Sequence analysis Multiple sequence alignment

Transcription

1 UMF0 Introduton to bonforats, 005 equene analyss Multple sequene algnent. Introduton Leturer: Marna Alexandersson 6 epteber, 005 In parwse algnent the resdues are algned n pars. The pars are sored usng the lkelhood rato and the total sore of an algnent would be EAA VF-T Pr( a, b odel) pab s( a, b) = log = log Pr( a, b rando) q q = s( E, V ) + s( A, F) + γ () + s(, T ) where s ( a, b) oes fro a substtuton sore atrx suh as PAM or BLOUM, and γ s the gap penalty funton (lnear or affne). How do we algn three or ore sequenes? In ultple algnent the resdues are algned n oluns. The dea s the sae, the resduals n an algned olun s assued to have dverged fro an anestral resdue. EAA VF-T GCA- A natural generalzaton would be where = s( E, V, G) + s( A, F, C) + s( A,, A) + s(, T, ) p s ( a, b, ) = q q (we skp the defnton of gap penaltes for now). But how do we obtan p ab? And what about when we want to algn four sequenes, how do we obtan p abd? We don't have enough data to estate these probabltes, the ore sequenes the ore data s requred. Moreover, exept for trval ases f hghly dental sequenes, t s usually not possble to unabguously reate a sngle orret ultple algnent. One reason beng that the evolutonary a ab b q a b

2 UMF0 Introduton to bonforats, 005 hstory of a sequene faly s not ndependently known, t ust tself be nferred fro sequene algnent. Thus, our ablty to defne a sngle 'orret' algnent wll vary wth relatedness of the sequenes algned. We therefore fous on subsets of oluns orrespondng to key resdues and ore strutural eleents that an be algned wth ore onfdene.. orng shees A sorng syste should take nto aount two portant features of ultple algnents Poston spef sorng: soe postons are ore onserved than others and thus dfferent postons are treated dfferently The evolutonary relatonshp between sequenes: sequenes are not ndependent and ther relaton affets the sorng. Ideally a ultple algnent would be sored based on the phylogenet tree, nludng all ts evolutonary events. Unfortunately we don't have enough data to paraeterze suh a oplex odel, and splfatons ust be ade. We use approxatons that partly or entrely gnore the phylogenet tree whle dong soe sort of poston-spef sorng of algnng struturally opatble resdues. Just as the postons were assued ndependent n the parwse algnent, any ultple algnent ethods assue ndependene between oluns n the algnent. uh a sorng funton an be wrtten where + ( ) = G ( ) s olun n the ultple algnent, ) s the sore for olun, and G s a gap funton (unspefed so far). Assue for now that possble ways to defne the sore ).. Mnu entropy ( ( ontans no gaps. There are several The bas dea of the nu entropy ethod s to try to nze the entropy for eah olun, and the bgger the varaton the hgher the entropy. Let = all resdues n olun j = the resdue n olun and sequene j = observed ounts of resdue a n olun a p = the probablty of havng resdue a n olun a j That s, for a ultple algnent the resdue j n olun, (that s, the ano ad or DNA base n sequene j at poston n the ultple algnent).

3 UMF0 Introduton to bonforats, 005 seq j...g D F H Y F V H G......G D A F H Y Y L F G......G D Y H Y F L F G......G D F H Y F M F G......G D F H F F A F G... j Fgure : Multple algnent. The th olun s denoted, and the j th resdue n the olun (belongng to the j th sequene n the algnent) s denoted. j Wth a beng the ount for a spef resdue a, let be the ount vetor,,..., K wth the ounts for eah the resdues n the urrent alphabet. For nstane, f we are algnng proten sequenes, the resdue a s one of the ano ads n the alphabet {A,C,D,,Y}, K = 0, and the ount vetor for s = { A, C, D,..., Y }. larly, f we are onsderng DNA sequenes the alphabet s {A,C,G,T} and K =. The probablty of observng a spef resdue a n p a = b a an be estated by where the su n the denonator runs over all possble resdues. For nstane, for ano ad Y n olun n the fgure above we would get p Y = The probablty of a olun would then be A + Pr( ) The nu entropy sore for a olun probablty of the olun. That s, ( ) C b + = a Y D p a a Y = = + would then be the negatve logarth of the = a a log p Ths s an entropy easure related to the hannon entropy n nforaton theory. Entropy s generally a easure of varablty, or nforaton ontent. When a olun onssts of only one or a few resdues t represents a hghly onserved poston n the sequenes, eanng that t s probably portant for the proten struture and funton. We say that a hghly onserved olun has low varablty, or hgh nforaton ontent. a 5

