Thomas W. Blackwell, Eric Rouchka and David J. States

Transcription

1 From: ISMB-99 Procdings. Copyright ' 1999, AAAI ( All rights rsrvd. Idntity by Dscnt Gnom Sgmntation Basd on Singl uclotid Polymorphism Distributions Thomas W. Blackwll, Eric Rouchka and David J. Stats Institut for Biomdical Computing, Washington Univrsity in St. Louis, 700 South Euclid Av., St. Louis, MO 63110, {blackwl, cr, Abstract In th cours of our fforts to build xtndd rgions of human gnomic squnc by assmbling individual BAC squncs, w hav ncountrd svral instancs whr a rgion of th gnom has bn squncd indpndntly using ragnts drivd from two diffrnt individuals. Comparing ths squncs allows us to analyz th frquncy and distribution of singl nuclotid polymorphisms (SPs) in th human gnom. Th obsrvd transition/- transvrsion frquncis ar consistnt with a biological origin for th squnc discrpancis, and this suggsts that th data producd by larg squncing cntrs ar accurat nough to b usd as th basis for SP analysis. Th obsrvd distribution of singl nuclotid polymorphisms in th human gnom is not uniform. An apparnt duplication in th human gnom xtnding ovr mor than 130 kb btwn chromosoms 1p34 and 16p13 is rportd. Indpndntly drivd squncs covring ths rgions ar mor than 99.9% idntical, indicating that this duplication vnt must hav occurrd quit rcntly. FISH mapping rsults rportd by th rlvant laboratoris indicat that th human population may b polymorphic for this duplication. W prsnt a population gntic thory for th xpctd distribution of SPs and driv an algorithm for probabilistically sgmnting gnomic squnc into rgions that ar idntical by dscnt (IBD) btwn two individuals basd on this thory and th obsrvd locations of polymorphisms. Basd on ths mthods and a random mating modl for th human population, stimats ar mad for th mutation rat in th human gnom. Introduction High throughput gnom squnc analysis has bn indpndntly prformd mor than onc on svral rgions of th human gnom. Comparing ths indpndntly drivd squncs dmonstrats that th distribution of SPs in th human gnom is highly non-uniform. This finding is striking bcaus SPs ar thought to aris by a mutation procss that occurs with approximatly uniform rats across th gnom. In comparing two chromosoms, sgmnts sharing a common ancstor ar said to b idntical by dscnt (IBD). Th ag of th last common ancstor for a sgmnt is Copyright 1999, Amrican Association for Artificial Intllignc ( All rights rsrvd. dfind as th coalscnc tim for that sgmnt. Gntic rcombination rsults in th intrchang of sgmnts btwn homologous chromosoms, so a pair of contmporary chromosoms will b composd of a patchwork of IBD sgmnts varying in ag. Th idntity of th last common ancstor for ach particular sgmnt will vary as wll. SPs aris as substitution mutations occurring along on or othr linag drivd from th last common ancstor. Sgmnts with a comparativly rcnt common ancstor will hav had littl tim in which to accumulat mutations, so w xpct that SPs in ths sgmnts will b spars. Convrsly, sgmnts with an ancint common ancstor will hav had mor tim during which to accumulat mutations and w xpct SPs to b dns in ths rgions. Th xpctd siz of an IBD sgmnt also dpnds on its ag. For a sgmnt with a rcnt common ancstor, fw gnrations will hav occurrd during which rcombination vnts could disrupt th rgion of idntity by dscnt which it rprsnts, so th sgmnt is likly to b larg. Loci with ancint common ancstors ar likly to hav had narby rcombination brakpoints and thus ar likly to b found in rlativly short IBD sgmnts. As a rsult, th distribution of th numbr of SPs pr IBD sgmnt is indpndnt of th ag of th sgmnt. (Tchnically, two chromosoms which diffr by a SP ar not strictly idntical in that rgion. Howvr, w will rfr to corrsponding sgmnts of gnomic squnc as IBD bcaus th majority of th squnc rmains idntical by dscnt.) To obtain data on SP distributions in th human gnom, w nd to compar squnc data drivd indpndntly from diffrnt individuals. Du to physical limitations of currnt squncing and cloning tchniqus, th gnom must b brokn down into smallr portions in th rang of 20 kilobass (kb) for plasmid clons to 250 kb for bactrial artificial chromosoms (BACs) and yast artificial chromosoms (YACs) [Lodish t al., 1995]. As th squnc data for ach of ths shortr rgions bcoms availabl, it would b hlpful to connct thm with adjacnt ovrlapping rgions prviously squncd. It is possibl that ovrlapping squncs could originat from diffrnt squncing cntrs. Sinc a complt squnc of ach human chromosom is dsird, a mthod to assmbl ths smallr squncs into largr contiguous rgions (contigs) is constructd.

