Recursive Dynamic Programming forAdaptive Sequence and Structure Alignment

Ralf Thiele, Ralf Zimmer, Thomas Lengauer

GMD SCAI, Schlot3 Birlinghoven, P.O. Box 1316D 53754 Sankt Augustin, Germany

Phone: +49 2241 14 2302, 2818, 2777 Fax: +49 2241 14 2656email: {Ralf.Thiele, Ralf.Zimmer, Thomas.Lengauer}@gmd.de

Keywords:Recursive algorithm, protein threading,sequence alignment, structural alignment, adaptive

combinatorial optimization, multiple alignment

Abstract

We propose a new alignment procedure that is capableof aligning protein sequences and structures in a uni-fied manner. Re, cursive dynamic programming (RDP)is a hierarchical method which, on each level of the hi-eratchy, identifies locally optimal solutions and assem-bles them into partial alignments of sequences and/orstructures. In contrast to classical dynamic program-ming, RDP can also handle alignment problems thatuse objective functions not obeying the principle ofprefix optimality, e.g. scoring schemes derived fromenergy potentials of mean force. For such alignmentproblems, RDP aims at computing solutions that areneat-optimal with respect to the involved cost functionand biologically meaningful at the same time. To-wards this goal, RDP maintains a dynamic balancebetween different factors governing alignment fitnesssuch as evolutionaty relationships and structural pref-erences. As in the RDP method gaps are not scoredexplicitly, the problematic assignment of gap cost pa-rameters is circumvented. In order to evaluate theRDP approach we analyse whether known and accept-ed multiple alignments based on structural informa-tion can be reproduced with the RDP method. Forthis purpose, we consider the family of ferredoxinsas our prime example. Our experiments show that,if properly tuned, the RDP method can outperformmethods based on classical sequence alignment algo-rithms as well as methods that take purely structuralinformation into account.

IntroductionAlignments are one-to-one mappings of elements oftwo or more structured sets of objects, such as se-quences of amino acids, physico-chemical profile vec-tors, or 3D-coordinates of atoms. Dynamic program-ming algorithms are capable of finding optimal align-ments, if the objective function (or scoring scheme)meets the principle of prefix-optimality. This meansthat optimal alignments of subsequences (or struc-tures) can be extended to optimal alignments of theoriginal sequences (or structures). Classical scoringmodels for sequence alignment meet this requirement.

This research is supported by the German Ministry forResearch and Technology (BMBF) under grant number413-4001-01 IB 301 A/1.

We are interested in threading a protein sequence in-to a protein structure. Threading or sequence-structurealignment is a version of the alignment problem thatmaps a sequence onto a structure and estimates thefitness of the resulting conformation. In order to beaccurate in this process, we have to account for spatialinteractions between residues or their atoms, explic-itly. Incorporating such interactions leads to scoringschemes that violate the principle of prefix--optimality.This problem can be circumvented by encoding thestructural information on the environment of each se-quence position in the form of one-dimensional profiles(Bowie, Liithy, & Eisenberg 1991). The advantage such a coarse description is that standard dynamic-programming algorithms can be used. A more pre-cise description of the structure entails an at leasttwo-dimensional representation, e.g., a contact ma-trix, describing interacting residues. As an approxi-mation, Jones, Taylor, & Thornton (1992) use a two-level dynamic-programming scheme (1989) for doingsequence-structure alignment. On the first level theirapproach takes pairwise interactions weighted by vir-tual energy functions (e.g., Sippl (1990)) into account,which rate the distance dependent preference of residuepairs forming interactions. Lathrop & Smith (1994)describe a branch&bound method for the optimal so-lution of the full fragment threading problem with suchpairwise interaction scores.

For a formally defined version of the threading prob-lem, Lathrop (1994) proved that the problem is NP-hard, if we allow for variable-length gaps in the align-ment and model nonlocal effects with pairwise interac-tion terms in the cost function. All such formal def-initions of the threading problem incorporate a largeset of parameters whose setting makes or breaks themethod. As a rule, these parameters entail a sizeableerror margin, because they are derived by statisticsover the sequence and structure databases. Therefore,finding the exact global optimum has to stand backbehind the goal of making the method adaptive to thedelicate signals that have to be found in the biologicaldata and robust to the statistical inaccuracies that popup along the way. For this reason, we chose to developa method that intelligently adapts to the changing pri-orities with which different fitness factors contributeto the overall cost of an alignment. Two examples for

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such fitness factors are evolutionary sequence homolo-gy and structural preferences, e.g., potentials of meanforce.

The hierarchical RDP method presented here com-putes near-optimal solutions with respect to the in-volved cost function by focusing on highly conservedregions with highest priority and considering match-ing/contacting regions on lower levels of the hierarchy.The procedure starts by identifiying sequence segmentsentailing most significant matches in the current prob-lem instance. By removing these matched segmentsfrom the current sequences, the problem is split intodisjoint subproblems. In order to avoid severe mis-takes caused by mismatched alignment portions com-puted early on--which can easily happen, due to lackof information--the method allows for handling sets ofa limited number of alternative subalignments on eachlevel of the hierarchy. This recursive divide&conquerprocedure terminates once the match score reaches theoverall noise level. Therefore, only a limited regionof the solution space, characterized by near-optimalalignment scores in significant regions of the align-ment, is searched. By leaving the gaps as the rest,which cannot be aligned at all, the RDP method hasthe additional advantage that gaps need not be scoredexplicitly. Scoring gaps is quite problematic, becausegap terms are not included in most scoring potentials.The RDP method has been implemented as part ofthe ToPLigu system (Toolbox for Protein Alignment)(Mevissen et al. 1994) developed at GMD.

