Mega Weaver: A Simple Iterative Approach for BAC Consensus Assembly

Transcription

1 Mega Weaver: Smple Iteratve pproach for onsensus ssembly aolong Wang, Maro Laura, o Yuan 3 *, and Fred. Wrght, 4 * epartment of ostatstcs, Unversty of North arolna, hapel Hll, North arolna 7599; epartments of omputer and Informaton Scence, and 3 omedcal Informatcs and Pharmacology, The Oho State Unversty, olumbus, Oho 430; 4 The Lneberger ancer enter, UN hapel Hll. * orrespondng authors: fwrght@bos.unc.edu bstract Herarchcal genome assembly can be dvded nto three dstnct stages: sequencng and assemblng shotgun reads for each of a seres of selected clones; assemblng the resultng fragments nto consensus sequences; and mappng and orentng the consensus accordng to external postonal nformaton. We report a new approach for consensus assembly that reles on teratve layouts of overlappng sequence, wth no need for pror maskng of repettve sequence. The approach ncludes major steps of qualty flterng and an teratve screenng algorthm wthn and between clusters of overlappng fragments. Each step ncludes numerous mnor steps desgned to detect false at mnmal expense n true. In contrast to dynamc algorthms, our approach attempts to mnmze false before attemptng to form consensus sequences. We show that false are reduced to a degree that fnal consensus assembly s straghtforward under a coordnate system descrbed n the paper. Usng human chromosome and a range of smulaton condtons, an average of 98.% false could be removed, whle 6.7% of true were not detected. The fnal assembled consensus sequences were nearly optmal, and support the usefulness of our approach for future herarchcal sequencng projects. Keywords: N sequence, consensus, assembly, lgorthm. Introducton espte the rapd progress over the last few years n sequencng large, complex genomes such as the human and mouse, the best strategy for sequencng and assemblng such genomes remans a matter of vgorous debate (Green 997; Weber and Myers 997; Waterston et al. 00). Genome researchers are well aware of the trade-offs nherent n a whole-genome shotgun approach vs. a clone-by-clone herarchcal approach (whch employs shotgun sequencng at the clone level). ertan opyrght 004, ustralan omputer Socety, Inc. Ths paper appeared at the nd sa-pacfc onformatcs onference (P004), unedn, New Zealand. onferences n Research and Practce n Informaton Technology, Vol. 9. Y-Png Phoebe hen. Ed. Reproducton for academc, not-for proft purposes permtted provded ths text s ncluded. economes of scale may favor whole-genome shotgun sequencng, but even recently ths vew has been questoned (Green 00). For the future sequencng of repeat-rch genomes, the herarchcal approach usng bacteral clones wll offer a contnued advantage n reducng repeat-nduced assembly errors (Waterston et al. 00). Thus, although the assembly of the human genome has moved far beyond the draft stage, computatonal mprovements n herarchcal assembly wll reman of contnued relevance. In the herarchcal strategy, a seres of mapped bacteral clones (bacteral artfcal chromosomes, s) are selected wth the ntent of coverng the genome wth a mnmum of overlap to reduce unnecessary sequencng costs. Each of the clones n ths tlng path s shotgunsequenced at (deally) 0X or greater coverage (Internatonal Human Genome Sequencng onsortum 00). Intal sequence assembly proceeds wth shotgun reads wthn each, formng one or more contgs (called fragments hereafter). The next step, whch s the focus of ths paper, nvolves the assembly of fragments from dfferent s nto longer consensus contgs (the consensus). The procedures for hghqualty consensus assembly have receved relatvely lttle attenton, although the consensus provdes crtcal nput for the fnal genome assembly. The fnal genome assembly nvolves numerous addtonal steps that are beyond the scope of ths paper, ncludng scaffoldng, orderng and orentng the assembled contgs usng external postonal nformaton and genomc landmarks. Numerous exstng approaches for assemblng shotgun reads (~500 bp) wthn clones of moderate sze (~50 Kb) (Peltola et al. 984; Huang 99; Huang and Madan 999; Green 994; Sutton et al. 995; Km et al. 999; Myers et al. 000; Pevzner et al. 00; atzoglou et al. 00). However, none of these approaches has been appled n full comparsons of s/ fragments across the genome, partly due to computatonal constrants. To our knowledge, only one publshed approach (Ggssembler, Kent and Haussler 00) has been desgned especally for consensus assembly usng pre-assembled fragments as nput, and formed the bass of the ntal publc human genome drafts (Internatonal Human Genome Sequencng onsortum 00; Kent and Haussler 00). Ggssembler also conducts the further steps of orderng and orentng the consensus nto mapped scaffolds (Kent and Haussler 00).