2 Mthods GnBank is usd as th rfrnc databas for human gnomic DA usd in building th contigs. Th rsults ar basd upon rlas 110.0, which includs squncs submittd to GnBank up until Dcmbr 5, 1998 [Bnson t al., 1998]. Th GnBank primat division is usd in ordr to crat stabl human contigs. In rlas 110.0, this is dividd into gbpri1, gbpri2, and gbpri3. Tabl 1 shows a brakdown of th squncs in th primat divisions by squnc siz. Squnc lngth (nuclotids) > 200, , , , , ,000-99, ,000-74, ,000-49, TOTAL > 25,000 2,644 umbr of GnBank ntris Tabl 1: Lngth of primat GnBank ntris. This tabl indicats th numbr of squncs in th primat divisions (gbpri1, gbpri2, and gbpri3) of GnBank rlas Som of th gnom squncing cntrs incorporat nighboring clon information into thir GnBank ntris. Tabl 2 shows som xampls of how this data is ntrd into th commnts sction. Us of this information could hlp in th cration of gnom contigs. Howvr, as Tabl 2 indicats, this data is not standardizd among th squncing cntrs. Th data is ntrd by hand in a mannr that is asy for a human to rad, but not asily parsd by a computr. Th ovrlap btwn two clons, if givn, is prsnt only in a positional mannr. An alignmnt btwn two ovrlapping clons is not givn. W crat most of th contigs using an automatd procdur. Th first stp is to rtriv human squncs from GnBank which ar gratr than 25 kb in lngth. Aftr ths squncs ar rtrivd thir nds ar sarchd against th primat division of GnBank for ovrlapping rgions at last 70 bas pairs (bp) long and at last 98% idntical. Ths sarchs ar prformd using wu2blastn vrsion 2.0 [Gish, ], th Washington Univrsity vrsion of BLAST [Altschul t al., 1990] with gaps for nuclic acid squncs. Whn ovrlapping clons ar found, thy ar mrgd togthr into a contig basd on th blast alignmnt. Discrpancis in th alignmnt rsulting from gaps and mismatchs ar markd by th charactr in th contig. Aftr a st of contigs has bn assmbld, thy ar compard against contigs found at th CBI [ and ORL [ wb sits. Any diffrncs ar lookd at in mor dtail. As a rsult of huristics usd in BLAST, in som cass th rportd highst scoring pairs do not corrspond to an optimal pairwis alignmnt. In som cass, th huristic sarch and assmbly rstrictions nd to b rlaxd for automatic assmbly to occur. Othr contigs nd to b assmbld by hand in ordr to crat th ovrlapping rgion. Sinc th volum of squncing data is growing xponntially, ths stps ar largly automatd using PERL scripts. Squncing cntr [sampl GnBank accssion numbr] Sangr Cntr [Z99715] Univrsity of Washington Gnom Squncing Cntr [AC004398] Whithad Institut for Biomdical Rsarch [AC005303] Washington Univrsity Gnom Squncing Cntr [AC002378] Baylor Collg of Mdicin [AC002523] Ovrlap information in COMMET sction Th tru right nd of clon 1114G22 is at 104. Th tru lft nd of clon 262D12 is at Ovrlapping Squncs: 5 : UWGC: g1248a010 (Accssion: AC004107) 3 : UWGC: g1248a139 Only 90.0 kilobass from th middl of this clon ar bing submittd. Th rmaindr ovrlaps ithr accssion AC (WICGR projct L281) or accssion AC (WICGR projct L351). EIGHBORIG SEQUECE IFORMATIO: Th clon bing squncd to th lft is BK085E05; th clon bing squncd to th right is DJ102K02. Actual start of this clon is at bas position 1 of DJ438O4. Bgining of squnc ovrlaps with AF007262, nd of squnc ovrlaps with AF (ot that Bginning is missplld hr) Tabl 2: Ovrlapping clon information. Th right hand column contains xampls of ovrlapping clon information from th COMMET sctions of th GnBank ntris idntifid in th lft column. Th ovrlapping clon information is typical for th squncing cntrs shown in th lft column. Difficultis Thr ar svral difficultis with trying to find ovrlapping nd sgmnts. On problm is that clons may not ovrlap with 100% idntity du to squncing rrors and polymorphisms. Th PERL scripts ar writtn in such a mannr as to allow ovrlapping squncs gratr than 98% idntical. This allows th possibility that som ovrlaps might b missd. Most ovrlapping sgmnts should b dtctd, howvr, sinc polymorphisms occur in th population at a rat of 7/10,000 [Taillon-Millr t al., 1998], and accptabl squncing rror rats ar 1/10,000 [Collins t al., 1998].

