These soutions require hardware speciaists who are abe to design such systems Moreover, it is not reaistic to design architecture for every singe bioinformatics probem In fact, the grid as an emerging infrastructure that provides seamess access to computing power and data storage capacity distributed over the different grid computing nodes is ideay quaified to knock the door of computationay intensive probems ike motif finding probem The rest of this paper is organized as foows: In Section II we describe the motif finding probem and the Brute Force agorithm In Section III, a brief expanation of the skip brute force agorithm is presented in addition to the expanation of the parae nature of the agorithm Section I describes the

2 grid-based impementation of the suggested approach Performance evauation is presented in section Finay, section I concudes our work and presents future enhancements II Motif finding probem The probem can be summarized as foows: Panted (,d)- Motif Probem: Find the motif consensus M which is a fixed but unknown nuceotide sequence of ength Suppose that M occurs once in each of t background sequences of common ength n Each occurrence of M is corrupted by exacty d point substitutions in positions chosen independenty at random Given the t sequences, recover the motif occurrences and the consensus M Pevzner and Sze[8] presented the chaenge probem(15,4) which makes a particuar parameterization to the panted motif probem The motif we are searching for is of ength =15, the aowed mutations d=4 and the number of sequences we are searching in is t=20 each of size n=600 The parameters of the chaenge probem are typica vaues for finding transcription factor binding sites in co-reguated gene promoter regions yeast [4] The Brute Force agorithm soves this probem by considering the set of a 4 possibe -mers It computes the tota distance of each -mer in that set to a other -mers in a t sequences The correct motif is the one that have the smaest tota distance aong a the other -mers The run time of this agorithm is O (4 nt) The running time for finding a motif of =11 is about 5hrs and it fais to hande onger motifs in reasonabe time To sove the chaenge probem, the running time of the Brute Force agorithm woud obviousy be too high III Enhanced Brute Force Agorithm- the skip Brute Force The idea behind our skip Brute Force agorithm is that it skips a the iterations that wi not ead to a correct soution The agorithm generates a possibe 4 -mers It then iterates over a the sequences examining the generated - mer with a the windows in the first sequence The agorithm then excudes a the generated -mers that are not matched with at east one window of the sequence Matching means that the hamming distance between the -mer and the window is ess than or equa to 4 In other words; a generated -mer of ength 15 with 4 permitted mutations is considered matched with a window if at east 12 identica positions at both of them are matched The agorithm then starts checking the next sequences and consequenty excudes unmatched -mers from the search in the next sequence The agorithm repeats this mechanism ti the end of the sequences A pseudo code of the sequentia skip Brute Force agorithm is shown in Fig1 The compexity of this agorithm is O(4 nt) at its worst case, just as the Brute Force The performance coefficient introduced by Pvzner and Sze to measure the performance is defined as foows: If K denotes the set of t, base positions in t occurrences of a panted motif, and P denotes the corresponding set of base positions in the t occurrences predicted by the agorithm Then the performance coefficient equas K P/KUP If the agorithm succeeds to recover a the positions of the panted motif correcty, this wi give a performance coefficient of 1, which is typicay the case of Brute Force The performance coefficient gives an indication of how many positions of the motif occurrences in the sequences have been predicted correcty by the agorithm 1for L = 0 to 4 _motifsize - 1 do % examine a possibe -mers 2 for Ti = 1 to t_sequences do % oop on a t sequences 3 motif_found = 0; 4 current_score =d_mutations; 5 for W = 1 to n_seqsize-_motifsize+1 do % oop on a windows 6 dist = compute_distance ( L, W); 7 if dist<= current_score 8 soutionmotif = Li; % this can be the motif 9 soutionposit(ti) = W; % save its position 10 motif_found = 1; % a suspected motif was found 11 current_score = dist; 12 if Ti = t_sequences % we reached the ast sequence 13 soution_found = 1; 14 end 15 end 16 if motif_found == 0 17 break; % Skip that Li, it is not the Motif 18 end 19 end 20 end 21 if soution_found 22 break; 23 end 24end Fig 1 Pseudo Code for Skip Brute Force Agorithm The brute force or skip-brute force agorithms are inherenty parae agorithms with we-defined points of synchronization and are thus we suited to impementation of Buk Synchronous Parae (BSP) computer A computer constructed with this paradigm is made up of a number of components each comprising three parts: parae threads, known as virtua processors; a point-to-point routing mechanism; and faciities for providing synchronization between some or a of the threads at a reguar time interva 2 The soution of a probem on the BSP computer consists of a number of super-steps, at one or more time intervas apart Fig2 shows the parae comparisons between the generated - mers and the windows of a given sequence on the components

