Parallel computing is frequently used to speed up computationally expensive tasks in Bioinformatics.a) pair-wise sequence alignments that are used as a first step to multiple alignment account for most of the CPU time in DIALIGN. Since alignments of different sequence pairs are completely independent of each other, they can be distributed to multiple processors without any effect on the resulting output alignments. (b) For alignments of large genomic sequences, we use a heuristics by splitting up sequences into sub-sequences based on a previously introduced anchored alignment procedure. For our test sequences, this combined approach reduces the program running time of DIALIGN by up to 97%.Herein, a parallel version of the multi-alignment program DIALIGN is introduced. We propose two ways of dividing the program into independent sub-routines that can be run on different processors: (By distributing sub-routines to multiple processors, the running time of DIALIGN can be crucially improved. With these improvements, it is possible to apply the program in large-scale genomics and proteomics projects that were previously beyond its scope. Multiple sequence alignment continues to be an active field of research in Computational Biology and a number of novel approaches have been developed during the last years, see  for an oet al. evaluated the capability of alignment programs to detect conserved non-coding sites in genomic sequences. These authors conclude that DIALIGN can produce alignments with high coverage and sensitivity, as well as specificity to detect constrained sites [DIALIGN  is a vered sites .anchored alignment option [Though DIALIGN produces alignments of high quality, it is slower than alternative multi-alignment programs. Especially if large genomic sequences are to be aligned DIALIGN is far more time-consuming than the above mentioned specialized programs for genomic alignment. A recently introduced t option  can be ut option -21. Herechain of local fragment alignments with maximum total weight score is identified. A fragment or fragment alignment is defined as an un-gapped local pair-wise alignment, and the weight score of such a fragment is calculated based on a P-value i.e. on the probability of its random occurrence, see [For multiple alignment, the DIALIGN algorithm works as follows: in a first step, all respective optimal pair-wise alignments are carried out. This means that, for each pair of input sequences, a nce, see  for a dence, see .N input sequences, N × (N - 1)/2 pair-wise alignments are to be calculated; fragments contained in these pair-wise alignments are then used to build up a multiple alignment in greedy fashion. If the maximum sequence length is bounded by some constant, the time-complexity of this algorithm as a function of the number N of sequences is as follows: Performing all pair-wise alignments takes O(N2) time. During the greedy procedure, O(N) independent fragments can be included into the multiple alignment; additional fragments would be either inconsistent or already contained in the existing multiple alignment. Accepting a single fragment takes O(N2) time since for each accepted fragment, so-called consistency frontiers are to be updated. These frontiers are used to decide if subsequent fragments are consistent with previously accepted fragments. Thus, the worst-case time complexity of our multi-alignment algorithm is O(N3). Test runs with real data show, however, that the real time-complexity is something between quadratic and cubic, see [For a set of bic, see  for a derelative proportion of CPU time used for pair-wise alignments decreases with the number of input sequences, as can be expected from the above theoretical considerations.The current version of DIALIGN uses an efficient algorithm to update the consistency frontiers. This means that, although performing all pair-wise alignments has a lower theoretical time complexity than processing the fragments from these alignments in the greedy algorithm, for realistic data sets most of the CPU time is spent on the pair-wise alignments. For example, for a set of 20 protein sequences with an average length of 367 amino acid residues, as much as 97.4 % of the CPU time is used to perform the 20 × 19/2 = 190 pair-wise alignments. However, the N × (N - 1)/2 pair-wise alignments to the available processors in order to balance the work load. Here, we are using a greedy algorithm to find a satisfactory work-load distribution in reasonable time: we first assign a processor to the pair-wise alignment with the longest expected running time, then assign a processor to the second-largest pairwise alignment etc.The pair-wise alignments that are calculated as the first step of the multi-alignment procedure are completely independent of each other. Thus, it is obvious that the total program running time can be crucially reduced by running these procedures on parallel processors. Here, an important point is to distribute the work load evenly to the different processors in order to minimize the total program running time. To this end, our algorithm first estimates the running time for each pair-wise alignment as a function of the sequence length. As outlined in , the runanchored alignment procedure has recently been implemented [CHAOS to identify a chain of high-scoring local alignments for each pair of input sequences . To select a consistent sub-set of these local alignments, a greedy algorithm is used, see [The quadratic time complexity of the original DI ALIGN algorithm for pair-wise alignment is clearly not efficient enough to align large genomic sequences. To improve the running time of DIALIGN for long sequences, an lemented ,24. For sed, see  for detatrie data structure to identify pairs of segments with a user-defined upper bound on the number of mismatches per segment pair. It defines a local alignment as a chain of such gap-free local alignments that are located within a certain distance from each other. Finally, the algorithm returns an optimal chain of such local alignments. After the consistency check, these alignments are used by our algorithm to define anchor points in order to narrow down the search space for the final pair-wise alignment procedure that is performed by DIALIGN as explained in [CHAOS uses a ained in .x is assigned to a residue y through one of the anchor points, this means that x is the only residue that can be aligned with y in the final output alignment. Whether or not x and y will be aligned depends on the degree of local sequence similarity that DIALIGN detects. Moreover, all residues to the left of x can be aligned only with residues to the left of y and vice versa, see Figure non-anchored alignment, then the result of the anchored alignment procedure will necessarily be the same as for the non-anchored procedure. In particular, this is the case if all anchor points are part of the optimal non-anchored alignment.To be precise, an anchor point is a pair of segments, one segment from each of the two input sequences; this way each position in the first segment is assigned to the respective position in the second segment. If a residue cutting positions to split the input sequences into smaller sub-sequences, and we reduce the program running time for DIALIGN by aligning these sub-sequences independently on multiple processors. This procedure is related to Stoye's well-known divide-and-conquer approach to multiple alignment [In the present study, we use selected anchor points as lignment  and to tlignment .non-additive weighting function w for segment pairs (fragments). If a large fragment f is split into two smaller sub-fragments f1, f2, the sum w(f1) + w(f2) is, in general, lower than the original weight w(f), see [It should be mentioned that, unlike the above outlined anchoring procedure, distributing sub-alignments to multiple processors may well affect the resulting output alignments, even if the selected cut positions are consistent with the optimal alignment. No matter how well our anchoring positions are chosen, we can generally not expect the optimal alignments of our sub-sequences to coincide with the optimal alignment of the original input sequences The reason for this behaviour is that DIALIGN uses a (f), see . As demoTo reduce the total running time of the alignment procedure as far as possible, our algorithm distributes the sub-sequence alignments evenly to the available processors. At the same time, it minimizes the loss of alignment quality that may be caused by splitting the sequences into too many subsequences. To this end, we first identify a chain of anchor points using CHAOS. The program then divides the sequences at every anchor point, thereby producing a large set S1 of pairs of relatively small sub-sequences. The running time for each of the corresponding sub-alignments is estimated as described above. Using these estimates, the sub-sequences in S1 are concatenated in such a way that a set S2 of larger sub-sequences is obtained that can still be evenly distributed to the available processors. Here again, we use a greedy approach to assign processors to sub-alignments. As a result, our algorithm minimizes the program running time by balancing the work load among the processors while it maximizes the length of the aligned sub-sequences, thereby reducing the possible loss of alignment quality.) that is a Linux-SMP cluster with two Pentium III processors (650 MHz) and 1 GB main memory per node. The nodes are connected by a Myrinet 1.28 GBit/s switched LAN. The software was also compiled and tested on a Sun fire with 8 processors and on an ordinary Linux-based workstation pool that generally exists in every institute.We decided to use the message-passing interface (MPI) ,28 for oat al. [genomic sequences has recently been investigated by Pollard et al. [existing approach, we do not evaluate the quality of the produced output alignments; the ability of our software to produce biologically meaningful alignments under various conditions has been evaluated in the above cited papers. Herein, we compare the running time of our parallel software to the original serial version of the program.The performance of existing multi-alignment software has been evaluated in detail. All programs have been extensively tested by their authors; in addition several independent studies have been carried out using numerous sets of real and artificial benchmark data. The quality of multiple-protein-alignment programs including DIALIGN has been systematically studied by Thompson at al.  and by Lat al. . The abid et al. . Since tp of processors. Using 64 processors, the running time for these data sets can be reduced by 94.82%, 90.80% and 75.90%, respectively, compared to the serial running time. The observed differences in the relative speed-up are due to the different proportion of CPU time that is spent on the pairwise alignments, see [As a first test example, we aligned sets of proteins with 20, 55, and 100 sequences, respectively. The program distributed the pair-wise alignments to different processors as described in section. Table nts, see . The larnts, see ). Furthents, see .bp . These pairs of subsequences were concatenated to obtain a set S2 of larger sub-sequences that can be evenly distributed to the available processors.Next, we looked at the improvement of program running time that can be achieved for large genomic sequences using the algorithm described in section. As a test example, we used a set of three syntenic genomic sequences from mouse, rat and human. Each of these sequences is around 1 MB in length. The program CHAOS identified a total of 15,818 anchor points; 4,294 for human/mouse, 4,072 for human/rat and 7,452 for mouse/rat. Most of these anchor points were consistent with each other, only 121 out of the 15,818 anchor points had to be discarded because of consistency problems [Using CHAOS anchor points, the serial version of our program took 267,574 s = 74 h 19 m 34 s to compute the multiple alignment of our input sequences on a single processor of our cluster. We estimate that, without the anchoring option, the original DIALIGN program would have taken around three weeks to align these sequences. By contrast, the parallel version of the program with 64 processors took only 6,583 s = 1 h 49 m 43 s to align the same sequence set, corresponding to a running time improvement by 97.5 %. With a speed-up from more than three days to less than two hours, DIALIGN can now compute long-range multiple alignments of genomic sequences that were, until recently, far beyond its scope.Göttingen Bioinformatics Compute Server (GO-BICS) at . The program code is available on request.The program will be available online through MS parallelized DIALIGN, installed it on the Kepler cluster, performed the test runs and wrote parts of the manuscript. KN and MK participated in the design of the project and manuscript preparation. BM supervised the project and wrote most of the manuscript. All authors read and approved the final manuscript.