3 Anothr difficulty is that th nd of a squnc may contain rptitiv lmnts. Prim xampls of this ar Alus and LIEs. In ths cass, blast will produc multipl hits to othrwis unrlatd squncs. It bcoms hard to dtrmin whthr or not two squncs should b assmbld into a contig whn th ovrlap btwn thm occurs in ths rpat rgions. Exampls of such squncs ar GnBank accssion AC004021, AC004202, and AC Th lngth of th ovrlap also varis gratly. Som squncing cntrs such as Washington Univrsity Gnom Squncing Cntr (WUGSC) and Sangr Cntr hav a rlativly constant squnc ovrlap lngth for known ovrlapping squncs. (In th cas for WUGSC it is 200 bp; for Sangr Cntr it is 100 bp.) For th assmbld contigs, th siz rangs from 0 bas pair ovrlaps from th Japan Scinc and Tchnology Corporation fforts on chromosom 21 to a 82,766 bas pair ovrlap btwn GnBank accssion HS326L12 and HS232G24 from th Sangr Cntr on chromosom X. Squncs with lss than a 70 bas pair ovrlap wr hand assmbld. Th GnBank ntris for ths squncs hav bn usd to aid in th dtction and assmbly of ths contigs. For th shortr ovrlapping sgmnts, running blast to find th alignmnt btwn two squncs taks a mattr of sconds, but for largr rgions, th tim spnt to find th alignmnt can tak hours. A thory for SP distribution in th gnom Gnrations => Individuals Shown in Figur 1 is a schmatic rprsntation for population gntics. Each point along th horizontal lin rprsnts an individual chromosom from th currnt population. Th jaggd lin tracs th linag of a particular locus through prcding gnrations. Th diamond indicats a substitution mutation which rsults in a SP in th currnt population. W adopt a nutral Wright-Fishr modl for population gntics. This consists of a random mating population of constant siz with diploid individuals and discrt, non-ovrlapping gnrations and no slction. Tim into th past and distanc along th chromosom ar both masurd as continuous variabls, with units of gnrations and nuclotids rspctivly. (Ths two continuous approximations ar known as a diffusion tim scal and an infinit sits modl.) Locations of rcombination brakpoints and of point mutations ar rprsntd by two indpndnt Poisson procsss for ach chromosom in ach gnration, with rats ρ and µ for rcombination and mutation rspctivly. Each rat givs th xpctd numbr of vnts pr nuclotid, pr chromosom, pr gnration. Considr n = 2 chromosoms chosn at random from th currnt day population. It is a standard rsult (rviwd in Tavar, 1984; Donnlly and Tavar, 1995) that at any singl locus, th tim T to th most rcnt common ancstor for ths two chromosoms has an xponntial distribution with man 2 gnrations and dnsity 1 T f ( T = ) xp. 2 2 W dfin th IBD sgmnt containing a givn locus to b a maximal rgion around th locus, within which no rcombination has occurrd in th linag lading to ithr of th two sampld chromosoms, in any gnration sinc thir most rcnt common ancstor. This dfinition is spcific to th pair of chromosoms in qustion. By construction, vry sit within this sgmnt has th sam coalscnc tim. If any singl nuclotid polymorphisms ar found btwn th two currnt day chromosoms within this sgmnt, thy must hav arisn by a point mutation, in on linag or th othr, in som gnration sinc th tim of th most rcnt common ancstor. Conditional on th coalscnc tim T, th lngth of an IBD sgmnt has an xponntial distribution with man 1 / 2ρ T. Marginal ovr T, this lngth L has dnsity 2ρ ρ f ( L, ρ) = + xp( 2ρ L). ( 1 L) 2 + ρ ( 1+ ρ L) (This xcluds rcombinations which might occur during th currnt gnration.) Marginal ovr th sgmnt lngth, th numbr of SPs occurring in an IBD sgmnt has a gomtric distribution with man µ / ρ, µ ρ Pr( ρ, µ ) =, ρ + µ ρ + µ and is indpndnt of th sgmnt s coalscnc tim. (This is a consqunc, rathr than an assumption of th modl.) Howvr, conditional on a sgmnt s lngth, th numbr of SPs found in it has a modifid ngativ binomial distribution, Pr[ X + 1] Pr( L,, ρ, µ ) = Pr Y 1 1+ µ L [ ] 1+ ( ρ + µ ) L 1+ ( ρ + µ ) 2 ρl ( + 1). L