3 (c) of the BSP mode [9] Of course a preiminary data preparation step shoud be performed before the start up of comparison processes This step extracts a the possibe windows from a given sequence Hence each -mer of the 4 - mers wi be compared with a the possibe (n-+1) windows The tota number of comparisons is (n + 1) * 4 Actuay there is no dependency between these comparison processes L-mer1,W1 Set of Possibe -mers L-mer1 : aaaaaaaaaaaaaaa L-mer2 : aaaaaaaaaaaaaac L-mer3 : aaaaaaaaaaaaaat L-mer4 : aaaaaaaaaaaaaag L-mer4 L : ggggggggggggggg L-mer1,W6 C1 P R C2 Comparison Process P R Sampe Sequence of Size 20: cctgatagacgctatctggc Possibe windows of size 15: Synchronization Contro Communication Medium W1: cctgatagacgctat W2: ctgatagacgctatc W3: tgatagacgctatct W4: gatagacgctatctg W5: atagacgctatctgg W6: tagacgctatctggc R=Point-t point Router P=Processor =irtua Processor (Thread) Cx P R L-mer4 L,W1 Fig2 Comparison processes using the BSP mode I Grid-based Impementation L-mer4 L,W6 The BSP mode was introduced to provide a bridge between software deveoped for parae machines and the architectures on which this software is utimatey impemented BSP was proposed as a possibe standard to faciitate the deveopment of genera purpose parae machines and increase the portabiity of software between these machines In order to impement the motif finding probem on a specific grid node consisting of mutipe computers, we have to correate the eements of the grid node to the components of the BSP [9] The message-passing programming paradigm is one of the odest and most widey used approaches for programming parae computers Its wide spread adoption can be attributed to the fact that it imposes minima requirements on the underying hardware The two key attributes that characterize the message-passing programming paradigm are: it assumes a partitioned address space; and it supports ony expicit paraeism The messagepassing interface MPI defines a standard ibrary for messagepassing that can be used to deveop portabe message-passing programs using either C or FORTRAN Most messagepassing programs are written using the singe program mutipe data (SPMD) approach In the SPMD programs the code executed by different processes is identica except for a sma number of processes We can obviousy see that the BSP mode components have the same attributes of the message-passing programming paradigm This makes the message-passing programming paradigm is the optimum choice for impementing the skip brute force agorithm on the grid [10] A EUMEDGRID Structure A set of grid nodes is impemented at different Mediterranean countries EUMEDGRID depoys gite as a stack of generic middeware Main gite components incude user interface giteui, virtua organization management service OMS, information service, workoad management system gitewms, ogging and bookkeeping utiity gitelb, computing services, data management, monitoring services, and secure access services Typica grid node structure is shown in Fig3 User Interface aows users to access Grid functionaities It is simpy a machine where users have a persona account and where the user certificate is instaed It is aso a gateway to grid services The user interface provides a command ine interface to perform some basic Grid operations such as: ist a the resources suitabe to execute a given job, submit jobs for execution, show the status of submitted jobs, cance one or more jobs, retrieve the ogging and bookkeeping information of jobs, retrieve the output of finished jobs, and copy, repicate and deete fies from grid The resource broker (RB) is responsibe for the acceptance of submitted jobs and for sending those jobs to the appropriate computing eement The resource broker retrieves information from Information cataogues so as to find the proper avaiabe resources depending on the job requirements Job s Submission UI RB WN CE Fig3 Grid Node Structure WN WN The computing eement (CE) is considered the Grid interface It is buit on a farm of computing nodes caed Worker Nodes It aso executes the basic queues functions The computing eement is responsibe for accepting jobs and dispatching them for execution to the worker nodes The state of an executing job is being watched by the Computing Eement LCGCE is the current CE service impementation of the production infrastructure, based on Gobus tookit The submitted jobs are being executed in the worker nodes (WN) Ony basic services of middeware are required in the Worker nodes such as: appication ibraries, Appication Programming Interfaces (API), and commands for performing actions on grid resources and data SE