The power of this approach strongly depends on the quality of the multiple alignments, which thus motivated development of theoretical concepts and strategies to improve alignment of conserved motifs within large sets of distantly related sequences.Certain protein families are highly conserved across distantly related organisms and belong to large and functionally diverse superfamilies. The patterns of conservation present in these protein sequences presumably are due to selective constraints maintaining important but unknown structural mechanisms with some constraints specific to each family and others shared by a larger subset or by the entire superfamily. To exploit these patterns as a source of functional information, we recently devised a statistically based approach called α isubunits, prolyl oligopeptidases, and transitional endoplasmic reticulum (p97) AAA+ ATPases.Here we describe a hidden Markov model (HMM), an algebraic system, and Markov chain Monte Carlo (MCMC) sampling strategies for alignment of multiple sequence motifs. The MCMC sampling strategies are useful both for alignment optimization and for adjusting position specific background amino acid frequencies for alignment uncertainties. Associated statistical formulations provide an objective measure of alignment quality as well as automatic gap penalty optimization. Improved alignments obtained in this way are compared with PSI-BLAST based alignments within the context of CHAIN analysis of three protein families: GWhile not entirely replacing PSI-BLAST based alignments, which likewise may be optimized for CHAIN analysis using this approach, these motif-based methods often more accurately align very distantly related sequences and thus can provide a better measure of selective constraints. In some instances, these new approaches also provide a better understanding of family-specific constraints, as we illustrate for p97 ATPases. Programs implementing these procedures and supplementary information are available from the authors. As the genome projects continue to generate sequence data, it is increasingly common to find protein superfamilies with thousands of members in the protein database. Given sufficient numbers of sequences, sensitive iterative search and alignment procedures, such as PSI-BLAST  and SAM contrast hierarchical alignment and interaction network (CHAIN) analysis [Certain protein families within these large superfamilies are often very highly conserved across distantly related organisms. Such proteins include, for example, certain metabolic enzymes, DNA replication and repair factors, certain structural proteins, such as actin, the motor protein dynein, and regulatory and signalling factors, such as protein kinases and Ras-like GTPases. While many of these proteins seem relatively well characterized, we still cannot account for the strong selective constraints preserving their observed high degree of sequence conservation across major taxonomic groups. Presumably these patterns of conservation contain implicit information regarding still unknown functional mechanisms. To access this information, we recently developed a statistically based approach, called analysis , that idAligning distantly related sequences presents unique algorithmic and statistical challenges because such proteins often only share a minimal structural core with sizable insertions occurring between, and even within, core elements. Classical dynamic programming-based multiple alignment procedures typically have considerable difficulty spanning across these insert regions because the log-odds scores associated with weakly conserved core elements are often too low to offset the substantial gap penalties that such insert regions incur. This problem is further exacerbated when core elements contain short insertions or deletions within them.To address this problems, we previously devised motif (or block) based multiple alignment procedures -6 that cAltschul at the National Center for Biotechnology Information (NCBI) likewise sought to address this problem through generalized affine gap costs , but theMore relevant to our purpose here, another drawback to the use of MUSCLE, MAFFT, and similar programs for CHAIN analysis is that these will align randomly generated sequences – a characteristic incompatible with the statistical basis of CHAIN analysis. MUSCLE and MAFFT perform well on small sets of relatively diverse representative sequences, such as the BALIBASE benchmark sets , becauseTo maintain statistical rigor in our formulations here, we will 'let the data speak' by modelling only those characteristics of the sequences that can be justified by the input data. Such an approach cannot be applied, however, to small benchmark alignment sets, because these lack sufficient sequences – less than the number of amino acids whose parameters are being estimated. Thus, while a rigorous statistical approach has severe limitations when applied to small datasets, it works very well when applied to large, diverse sets of distantly related sequences, as demonstrated, for example, by some of our earlier analyses -16.Two other theoretical issues, which are important to the multiple alignment problem, are devising an objective measure of alignment quality and an efficient strategy for finding the best alignments based on this measure. Our previous methods -6 addresα subunits, which belong to the P loop GTPase class [α,β-hydrolase fold class [Within this MCMC sampler we implemented specific operations on the alignments, including those allowing for realignment of a sequence against the alignment model, shortening or lengthening of blocks, and creation of recombinant alignments. Such operations function like catalysts to help the sampler avoid or more quickly escape from local optima. Here we expand on the number of these operations and modify our Bayesian model to allow for short insertions or deletions within blocks. In theory, such an approach could be used to sample representative multiple alignments from the posterior distribution, which is relevant to CHAIN analysis because this could be used to adjust position-specific amino acid frequencies for alignment uncertainty. Doing so for the model and operations described here, however, is non-trivial and thus is a topic for a future publication built upon this one. Our primary objective here is merely to obtain the optimal alignment. Thus we also introduce various annealing-like strategies for luring the sampler toward optimum alignments. These include simulated annealing, which is applied within sampling routines, and other intervention strategies. Our primary motivation for developing and implementing these concepts and strategies is to improve CHAIN analysis, as is illustrated here for G-protein se class , prolyl ld class ,19, and ld class , which bld class -23 withild class ,24,25.The fundamental problem addressed here is to identify the essential features – the common structural core – characteristic of a large set of distantly related proteins. Given an input sequence set, we build a Bayesian statistical model with adjustable parameters to reflect the relationships among the proteins. We also design a stochastic search algorithm, with an MCMC sampler as its backbone, to explore possible alignments and corresponding model parameters in order to find alignment models that best 'explain' the input data. The model parameters specify, for example, the number and lengths of the motifs, their locations within each sequence, the residue frequencies observed at each position in each motif, and other properties (described below). We may thus envision our sampler as searching through a discrete space where each point, corresponding to a particular alignment, has a probability associated with it. The probability function appears fairly smooth inasmuch as nearby points  have roughly comparable probabilities. As the sampler traverses from one point to another, it favors moves toward the better alignments, that is, toward that part of the alignment space with greater posterior probability. Since it is computationally prohibitive for the sampler to consider many transitions at one time, a key design issue is the selection of allowed transitions between points.We first define the alignment model in precise mathematical terms, which provides a scoring scheme that allows us to judge which alignment is better than another. Here, for the sake of conciseness and readability, we will keep the discussion on a conceptual level whenever possible. Interested readers can consult our earlier publications for further details ,6.m co-linear ungapped motifs, of width w1,... , wm, respectively. Each motif is modelled by a position specific frequency matrix Θi, whereas residues outside the motif blocks follow a common frequency distribution. Independent prior Dirichelet distributions are employed for these frequency parameters.As illustrated in Fig. m and the wi's are unknown, we assume that they are uniformly distributed in a certain range a priori . Then the posterior alignment distribution is:Since both ori (see  for detaP(A | S) ∝ P(A) ∫ PP(Θ)dΘ.P(A | S), the so-called "maximum a posteriori (MAP)" score.Based on this distribution, our algorithm (as implemented in the PROBE program ) attemptg, are given in Methods.A major drawback of the previous block-based alignment approach is that it disallows insertions or deletions within motif blocks. Here we describe hidden Markov model (HMM) ,27 strucp = 1/220) and an extension penalty of 2.5 bits. Then, for example, the overall MAP would need to improve by 25 bits in order to justify a 'surgical operation' on a sequence involving an insertion of three dummy residue  or a deletion of three residues . The statistical problem is thus that of finding the right penalty so that the sampler only adds insertions or deletions when the data provides sufficient justification. In a Bayesian context, this justification is based on the posterior inference of the overall number of insertions and deletions from what it finds in the aligned sequences.For an intuitive notion of how within-motif penalties influence the total MAP score, consider a gap-opening penalty of say 20 bits  slightly, with the equilibrium distribution of the chain being the target distribution. A MCMC scheme is usually constructed in two steps: (i) propose a new state according to a certain reversible transition rule, and (ii) accept or reject the proposal according to the probability ratio between the proposed and the current states .g one obtains a set of "typical" alignments according to the posterior distribution, which provides information regarding