4 Hr, X and Y ar indpndnt Poisson-distributd 2 ρ +µ L+ 1 2 and random variabls with mans ( ) 2 ρ + rspctivly. Thir Poisson cumulativ L 1 2 distributions simply giv a convnint rprsntation for valus of th incomplt gamma function. Th locations of th obsrvd SPs ar uniformly distributd within th boundaris of th sgmnt, conditional on L and. 0.3 Whn R is larg (~10 5 ), w introduc an approximation to furthr acclrat th calculation. Lt r b th rsolution of a sgmntation. By this w man that w will only considr sgmnt boundaris placd at an intgr multipl of r across th rgion. In this cas, only R/r sgmnt boundaris nd b considrd and for ach of ths, only R/r possibl trminal sgmnts nd b considrd. Th calculation tim is thn O((R/r) 2 ). Thus, by limiting th rsolution to 10 nuclotids, a factor of 100 improvmnt in run tim is achivd. In practic, no signficant diffrnc in rsults was obtaind for rsolutions of 10, 20, 50 or 100 nuclotids. Rsults probability nuclotids 10, ,000 1,000,000 Shown in Figur 2 is th probability distribution for th log of th IBD sgmnt lngth for random mating populations of 1 million, 100,000 or 10,000 individuals. Th man IBD sgmnt lngth dos dpnd on th population siz, and for all population sizs, th distribution of IBD sgmnt lngths is xtrmly broad. Givn a rgion of th gnom containing a numbr of SPs, and som hypothtical sgmntation S into intrvals that ar IBD, th liklihood for S is calculatd as th product ovr all sgmnts marginal ovr all possibl sgmnt coalscnc tims of th probability that an IBD sgmnt of that ag would hav th hypothsizd lngth L and numbr of SPs at th obsrvd locations. Thus th ovrall sgmntation liklihood is just 1 L ( S) = Pr( L, T ) f ( L T ) f ( T ) dt. L sgmnts 0 Sinc w do not hav a way of knowing which of th many possibl IBD sgmntations dscribing a rgion corrsponds to th tru gntic history, w marginaliz ovr all possibl IBD sgmntations for th rgion. This is accomplishd using a dynamic programming approach [Lawrnc and Rilly, 1985]. Givn a st of all possibl sgmntations for a rgion of lngth R, to sgmnt a rgion of lngth R+1 w must ithr xtnd a trminal sgmnt or start a nw sgmnt. Th liklihood of ach sgmnt dpnds only on its lngth and SP contnt so th problm is partitionabl and dynamic programming can b applid. Sinc thr ar R possibl trminal sgmnts ranging in lngth from 1 to th full lngth of th rgion, th calculation rquirs linar storag and O(R 2 ) tim. Two ovrlapping clons from diffrnt chromosoms An intrsting rgion occurs btwn two ovrlapping clons originating from two sparat chromosoms. Th first ntry is GnBank accssion AL and th scond ntry is GnBank accssion U Th 135 kb AL is squncd by Sangr Cntr and is annotatd as 1p Th 171 kb ntry U95738 is squncd by Th Institut for Gnom Rsarch (TIGR) and is annotatd as 16p According to th blast hits, AL lis compltly within U95738 with 100 mismatchs, 74 of which ar transitions (A<->G; C<->T) and 26 ar transvrsions. Thr ar also 22 gaps composd of 123 indl vnts. Th ratio of transitions to transvrsions is consistnt with a biological origin for ths squnc discrpancis. On avrag substitution mutation is xpctd to produc twic as many transitions as transvrsions [Li t al., 1996] whil a random rror procss (such as squncing rror) would b xpctd to produc a two-fold xcss of transvrsions. W obsrv thr tims as many transitions