4 The storage eement (SE) provides uniform access to storage resources It may contro simpe disk servers, arge disk arrays or Mass Storage Systems Information service provides information about the Grid resources and their status Monitoring service has a set of monitoring toos designed for grid systems It provides basic data about Grid ike the number of each site s CPUs, the number of submitted jobs, the number of executing jobs, the number of waiting jobs, the number of each site s free CPU, the avaiabe storage space, etc Secure access service decides resource access poicy, authentication, an authorization mechanisms B MPI Program Based on the nature of the probem and the huge number of concurrent comparisons, we introduced a nove approach Since a the impementations of agorithms simiar in nature to brute force are based on the generation of the possibe - mers through oops, we here assumed that the possibe -mers are distributed eveny among the different worker nodes On the other hand, a the sequences wi be submitted to a the worker nodes This means that each worker node wi have a compete set of a the sequences and a portion of the possibe -mers Typica execution steps after data distribution of both the -mers and the sequences are isted in Fig 4 Step 1: For a worker nodes; expand each sequence to provide(n-+1) windows Step 2: For a worker nodes; perform the comparison process between each window of the first sequence and the resident -mers of the worker node Step 3: For a worker nodes; excude the unmatched -mers Step 4: Repeat steps 2 and 3 on the next sequence unti the end of sequences Step 5: Coect resuts and then dispay it Fig4 MPI Program steps for impementing skip brute force Performance Evauation and Resuts A test of the performance of the Skip Brute Force agorithm on synthetic probem instances is performed Probem instances are generated according to the panted (, d)-motif mode We foowed up the FM mode described by Pvzner and Sze[8] Probem instances are produced as foows: First, a motif consensus M of ength is chosen by picking bases at random Second, t=20 occurrences of the motif are created by randomy choosing d positions per occurrence (without repacement) and mutating the base at each chosen position to a different, randomy chosen base Third, we construct t background sequences of ength n=600 using n*t bases chosen at random Finay, we assign each motif occurrence to a random position in a background sequence, one occurrence per sequence A random choices are made uniformy and independenty with equa base frequencies For each set of parameter and d, we ran 10 test cases and recorded the average running time of each agorithm In order to evauate the grid-based impementation; we need to define the expected number of matching operations First we define the probabiity P d to find a random -mer in a given sequence with up to d mutations [2] This is shown in (1) Additionay, we define the expected number of the required matching operations E(, d) to find the correct impanted motif as in (2) We then deduce for a probem of size n=600, t=20, the expected matching operations to be as in tabe 1 P d = (1) E(,d) = (2) Matching operations constitute the most time consuming part of the agorithms athough it coud be performed concurrenty Unit matching time is defined as the time required carrying out a set of comparisons in order to decide whether an -mer is matched with a corresponding window of a given sequence or not Unit matching time depends of course on the ength of the window A comparison process for an - mer of size 15 wi be different from that of ength 11 Typica Unit Matching Time running on Dua Core, 25 GHz, 2GB RAM (the defaut machine specifications for a the worker nodes in our experiments) for different and d vaues is shown in Tabe 2 Tabe 1: Expected matching operations for different (, d) d Expected Matching Operations x x x x x Assuming that the sequences and the possibe -mers are initiay stored as data fies on the computers, a typica anaysis of the expected sequentia impementation time T s of Skip Brute Force agorithm on a singe computer machine is given by (3) T s = T expand + T comp + T save (3) Where; T expand is the time needed to expand the sequences such that a compete set of windows is generated for each sequence, T comp is the time needed to perform comparison processes, and T save is the time needed to save the resuts to a data fie The MPI impementation time T MPI on the grid is given by (4): T MPI = T expand + (T comp /P) + (T save /P) + T comm (4)