Our first experiments on biological data show thatthis effective limitation of the search through the solu-tion space does not prevent our method from comingup with biologically meaningful solutions of the thread-ing problem. Even more, based on a mix of sequenceand structure information the RDP method is able toalign sequences on which both exclusively sequence-based methods as well as exclusively structure-basedmethods fail. To our understanding, the essential el-ement of this performance is that we trade the goalof exact optimization with an adaptivity of the algo-rithm to the varying significance of different criteriacontributing to alignment fitness instead of optimizingonly one fitness criteria.

The paper is organized as follows: The first sectionputs the different versions of alignment problems into auniform formal setting. The following section describesthe general RDP method. The third section discussesvariants of letting sequence and structure informationguide the alignment process. As a running example,we discuss ferredoxins, which are proteins containingiron-sulfur ([Fe-S]) clusters, but otherwise are quitediverse in sequence and structure. Because of theirimportance in basic metabolic pathways and of theirubiquitous occurrence in a number of organisms includ-ing algae, plants, and archaebacteria ferredoxins arequite old and have undergone substantial evolutionarychanges in sequence and structure. These changes, onthe one hand, and a striking sequence and structural

conservation in connection with the coordination of the[Fe-S]--cluster as well as the protein’s electron transferfunction, on the other hand, make this protein familyan interesting object for all kinds of alignments. Thelast section interprets some RDP alignments of ferre-doxins and presents some preliminary analysis of RDPalignments by comparing them to alignments from dif-ferent sequence and structure alignment databases.

Formal background

For the context of this paper, we define an align-ment formally as a homomorphism f between two or-dered or otherwise structured sets A and B. This set-up includes sequence alignment, as well as sequence-structure alignment (threading) and structure compar-ison. A structured set (e.g., a sequence, a tree, a graph)is a set of elements (residues, letters, vertices) with binary relation on the elements. An alignment is ahomomorphism, e.g., a relation-preserving partial in-jective mapping between two structured sets. In thisterminology, sequence-structure alignment is a homo-morphism between two protein sequences, whose ele-ments are ordered by their position in the sequence.In addition, the image sequence has an associated pro-tein structure, which is represented by an additionalrelation indicating spatial adjacency between residues.By the homomorphism, this relation is imposed on thepre-image sequence. An example for such a homo-

Figure 1: A sequence-to-structure alignment. The arrowsemaztating from residue i in the structure B denote inter-actions to spatially close residues in B.

morphism between a sequence A and a structure B isshown in figure 1. Thus, the alignment problem canbe formalized as follows:

Given two sets A and B with relations RA C A × Aand RB C_ B x B,

find an injective, partial homomorphism f : A ---, B(f : A’ ~ B’ bijective),

which optimizes a scoring function ¢(f, A, B).

Thiele 385

The scoring function ¢ is usually specified as a sum ofthe following functions on subsets:

¢(f, A, B) = M(f, A’, B’) + I(f, A \ A’) + D(f,

where M scores the matched parts A’ = pre-image(f) and B’ = image(f), I scores insertions, i.e.,elements in A\A’, and D scores deletions, i.e., elementsin B \ B’. In the context of biological applications theI and D parts are usually realized as affine cost func-tions gi + ge * k, where the gap-insertion penalty giis accounted for every gap, regardless of the length k,and the gap-extension penalty ge is charged for ev-ery insertion and deletion. The exact definition of theM-term depends on the specific kind of problem tobe dealt with. For classical sequence alignment, thisterm reduces to the Dayhoff-matrLx (Dayhoff 1978),for threading, it consists of distance-dependent energyterms (Sippl 1990), for structure comparison it involvesthe rms distances of superposed elements.

Recursive dynamic programmingThe main idea of the alignment approach proposed inthis paper is to recursively decompose the problem intosmaller subproblems. In order to do so, the algorithmuses a method for computing a reliable partial solu-tion of the alignment problem. In a first step, we useclassical local alignment algorithms based on dynamicprogramming, here. But, in general, we can use anyalgorithm for this purpose that computes a convinc-ing subsolution. We call such an algorithm an oracle.The solution computed by the oracle splits the align-ment problem into disjoint subproblems, each one per-taining to a portion of the problem that has not beenmatched yet by the oracle. We apply the oracle recur-sively to each of these subproblems, in order to extendthe matched regions in the alignment. This process ter-minates if the oracle finds no more significant matches,i.e., subalignments whose scores rise above the overallnoise level.

In order to avoid the known drawbacks arising fromrestricting the attention to optimal solutions and tocircumvent the inaccuracies involved in the choice ofparameters (e.g., pseudo-energies rather than real en-ergies), we collect sets of suboptimal but near-optimalsolutions for each of the subproblems under consider-ation. The size of such sets can be tuned to a suitablebut limited value.

Figure 2 sketches the recursive decomposition of asequence-alignment problem into subproblems and theassembly of the alignment from the solutions for thesesubproblems. For clarity, we show only one solutionfor each subproblem.