the most likely alignment(s) supported by the data and its variability. In practice, however, one may wish to find the optimum of this function and explore only around this optimum considering the difficulty of summarizing a set of distinct alignments in a meaningful way. MCMC is also an important ingredient of an optimization technique termed "simulated annealing" [The broad utility and general applicability of these techniques are exemplified and popularized by recent developments in statistics: if one can sample from nealing" , of whicThe elementary mathematical operations of addition and subtraction define a means of transitioning between points in the discrete space of natural numbers. "Global" operations, such as multiplication and integer division, allow transitions between more distant points in this space. Likewise, we define both elementary and global operations on multiple alignments as a means of transitioning between points in alignment space. In this case a set of unaligned sequences  serves the same role as the natural number zero. Formal mathematical descriptions of the alignment and of certain simple operations are provided in our earlier papers ,6. SinceThere are two issues to consider in the design of multiple alignment operations. First, the reversibility of MCMC algorithms requires that every operation have an "inverse" so that the sampler can readily transit in either direction. Second, to help find the optimal alignment according to our Bayesian model, which is our main objective, annealing techniques and less restrictive acceptance rules should be considered for certain complex operations. By doing so the target alignment distribution has to be distorted to some degree, though the global optimum of the distribution remains the same.All alignments described here are collinear multiple alignments (CMAs), which are defined to contain zero or more motif blocks arranged collinearly in each sequence. Partial or complete deletion of any motif from a particular sequence is modelled by aligning that motif against null residues ('-'), which the sampler may insert anywhere in the sequence. Sequences may also contain more than one repeat of the entire protein domain, each of which is modelled by the full set of motifs.  For clarity, we describe operations deterministically, though it should be kept in mind that our sampler applies these stochastically.The HideInsert operation (inverse ShowInsert) is applied to 'surgically' remove a region of the sequence that appears to correspond to a typically short insertion within a conserved motif. This operation thus changes the real sequence into an idealized sequence that, presumably, more closely resembles the canonical characteristics of the protein class. As a result, the sampler needs to maintain both a real and an idealized version of each protein's sequence and to store the operational derivation used to obtain the ideal sequence from the real. Algorithmically it is convenient to deal with insert regions in this way because otherwise the sampler would need to look up the locations of insertions and deletion within each sequence when applying other operations. The FillDeletion operation (inverse UnfillDeletion) likewise converts a sequence that contains a deletion of either part of or all of a motif into an idealized sequence in which the deletion has been filled in with null or 'dummy' ('-') residues. Note that HideInsert and FillDeletion merely define data structure interconversions that allow basic operations, which were initially defined for ungapped motifs, to be efficiently applied to gapped motifs.disallow gaps within motif blocks.The Align operation assigns motif positions within a sequence and thereby adds that sequence to the alignment, UnAlign removes the sequence from the alignment. Note that these operations The AddColumn and DeleteColumn operations add and remove aligned columns, respectively. Note that these operations may add or remove columns internal to a motif as well as at the edges. Moreover, AddColumn may also insert a column an arbitrary number of residues beyond the current edge of a motif. This is important for motif 'fragmentation' ,30, a prElementary operations can be combined in a coordinated manner in various ways to produce compound operations that better facilitate escape from local traps. For example, GapAlign (inverse UngapAlign) combines the row operation Align with the sequence operations HideInsert and FillDeletion in order to add a sequence to an alignment with insertions and deletions. The GapAlign operation is performed using dynamic programming to obtain a gapped alignment of a sequence against a statistical model of the current alignment. The trace back procedure determines how to apply the HideInsert and FillDeletion operations to the true sequence and how the Align operation is then applied to the resultant idealized sequence.We define several compound operations on a motif block: AddBlock, ShiftRight, and TrimRight . Another compound operation, MoveColumn, which transfers a column from one position to another within a block, is its own inverse. Conceptually, AddBlock and DeleteBlock simply iteratively apply the AddColumn and DeleteColumn operations, respectively. Because our motif alignments are collinear, the position of an added block within each idealized sequence must be specified in a manner consistent with this collinear arrangement and, in order to add a new block in this way, the sampler may need to insert null residues at certain positions within some of the idealized sequences. This is an example of operational flexibility. Similar operational flexibility is required for the ShiftRight and ShiftLeft operations, which remove one or more columns from one end and append it to the other end of a motif. TrimRight and TrimLeft allow poorly conserved residues to be trimmed from a motif block based on their relative entropy. These operations thus provide a means to manually edit motif-based alignments as discussed below.Three compound operations involving two motif blocks are: TransferColumn, Splitblock and FuseBlocks. TransferColumn deletes a column from one block and adds it to another block. Splitblock splits a single block into two leaving two contiguous motif blocks in each of the idealized sequences. During future realignment operations the sampler typically induces these abutted blocks to drift apart. Splitblock's inverse operation, FuseBlocks, merges two blocks into one, which typically requires forced realignment of motif positions in each sequence in order to join the blocks together. All such forced realignments are followed by additional optimization via sampling prior to deciding whether to reject or accept this new configuration. We thus typically have to violate the MCMC's acceptance-rejection rule to enable such a move, which distorts the target distribution. The awkwardness of this procedure may be advantageous, however, inasmuch as it forces the sampler out of local traps in alignment space. Fig. As an aid to locating the optimum alignment, we define recombination operations that combine the best features of two distinct, fairly well refined alignments. These operations require that the sampler first generate a population of fairly well refined alignments starting from distinct, randomly selected points in alignment space. All of these input alignments must, of course, contain the same set of sequences.The Recombine operation must be applied to two alignments that are fairly similar because the sampler needs to locate at least one crossover point between them. A crossover point is a set of positions, one position in each aligned sequence, such that the same set of blocks in the first alignment lie to the left of each of those points, while the same set of blocks in the second alignment lie to the right of each point. Because this requirement often proves difficult to satisfy for every sequence, we define the Recombine operation flexibly by allowing a certain number of sequences to violate this rule. In this case, violating sequences are removed prior to recombination and sampled back in afterwards (using the GAPALIGN operation).both input alignments. More precisely, we first find the common blocks shared by the two alignments, where a common block is defined as two aligned motif blocks  that overlap within corresponding sequences. To allow for some flexibility, these are defined as blocks for which at least some minimum fraction (say 50%) of the sequences are consistently aligned in both input alignments.  Then, for each pair of common blocks, we find the sub-block shared by both blocks. Next, we create a new alignment containing only these Intersecting sub-blocks. Finally, sequences that were inconsistently aligned between the two starting alignments are sampled back into the resulting alignment. The Intersect operation allows the sampler to be reinitialized starting with a consensus alignment that aligns only those regions with high likelihood scores and eliminates those regions about which the sampler is less certain. Subsequent sampling will then extend these sub-blocks, add new blocks, and explore more extensively the alignment space.The Intersect operation takes as input two distinct alignments and produces a new alignment containing only those aligned columns common to corresponding motifs in There are no absolute rules on how to choose parameter settings for these algebraic operations, such as, for example, the maximum increase in motif length allowed during the MoveColumn operation or the number of disordered blocks to tolerate for the Recombine operation. We find, in fact, that it often matters little which settings are used and the slight degree to which it does matter depends on the particular protein class being analyzed. As a result, any biologically reasonable parameter settings work well. For example, since weakly conserved motifs are never a hundred residues long, motif blocks typically should be limited to no more than, say, fifty residues in length. Nevertheless our algorithm tolerates unreasonable parameter settings, because then it either simply rejects the corresponding alignment space transitions (though with some degradation in performance) and/or learns to avoid applying useless operations through its memory module, as described below.Having specified various operations on the alignment space, we now need to specify when and how often to apply them, as well as how to escape from local traps and thus to most rapidly converge on an optimum or nearly optimum alignment.Since some of the alignment operations are computationally expensive, it would be helpful to avoid applying them over and over again when this proves to be unfruitful. For example, if the sampler has already converged on the correct number of motifs, applying the AddBlock operation may be a waste of time. On the other hand, we don't want to eliminate any operation entirely, as at some point it may be useful. To do this we define both short-term and long-term sampling memories. The short-term memory allows a rapid response to sudden changes while the long-term memory adds stability so that the sampler does not over respond to short term trends. Details are given in Methods.