2 Ggssembler reles on external mappng nformaton (va fngerprnt clone contgs, FP) to pre-dentfy groups of s wth presumed overlap. Each FP typcally ncludes only 0-00 s, and so by restrctng consensus assembly to an FP the computatonal burden s greatly reduced, and smaller regons may be less prone to error produced by modestly repettve sequence. However, the FP s created usng a statstcal evaluaton of restrcton enzyme dgeston patterns (Gllett et al. 996; Soderlund et al. 997), nevtably contanng mappng errors. The extent of FP mappng error has not been carefully documented, and the FP map repostory ( s manually edted to accord wth other data sources. Several lnes of evdence suggest the FP mappng error s nontrval: () overlappng sequences show that the tlng coverage of the human genome, selected va FP to acheve unformty on the genome wth no multple, often s n fact redundant to a depth of several-fold coverage; () by comparng the orgnal FP map (June freeze) wth the NI uld 30 of the human genome, we found that the FP map (except the fnshed chromosomes and ) show substantal devaton from the assembly; (3) sequence comparsons of s across FPs on many chromosomes exhbt sequence overlap that can be parsmonously explaned as msplacement of s n FPs. Moreover, the breakponts between FP contgs do not necessarly represent sequencng gaps, so that s straddlng the breakpont are not compared n Ggssembler; and (4) ntegraton of ndependently mapped-consensus transcrpts nto ndvdual s show sgnfcant nconsstences (5%) for the order and orentaton of correspondng s n the publshed human genome draft (Zhou et al. 00). The Natonal enter for otechnology Informaton (NI) s now responsble for the regular updatng of human genome assembly. The NI assembly does not requre FPs for clusterng s, accordng to the bref ntroducton on the NI ste ( However, the procedures n creatng the consensus are not fully detaled, so t s dffcult to assess how mprovements may be made. In addton to computatonal burden, another major obstacle n large, complex genome assembly arses from the consderable amount of repettve sequence n the genome, causng msassembly f not handled carefully. Hghly repettve sequences are commonly masked when conductng genome assembly (Kent and Haussler 00), although at the scale of fragments, these repeats may be unque enough to warrant retenton for the consensus. Moreover, t may be dffcult to specfy repeat sequences before attemptng the assembly. In ths report, we propose a new algorthm (Mega Weaver) for assemblng fragments nto a consensus based on all-by-all comparson of fragments, wthout relyng on any predefned clusters of s. In general, t apples the overlap-layoutconsensus framework famlar n genome assembly. However, our approach focuses more on cleanng up false before fnal layout and consensus phases,.e., dentfyng parwse matches of fragments that are not consstent wth a fnal layout. fter ntal flterng of low-qualty, Mega Weaver uses an teratve procedure to remove false and mnmze the nfluence of repettve sequences. Mega Weaver does not requre repeat-maskng of the nput fragments. s we wll later document, true sequence can be readly dentfed n chromosome-wde comparsons usng our approach, and the ndcatons are that t wll scale up to genome-wde comparsons. Moreover, the great majorty of false can be dentfed and removed. We conducted careful smulaton studes to evaluate ths algorthm usng human chromosome as a hypothetcal genome. The results show that Mega Weaver can generate near-optmal consensus assembly for realstc tlng coverage and sequencng error rates.. Methods Input fragments ll ntal leaner leaner leanest onsensus Overlap detecton Qualty flterng Screenng wthn clusters (SW) Screenng between clusters (S) onsensus assembly Fgure. Procedure for consensus assembly Mega Weaver takes preassembled fragments as nput, and produces consensus sequence as output. It frst dentfes all parwse and conducts qualty flterng to elmnate low qualty (lkely false). fter qualty flterng, two subsequent teratve procedures are performed to dentfy addtonal false. Fnally, consensus sequences are generated through sequence layout wth the cleaned. In addton to a genome-wde sequence algnment, the use of teratve procedures allows effcent valdaton of across the genome a key feature that dstngushes Mega Weaver from other greedy assembly algorthms. Fgure shows the overall schema of our assembly procedure. Overlappng fragments (dentfed va Megablast, Zhang et al., 000) are used to defne clusters (descrbed further n Methods) of possbly contguous sequence, and screenng wthn clusters (SW) and screenng between clusters (S) proceed teratvely. The teratons are further detaled n Fgure, and nvolve swappng of query/subject denttes of fragments to accord wth the Megablast nput format.