Each recursive refinement step of the RDP proce-dure expands the partial information currently avail-able about the final mapping f to regions of the align-ment problem that have not been matched yet. Inthe case of threading, the interactions between alreadyaligned regions in the structure B and the rest of thestructure can be analyzed in order to find additional

386 ISMB-95

Merge

~ %valuation ~,k 2’

Figure 2: Diagrammatic sketch of the RDP method.

appropriate matches with the sequence A. Using thepartial alignment in its reverse direction, we carry outthis analysis inside the sequence A, rather than in B.This is a more accurate model than the frozen approxi-mation (Godzik, Kolinski, & Skolnick 1992), which us-es the structural setup of B for this purpose and doesnot take into account that residues of A are alreadymapped onto the interaction partner sites by f.

Figure 3: AND-OR tree representing the ~t of solutions.A subsolution for node SP2 on the bottom level may de-pend on all of the encircled part of the tree.

The RDP procedure constructs a AND-OR-like so-lution tree as depicted in figure 3. The nodes P andSPi (OR nodes) in the tree represent subproblems be solved. The nodes Ai (AND nodes) represent solu-tions for the problem represented by their father node.As alternative (optimal or suboptimal) solutions areallowed for each subproblem, there are multiple sub-solutions Ai connected via edges to their respectivefather node SPi or P.

In general, the outcome of the method depends onthe order in which the subproblems are solved, e.g., forthreading a subsolution for node SP: on the bottomlevel in figure 3 may depend on the encircled part ofthe tree via spatial interactions in the structure. Thusthe order of evaluation of the subproblems is an ob-ject of algorithm tuning. As usual for branch&boundmethods, open subproblems are maintained in a prior-ity queue. The criterion by which this queue is sorteddetermines the order of evaluation, e.g., breadth-first,or by decreasing size of the subproblem, or by increas-

ing expected score for a solution of the subproblem.A more sophisticated approach is to order the sub-problems according to some appropriate notion of sig-nificance, to reevaluate this notion regularly, and toreorder the queue accordingly.

The implementation of the top-down recursive re-finement phase depends on the type of informationthat is processed (e.g., pure sequence information, localstructure, or interactions between residues) and on thepartial solutions already computed on the same leveland on upper levels. There are several possible levelsof sophistication here: The simplest concept is to ig-nore dependencies on brother or ancestor subsolutiousaltogether. This option is chosen if the alignment iscomputed on the basis of the classical scoring schemesfor sequence alignments.

On the other hand, the optimization of a pairwiseinteraction score necessarily implies dependencies onpositions distributed all over the alignment. There aretwo types of such dependencies: Backward dependen-cies are depedencies between the solution of the cur-rently solved subproblem and solutions of previouslysolved subproblems. In order to take backward depen-dencies into account, the algorithm needs to maintainnot only the score but all subsolutions realizing thisscore. In a standard dynamic-programming settingthis requirement exceeds available resources in timeand space. Forward dependencies exist between thesolution of the current subproblem and its extensionstowards the overall solution. These dependencies mayrender currently suboptimal solutions optimal lateronin the algorithm and vice versa. Thus, forward depen-dencies not only pose even more serve problems w.r.t.resource demands but may even destroy the acyclici-ty of the dependency graph between the subproblems.By constructing the alignment not from the left orright ends of the sequences but from those segmentsfor which significant and reliable alignments can be de-rived, the RDP method heuristically circumvents theproblems occuring from backward as well as from for-ward dependencies. RDP considers backward depen-dencies only on reliable solutions which are artificiallyrestricted in number via the number of allowed alterna-tives and the number of returned solutions after evalu-ation and ranking. Whether a dependency is backwardor forward depends on the order of evaluation of thesubproblems. By computing the significant parts of thealignment with highest priority forward dependenciesonly exist to subproblems, which pertain to less sig-nificant regions of the alignment. Therefore, the RDPmethod limits the mistakes made by neglecting forwarddependencies to be within a certain range.

Different versions of the RDP procedure essentiallydiffer in the kind of oracle that they use. In the follow-ing, we concentrate on oracles that also take structuralinformation into account. For this purpose, we con-sider the following three types of oracle which differin the degree to which structural information is ex-ploited. For illustration, refer to Figure 4. This

Structure B ~

counter ~ ~ ![ probe ] _~ Ai:~Ai20_J

B~BkBk+ i probe

Figure 4: Probe and inverse probe alignmentfigure shows a section of a protein structure B on-to which already a few parts of sequence A (e.g., allnodes labelled with a Ai) have been mapped. Thepairwise interactions within the structure are depictedby edges between the interacting residues. For clar-ity, we direct the edges from the residues in B thathave been matched already to the residues in B thathave not been matched yet. On the next level of theRDP procedure, we want to match the residues thatare adjacent to already matched residues in B to ap-propriate regions in A. In the figure, these are residues(Bk+l,..., Bk+3) and (Bk÷x-3,..., Bk+x-1). We these residues a probe PB. The oracles differ in theprocess, with which they find regions in A that matchthe probe PB. The already matched residues in Bthat give rise to the probe PB are called the counter-probe. In Figure 4, the counterprobe is composed ofthe residues (A~I,..., A~3) and (Ailg, Ai20).

Oracle 1. Sequence probe: Find a match for the probePB on the basis of some kind of classical sequence align-ment. This oracle does not evaluate any structure fit-ness and resides entirely on evolutionary similiarity butfocusses selectively on residues interacting with morehighly conserved regions.