π (X). As the sampler converges on near optimum alignments, typically it has difficulty 'dropping' into the global optimum of π (X) because the chance of selecting the highest probability alignment is still very small due to the sheer number of near optimum alignments. This is true for the same reason that the most likely outcome of obtaining exactly 5,000 heads and 5,000 tails in 10,000 flips of a fair coin is extremely unlikely.Let the target alignment distribution be denoted generically as π (X) to some exponent, renormalizing it and using the "powered-up" distribution, denoted as πT(X) ∝ πT 1/(X) with the "temperature" parameter varying from a very large value to near-zero, for sampling. This procedure is a key component of simulated annealing [T → 0), we raise the probability of high-density points and lower the probability of low-density points, so as to allow the best alignment to win out over alignments that are nearly as good. If the temperature is lower too abruptly, however, the sampler may get trapped in a sub-optimum alignment, so that the annealing strategy needs to be devised carefully.A standard way around this problem is to take power of nnealing , which hT = 1) probability densities of the sampled alignments. If the variance of log π (X) in a given number K of consecutive iterations at a given temperature is below a certain threshold (so that the posterior probabilities barely change), the sampler may be stuck in a  optimum, and the thermostat raises the temperature a bit. On the other hand, if the log π (X) are varying wildly and, in particular, if they are greatly diverging from the best  alignment found thus far, then the sampler may be wandering away from near optimum alignments and the thermostat lowers the temperature. This approach thus attempts to keep the sampler just above its 'glass transition temperature' [Tg. Details are given in Methods.We have built a 'thermostat' into the sampler that keeps track of variations in the , the user can modify this parameter. As an alternative strategy, two or more programs may also be run in parallel until they both converge on the same alignment.When painting a picture, it is helpful to first draw a rough sketch so that details will end up in the right place relative to each other. Similarly the sampler uses the following progressive refinement strategy to avoid being too "shortsighted."g.There are five stages to this strategy. In the first stage, the sampler applies the Align operation, which aligns the sequences against contiguous ungapped blocks; it also applies compound ungapped motif operations. The initial numbers of block motifs and columns in each block are sampled from binomial distributions with means between roughly 5~10 blocks and 10~30 columns each, respectively. In the second stage, which is introduced after the sampler begins to converge on a local optimum under the ungapped block-motif model, elementary and compound column operations are introduced, which allow these ungapped blocks to 'fragment', thereby permitting nonconserved columns to be ignored by the alignment model . Recomba priori parameter settings chosen before the analysis, fails to split this motif into two blocks. In this case, a biologically more meaningful alignment may be achieved by manually intervening to split this ungapped region . To accommodate such tweaking, we thus allow manual application of various operations. We find that splitting and trimming of aligned blocks are particularly helpful in this regard. Such manually modified alignments then may be reintroduced into a population of similar alignments for recombination and selection via our genetic algorithm [Despite attempts to codify and fully automate optimization of a multiple sequence alignment, the algorithm may still create an alignment model that lacks certain properties observed to be biologically important for a particular class of proteins. Take the situation, for example, where a motif, which occurs as a single block in most of the proteins, is split in two by a sizable insertion in other proteins and where the sampler, due to the lgorithm  followedGibbs-like sampling with multiple operations), GARMA  and GAMBIT . GARMA recombines the output alignments provided by GISMO and then applies simulated annealing strategies on the recombinants. GAMBIT performs on a single alignment the same optimization procedures that GARMA performs on recombinants. Manual application of alignment operations may be performed using another program, TweakAln. These programs along with sample alignments are available from the authors. Multiple alignment of thousands of sequences in this way may take substantial time , but this is not critical because, once performed for a particular protein class, such an alignment can be updated readily by seeding the sampler with a previously optimized alignment. Here we apply these programs to several large protein classes within the context of CHAIN analysis, which is our primary reason for generating such alignments.The theoretical concepts and strategies just described were implemented in the programs GISMO  the background are subject to strong constraints. In Figs α subunits. G proteins [α, a β and a γ subunit, that mediate transduction of extracellular signals to the cellular interior. As do many members of the P loop GTPase class, the Gα subunit functions as a binary switch that is turned on by binding GTP in response to the signal and thereby relays this information to downstream components of the pathway. This switch is turned off by hydrolysis of GTP to GDP, an event mediated by GTPase activating proteins (GAPs).We first examine in this way G protein proteins  are heteα subunits are unique among such GTPase switches inasmuch as their GAP domain is contained within the Gα polypeptide chain itself rather than existing as a distinct protein. This unique arrangement presents particular difficulties for CHAIN analysis because, during subsequent iterations, the PSI-BLAST algorithm tends to slightly overextend the alignment beyond Gα's region of homology to other P loop GTPases and into the C-terminal region of the GAP domain. As a result, the foreground patterns for the Walker A motif are mistakenly aligned against the C-terminal end of the GAP domain . AAA+ Ais known . These Aπ interaction with an alanine  to AAA+ ATPases Fig. , it intrWith a view to improving alignments for CHAIN analysis, we have enhanced our earlier motif-based methods by developing (i) a HMM for insertions and deletions within motifs, (ii) an expanded algebraic system of operations on multiple alignments and (iii) various annealing and sampling strategies that facilitate rapid convergence on optimum or near optimum alignments. Furthermore, our approach, due to its rigorous statistical basis, fills a gap left by current multiple alignment methods inasmuch as it aligns only those characteristics of the input sequences that may be justified statistically. Thus it is useful for statistical analysis of conserved patterns in multiple alignments. Our statistical model likewise provides objective criteria for evaluating curated alignments, thereby guiding manual application of various operations. In the future, our MCMC sampling methods could be used to estimate alignment uncertainties, which will be useful for estimating background amino acid frequencies for CHAIN analysis. These approaches also serve as a starting point for further enhancements that integrate MCMC sampling, HMM and PSI-BLAST methods, which, based on our earlier analyses , seem liWhen this motif-based approach was applied to CHAIN analysis of families belonging to large and diverse protein classes, we found numerous examples, three of which are described here, where this does a better job of revealing subtle, biologically important sequence features than does PSI-BLAST. This is in large part due to the ability of our statistical model and sampling strategies to find weakly conserved islands of homology within a sea of essentially nonconserved regions. While this motif based approach will not become the default method for CHAIN analysis – especially considering that PSI-BLAST alignments also may be optimized using these approaches – it, nevertheless, often more accurately aligns very distantly related sequences and thus can provide a better measure of selective constraints in this situation.ith motif is:We model gaps within motif blocks through the HMM shown in Fig. i ≤ m and 1 ≤ x <wi and where M, I, and D denote match, insertion and deletion states, respectively. The probability matrix for transitions between motifs is:where 1 ≤ i <m and where these transitions each emit a string of zero or more residues. Note that the contribution to the log-posterior probability of the lengths of these strings and of their emission probabilities (as well as those of M and I states) are specified by our ungapped statistical model [where 1 <al model , upon whA, let f(A) be its log-posterior probability as in [i within each sequence Sk is associated with a "path" through the HMM indicating its alignment against motif model Θi. Let the collection of these paths be Λ. Next, we denote the total number of transitions of type M → M, M → I, ..., byFor a given alignment ty as in . If we aNmm, Nmi, Nmd, Nim, Nii, Ndm, Ndd.It then follows that the likelihood of the gap parameters iswith independent prior distributionsαo, βo, 1 - αo - βo) ~ Dirichlet,, and βe ~ Beta,ao, bo, nm, ae, ni, be, nd are prior pseudo counts given by the user. The corresponding maximum likelihood estimates (MLEs) arewhere The joint posterior distribution for the alignment and gap parameters isg ∝ P × P(A) Λ h P,P × P(A) is computed the same way as in the original block-motif model [where if model , andP = Dirichlet × Beta × Beta.Given the alignment Λ, we have the conditional posterior distributionSampling on this distribution can be performed by drawing the following random variables:α and β to getFor computational efficiency, we integrate out the g with h(Λ) replacing h P in our previous formula [This gives rise to a new posterior  