as transvrsions. Intrstingly, although ths two squncs ar 99.9 prcnt idntical, thy now appar to hav bn drivd from diffrnt chromosomal locations. Th Sangr cntr confirms th FISH localization of thir clon on chromosom 1p. Th sourc clon for th longr TIGR squnc was mappd by FISH at th California Institut of Tchnology. That data shows FISH signals on both chromosoms 1p34 and 16p13 (Figur 3). Togthr, ths FISH data ar consistnt with th prsnc of a duplication vnt btwn chromosoms 1 and 16 occurring so rcntly that th human population may b polymorphic for this duplication. Othr possibl xplanations includ prob contamination or a chimric BAC. Thr is no rason to suspct th formr and w ar not awar of any documntd xampls of chimric BACs. Furthr, Pitr d Jong [prsonal communication] has survyd ovr 400 BACs from th RPCI-11 library looking spcifically for vidnc of chimrism and found non.

5 log sgmnation liklihood = 10 5 = 10 4 Figur 3: FISH rsults for GnBank accssion U This FISH imag indicats a homology btwn chromosoms 1 and 16. (Imag courtsy of California Institut of Tchnology) ( Th distribution of singl bas polymorphisms across this 134 Kb intrval is shown in Figur 4. Th distribution is highly nonuniform with som intrvals spanning 10 Kb with no polymorphisms at all and othr intrvals of 100 nuclotids containing multipl SPs Shown in Figur 4 is th distribution of SPs along th ovrlap rgion btwn squncs U95738 and AL Ovrall this ovrlap spans 134 kb with 100 squnc discrpancis (74 transitions and 26 transvrsions). Th dynamic programming algorithm dscribd abov was usd to calculat IBD sgmntation liklihoods for all possibl sgmntations at a varity of population sizs and singl point substitution rats. In all cass a uniform population with random mating was assumd. For th purpos of this analysis, th rcombination rat was fixd at on rcombination pr 10 8 nuclotids pr gnration (on cntimorgan quals on mgabas). Whil it is known that th rlationship of gntic to physical distanc varis across th gnom and in som locations is vn sx spcific, ths variations ar rlativly modst in comparison to th assumptions w hav mad about population siz and mating bhavior. Rsults ar shown in Figur 5 blow. Calculations wr prformd with a rsolution (s abov) of 10, 20, 50, and 100 nuclotids. o significant variations with rsolution wr obsrvd E E E E-06 mutations pr nuclotid pr gnration Shown in Figur 5 is th calculatd liklihood for all possibl IBD sgmntations of th U95738/AL ovrlap as a function of point substitution mutation rats givn a rcombination rat of on pr 10 8 pr nuclotid pr gnration (on cntimorgan quals on mgabas) and a homognous population of 100,000 or 10,000 individuals. Th bst fit is obtaind with a mutation rat modratly in xcss of th rcombination rat and a population siz of roughly 10,000. Discussion In this papr w prsnt xprimntal vidnc for nonuniform distribution of SPs across th human gnom and driv thory for th xpctd distribution of SPs in th gnom. Intrstingly, th obsrvd non-uniform distribution can b accountd for by th intrplay of two uniform and random procsss, singl point mutation and rcombination. A striking finding is th vry broad distribution of xpctd IBD sgmnt lngths and ags. Anothr intrsting rsult is that th random numbr of SPs pr sgmnt is indpndnt of th IBD sgmnt s ag. Givn th small numbr of SPs that occur, it is not possibl to dtrmin which of th many possibl IBD sgmntations corrsponds to th tru gntic history of th intrval bing analyzd. Instad w apply a dynamic programming approach to calculat th liklihood marginalizd ovr all possibl sgmntations of th rgion. Using this approach w obtain an approximat stimat for th point substitution rat in th human gnom ovr th tim to coalscnc, roughly a fw hundrd thousand yars. This stimat dpnds on knowldg of th rcombination rat, which is wll-stablishd from pdigr gntics, and assumptions about population structur and history for th human spcis (rviwd in Jord, Bamshad and Rogrs, 1998). For assumd population sizs diffring by an ordr of magnitud, th drivd mutation rat diffrs by a factor of four. Th singl point substitution mutation rat stimatd hr is in agrmnt with stimats drivd through