Oracle P. Structure probe: Find a match for theprobe PB based on the structural fitness to the coun-terprobe. We use interaction potentials in order toevaluate this fitness. This oracle does not consider anysequence homology measure.

In general we expect both sequence homology andstructural fitness to contribute to the alignment score.Therefore, we consider the following oracle:

Oracle 3. Mixed probe: Find a match based on bothsequence homology (sequence probe) and structure fit-hess (structure probe) with appropriate weights. Dy-namically change the weights during the algorithm.

It is an essential factor of the efficiency of the RDPprocedure that all of the above oracles can be comput-ed using the extensions of the classical dynamic pro-gramming method implemented in ToPLign.

A tour through DelphiIn this section, we report on preliminary experimentsthat tell us what kind of information we should appro-priately make available to the oracle. We discuss thedifferent versions of alignment for different applicationsseparately.

Thiele 387

Sequence alignment

In order to be able to discriminate more between differ-ent sequence alignments than the typical Dayhoff-typescore functions (Dayhoff 1978) are able to do, we usethe concept of a path-contour map. The path-contourmap is a matrix representation of the solution spacefor an alignment problem. Entry (i, j) in the matrixcontains the score of the optimal alignment of the twosequences A and B that matches position Ai to po-sition Bj. The path-contour map can be efficientlycomputed for all kinds of global and local alignmentsin time O(mn) (Mevissen el al. 1994).

! []I

~.?! .:..i~!~:/:iii ~ ~ ¯PDI32fx:5

Figure 5: Global sequence alignment (2FXB vs. 1FDX)

A path-contour map can conveniently be visualizedby colouring the matrix w.r.t, score (see Figures 5,8,and 9). The set of optimal alignments forms a setof ridges and/or plateaus coloured white in the path-contour map. The colour of a position in the path-contour map gets darker with decreasing score of thealignment containing the respective match. Therefore,near-optimal alignments form the light regions aroundthe optimal alignments.

The path-contour map gives us information not onlyon suboptimal alignments but also on the reliabilityof different regions in the alignment (Mevissen el al.1994; Mevissen & Vingron 1995). This information isvital to the oracles, especially to those that are used inthe upper levels of the RDP procedure. Intuitively, thereliability of an alignment position is correlated withthe gradient that occurs close to this positions in thepath-contour map.

Sequence-structure alignment

For sequence-structure alignment (or threading) theestimate of fitness is mostly based on some kind ofpseudo-energy function. It is quite tricky to derivemeaningful pseudo-energy functions and many pro-posals have been made in the literature (Bryant Lawrence 1993; Hubbard 1994; Maiorov & Crippen1992; Miyazawa &5 Jernigan 1985; Sippl 1990). Mostof these energy potentials of mean force include termsthat evaluate a specific interaction in the given struc-ture. For instance, the interaction between the posi-tions i and Jl of the structure B in figure 1 is scoredaccording to the residues of the sequence A that are

mapped onto the positions i and jl via the homomor-phism f. We can make two general observations on

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Figure 6: Comparison of sequence, interaction, and com-bine~ score for I0000 optimal ~d suboptimM alignmentsof IFDX ~th the ferredo~d~ 2FXB from BACILLUSSTHERMOPROTEOLYTICUS (sorted w.r.t, decreasinginteraction energy)

the role played by pseudo-energies in the evaluation ofsequence-to--structure fitness. The first observation isillustrated by Figure 6. This figure shows the overallpseudo-energies of 10000 threadings of the ferredoxin2FXB into the ferredoxin 1FDX, sorted in decreasingorder (black curve). All of these threadings are, by def-inition, near-optimal w.r.t, their sequence-alignmentscore. In the figure, this score is shown in light-gray.A mixed score amounting to the sum of the sequencescore and the pseudo-energy of the alignment is shownin dark-gray. The figure shows that pseudo-energiesare able to discriminate between the large number ofnear-optimal and thereby mostly similar alignments.The challenge is to tune the energy potential to op-timizing structural fitness within the space of near-optimal sequence alignments.

The second observation is that energy values cannotonly be used as a tool for discriminating between differ-ent alignments globally, but rather that we can use thepotentials in order to single out local regions in thestructure, which dominate the sequence-to-structurefitness. Figure 7 presents two renderings of the ener-gy distribution for the threading of 2FXB into 1FDX.Part (a) of the figure shows a map, in which entry (i, represents the energy contribution (Russell & Barton1994) of residue j in 2FXB when it is singly mappedonto residue i in 1FDX (frozen approximation). Entry(i, j) of the map in part (b) of the figure represents thedifference between that energy value and the energycontribution of the original residue i in 1FDX. In allthree diagrams the cysteine residues coordinating the[4Fe-4S] clusters of the ferredoxins show up dramati-cally. Such clear signals can be analyzed in a prepro-cessing step of the RDP procedure and be used by theoracle to rate the reliability of subsolutions containing

388 ISMB--95

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Figure 7: ’Energ~v; plots of positional contributions (a) single positions, (b) in comparison to the native sequence

the correctly mapped cysteines.

Structure comparison with RDPA common approach to comparing protein structuresis to superpose their 3D-coordinates and to computethe root-mean-square (rms) deviation of the assignedresidues or atoms. In order to compute the superpo-sition efficiently, the matching of residues or atoms isassumed to be given, for instance, via a sequence align-ment. However, the structure comparison can only beas good as the sequence alignment which forms its ba-sis.