formula  and freeK1 residues and one deletion in every K2 residues. Then we setSuppose that we expect to see one insertion in every no to reflect the strength of this conviction. We suggest using priors reflecting conservative gapping where, for example, K1 = K2 = 1000 and no = nM N, where  is the total number of match positions in all of the motifs and N is the total number of aligned sequences.and set L1, and deletion length of L2, then we letFor gap extension prior probabilities, if one expects to see an average insertion length of n1 to be equal to the total number of expected insertions within motifs nM / K1. Likewise, n2 is set equal to the expected number of deletions nM / K2. In order to have different gap parameters for each motif, one need only keep specific counts of insertions and deletions for each motif, as the formula h(Λ) then applies to each motif individually, and we only need to multiply these h functions together when computing the total 'penalty'.We set the prior pseudo counts No  that a type "o" operation has been applied and the number of times no that it was "successful" . The same is done for short-term memory except that in this case we monitor the number of short-term successes mo over Mo previous applications . At the next iteration, we then assign a probability  of applying this operation, where ws ≥ 0 and wl ≥ 0 are the weights given to the short and long-term memories, respectively, and where wp ≥ 0 specifies the minimum frequency at which this operation is applied. Typically, we set ws = wl = 1 and 0.2 ≤ wp ≤ 0.66, so that operations that previously proved to be unfruitful will only be performed about one-tenth to one-third as often as those that always yield improvements in the alignment.For long-term memory we monitor among the sampler's previous iterations the number of times T' = 300/T and, thus, πT'(X) ∝ πT 300/(X). On this 'pseudo-degrees-Kelvin' scale sampling from the true distribution π (X)  corresponds to sampling at 'room temperature'. After a period of sampling at room temperature until 'convergence', which is defined by the sampler's failure to improve the MAP after a specified number of iterations, simulated annealing is initiated. During this stage, whenever the probability densities of the sampled alignments averaged over say 20 iterations fluctuate by more than some maximal value, say Δlog(p) ≥ 50 nats, the temperature is lowered by 1–5°. If, on the other hand, the probability densities of the sampled alignments fluctuate on average less than some minimal value, say Δlog(p) ≤ 5 nats, the temperature is raised by say 1°.  This period of thermostatic sampling is again applied until convergence.We define an intuitive sampling temperature ad hoc approaches conceptually similar to the statistically rigorous procedures described in Methods, which were designed by JSL. AFN implemented the procedures and performed the sequence analyses. Both authors wrote and approved the final manuscript.AFN developed the algorithmic strategies and early


Multiple sequence alignment algorithms are very important tools in molecular biology today. Accurate alignment of proteins is central to several areas such as homology modelling, docking studies, understanding evolutionary trends and study of structure-function relationships. In recent times, improvement of existing progressing programs and implementation of new iterative algorithms have made a significant change in this field.We report an alignment algorithm that combines progressive dynamic algorithm, local substructure alignment and iterative refinement to achieve an improved, user-interactive tool. Large-scale benchmarking studies show that this FMALIGN server produces alignments that, aside from preservation of functional and structural conservation, have accuracy comparable to other popular multiple alignment programs.The FMALIGN server allows the user to fix conserved regions in equivalent position in the alignment thereby reducing the chance of global misalignment to a great extent. FMALIGN is available at  The advent of large genome projects has led to an explosion of sequence data in public databases. Analysis of protein families, understanding their evolutionary trends and detection of remote homologues are now the primary objectives. Genome annotation and analysis tools like fold prediction, homology modelling, protein-ligand docking and clustering algorithms rely heavily on accurate multiple alignments to provide a genome-wide perspective.The most popular approach for multiple sequence alignment has been the progressive alignment method . A multiIn this paper, we present an alignment algorithm that combines the properties of both progressive alignment methods and iterative refinement algorithms. This algorithm offers the user the selective advantage of guiding the course of alignment by simultaneous inputs of multiple conserved motif regions that in turn guarantees retention of structure/function in the final alignment. FMALIGN is an alignment server that provides the user to obtain a control over the alignment by providing important conserved regions as input to the alignment program to achieve a more structurally relevant and functionally useful alignment of protein sequences. It employs the sequential branching method to identify the closest pair of sequences and subsequently includes the next closest sequences to generate a guided tree using UPGMA , which iThe algorithm of FMALIGN (Fixed Motif ALIGNment) program combines three main criteria: (a) Progressive global alignment method, (b) substructure  conserved region fixation and (c) iterative refinement of alignment with identification of more conserved regions. The procedure involves three steps: (i) identification and fixing of the specified sequential conserved regions. This alignment method requires specific regions of the sequences to be aligned as anchor and these anchors are generally meant for sequentially conserved parts which do not undergo many changes. (ii) derivation of the progressive multiple sequence alignment guided by the tree. During this step, excluding the fixed anchored regions, the rest of the sequences are divided into several sub-segments that are aligned employing a dynamic alignment algorithm in a sequential order from N to C-terminus. The phylogenetic guide tree has been derived using Unweighted Pair Group Method with Arithmetic Mean (UPGMA)  which isFMALIGN server can accept amino acid patterns for multiple motifs provided by the user. It also provides option to the user to search motifs within their sequences using FINDMOTIF routine or to obtain them for the alignment by providing a link to SMoS , a strucTo assess the performance of FMALIGN in comparison to other programs, Sum-of-Pair-score (SPS) and Column-Score (CS) alignment scoring scheme  are applFMALIGN derived alignments retain high degree of conservation in secondary structures. Six members from the globin family were selected comprising a wide range of sequence identity between them (7% to 61%). Conserved regions for six aligned globin sequences were identified by the FINDMOTIF routine starting from CLUSTALX  alignmenIn order to evaluate the FMALIGN server, the results have been compared with 10 other alignment programs and objective criteria were employed to assess the quality of an alignment. We selected the BAliBASE benchmark alignment database  to compaReference 1 alignments consist of a small number of equidistant sequences of similar length, i.e. the percent residue identity (% ID) between any two sequences is within a specified range and no large extensions or insertions have been introduced.Reference 2 contains alignments of a family of closely related sequences with >25% ID, plus up to three 'orphan' sequences . It is designed to evaluate program accuracy according to two criteria: (i) the stability of the family alignment when orphans are introduced into the sequence set and (ii)the quality of the alignment of the orphan sequences.Reference 3 checks the ability of the programs to correctly align equidistant divergent families into a single alignment. The reference alignments consist of up to four families, with <25% ID between any two sequences from different families.Reference 4 and 5 contain alignments of upto 20 sequences including N/C-terminal extensions (upto 400 residues) and insertions (upto 100 residues), respectively.This dataset is designed to study the effect of sequence length and percentage identity on the performance of the alignment program and provides a basis for the remaining tests. The overall performance of FMALIGN server for this dataset is comparable to the two best performing alignment programs, like PRRP  and CLUSIt is possible to assess the performance of the methods to align divergent 'orphan' sequences (10–20% ID with the family and between orphans) with a family of highly related (>25% ID) sequences using this data set. It is also interesting to observe the disruption of the family alignment due to the introduction of orphans. Figure This allows the assessment of the programs to correctly align approximately equidistant divergent families (<20% ID) composed of highly related sequences (>25% ID) into a single multiple alignment. Figure This dataset includes large N/C-terminal extensions to investigate whether the programs are capable of aligning the core blocks flanking the extensions. No large internal insertions are introduced at this stage. Mostly local alignment strategies out-perform the global methods. PILEUP  is the only program based on a global alignment method which does reasonably well compared to other global methods. Performance of FMALIGN is comparable to the best three methods  are calculated using a standard program kindly provided by the authors of BAliBASE. The inter-motif regions are aligned in FMALIGN by normal progressive alignment using standard substitution matrices like BLOSUM62. The gap penalties used in this version of FMALIGN are all maintained according to standard multiple alignment parameters. Benchmarking at the superfamily level has also been done utilizing both structural and sequential conserved regions. The dataset is wide enough to include proteins from different structural classes and of different length. The average sequence identity for this dataset was less than 30% since the proteins are related at the superfamily level. The performance of FMALIGN has been tested against one of the best performing multiple sequence alignment (T-Coffee) as well as structure based alignment tool (COMPARER). Studies on large and different datasets revealed an overall better performance of FMALIGN server for all categories in BAliBASE benchmarking database. It works especially well at lower sequence identity range, such as superfamily level, where no two proteins are more than 25% identical to each other in comparison to other popular methods like CLUSTALX and T-Coffee. It is well-known that automatic multiple sequence alignments at poor sequence identity are often subject to careful manual validations and improvements to avoid offsets of critical functionally important residues. FMALIGN can sensitively address this issue to avoid manual intervention subsequent to final alignment. FMALIGN-derived alignments also show a high conservation of secondary structural elements and provide better alignments for comparative modelling. The implementation of this alignment algorithm can be used to include new members into an existing protein superfamily with the help of motif regions that provide a reliable approach to connect protein sequences with their structural homologues within a particular superfamily. FMALIGN is available via the following URL S.C. had carried out the benchmarking, was involved in the development of the server and has written the first draft of the manuscript. N.B. had written the initial part of the code and P.A. has written the latter part of the code and developed a web server. R.S. had initiated the idea, was involved in discussions and in the critical reading of the manuscript.Fixed Motif ALIGNmentFMALIGN SPS Sum-of-Pairs Score