5 Where; P is the number of worker nodes, and T comm is the communication and synchronization time of the depoyed grid eements Tabe 2: Unit Matching Time d Unit Matching Time E E E E E-07 A Experimenta Resuts Typica experimenta resuts for the execution time of skip Brute Force agorithm on a singe, 24, and 96 worker nodes are isted in tabes 3, 4, and 5 respectivey It is cear that as increases, the execution time increases Aso we can see that as the number of WNs increases, the execution time decreases whie the communication time increases Typica LAN setup of the computationa grid node on which we conducted our experiments consists of 4 LAN switch each has 24 10/100 Mbps UTP ports and 4 ports each of 1Gbps (upink modues) A typica star topoogy is impemented such that one switch connects the other 3 switches Each switch connects 24 WNs with a rate of 100 Mbps for each WN Tabe 3: Impementing the skip Brute Force Agorithm on a singe machine d T expand T comp P=1 T save Ts Tabe 4: Impementing the skip Brute Force Agorithm on computing grid has 24 Worker Nodes d T comp T save P=24 T comm T MPI B Performance Evauation speedup of an agorithm using P processors is defined as S P = t s / t P where t s is the execution time of the best avaiabe sequentia agorithm and t P is the execution time of the parae agorithm Amdah s aw states that the speedup given P processors is as in (5) S P = T s / ( f T s + (1-f) T s / P ) = P / ( 1 + (P-1)f ) (5) Where; f is the fraction of the computation that is sequentia and cannot be divided into concurrent tasks It is obvious that f is directy proportiona to T expand, and T comm Aso f is inversey proportiona with the probem size since the tota sequentia execution time is affected by it Hence; f is given by (6) f = (T expand + T comm )/ T s (6) Tabe 6 shows the Speedup S P for different and d It is cear that the impementation of the motif finding probem using skip brute force on the grid yieds a considerabe enhancement in the speed of the agorithm Tabe 5: Impementing the skip Brute Force Agorithm on computing grid has 96 Worker Nodes D T comp T save P=96 T comm T MPI On the other hand, severa impementations for soving motif finding probem on Matab can be used in comparisons Of course much more enhancement is achieved if we compared our resuts with the Matab impementation of Brute Force agorithm running on an AMD 5500 X2+ processor and 2GB RAM This is shown in Tabe 7 We can see that a boost factor of 6419 is achieved when 96 worker nodes are depoyed as compared to the run time of Matab impementation Tabe 6: Speedup S P for different, d, and f vaues P=24 P=96 d f Sp f Sp

6 I Concusion and Future Directions Motif finding probem has been considered as one of the most chaenging research topics for the scientists of bioinformatics In this paper, we presented a grid-based soution that aimed at speeding up the soution of the probem We introduced an enhanced version of the Brute Force agorithm caed skip Brute Force We depoyed message-pass interface to paraeize the probem We then impemented the soution on EUMEDGRID infrastructure Resuts showed the achievement in terms of execution time such that the gridbased impementation provides a good speedup factor We can see that the experiment is conducted on a norma infrastructure that consists of traditiona PCs connected to LAN switches and MPI code written in C anguage This means that no need for speciaized or sophisticated hardware infrastructures that costs very much [6] E Eskin and P Pvzner, Finding composite reguatory patterns in DNA sequences, Bioinformatics S1, , 2002 [7] G Hertz, G Stormo, Identifying DNA and protein patterns with statisticay significant aignments of mutipe sequences, Bioinformatics 15(7-8), , 1999 [8] P Pvzner and S H Sze, Combinatoria approaches to finding subte signas in DNA sequences, in the Proceedings of the 8th Internationa Conference on Inteigent Systems for Moecuar Bioogy, , 2000 [9] A Chamers and J Tidmus, Practica Parae rocessing, An Introduction to Probem Soving in Parae, Internationa Thomson Computer Press, 1996 [10] A Grama, A Gupta, J Karypis, and Kumar, Introduction to Parae Computing,, 2 nd Edition, Addison Wesey Pubishing Inc, 2003 We strongy beieve that such appicabiity of grid computing can greaty improve the way the bioinformatics research is impemented This paper is a step towards a compete suite of grid-based impementations in the fied of bioinformatics Tabe 7: Comparison with Matab Resuts d Matab Run Time TMPI P=24 P=96 Boost Factor TMPI Boost Factor REFERENCES [1] SRajasekaran, S Baa, and CH Huang, Exact agorithm for panted motif chaenge probems, in the Proceedings of Asia-Pacific Bioinformatics Conference, , 2005 [2] T L Baiey, N Wiiams, C Miseh, and W W Li, MEME: discovering and anayzing DNA and protein motifs, Nuceic Acid Research 34, W369 W373, 2006 [3] A Brazma, I Jonassen, J io, and E Ukkonen, Predicting gene reguatory eements in siico on a genomic scae, Genome Research 15, , 1998 [4] J Buher, M Tompa, Finding motifs using random projections, Journa of Computing Bioogy, o 9, pp , 2002 [5] C E Lawrence, S F Atschu, M S Boguski, J S Liu, A F Neuwad, and J C Wootton, Detecting subte sequence signas: a Gibbs samping strategy for mutipe aignment, Science 262, , 1993