3 . Sequence ata Qualty flterng Remanng SW Swtchng query and subject Outputted Remanng S The nput sequence data conssts of fragments preassembled from shotgun reads (possbly ncludng full-length s as a specal case). The assembly of fragments (often wth PHRP, ensures that for the most part no true reman between fragments wthn the same. s ths paper was prepared, the average length of fragments from the publc human genome assembly had reached ~60 kb, whle an ever-ncreasng number of s had reached the fnshed stage as a sngle consensus of ~50 kb. The current generaton of sequencers has an error rate on the order of 0 - per bp or less (Ewng and Green, 998). Wth sequencng depth of coverage at ~8X or more (Internatonal Human Genome Sequencng onsortum 00), the unresolved error rate n fragments s perhaps 0-4 or lower, and thus the effects of sequencng errors are not heavly emphaszed n ths report. However, several of our smulaton condtons do consder the effects of conservatvely hgh error rates n the fragments (up to 0 - per bp). No repeat maskng or other sequence preprocessng s requred. Sequence qualty nformaton s not requred, although we do account for reduced qualty at the ends of each fragment.. Identfyng parwse onvergent Outputted Swtchng query and subject leaned Fgure. Iteratve procedures for screenng false wthn and between clusters The frst step of our assembly process s to fnd all parwse between fragments across a whole genome or chromosome (assumng s have been correctly assgned to chromosomes). Several exstng programs can be used to dentfy, and provde useful scores for overlap qualty. We have found that Megablast (Zhang et al. 000) can perform ths task effcently, and s easly mplemented on standard workstatons. Fgure 3 shows the structure of a typcal overlap wth detals of algnment procedure, detectable by Megablast under output opton - 3. Megablast compares socalled query sequences to subject (database) sequences. For our purposes we need to perform all N(N-)/ parwse comparsons of N total sequences, and there s no meanngful dstncton between query and subject. However, we adopt ths nomenclature to adhere to the Megablast format. In order to obtan hghly accurate overlap postons (q, q, s, and s, see Fgure 3), we set the flter opton for runnng Megablast as F F. However, applyng ths opton to the full-length fragments dramatcally onvergent slows Megablast, and we have devsed a two-stage strategy to speed up the process. In the frst stage, the two ends of each sequence are cut off at a specfed length (e.g. 500 bp) and used as query. These end query sequences are then compared wth full-length subject sequences. lthough the creaton of end queres doubles the number of comparsons, the total comparson tme s greatly reduced. The choce of end query length nvolves nherent trade-offs n specfcty and computng tme, and nvald wll ncrease the burden for the second stage. We determned from our smulatons that end Query sequence L Q q q s s L S Fgure 3. typcal parwse sequence overlap. L Q and L S are lengths n bp of the sequences. ase postons q and q, and s and s, counted from the left ends of the sequences, defne the overlap regon wth respect to each sequence. ase matches are ndcated by vertcal bars, along wth msmatches (dashed bars) and gaps (no bars). hangng end s defned as the shorter of any unmatched ends of the two sequences. sequences of 500 bp were suffcent to detect nearly all true wth hgh effcency. The second stage s to verfy potental parwse n Megablast by performng full-length comparsons of only those sequences dentfed as overlappng n stage one. The net effect of the two-stage approach was to reduce the computng tme for the parwse comparsons by ~ 5 tmes or more. Our smulaton studes usng chromosome as a hypothetcal genome ndcate that ~99.9% of true can be dentfed usng the above approach, wth Megablast false algnment expectaton set to e-0 (opton -e ). However, false caused by repettve sequences can account for more than half of all detected, dependng on the average sequence length and error rates..3 Intal qualty flterng Hangng end Subject sequence Smply ncreasng the strngency (opton -e ) cannot remove all false, especally those wth hgh overlap qualty, whle hgher strngency wll exclude many true of moderate qualty. We have consdered a number of qualty ndcators derved from Megablast output, and have found percent dentty, length of overlap regon, length of hangng ends, and dfferences n lengths of overlap regons to be the most useful. fragments that are fully contaned n several other sequences, or contaned n the same sequence multple tmes, are consdered suspcous and are also removed at ths step. Further removal of false n the remanng s only possble by checkng for mutual compatblty of by consensus layout. Mega