6 psudogn analysis. For xampl, Li t al. hav xamind point substitution rats for a numbr of psudogns idntifid in primat spcis. Comparing human to old world monky spcis, thy find substitution rats varying btwn and [Li t al., 1996]. Ths spcis ar thought to hav divrgd roughly 25 million yars or 1.25x10 6 gnrations ago, assuming a gnration tim or 20 yars. Th corrsponding point substitution rats ar 4-8x10-8 substitutions pr nuclotid pr gnration. Our stimat for th human point substitution mutation rat is indpndnt of many of th assumptions mad in traditional molcular clock calculations. First, w ar calculating th mutation rat with rspct to th rcombination rat and thrfor do not nd to mak assumptions about th avrag gnration tim for th spcis. Scond, th tim scal is infrrd from th SP distribution obsrvd in th gnom, and w do not nd to mak rfrnc to th fossil rcord. Our rsults suggst that SPs found in isolation (no othr SPs in clos proximity on th gnom) ar likly to hav bn drivd from a rlativly rcnt mutation vnt whil SPs found in clustrs ar mor likly to hav bn drivd from a comparativly ancint ancstor. If thr has bn stratification of th human population, th oldr SPs ar mor likly to b prsnt in all contmporary branchs of th population and thus might b prfrrd for us as gntic or diagnostic markrs. Jord, L.B., Bamshad, M. and Rogrs, A.R., (1998) Using Mitochondrial and uclar DA Markrs to Rconstruct Human Evolution. BioEssays, 20(2): Lawrnc, C.E., Rilly, A.A. (1985) Maximum Liklihood Estimation of Subsqunc Consrvation. Journal of Thortical Biology, 13(3): Li, W.H., Ellsworth, D.L., Krushkal, J., Chang, B.H.J., and Hwtt-Emmtt, D. (1996) Rats of uclotid Substitutions in Primats and Rodnts and th Gnration- Tim Effct Hypothsis. Molcular Phylogntics and Evolution, 5: Lodish, H., Baltimor, D., Brk, A., Zipursky, S.L., Matsudaira, P., Darnll, J. (1995). Molcular Cll Biology. w York: Scintific Amrican Books. Taillon-Millr P., Gu Z., Li Q., Hillir L., Kwok P.Y., (1998) Ovrlapping Gnomic Squncs: a Trasur Trov of Singl-nuclotid Polymorphisms. Gnom Rsarch, 8(7): Tavar, S. (1984) Lin-of-dscnt and Gnalogical Procsss, and thir Applications in Population Gntics Modls. Thortical Population Biology, 46: Acknowldgmnts W wish to thank Brndan Loftus of th TIGR Cntr and Andrw King of th Sangr Cntr for assistanc in rviwing clon origins and FISH data and th Caltch Gnom Cntr for prmission to rproduc Figur 3. This work was supportd by th Dpartmnt of Enrgy undr grant DE-FG02-94ER61910 and by th ational Instituts of Halth undr grant R01 HG Rfrncs Altschul, S.F., Gish, W., Millr, W., Myrs, E.W., Lipman, D.J., (1990) Basic Local Alignmnt Sarch Tool. Journal of Molcular Biology, 215: Bnson, D.A., Boguski, M.S., Lipman, D.J., Ostll, J., Oulltt, B.F., (1998) GnBank. uclic Acids Rsarch, 26(1):1-7. Collins, F.S., Patrinos, A., Jordan, E., Chakravarti, A., Gstland, R., Waltrs, L., (1998) w Goals for th U.S. Human Gnom Projct: Scinc, 282(5389): Donnlly, P. and Tavar, S., (1995) Coalscnts and Gnalogical Structur Undr utrality. Annual Rviw of Gntics, 29: Gish, W., ( ). unpublishd.