4 UMF0 Introduton to bonforats, 005 The nu entropy s a onvenent easure, beause the ore varable the olun, the hgher the entropy. A opletely onserved olun would sore 0. Thus, a good algnent ould be defned as the one nzng the total entropy. P sores (u of Pars) = ( ) ( ). The standard ethod of sorng ultple algnents does not use a phylogenet tree and t assues ndependene for the oluns. Coluns are sored by a 'su of pars' (P) funton usng a substtuton sorng atrx. For nstane, the sore of the olun E V G beoes the su of all parwse sores where s oes fro PAM or BLOUM. = s( E, V ) + s( E, G) + s( V, G) Forally, for olun a ultple algnent of N sequenes, the total sore s j k = ( ) = s(, ). (Note: the seond su s over all j =,..., N and k =,... N suh that j < k. Ths s to avod sung over the sae par twe, sne s ( a, b) = s( b, a).) One proble wth P sores s that the dfferent pars n the ultple algnent ght not be at the sae evolutonary dstane. Hene usng the sae sorng atrx ght not be far on the dfferent sequenes. Wth P sores we assue that any of the sequenes ould be the anestor of the others. j< k

5 UMF0 Introduton to bonforats, 005 Fgure : Evolutonary trees. The left tree s an exaple of a real stuaton, wth organss at dfferent evolutonary dstanes. The tree to the rght s the assupton n the P sores ethod, where all sequenes are assued to be at equal dstanes of the anestor. Ideally we would lke to odel the oleular sequene evoluton. Gven the orret phylogenet tree for the sequenes, the probablty of a ultple algnent would be the produt of the probabltes of all the evolutonary events neessary to produe that algnent. Ths s a very oplex odel and not enough data to estate the paraeters.. Mult-densonal dyna prograng In dyna prograng for parwse algnents (suh as Needlean-Wunsh for global algnent) we oputed an n atrx F where F (, j) = sore of the best algnent up to (, j) and we flled the atrx n a tabular fashon by alulatng these values reursvely. It s possble to generalze dyna prograng as used n parwse algnent to ultple algnents, but the forals beoes tedous and the algorths requre a lot of eory and any oputatons and would be restrted to only sall probles. For three sequenes we would need a ube, for four sequenes a four-densonal hyperube and so on, suh that the atrx F would have as any densons as sequenes.. MA (Multple equene Algnent) A lever algorth for redung the volue of the ultdensonal dyna prograng atrx was pleented n a ultple algnent progra alled MA. MA an optally algn up to seven proten sequenes of reasonable length (00-00 resdues). (Meanng that we are guaranteed to obtan the optal soluton for suh a proble. Most ultple algnent algorths annot guarantee that the soluton found s the optal one, sne t s not possble to searh through the all). 5

6 UMF0 Introduton to bonforats, 005 The P sorng syste s used n MA. Assue we want to algn N sequenes, and let denote a parwse algnent between sequenes k and l. Then the sore for the ultple algnent s = ( a ) k< l (Agan we are sung over all ndex obnatons k < l N.) If, aong all possble parwse algnents between sequenes k and l, â s the best one, then naturally, MA uses a lower bound ( a ) ( aˆ ). β and only onsders parwse algnents of hgher sore β ( a ). For eah sequene par seq k and seq l we reate a subset of possble algnents suh that n eah oordnate obnaton n the algnent ( k, l ) the sore for the best algnent gong through that pont s greater than β. To understand ths a lttle better, let us onsder the -densonal dyna prograng atrx below, wth seq k on the X-axs and seq l on the Y-axs. Reeber how eah possble algnent of the two sequenes an be represented as a path through the atrx, and how the atrx ontans all possble algnents between the two sequenes. Now, nstead of searhng through all paths gong through every pont n the atrx we ntrodue a threshold. A oordnate obnaton, n the atrx wll be nluded n the searh spae used later, f the hghest sorng path aong all those gong through that pont has a sore that s greater than β. a seq l seq k Fgure : Redued searh spae. Eah pont n the atrx s heked and s nluded f the hghest sorng path gong through that pont has a sore that s hgher than the threshold β. Ths s done for all pars of sequenes and then the ult-densonal dyna prograng algorth s perfored n ths subset of the hyperube. 6

7 . Progressve algnent UMF0 Introduton to bonforats, 005 Probably the ost oonly used approah to ultple sequene algnent s progressve algnents. The dea behnd progressve algnents s to use dyna prograng to buld a ultple algnent, startng wth the ost related sequenes and then addng sequenes or groups of sequenes progressvely. Progressve algnent tself s heurst, even f the parwse algnents are not, suh that there s no guarantee that the fnal ultple algnent s the optal. But t s fast and effent, and n any ases the resultng algnents are reasonable. Most progressve algnent algorths buld a gude tree, renderng the evolutonary relatonshp between the sequenes. The algorths dffer n several ways:. In the way they hoose algnent order.. In whether one sequene s algned at a te to a growng algnent, or whether subalgnents are bult and then algned to eah other.. In how to algn and sore sequenes to exstng algnents.. The Feng-Dolttle algorth The Feng-Dolttle algorth s one of the frst progressve algnent algorths. The proedure s as follows: () Perfor parwse algnent of all N sequenes (= N ( N ) / pars). Convert the algnent sores to evolutonary dstanes usng a noralzed perentage of slarty. () Construt a gude tree fro these dstanes (usng lusterng), dsplayng the evolutonary relatonshps. () Algn the ost related sequenes n the tree usng dyna prograng. (v) Algn the sequene ost losely related to the exstng algnent, or the next ost related par to eah other, or two subalgnents. In () and (v): equene sequene algnent: regular parwse algnents. equene subalgnent (group): parwse to eah sequene n group. Hghest sorng algnent deternes the algnent to the group. Group group: all parwse algnents between groups are perfored, and the best deternes the algnent. Parwse PAM sores and affne gap penaltes are used. After eah algnent gaps are replaed by a neutral harater X, so that algnent to that harater has no penalty sore n sueedng algnents. In ths way gaps are always kept. When addng a sequene to a group, new gaps ay be ntrodued to keep the algnent onsstent, but no gaps are reoved. The sde effet s that gaps tend to our n the sae oluns n subsequent parwse algnents. The ethod for onvertng algnent sores to dstanes does not need to be espeally aurate, as the goal s only to reate an approxate gude tree. Feng-Dolttle alulate the dstane D as D = log eff = log obs ax rand rand 7