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Figure 8: Global ¢/~b angle alignment (2FXB vs. 1FDX)

A statistical analysis of the sets of protein struc-tures and sequences (Orengo 1994) shows that thereare many proteins with remarkably low sequence sim-ilarity that nevertheless share the same overall struc-ture. For such proteins, it is very hard to produce ameaningful sequence alignment as a starting point fora structure comparison and it would be better to derivea structural alignment directly. Here, we present twomethods of detecting information on structural simi-larity of local substructures which can be exploited bythe RDP method.

First, we can compare protein structures as se-quences of rotation- and translation-invariant dihedral¢/¢ angles. Local alignments of sequences of ¢/¢ an-gles can be used as oracle for the RDP method in orderto compute structure-alignments which figure out lo-cal structural similarities between structures. In the

ToPLign tool environment (Mevissen et ai. 1994) suchsequences can be aligned via dynamic programmingjust like sequences of amino-acid identifiers and theRDP method can be guided by information from theassociated path-contour maps similarly as in sequencealignment. Figures 5, 8, and 9 contrast the effectsof aligning sequences of ¢/¢ angles derived from thestructures versus aligning the sequences of the aminoacids themselves. The amino-acid sequence alignmentuses Dayhoff homology scores with standard gap penal-ties, whereas the ¢/¢ alignment uses the rms deviationof the angles of the corresponding amino acids with ap-propriate gap penalties. The figures show differencesas well as points in common amongthe two kinds ofalignments, which can be the basis for reliability crite-ria used by the oracle.

Second, we can superpose all short fragments of fixedlength of the first structure with all fragments of thesame length in the second structure via standard frag-ment superposition methods (McLachlan 1982). Sucha preprocessing step produces a list of similar frag-ments sorted by their rms deviation. Part (c) of Fig-ure 9 shows a rms-distance matrix for superpositionsof fragment of length 8 taken from 1FDX and 2FXB.Now, the oracle of the RDP method reduces to efficienttable-lookups in this list and the RDP procedure com-bines the fragments into structure alignments in such away that all mutually consistent segments of two givenstructures, which are structurally similar, are coveredby the alignment. If we like, the method guaranteesthat the matched parts are still compatible with thesequential order prescribed by the sequence of the pro-teins.

Multiple alignments

The RDP method can also be applied to multiple align-ments. Using the method, we can first identify consis-tent local matches in the p airwise alignments and thansplit up all participating sequences according to suchalignments. Doing so, sequence patterns often showup with much more significance than with usual SOPor tree alignment. The result is an increased relia-bility and efficiency of the method. Figure 10 showsthat the first consistent match drastically reduces thesearch space left over for the recursive procedure. Forinstance, in the plots of the second row only the non-black regions of the matrices have to be searched bythe algorithm, after the first reliable segment of thealignment has been found.

Experimental resultsFigure II shows an HSSP-alignment (Sander ~ Schnei-der 1991) of 36 homologous ferredoxin sequences thatcan be derived almost identically via a dynamic-programming-based tree alignment. It is an inter-esting observation that, despite of the unquestionablemultiple alignment of the sequences and the assumedfunctional conservation with a [Fe-S] cluster (and sup-posedly similar structure), almost all positions have

Thiele 389

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: lllgllUn~ ~ hum I~ iUnmll~ll~lll~UllnlllUUWUlUUl~P00598.._02 : ATTZIIEACTSCOAC’DPECPYDAISDS nl"VZ D/LDTCZ~ACAQVCPYDAP ....P00195.._03 : ATE IlDSCVSCGAC&$ECPYNAISDS l~l DADTCIDCfllC~I~CPVgAPqQZ-P00196.._04 : AW¥ZWDSCVSCSACAflECPVSAITDTQYVZ D~DTCIDCe|C JJIVC~VQAP|QZ-P00%97.._05 : AT~ZTDQCX|CGLC~P£CPYEkI$£SYLYZD &D[CZ~3g/Ci]ITCPqD& ....P00194.._06 : kYI IEETCZSCeACJAECPV|AI~eDT ZFVVNADTCID~BCMIVCPVSAPVA’e-

P2~845.._07 : ATI Z LDTCVSCQACAAECPVDAISDTQWVZ DADTCZDC~|CANVCPVSAPVQZ-P07508.._08 : AyFZTDACTSCSAC]~S£CPVSPISPSVTVZ DADACZKCEACA|VCPYDA~QX-P14073.._09 : ATI ITDECTACSSCADQCPVBAISgS ZTET DEAr CT~ICADQCPYBAIYPEDPO0200.._10 : ABI TTDECZSCQACAkleCPVEAZIIEGTTEYDADTCTDCGACBA VCPTSAVW AE"P0~123.._tl : ..... RCTVC~DCIiP¥CPTgSIQgO ZTYT DAD~C~£CAD~L~¥CPVD ......PO020S.._12 : ~LTTTE~CTTCSACEPECPTSAZSAE lTYl DIASCTECVO~AA¥CPAE ......P00201.._13 :-b’VZSD~CVECS~C&STCPTSAZEEET|TYTTDSCZD~ACE~VCPT~AZSA~-P254~.._14 :-YVIIEPCVDDE~CIZECPVDCZTS~RLTZBPDE~DO31CEPVC~PVE~ZTTEDP05204.._15 : ALTZTEECTTCgAC~ECPVTAZSA6 lTYl DAITCWECAQCVAVCPAE ......P00205.._15 : ~H~ZTEEC’ZTCAAC~BCPVIlZSAE lYI¥ DESVCTDCESCVAVCPVD ......P05216.._17 :-TYZAEP~"4DVI~CIEBCPVDCZT~eR~qLTZBPDECVDC~ACEPVCPVE~ZTTEDP13275.._18 :-~Zk~P~DTIkCI~ECpYDCI~IL~L~I";~D~C"WDC~kCEP¥CP¥EkI¥¥~DP53941.._19 : PElf ITSPCISHAC~TCPYDAZEUBSQT~ZDPDLCZDCS ~CEP¥CPVlAITQEEP14935.._20 : ..... EC~VCflDCEP¥CPCQSZ~DDBTgZEADSCMgCtDCLOVCPYD ....P00215.._21 : ..... DCCI~D~AC55¥CPV|LY~|LDP~I~SDCI~CEACES¥CP¥~A ....P$27%2.._22 :--ZZL.~QCTQCgkCEFBCPI~&¥u~EYV[DP’~IiCII~CI~C~S¥CP¥SS~--~