4 Weaver uses teratve procedures to dentfy and remove ncompatble (descrbed below). Under a varety of scenaros, the algorthm can relably reduce false to less than % of all presumed whle retanng ~95% of true (see Results)..4 Screenng false wthn clusters (SW).4. lusterng and hash tables Ths step dentfes groups (super clusters) of fragments that are mutually connected through transtve parwse. Parwse overlappng fragments Parwse Overlaps E E F G Hash table lusters that reman after the ntal qualty flterng are frst grouped nto clusters (contanng or more fragments), each of whch has one common (subject) sequence that wth all other (query) sequences n the cluster. Super clusters are formed by groupng together all clusters that share one or more sequences (query and/or subject) (Fgure 4). y defnton, fragments from dfferent super clusters do not overlap. Thus, overlap valdaton va sequence layouts need only be performed wthn each super cluster, greatly reducng computaton. Effcent overlap valdaton va sequence layout requres rapd retreval of parwse overlap nformaton, for whch we use hash tables. Once super clusters have been generated, one hash table stores all the parwse for each super cluster, usng parwse sequence Is as the keys..4. coordnate system and ftness scores Overlap valdaton s carred out by buldng a sequence coordnate system for each cluster n the super cluster. The system assgns a par of coordnate values (P, O) to each fragment based on ts overlap poston wth the common subject sequence S (Fgure 5a). P specfes the base poston of the sequence left end n the coordnate system; O specfes the sequence orentaton. The common sequence S s set at the orgn wth coordnate (P E E F G Super-cluster Fgure 4. reaton of a super cluster and hash table based on parwse. = 0, O = ), whle the coordnate for any other sequence (Q ) n the cluster s determned by P = s q, P = s ( LQ O = q + ), O = f f s s < s > s where s, q, and L Q are defned as n Fgure 3. fferent clusters n the same super cluster have dfferent orgns, and thus dfferent coordnate systems. The coordnate system facltates sequence layout and comparsons. We also fnd t useful to defne a ftness score F, a smple measure of how well each fragment fts n a cluster, later used to decde whether the sequence s lkely to belong to the cluster. The ftness score s the sum of overlap scores that sequence has wth the remanng sequences n the cluster, or F score,, = j j where score j s the Megablast overlap qualty score for sequences and j..4.3 ompatblty checks The coordnate system for each cluster assumes that between queres and the common subject are true, so that all n the cluster should be mutually compatble. We can easly perform compatblty checks between nferred (based on the coordnate system) and the observed obtaned from Megablast sequence comparson. To nfer the overlap between two sequences Q and Q, we compute the base postons for ther rght ends (P rght and P rght ) n the cluster coordnate system. Gven the coordnates for the left ends of Q and Q (Fgure 5b), t s apparent that P rght = P left + L, P rght = P left + L, where P left and P left are the base postons for the left ends of Q and Q, and L and L denote the respectve sequence lengths. If P left > P rght or P left > P rght, then there s no overlap expected between Q and Q ; a b oordnate system Q (P, -) (0, ) (P, ) Overlap expected Q q q Q s s P left P left P rght S P rght No overlap expected P left Q P rght P left S S Q Q P rght Fgure 5. (a) oordnate system bult on a subject sequence for a cluster of three sequences. The subject sequence S (left end) s placed at orgn; query sequences are placed accordng to ther wth the subject sequence. (b) oordnate system gvng the expected overlap between two sequences n a cluster.