Accurate multiple sequence alignments of proteins are very important in computational biology today. Despite the numerous efforts made in this field, all alignment strategies have certain shortcomings resulting in alignments that are not always correct. Refinement of existing alignment can prove to be an intelligent choice considering the increasing importance of high quality alignments in large scale high-throughput analysis.We provide an extensive comparison of the performance of the alignment refinement algorithms. The accuracy and efficiency of the refinement programs are compared using the 3D structure-based alignments in the BAliBASE benchmark database as well as manually curated high quality alignments from Conserved Domain Database (CDD).Comparison of performance for refined alignments revealed that despite the absence of dramatic improvements, our refinement method, REFINER, which uses conserved regions as constraints performs better in improving the alignments generated by different alignment algorithms. In most cases REFINER produces a higher-scoring, modestly improved alignment that does not deteriorate the well-conserved regions of the original alignment. The reliability and accuracy of many bioinformatics methods such as homolog identification, comparative modeling, phylogenetic analysis and others depend heavily on the quality of multiple sequence alignments. Heuristic approaches such as progressive and iterative methods are generally used to obtain multiple sequence alignments in a computationally efficient manner. In progressive approaches, a multiple alignment is generally built up gradually by aligning the most similar sequences first and successively adding in more distant relatives. A number of alignment programs apply this strategy -3 by conDespite the numerous efforts made in this field, each of these strategies has weaknesses that can result in alignments that do not reflect the correct evolutionary relationships. This persistent difficulty of course reflects the fact that aligning multiple sequences is a highly non-trivial task  whose accuracy in practice depends largely on the choice of input sequences, the objective function and the heuristics employed. Therefore, the application of an alignment refinement algorithm to an existing or automatically-generated alignment can be helpful for detecting alignment problems. Alignment refinement as a post-processing operation is particularly worthwhile considering the increasing importance of high quality alignments in large scale high-throughput analysis.et al., , norMD score range  and information content range ) performing alignment refinement is most often beneficial. At higher levels of input alignment quality , however, it is also encouraging that refinement can provide moderate improvement yet seldom results in significant degradation.As the quality of an alignment improves, refinement procedures reach a point of diminishing returns. It is therefore useful to identify the circumstances under which refinement is most likely to be helpful. We explored this issue by correlating the improvement of alignment accuracy under refinement (in terms of SP score) and the quality of the initial alignment as measured by its objective score, focusing on the REFINER method. Figure We used the program Hmmsearch from the HMMER 2.3.2 package  to perfoThe database search sensitivities at 1% and 5% error rates are given in Table Finally, we compare the average computation time required for each of the refinement algorithms. The CPU time cost is an important practical factor that influences the utility of an algorithm to a great extent. Table Although the computational complexity may be similar for RF and REFINER due to their similar approaches to the problem, implementation differences appear to account for the disparity in speed between the two methods. Specifically, RF is a Perl script which performs multiple system calls within its innermost iteration loop, including invocations of the program(s) Muscle and/or ClustalW to perform sequence realignment operations. In contrast REFINER is a C++ binary that has no nested system calls and includes a fast dynamic programming engine to do sequence realignment operations.The alignment of multiple sequences is a very important task and still remains a challenging problem. Acknowledging the difficulty of that challenge, an alternate approach to the underlying problem has been examined here: augmenting alignment-generation procedures with a separate alignment-refinement algorithm capable of repairing those errors that remain. Iterative refinement algorithms generally attempt to improve the overall quality of alignment by employing objective functions and heuristics to obtain an optimal alignment. Most iterative refinement methods face the challenge of how to escape from sub-optimal alignments. Therefore, the main differences among the existing methods lie in the effective definition of an objective function and intelligent design of the method's heuristics.In this study we conducted an extensive comparison of the performances of three different alignment refinement algorithms. The accuracy and efficiency of the refinement programs such as, RASCAL , RF methi.e., higher ranges of the input's objective score) although REFINER still found improvements, the impact of refinement is reduced. This might indicate that those alignments were already been optimized and therefore were less prone to changes.Further, we tried to identify the range of initial alignment quality in which REFINER is most successful at improving the alignment. High-quality input alignments are difficult for refinement algorithms to improve without also making additional deleterious modifications. Because the good input alignments also tend towards higher objective scores, for these purposes the input alignment's objective score is viewed in a general sense a proxy for the difficulty that alignment presents to a refinement algorithm. The impacts of refinement by the REFINER algorithm are very prominent in the lower ranges of initial alignment quality where REFINER provided significant improvements. For higher quality input alignments . We are not aware of another analysis like the one presented here, and believe that it will be helpful to researchers in the sequence analysis field when attempting to decide if their alignment tasks can benefit from the use of one or more refinement programs.Our previous study  establisWe used the BAliBASE 3.0  alignmenet al., 2006 [The REFINER algorithm refines an existing alignment by systematically realigning each sequence to the profile constructed from the remaining sequences in the family. The algorithm performs one or more iterations of refinement; each iteration contains a phase of 'block shifting' followed by a 'block editing' phase. The refinement is constrained by the block model defined for a given alignment, where a block is a region containing no gaps on any sequence; a block is specified simply by a start position and residue length. The order in which the sequences are realigned  is randomized to avoid bias and make the use of multiple iterations more effective. Convergence is declared when no further improvement of overall alignment score is observed or all iterations have been performed. A detailed description of the algorithm can be found in Chakrabarti l., 2006 .et al., [N2 iterations, where N is the number of sequences. Two different programs were used to align sequences in this protocol; ClustalW [The Remove First (RF) scheme from Wallace et al.,  is similClustalW , which mClustalW , which mThe refinement program RASCAL  uses a dSix multiple alignment programs were used to generate alignments as inputs for the refinement algorithms. These are: ClustalW version 1.83 , Muscle When using the BAliBASE benchmark, we used the bali_score  program In the case of CDD alignments we evaluate the refined alignments by calculating the objective scores SCORECONS  and norME-values of 10-80 or less, from all the entries in the MMDB structure database [Another way to validate alignment refinement methods is to examine the performance of a refined alignment in homology-based database searches. To compare the database search sensitivity of the profiles or Hidden Markov Models (HMMs) computed from alignments before and after the refinement procedure, we first constructed a list of true positives for the conserved domain families from set_280. True positives here were defined as those proteins/domains which were structurally similar, as defined by the VAST algorithm , to the database .We used HMMER  to test CDD Conserved Domain DatabaseSP Sum-of-PairsHMM Hidden Markov ModelsPSSM Position Specific Scoring MatrixCPU Central Processing UnitS.C. had carried out the benchmarking, was involved in the development and validation of the algorithm and has written the first draft of the manuscript. C.J.L and P.A.T were involved in development of the program. T.M.P and S.H.B were involved in discussion and critical reading of the manuscript. All authors were involved in the design of the algorithm. S.C, C.J.L, A.R.P, T.M.P and S.H.B participated in discussions and writing the final version of the paper.