Pt8082.._23 :-TVYTDBCISCIDCYEVCPVDC¥1r~|TL¥II~DECIDC~VCEPECPADAZLODTP03942.._24 : pB¥I(~pCZ~VWSC¥EVCP~CZY~DQFTI BPEECIDC~ACYPACPV|AZTPImP06253.._25 : ..... DXCZJ@VC~]tVCPI~LPQLI|YSIDWSVCIFC~|C¥BTC~PTB .....P002~.._26 : ALRZT~CZ|~IVC~ECP|aAISDETYTZ~SLCI~CV~EVCPVD- ....P00202.._27 :ATV|ADECS~C~TCVDECP|QAIgI~ZAYVDIDEC¥ECSACEEtCPNQA’rIvE~$FD2. PDB_28: ~WTDWCIKCWDC¥EVCPYDC~Y~|FL¥I BPD~CIDC~LCEPECPA~AZ~SEDP0021"~.._2t) :-PWTD|CIKCWDCVEVCPVDCTY~3FLVZNPDBCZDCALCEPECPAQA’rFsEDP08811.._30 :-FVl~D|CIXC~DC~CPYDCT¥~WLVI BPD~CIDCA LC~PECPt qt ZFB£DP00259.._31 : ..... DLCI~D~SCZT~CPV~iVFQWEJLDP¥BQQACIFCS~CV|VCP¥~ZD¥1PP23481.._32 : ......... PCL~VC~I~DDAI EES LCZOC| LCJVVCPWS~ZSIS~}

POO211.._3~ : --VDSDICI~C~CWDVCP~VYS~WAVPVBEEECLOCESCIE¥C~BI---~P18776.._34 : ITy~SZSCIBC~ECT~¥CPSC~JIHE|F~VVDED¥CIOC~YCBRICPT~IPQTn

5 di~terent :368686C25DS671ABSt166T~89~E8726789154188169612783-qB766dis s tJIIll&~" :

e lutjowa~~t3erXty : A~/ITD~IS~AG~2~CpVDAI$2~IIVI 5AD[CII~SAC2P¥CPYeAI--[-ab|.uJort~y: I D CI C~AC ECP¥ AI ¥1D D CIDC5 C ¥CP¥ A |-¢onle~red : 412513092053391139951231100125323193392192949931521133~a~i&billt y : 577676906946608860048TS889587467680660780784005857886(~entropy : 2543436036233055200253345564413435033044L¢3~ 20035138533scor~ :1 II I II IIIC CPI II I Clio c Icll I Irellabl~l~y : 885877?8778888777997555555855888778~897787789988877758

Figure 11: Multiple alignment of 36 ferredoxins

In a multiple tree alignment the signals of the fewconserved residues are amplified by the stepwise ex-tension of the alignment starting with closely relatedsequences and then extending to more unrelated se-quences. Pairwise sequence alignment is not adaptiveto conserved regions, in this sense. Therefore, ferredox-ins are quite challenging examples for deriving mean-

ingful pairwise alignments without taking informationbeyond the pairwise sequence homology into account.

We have performed the following two initial experi-a)

~l~O~ elr’t’~l alJ.(~zlne~l.t "v~.I-]SSP (IFI~(; mean 96.1%)~

e4r.l~.-Ltyof lq~a]~ vs. ~ (IFDX; mean 99.3%) [--’l

20

.~ ~,~. ~ ,-~_____~___~_85 90 95 I00

b) ~cr~l~ c~ glc~l a]_~VS.3dsli(IFEM; mean 61.9%)

Slmilarity of lq]P al~s. 3dali(iFDX; mean 62.6%) [~

20

I0 ~ ~r’n .

20 30 40 50 60 70 80 90 i00

Figure 12: Capability of reproducing (a) ItSSP- and (b)3Dali-alignments for ferredoxins

ments with the RDP method: First, we have analyzedthe agreement of sequence alignments computed by theRDP method with other alignments reported in the lit-erature. Second, we have tested the capability of RDPto detect structural issues.