5 otherwse they should overlap. If Q and Q are expected to overlap, then the expected overlap regon (q and q ) on sequence Q (as query) s q q q q = max(, P = mn( L, P = L = L left P rght max(, P mn( L, P left P left + ) left + ) for O =, or Pleft + ) + for O =. P + ) + rght left The expected overlap regon (s and s ) on sequence Q (as subject) s s s s s = max(, P = mn( L, P = L = L left P rght max(, P mn( L, P left P left + ) left + ) f O =, or Pleft + ) + f O =. P + ) + rght left Note that f q > q, the assgnments of q and q (and s and s ) must be swapped, because for detected by Megablast, q s always less than q. lso, we requre that the nferred overlap satsfy the same qualty requrement (overlap regon length) used for flterng parwse n the ntal qualty flterng step; otherwse no overlap s nferred. Wth the hash table, t s easy to check the compatblty of observed vs. nferred between Q and Q. ompatblty s assumed f there s nether nferred nor observed overlap between Q and Q, or the nferred overlap devates from the detected overlap wthn allowable lmts for boundares of the overlap regons. Each compatblty check of Q and Q also nvolves the orgn sequence S. In case of ncompatblty, f the ftness scores of Q and Q are both greater than that of S, then both Q and Q are removed from the cluster; otherwse the sequence wth the smaller ftness score s removed. In ths manner, all pars of query sequences n the cluster are compared, and ncompatble sequences removed. When a sequence s removed, the ftness scores for the remanng sequences are updated to account for ths removal. fter the SW step has removed ncompatble sequences for all clusters n the super cluster, the cleaner are output from the correspondng hash table for the remanng sequences n each cluster. When ths s completed for all super clusters, one teraton of SW s complete. The next teraton of SW begns by swtchng the roles of query and subject sequences, so that query sequences from the prevous teraton are taken as subject, and the prevous subjects become queres. The clusterng, hashng and compatblty steps are agan performed, and so on. The teraton proceeds untl no more (false) can be removed (Fgure ), and we then descrbe SW as convergent. The teratons do not requre the Megablast comparsons to be repeated, and so the entre procedure can be performed effcently..5 Screenng false between clusters (S) The SW procedure ensures that fragments wthn clusters are compatble wth each other. However, some of the fragments, n partcular sequences at the ends of cluster layouts, or regons wth low sequence coverage, may have spurous compatblty wth other sequences n the cluster. Screenng between clusters (S) provdes an addtonal opportunty to dentfy false nvolvng such sequences, and merges compatble clusters to form longer consensus sequences. Lke SW, S s an teratve procedure (Fgure ). It begns by usng the convergent SW output, and the later teratons nclude the clusterng and hashng steps as descrbed for SW. The compatblty checks, however, are performed between clusters. For each super cluster, two clusters, denoted and, are compared at a tme to see f they have any drectly shared sequences. If there are no shared sequences, then S contnues wth another par of clusters. If there s more than one sequence shared, compatblty of the shared sequences s checked. Ths requres that the coordnates of the shared sequences n be converted to those n based on one of the shared sequences, called the anchor (denoted ). Let ( P, ) be the O (, O coordnate/orentaton of n, and P ) the correspondng coordnate n. Then coordnate O (, O ( P, ) for any other sequence S n can be converted to P ) for by: or ( P P ) + P, O O O P = =, f O =, P O O. = ( P + P + L ) P L, O = O, f If the converted coordnate of a shared sequence devates from ts orgnal coordnate by more than a specfed value, a penalty score s recorded for each of the shared sequence and the anchor. Otherwse a penalty score of 0 s recorded. Each of the shared sequences s taken as anchor sequence n turn, and a total penalty score s calculated for each shared sequence by summng all ts penalty scores recorded under all anchor sequences (ncludng tself). The shared sequence wth largest penalty s removed, and the total penalty scores for sequences ncompatble wth the removed sequence (ether anchor or non-anchor) are reduced by. The process contnues untl all remanng shared sequences have a zero total penalty score. If only one sequence s shared by and, there s no need for a compatblty check. The shared sequence may be valdated n later comparsons, or (as a conservatve measure) dropped from the cluster n whch t has the smaller ftness score.