In addition, multiple-alignment strategies for binding profiles and tree-building methods are tested for their efficiency in constructing generalized binding models. A new method for automatic determination of the optimal number of clusters is developed and applied in the construction of a new set of familial binding profiles which improves upon TF classification accuracy. A software tool, STAMP, is developed to host all tested methods and make them publicly available. This work provides a high quality reference set of familial binding profiles and the first comprehensive platform for analysis of DNA profiles. Detecting similarities between DNA motifs is a key step in the comparative study of transcriptional regulation, and the work presented here will form the basis for tool and method development for future transcriptional modeling studies.Transcription factor (TF) proteins recognize a small number of DNA sequences with high specificity and control the expression of neighbouring genes. The evolution of TF binding preference has been the subject of a number of recent studies, in which generalized binding profiles have been introduced and used to improve the prediction of new target sites. Generalized profiles are generated by aligning and merging the individual profiles of related TFs. However, the distance metrics and alignment algorithms used to compare the binding profiles have not yet been fully explored or optimized. As a result, binding profiles depend on TF structural information and sometimes may ignore important distinctions between subfamilies. Prediction of the identity or the structural class of a protein that binds to a given DNA pattern will enhance the analysis of microarray and ChIP–chip data where frequently multiple putative targets of usually unknown TFs are predicted. Various comparison metrics and alignment algorithms are evaluated . We find that local alignments are generally better than global alignments at detecting eukaryotic DNA motif similarities, especially when combined with the  motifs). Comparison of these motifs not only provides insights into the evolutionary process they undergo, but it also has many important practical applications. For example, motifs that are found to be “similar” can be combined to form generalized profiles, which can be used to improve our ability to predict novel DNA signals in the promoters of co-expressed genes, and thus facilitate a more accurate mapping of gene-regulatory networks. However, to date there is no comprehensive platform that will allow for an efficient analysis of DNA motifs. Furthermore, the efficiency of the methods used to assign similarity between DNA motifs has not been thoroughly tested. This paper takes an important first step towards this goal by evaluating available comparison strategies as applied to DNA motifs and by generating an improved familial profile dataset.Transcription factors are primary regulators of gene expression. They usually recognize short DNA sequences in gene promoters and subsequently alter their transcription rate. It is known that structurally related transcription factors often recognize similar DNA-binding patterns (or  Transcription factor (TF) proteins usually recognize a small number of DNA targets via the formation of sequence-specific and nonspecific molecular interactions. Understanding the evolution of TF DNA-binding preferences will not only provide useful insights on the mechanism of DNA recognition, it will also allow more accurate prediction of genomic regulatory elements, which still constitutes a major hurdle in understanding cellular gene regulatory networks. Furthermore, high-throughput studies, such as microarray and ChIP–chip, generate a number of DNA motifs that are putative targets of usually unknown TFs. In this study, we present an alignment and comparison platform that is optimized for DNA motifs, thereby allowing for their efficient analysis and enabling and formalizing their evolutionary study. This platform is called STAMP, for similarity, tree-building, and alignment of DNA motifs and profiles.position-specific scoring matrices (PSSMs) assume independency between the base positions )HTW) G). The IRF family consists of wHTH proteins that bind as homodimers via nonpalindromic direct repeats [The method we used to determine the optimal number of clusters is similar to the Calinski and Harabasz statistic , but the repeats  or as mo repeats . The IRFOur algorithm also correctly recognized three subfamilies in the major bHLH family. The six members of the bHLH-zip subclass  are clustered together, whereas the remaining four “standard” bHLH proteins  and bHLH complexes  form two separate clusters. Examination of the FBPs of these clusters  shows clAT-hook family of TFs [HMG-box proteins [not identical, but they show significant overlap in four highly informative nucleotide positions (consensus: AACA)  . Neverths: AACA) . NotablyWhen the two zinc-finger families were included in the analysis, the overall structure of the tree and the clusters remained the same, pointing to the stability of our multiple alignment and clustering algorithm. Most of the GATA proteins formed a new cluster, whereas all DOF proteins joined the cluster of the two IRF proteins. This is because the DOF consensus target sequence (AAAG) is part of the IRF motif . The croThe STAMP platform, introduced in this study, contains all tested algorithms and can be efficiently used in BLAST-like searches against a database of PSSM models. Various datasets (including TRANSFAC and JASPAR motifs) are currently supported. In the future, it would be useful to incorporate other similarity metrics, alignment methods, and tree-building algorithms into the platform in order to allow for further exploration of optimal methods. Note, however, that it may not be possible to implement all of the known tree-building algorithms for motif alignment. Other distance-based methods (such as neighbour-joining ) rely heIn summary, we expect that the methods and the results described in this study will facilitate the exploration of DNA-binding preference evolution amongst related transcription factors and will have a significant impact in many areas of gene research.L is composed of a set of 4 × L weights (columns). Each column, X, follows a probability distribution, {xp(b)}bA,C,G,T}∈{, with the base-probability values reflecting the preference of the TF for the corresponding base in this position. The probability values can be estimated from the observed base counts {xn(b)}bA,C,G,T}∈{. We denote the estimated values f(X) = {xf(b)}bA,C,G,T}∈{. In practice, Xp are estimated from Xn plus some pseudocounts to reduce small-sample biases and to avoid zero probabilities. The assumption of independence between positions is not entirely accurate, but acts as a useful approximation [A PSSM model of length ximation –34. In tX and Y, with total number of aligned sequences XN and YN and (estimated) frequency distributions off̂(X) =  andf̂ (Y) = , respectively. We denoteX̄ andȲ the average frequencies in the two columns.Six metrics  are compPearson Correlation Coefficient (PCC). PCC is a popular similarity metric that has been used by us and others in comparing DNA models [A models ,32,35. PA models  found PCp-Value of chi-square test (pCS). Schones et al. [Kn(b) in the pCS formula represents the observed count of base b in column K  plus one pseudocount. The expected occurrence of base b in column K is given by KN·bN)/N, where KN is the total number of counts in column bK, N is the total number of counts for base b in the two columns, and N is the sum of counts in both columns. The p-value is calculated from the s et al.  used thea column . This coAverage Kullback–Leibler (AKL). The Kullback–Leibler distance (or relative entropy) is the weighted log-likelihood ratio distance between two distributions. The standard Kullback–Leibler is noncommutative and hence is not a true metric. However, it is frequently used in comparing TF–DNA preference probability distributions since it has an important quality: more weight is placed in the high-probability bases, where TF–DNA modeling algorithms need to be more accurate. Kullback–Leibler distance has been employed in the T-Reg Comparator motif similarity software tool and elsewhere [average Kullback–Leibler score from an arbitrarily defined maximum (10.0) to convert it to a similarity score. A theoretical maximum score cannot be defined for the AKL column distances, but more than 99% of the column-to-column scores in the TRANSFAC database [lsewhere ,37,38. Idatabase  were fouSum of squared distances (SSD). SSD is a simple scoring metric that was employed by Sandelin and Wasserman in their construction of FBPs [ of FBPs . Note thAverage Log Likelihood Ratio (ALLR and ALLR_LL). The ALLR statistic was introduced by Wang and Stormo [informative  column distributions. Kn(b) is the observed count of base b in column K  and refp(b) is the background probability of base b. In this study, refp(b) is assumed to be 0.25 for all bases. The ALLR metric has a skewed scoring distribution; the minimum score (≤−10) is much smaller than the maximum score (2). Therefore, we also tested a modified ALLR measure, termed ALLR_LL, in which the lower score was bounded by −2.d Stormo ,39 as a I(C) = fI(G) = fIf(T) and If(A) set such that the column information content had a specified value I. This column is denoted the “true” column centre, or α parameter = 20). The sum of nucleotide counts in each of the random columns was set to 30 to reflect the mean number of binding site instances used to construct TRANSFAC PSSMs. Another one million columns were sampled from a Dirichlet distribution centered on the zero information content columnref(A)f = ref(C)f = ref(G)f = ref(T)f = 0.25.Information content–specific PSSM columns were constructed with p-values based on simulated PSSMs [http://forkhead2.cgb.ki.se/jaspar/additional) that reflected the properties of PSSMs in the JASPAR database.To avoid length biases when comparing motifs of different lengths, we used the method of Sandelin and Wasserman for the calculation of empirical ed PSSMs . ConstruPairwise motif alignment. Needleman–Wunsch global alignment [lignment ,41 and Slignment  were tesMultiple-motif alignment. Two multiple-alignment strategies are tested. One is a progressive profile alignment strategy, which relies on the preconstruction of an approximate guide tree using UPGMA. The multiple alignment is built up by progressively aligning the nodes on the guide tree in order of decreasing similarity. In this way, each internal node contains a “familial” profile. The alignment at the root node will represent the final multiple alignment. The second implemented strategy is iterative refinement alignment, which aims to combat the problem of local minima, common in the progressive alignment methods due to “frozen” subalignments [ignments . IteratiTree-building algorithms. We implemented two similarity-based tree-building algorithms: an agglomerative method  and a dd (UPGMA ). UPGMA d  [CH) [CHlog