Let us turn to the former experiment. Here, we takethe HSSP and 3Dali alignments of ferredoxins as thestandard of truth. For the aim of comparison we de-compose the given multiple alignments into pairwisealignments. A score for the similarity of two pair-wise alignments can be computed elegantly using theToPLign (Mevissen el al. 1994) profile alignment ofalignments. To be precise, we align the two align-ments such that the number of column-wise agree-ments between them is maximized. Here, an agree-ment is counted if the matched columns are identicalin both alignments. Figure 12 compares the percent-age of agreement between HSSP (part a)) and 3Dali(part b)) alignments, on the one hand, and standard

390 ISMB-95

n

[]

I

Im

¯ |

1FDX :~YVINDSCIAC--GACKPECPVN-I IqGSIY-AIDADSCIDCGSCASVCPVGAPNPED ...................5FD1 : AFYVTDNCIKCKYTDCVEVCPYDC f~’EGPNFLVIHPDECIDCALCEPECPAqAIFSEDEVP ................2FXB : ............................ PKYTIYDKETCIACGACGAAAPDIYDYDEDGIAYYTLDDNQGIYEVPDIconsensus: ............................ CI C C P ED ...................

Figure 10: Path-contour matrices of all pairwise sequence alignments of 3 ferredoxins before and after fixing the best scoringcompatible region (matching the cluster of 2FXB onto the 2nd clusters of 1FDX / 5FD1) and the corresponding alignment.

global alignment (filled bars) and RDP (unfilled bars),on the other hand.

The results show that RDP outperforms classicalglobal alignment both with respect to the numberof exactly recreated alignments and with respect tothe average number of identically reproduced matches.The results are much more striking for HSSP align-ments than for 3Dali alignments. As discussed belowin more detail, the single [Fe-S] cluster of ferredoxinswith only one cluster can be structurally mapped onboth [Fe-S] clusters of ferredoxins containing two clus-ters. This ambiguity is reflected in part (b) of figure12 by alignments having an agreement with the 3Dalialignment less than 50 %.

The quality of the RDP method, as it is exhibitedby these experiments, is especially striking in view ofthe fact that the RDP method does not compute opti-mal solutions and the power of structural informationcannot be put to full use in pure sequence alignment.We believe that the method is superior because of itspower of adaptively focussing on significant regions ofthe alignment.

We now turn to the second experiment. Figure13 shows several sequence- and structure-based align-

ments of 1FDX, which has 54 residues and two [4Fe-4S] clusters and 2FXB with 81 residues and only one[4Fe-4S] cluster. In 1FDX, the two clusters are coordi-nated via four cysteine residues at positions 8, 11, 14,and 45, for the first cluster, and at positions 18, 35, 38,and 41, for the second cluster. The single cluster in2FXB is coordinated via the four cysteine residues atpositions 11, 14, 17 and 61. The four cysteine residuesthat participate in the coordination of each of the twoclusters in 1FDX occur in the motif CxxCxxCxxxCP,which is characteristic for ferredoxins. The last cys-teine residue occurs only in the ferredoxins that havetwo [4Fe-4S] clusters, i.e., only in 1FDX but not in2FXB. The parts of the protein containing the clus-ter are sequentially and structurally highly conserved.However, because of the small difference in the mo-tiffs defining the cluster-coordinating sites, both globaland local and both sequence and structure alignmentmethods are trapped: They search for and find themotif CxxCxxCxxxCP. The global, local, and 3Dalialignments correctly match the first sequence motifCxxCxxCxxxCP, but then fail to align the second partwith the fourth cysteine coordinating the cluster (45in 1FDX and 61 in 2FXB) or match it incorrectly.

Thiele 391

Global alignment oGm~uted with ToPLignlIFDX : A- YVI - -ND S~IA~GAEy~ EC P .................. VNI IQGSIYAIDA ..... DSC - I DCG S CASVC PVGAPNPED2FXB : PKYTIVDKET~IA~GA~GAAAPDIYDYDEDGIAYVTLDDNQGIVEVPDILIDDMMDAFEG~PTDS IKVADEPFDGDPNKFELocal alignment computed with ToPLiguzIFDX: . . .AYVINDSCIA~GA~KPECPVNIIQGSIYAIDADSCIDCGSCASV~PVGAPNPED ..................................2FXB: PKYTIVDKET~IA~GA~GAAAP ...... DIYDYDEDG .................... IAYVTLDDNQGIVEVPDILIDDMMDAFEG~P...structure alignment £ro~ 3Dallm1 FDX : - - -AYVI ND SC IA~GAE~P EC P -VN-- I IQG- S IYAIDADSC I DCGSCASVCPVGAPNPED .............................. . ..i fxb : PKYTIVDKET~IA~GA~GAAAPDIYDYDEDGI ............................. AYVTLDDNQGIVEVPDILIDDMMDAFEC~P...StruQturo allgv-~t from GBF!IFDX : AYVINDSCIACGACKPF~PVNI IQGSIYAIDADS~ID~GS~ASVCPVGAPNPED ...................................... . . .2FXB: PAY .......... afeg~Lptdsik---TIVDKET~IA~GA~GAAAP-DIYDYDEDGIAYVTLDDNQGIVEVPDILIDDMMDafegF~ptdsik. . .S~e~CO Alig~""~ co~:~l.ted with RDP:IFDX : - -AYVIND- -S~IA~PEC PVNI IQGS I YAI DADSC I ..... DCGSCASV .............. CPVGAPNPED ...........2FXB : PK-YT IVDKET~IA~P ...... DIYDYDEDGIAYVTLDDNQGIVEVPDILIDD~4MDAFEG~PTDS IKVADEPFDGDPNKFEgtru=ture alignment oom~uted with RDPzIFDX : - -AYVIN-DS~IA~GAE~PECPV-NI IQG- -- S IYAIDADSC I DC - ................ GSCASVCPVGAPNPED ..............2FXB: PKYT IVDKET~IA~GA~GAAA- - PD I Y DYDEDG IAYVTL ...... DDNQGIVEVPDI LI DDMMDAFEC~PTDS I K- - -VADEPFDGDPNKFE