8 UMF0 Introduton to bonforats, 005 where obs s the observed parwse algnent sore, ax s the axu sore (the average of the sore of algnng ether sequene to tself), and rand s the expeted sore for algnng two rando (ndependent) sequenes of the sae length and resdue oposton. The last one, ay be alulated by rando shufflng of the two sequenes, or, as n Feng-Dolttle, by an approxate alulaton. One proble wth the Feng-Dolttle algorth s that all algnents are deterned by parwse sequene algnents, gnorng the poston-spef nforaton obtaned one an algned group has been bult up. rand Exaple. Assue that we have four sequenes,,, and, and that parwse algnents of all pars (6 possble pars: (, ),(, ),(, ),(, ),(, ),(, ) ) gves an evolutonary tree Fgure : Evolutonary tree based on parwse algnents between all possble pars.. Algn the two ost losely related, and.. Algn and. 8

9 . Algn the two algnents, ) and, ). ( UMF0 Introduton to bonforats, 005 ( new gap 5. Profles A speal varant of ultple algnent are proten profles. Profles are nueral representatons (that s, sores) of ultple sequene algnents that represent the oon haraterst of a proten faly. The profle s then used to deterne whether a new proten sequene belong to the faly or not. Exaple. In a proten soe postons are ore portant than others to the proten struture and funton, and suh postons tend to be ore onserved than less portant ones. A proten faly an therefore be represented by ts onservatonal pattern. These patterns an be wrtten n a regular expresson: a proten pattern of a haraterst regon n Cu/Zn uperoxde Dsutase an be wrtten as [GA] [IFAT] H [LIVG] H x() [GP] [DG] x [TADG] Eah poston n pattern s separated by a hyphen. x eans any resdue. [GA] eans G or A. {A} eans that A s a forbdden resdue n that poston (none n the exaple). ( ) surrounds repeat ounts, suh that x() eans x twe, for nstane two arbtrary resdues. < or > sgnfes the begnnng or end of the proten sequene. H stands for a opper lgand n ths exaple. For nstane, n Drosophla yakuba (a frut fly) a Cu/Zn uperoxde Dsutase proten sequene s vvkavvn gdakgtvffe qessetpvkv sgevglakg lhgfhvhefg dntngssg phfnpygkeh gapvdenrhl gdlgneatg dptkvstd sktlfgads grtvvvha daddlgkggh elskstgnag arggvg akv wth the underlned subsequene beng G-F-H-V-H-E-F-G-D-N-T. 9

10 UMF0 Introduton to bonforats, 005 A otf s a bologally onserved regon, suh as a proten n doan or proten bndng regulatory regon. A pattern s a otf desrbed usng a gven syntax, suh as the one n the exaple above. A profle s a sore atrx desrpton of a otf. The advantage of profles over regular ultple algnent s that they an fnd slartes n very dstantly related proten sequenes. Answers gven by usng profles an be: What sgnfes a gven proten faly? Whh faly does ths new sequene belong to? Whh resdues are seen at a gven poston n a ultple algnent? What are the frequenes of the observed resdues? Whh postons are onserved n the sequene? A profle s a poston spef sorng atrx (PM) that has N rows and 0+ oluns. N s the length of the proten sequene, and there s a olun for eah possble ano ad and usually one for gaps. A C D Y Gap. k. N M kj Fgure 5: A profle M s slar to a PAM or a BLOUM sorng atrx, exept that t s spef to the otf n queston. It has the 0 ano ads (an the gap) on the horzontal axs n the proten postons on the vertal axs. M s the sore for observng ano ad j at poston k n the otf. In the sae anner as for regular ultple algnent, the sore for a olun would naturally be based on the probablty of observng all the urrent ano ads together. For a ultple algnent of three sequenes we would then need to estate probabltes p ab for all obnatons of three resdues, for four sequenes p abd and so on. To ths we would need and ense aount of sequene data and known algnents, and t s sply not possble. However, we an get farly good estates for pars of resdues, suh as n the PAM or BLOUM sorng atres. Thus, good approxatons of the M sores should be based on the parwse sores. kj kj 0