6 fter the compatblty check for shared sequences, coordnates for all unque sequences n are converted to those of wth any compatble shared sequence as anchor. The converson merges the two clusters and adopts sequence n overlappng regons. omparsons of unque (non-shared) sequences from and are conducted n the same manner as for SW. The compatblty check terates by swappng the roles of query sequences and subject sequences n the same manner as for SW. t the end of the S teratve procedure, each super cluster becomes one or more dsjont clusters, whch are then ready for assembly. For realstc tlng coverage n a draft assembly stage of a complex genome, the combnaton of qualty flterng and the SW and S teratve procedures reduces false to < % of detected, whle retanng > 95% of true (see Results)..6 ssembly of consensus sequences Wth the cleaned, consensus assembly now becomes straghtforward: smply jon overlappng fragments, followng the coordnate system wthn each cluster. Mega Weaver outputs the fragments, cluster Is, and poston nformaton. The fnal step s to perform multple algnments of fragments to form a consensus. ecause the remanng fragments have been extensvely cleaned, msassembly s very lmted. In our smulatons, the assembly results were nearly optmal n the sense of reconstructng true (see Results). 3. Results Smulaton studes were carred out to assess the performance of Mega Weaver n assembly of consensus sequences. The complete sequence of human chromosome, after removal of sequencng gaps, was used as a 33.5 Mb hypothetcal genome. The chromosome sze and the amount of repettve sequence (4% tandem and nterspersed, unham et al. 999) make t deal for smulaton studes (atzoglou et al. 00). We consdered several condtons that nfluence assembly qualty, ncludng tlng coverage, average fragment length, and sequence error rates. Tlng coverage s the total length of all fragments dvded by the genome length, whch should not be confused wth the shotgun coverage used n creatng fragments. Each condton corresponds to one set of smulatons. The frst set of smulatons used fve degrees of tlng coverage (X,.4X,.8X,.X, and.6x) wth a fxed average fragment length of ~47kb and zero sequence error rate. For the second set of smulatons, eght dfferent average fragment lengths (0kb, 0kb, 30kb, 40kb, 60kb, 80kb, 00kb, and 00kb or complete clone) were used wth a fxed tlng coverage of ~.5X and zero sequence error rate. The last set of smulatons used fve sequence error rates (0%, 0.0%, 0.05%, 0.5%, and %) under fxed tlng coverage of.5x and average fragment length of 0 kb. The condtons are not exhaustve, but reflect the wde range of coverage lkely to be encountered as a genome moves through successve stages of draft assembly. Each clone was smulated by frst choosng a random length n the range kb, and then choosng a startng bp poston unformly on the genome. lthough one ntent of the FP map had been to ad n tlng path selecton, we fnd that our smulatons do not appear to be dramatcally dfferent from the observed human genome coverage. Each was fragmented by nsertng random gaps accordng to the specfed average fragment length. Sequence errors were ntroduced at a specfed rate per bp for each fragment. For each condton, 0 replcate smulatons were conducted. Parwse were dentfed as descrbed n METHOS wth Megablast optons -e e 0, - 3, and -F F. Qualty flterng and the SW and S overlap procedures requred a 00 bp mnmum overlap length, 3 bp maxmum hangng end, 3 bp maxmum dfference n overlap regons, and 95% mnmum overlap dentty. Megablast comparsons were performed usng a small Lnux cluster (8 nodes, 6 processors at GHz), and the remanng steps performed on a sngle Lnux workstaton. 3. Performance n screenng false We evaluate the effectveness of the screenng procedures False overlap % False overlap % False overlap % a Tlng coverage (X) c e ve. fragment length (kb) Sequence error rate (%) True overlap % True overlap % True overlap % b Tlng coverage (X) d f ve. fragment length (kb) Sequence error rate (%) Intal status fter qualty flterng fter SW fter S Fgure 6. Performance of Mega Weaver n screenng false. (a, b) effect of tlng coverage wth average fragment length 47kb; (c, d) effect of fragment length wth tlng coverage.5x; (e, f) effect of sequence error rate wth fragment length 0kb and tlng coverage.5x. Results were averaged for 0 replcates under each condton.