Figure 13: Sequence and Structure alignments for 1FDX and 2FXB

The GBF structure alignment (Lessel & Schomburg1994) optimizes the structural superposition ignoringthe sequence order. The resulting alignment identi-fies a whole cluster by mapping the CxxCxxCxxxxPmotif of 2FXB onto the second CxxCxxCxxxCP motifof 1FDX and also correctly identfies the region aroundthe fourth cysteine in the first motif. This results in 43superposed Ca atoms at arms distance of 0.96/~. How-ever, for comparative modeling, this alignment couldbe quite misleading because it is not in accordance withthe sequence order.

Both the sequence- and structure-based RDP align-ment correctly find the structurally significant match-es (see Figure 13). Furthermore, the order of thealignments respects the sequence order, in contrastto the purely structural alignment. The RDP align-ment maps the CxxCxxCxxxxP motif of 2FXB on-to the first Cx.xCxxCxxxCP motif of 1FDX and thefourth cysteine 45 of 1FDX correctly onto cysteine 61of 2FXB. Even the long segment that is not aligned inthe structure-based RDP alignment is consistent withthe structural properties, because the helix in this re-gion is longer in 2FXB than in 1FDX. This fact pro-hibits 2FXB from coordinating a second cluster. Thesuperposition associated with this alignment covers 43amino acids with an rms of 1.25/~.

This experiment gives evidence for our hypothe-sis that combining evolutionary sequence informationwith information on structural preferences can detectstructurally meaningful alignments even where meth-ods purely based on sequence information or purelybased on structure information are being misled. En-couraged by the results presented in this paper, weare equiping the RDP method with additional vari-ants of sequence and structure information. In thenear future, we will run extensive experiments on se-quence and structure data and rate the RDP methodin comparison to other existing methods for aligningsequences and/or structures.

ReferencesBowie, J.; Lfithy, R.; and Eisenberg, D. 1991. A methodto identify protein sequences that fold into a known three-dimensional structure. Science 253:164-170.Bryant, S., and Lawrence, C. 1993. An empirical energyfunction for threading protein sequence through the fold-

Lug motif. PROTEINS: Structure, Function and Genetics16:92-112.Dayhoff, M. O. 1978. A model of evolutionary change inproteins. Atlas of Protein Sequence and Structure, Sup-plement 3 5:345-352.Godzik, A.; Kolinski, A.; and Skolnick, J. 1992. Topologyfingerprint approach to the inverse protein folding prob-lem. JMB 227(1):227-238.Hubbard, T. 1994. Use of E-strand interaction pseudo-potentials in protein structure prediction and modelling.In Lathrop, R., ed., Proceedings of the BiotechnologyComputing Track. IEEE Computer Society Press.Jones, D.; Taylor, W.; and Thornton, J. 1992. A newapproach to protein fold recognition. Nature 358:86-89.Lathrop, R., and Smith, T. 1994. A branch-and-boundalgorithm for optimal protein threading with pairwise(contact potential) amino acid interactions. In Proceed-ings 27th Hawaii International Conference on System Sci-ences, volume V. Los Alamitos, CA: IEEE.Lathrop, R. 1994. The protein threading problemwith sequence amino acid interaction preferences is NP-complete. Protein Engineering 7(9):1059-1068.Lessel, U., and Schomburg, D. 1994. Similarities betweenprotein 3-d structures. Protein Engineering 7(10):1175-1187.Malorov, V., and Crippen, G. 1992. Contact potentialthat recognizes the correct folding of globular proteins.Journal of Molecular Biology 227:876-888.McLachlan, A. 1982. Rapid comparison of protein struc-tures. Acta Crystallographica A 38:871-873.Mevissen, H., axtd Vingron, M. 1995. Quantif~ng thelocal reliability of a sequence alignment, submitted.Mevissen, H.; Thiele, R.; Zimmer, R.; and Lengauer, T.1994. Analysis of protein alignments - the software envi-ronment toplign. GMD Technical Report (in preparation).Miyazawa, S., and Jernigan, R. 1985. Estimation ofeffective interresidue contact energies from protein crys-tal structure: Quasi-chemical approximation. Macro-molecules 18:534-552.Orengo, C. 1994. Classification of protein folds. CurrentOpinion in Structural Biology 4(3):429-440.Russell, It. B., and Barton, G. 1994. Structural featurescan be unconserved in proteins with similar folds. Journalof Molecular Biology 244(3):332-350.Sander, C., and Schneider, R. 1991. Database ofhomology-derived protein structures and the structuralmeaning of sequence alignment. PROTEI’VS: Structure,Function and Genetics 9:56-68.Sippl, M. 1990. Calculation of conformational ensem-bles from potentials of mean force: Aa approach to theknowledge-based prediction of local structures in globularproteins. Journal of Molecular Biology 213:859-883.Taylor, W., and Orengo, C. A. 1989. Protein structurealignment. JMB 208:1-22.

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