7 by two measures: the proporton of false among detected (deally 0%), and the proporton of true that were correctly detected (deally 00%). Fgure 6 shows the results for each step of the screenng procedure (ncludng ntal Megablast output, qualty flterng, SW and S) for each of the three sets of smulatons. It s apparent that nearly 00% of true were detected wth Megablast under all of the condtons examned (Fgure 6b, d, f). However, the ntal contaned up to ~68% false, and 8% false even when full-length clones were used (Fgure 6a, c, e). The proporton of false n ntal Megablast output depended on average fragment length more than tlng coverage and sequence bp error rate (Fgure 6a, c, e). fter the entre screenng procedure, false were reduced to 0.9%-.9% for the entre range of condtons consdered. Ths eventual reducton dd not depend much on the condtons examned, an ndcator of the robustness of our algorthm. t the same tme, the losses n true were tolerable an average loss of 6.7% over all smulaton condtons. The greatest loss of true (~5%) occurred wth the hghest sequence error rates (% and 0.5%), and short average fragment length (0kb). For full-length clones (the other extreme), the loss was only 0.8%. Sequence error rates seemed to have the greatest nfluence on loss of true, assumng a relatvely low average fragment length (0kb). Longer fragment lengths would correspond to greater depth of sequencng coverage, for whch the remanng errors n fragments would be at the extreme low end of our range. The steps n the screenng procedure dd not contrbute equally to the reducton of false and loss of true (Supplemental Fgure S on our web ste). The most effectve steps were qualty flterng and SW, whch together reduced false by 94.%, but also accounted for 50.5% of the loss n true. y contrast, S succeeded n reducng false by only 3.8% of the total. 3. Performance n consensus assembly The overall qualty of after the screenng procedure largely determnes the qualty of the fnal consensus assembly. Fgure 7 compares the total number, average length, and coverage of consensus sequences assembled wth the cleaned, compared to the best possble assembly usng the known genomc postons of all fragments. It s evdent from the fgure that our assembly after the cleanng procedures was nearly optmal. The performance dd not vary greatly by smulaton condton, except n the worst case wth sequence error rate % and average fragment length 0kb. The nfluence of the three sets of smulaton condtons on the overall assembly qualty were as expected. We further evaluated the qualty of each assembled consensus sequence by comparng t to the true consensus nferred from known genomc postons of fragments (supplemental Fgure S on our web ste). Most consensus sequences (average 94%) were correctly assembled,.e., the correspondng fragments were postoned and orented correctly (n proper order and postoned to wthn 3 bp). Moreover, the correct consensus sequences formed an average 95.5% of the total length of assembled consensus sequences. Usng full-length clones yelded ~99.8% correct consensus sequences, and 99.6% of the assembly length. 3.3 Performance n larger genome assembly To assess the performance of our algorthm for consensus assembly of a larger hypothetcal genome, we performed addtonal smulatons by jonng end-to-end all human chromosome fragments (NI uld 30). Ths genome length s 54 Mb, ncludng over 5% repettve sequence. Smulatons were carred out under fxed tlng coverage.5 X and sequence bp error rate 0.%, wth two dfferent average fragment lengths, 0 kb and 00 kb (complete sequences). Fve sequence data sets were smulated for each of the two condtons. Parwse were detected and teratvely screened usng the same crtera as above. fter qualty flterng and teratve screenng of false, false were reduced to ~6% on average for the shorter fragments (0kb), but only ~0.% for the longer fragments (00 kb). Loss of true was ~7% wth 0kb fragments, and ~5% for the 00 kb fragments. These results ndcate that the algorthm can be scaled up for larger genome assembly wthout substantal reducton n performance. 4. scusson Sequence errors and repettve sequences are two major obstacles to the assembly of complex genomes. Even usng full-length sequences, false (after qualty flterng) caused by repettve sequence were as great as 3% (Fgure 6c). Ths percentage ncreases consderably when consderng fragmented sequences wth sequence errors that reman n the fragments. Some of the ssues n consensus assembly are smlar to that encountered n wholegenome shotgun assembly (atzoglou et al. 00), and the detecton of false s central to genome assembly. However, compared to ndvdual shotgun reads, the greater length of fragments allows the assembly procedure to focus mmedately on layout compatblty of fragments rather than more elementary ssues of sequence qualty. The effcency of the overlap comparsons detaled here enables the use of teratve procedures not consdered n Ggssembler (Kent and Haussler 00). Most greedy or dynamc algorthms (Staden 98; ean and Staden 99; Kent and Haussler 00) process one sequence (raw nput sequence or exstng contg) at a tme, ether creatng a new contg or extendng an exstng contg. False are dentfed and removed as the consensus s extended. Our smulaton study has demonstrated that our teratve approach can remove the majorty of false nvolvng repettve sequences relably and effectvely, to the pont of nearly achevng optmal assembly and

8 a b c onsensus coverage Number of consensuses ve. consensus length (kb) overage (X) ve. Fragment length (kb) Sequence error rate (%) Expected ctual Fgure 7. Performance of Mega Weaver n consensuses assembly. olumns a, b, and c show the effects of coverage, average fragment lengths, and sequence bp error rate, respectvely, on the qualty of assembly. ncludng false to <% of ncluded sequence (whch s further mproved n later fnshng steps). We found that average fragment length, and (to a lesser extent) tlng coverage and sequence error rate were mportant determnants of the qualty of consensus assembly. Sequence error rate dd show some mpact when usng relatvely short fragment sequences (e.g. 0kb). The assembly appears farly robust to varatons n tlng coverage, average sequence length, and reasonable sequence error rates. Thus, f fragments have been assembled largely correctly, ths algorthm can provde a useful ntermedate step to full genome assembly, wthout requrng pror poston nformaton. The fact that fragments are suffcently unque to perform ths assembly on the scale of human chromosome (and lkely larger) suggests that alternate herarchcal strateges nvolvng random selecton may be feasble. For such a strategy, the potental extra costs n sequencng (va redundant sequenced s) must be weghed aganst the costs and accuracy of creatng the FP-based tlng path. Mega Weaver code s freely avalable at 5. cknowledgments Thanks to r. Wllam Lemon and Hao Sun for helpful dscusson. Ths research was supported n part by GM to F..W. 6. References atzoglou, S., Jaffe,.., Stanley, K., utler, J., Gnerre, S., Maucel, E., erger,., Mesrov, J.P. and Lander, E.S. (00): RHNE: whole-genome shotgun assembler. Genome Res. (): unham, I., Shmzu, N., Roe,.., hssoe, S., unham, I., Hunt,.R., ollns, J.E., ruskewch, R., eare,.m., lamp, M., et al. (999) The N sequence of human chromosome. Nature 40 (676): Ewng. and Green P. (998): ase-callng of automated sequencer traces usng Phred. II. Error probabltes. Genome Res. 8(3): Gllett, W., Hanks, L., Wong, G.K., Yu, J., Lm, R. and Olson, M.V. (996): ssembly of hgh-resoluton restrcton maps based on multple complete dgests of a redundant set of overlappng clones. Genomcs 33 (3): Green, P. (997): ganst a whole-genome shotgun. Genome Res. 7(5): Green, P. (00): Whole-genome dsassembly. Proc. Natl. cad. Sc. 99(7): Huang, X. (99): contg assembly program based on senstve detecton of fragment. Genomcs 4(): 8-5. Huang, X. and Madan,. (999): P3: N sequence assembly program. Genome Res. 9(9):

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