performed the best. The CHlog formula is given in B and W representing the between and within cluster sum of squared errors, n is the number of matrices , and g is the current number of clusters in the hierarchy. Error here refers to the negative logarithm of the motif comparison p-value (described above). In contrast to the original Calinski and Harabasz statistic, the B and W are log-transformed to avoid the tendency of the denominator towards zero, which results from the relatively small size of the datasets in which we operate. This logarithm transformation means that the estimate for the optimal number of clusters on the tree (K) is the value of g that minimizes CHlog . The suitability of the above metric to the current application domain was confirmed by evaluating its performance in a dataset with a small number of tightly clustered motif groups (see er (HTW)  and CaliTW) [CH) , and oneoups see .For the purposes of testing the accuracy of various motif-alignment and tree-building strategies, we compiled two datasets that contain the motifs of the families with four or more profiles in JASPAR  and TRANTable S1Average is the weighted average. Overlapping (overlap) and ungapped (ungapped) alignments are specified. Gap extension is equal to half the gap opening.Performance is measured as the percent of motifs whose structural class are correctly recovered via the best hit in database searches. The two datasets used in this comparison are taken from JASPAR and TRANSFAC. While accuracy was measured over the complete dataset, the results below report separately the performance for the nonzinc-finger families  and the zinc-finger families . (243 KB DOC)Click here for additional data file.http://www.pdb.org) accession numbers: 9ANT, 2EZD, 1HRY, 1IF1, 1DH3, 1BC8, 2NLL, 1H88, 1PDN, 1SVC, 1SRS, 1MDY, 1AN2. The HNF3_Mod structure was provided by Kirk L. Clark and Stephen K. Burley .The structures we used in


Finally, we extensively discuss how module finding methods and ab initio motif finding methods can be extended to take phylogenetic relations between the input sequences into account, i.e. we show how motif finding and phylogenetic footprinting can be integrated in a rigorous probabilistic framework. The article is intended for readers with a solid background in applied mathematics, and preferably with some knowledge of general Bayesian probabilistic methods. The main purpose of the article is to elucidate that all these methods are not a disconnected set of individual algorithmic recipes, but that they are just different facets of a single integrated probabilistic theory.Over the last two decades a large number of algorithms has been developed for regulatory motif finding. Here we show how many of these algorithms, especially those that model binding specificities of regulatory factors with position specific weight matrices (WMs), naturally arise within a general Bayesian probabilistic framework. We discuss how WMs are constructed from sets of regulatory sites, how sites for a given WM can be discovered by scanning of large sequences, how to cluster WMs, and more generally how to cluster large sets of sites from different WMs into clusters. We discuss how 'regulatory modules', clusters of sites for subsets of WMs, can be found in large intergenic sequences, and we discuss different methods for  For any length-l sequence s there will be a well-defined  binding free-energy E(s) to the regulatory factor. A key assumption            . Unfortunately, there is no simple way of determining a reasonable distribution P(σ) and the sum would generally involve a large number of terms. This author is not aware of any algorithm that currently implements this general scheme.Let gorithms ,50,51 inσ* is chosen that best fits the alignment and the sequences in it. Note first that, since WMs have a fixed width, a site in the reference species can only occur in another species if the corresponding segment in that species is gaplessly aligned with the site in the reference species. Therefore, we first check which of the other sequences in Si,l]    [we find which other sequences are ungapped at the segment and choose which of these are evolving according to the WM based on the probabilities of the individual sequence segments under the WM. The generalization of equation (20) is then simplyInstead of looking at one sequence segment at a time, we can of course also use this formalism to calculate sums of the probabilities of all possible binding site configurations as in section "Finding WM matches". Instead of calculating the probability n here always refers to the nth base in the reference sequence.Note that position Finally, using this formalism we can of course also search for regulatory modules in multiple alignments in complete analogy with the equations in section "Finding clusters of binding sites: regulatory modules".Drosophila it was shown in [This procedure has been implemented for two-species alignments in the Stubb algorithm . Applyinshown in  that usiP(D|w) of the data given a WM w using expectation maximization, and one using Markov chain Monte-Carlo sampling to find the site configuration c that maximizes the posterior P(c|D). These methods can also be extended in a straightforward way to multiple alignments and we now discuss these in turn.In section "Motif finding" we discussed two approaches to motif finding, one based on maximizing the probability P(D|w) of the alignment given the WM w. The evolutionary model that is used by PhyME to score ungapped alignment blocks P is precisely the simplified model of equation (76). However, like MONKEY and in contrast to MotEvo, PhyME assumes that either all branches in the tree evolved according to the WM model, or that all evolved according to background.The PhyME algorithm implements an extension of the MEME algorithm to multiple alignments of orthologous intergenic sequences from related species. It uses a reference species and considers all configurations of binding sites that can be assigned to the reference species in the same way as discussed in the previous section, i.e. it uses equation (81) to calculate the overall likelihood P(D|w) with respect to the WM PhyMe needs to solve, for each column k in the WM, the equationsTo maximize P(s|w) with respect to the WM components dP/dP itself. Here it becomes particularly advantageous that in the simplified model (76) the probability Pαβ is such a simple function of the WM components. We do not discuss the mathematical details of solving (82) here except for mentioning the fact that it involves an iterative procedure similar to EM that leads to a local optimum in P(D|w).Note that for the single sequence case, the derivative of P(D|w) conditioned on the WM, we condition on a particular binding site configuration c and calculate the probability P(D|c) by integrating over all possible WMs w.We now discuss extending the motif sampling approach of section "Motif sampling" to alignments of phylogenetically related sequences. Remember that in the motif sampling approach, instead of summing over all possible binding site configurations to calculate the probability c of binding sites that can be assigned to the input data D, and calculate the probability of the data P(D|c) for each possible configuration. Whereas for single sequences the space of all possible configurations existed simply of all ways in which sets of non-overlapping windows can be assigned to the sequences, i.e. see Fig. Instead of a set of single sequences the input will now generally consist of a set of multiple alignments of orthologous non-coding sequences or a combination of multiple alignments and single sequences. As in section "Motif sampling" we want to consider all possible configurations s is given for each multiple alignment and that the set of binding ste configurations for the alignment is simply the set of all binding site configurations for the reference species. In the PhyloGibbs algorithm [Above we assumed that a reference sequence lgorithm  there isP(D|c) for every possible such configuration c. This probability P(D|c) is given by an equation essentially identical to equation (61). However, instead of single background bases σ with probability bσ we will now have alignment columns S with probability P as calculated in section "Probability of an orthologous set of bases". The set of sequences Sw assigned to a WM w will now generally consist of several ungapped segments from the multiple alignments, i.e. alignment blocks, and possibly some single sequences as well, see Fig. P(Sw) will again be an integral over all possible WMs but the integrand in this case will be considerably more complicated. For simplicity let's focus on a single column from the set Sw of sequence segments and alignment blocks. For simplicity assume that this column from Sw contains two independent columns S, and P(Sw) would then be formally given byNext we need to calculate T is the phylogenetic tree of alignment column S, P and P(w)  are given as in equations (78) and (79). To calculate the integral notice that, formally, the expression P is a polynomial in the WM components of the following formwhere ck depend on the branch lengths in the tree and the P(w) can of course also be written in this form. Denote its prefactors where the prefactors Note that each monomial term of the form P(Sw) in this way. However, the number of terms in the above sum grows exponentially both with the number of sequences in each alignment and, more importantly, with the number of alignments under the integral. That is, if the configuration c contains 10 multiple alignment segments for WM w, then even if there were only 10 terms for each alignment column P, there would still be 1010 terms in total. In practice we thus have to resort to approximations of the above integral. The approach that is taken in the PhyloGibbs algorithm is to approximate the expression P with a monomial for each alignment column, i.e.So in principle we can analytically determine the value of the integral xα may be non-integer. The prefactor c and the exponents xα are set such that the first moments of the approximation match those of P. That is, we demand thatwhere the andβ. As shown in [c and the relative sizes of the xα but leaves ∑α xα still free. The absolute magnitude of the xα we set so as to approximate the second moments, i.e. such thatfor all shown in  this fixβ and γ. With these approximations the integral for P(Sw) becomes simplyfor all combinations of x = ∑α xα and the variables with a tilde are those of the approximation to P(w). The crucial point of this approximation procedure is that, at the start of the algorithm, we can determine these approximations, i.e. the values of the xα, for every multiple alignment column S that occurs in the input data once and store the results. We thus replace the complex expression P with the simple expression S. After that, when we are sampling different configurations, the expression P(Sw) can be as efficiently calculated as for single sequences. That is, we can simply use equation (62), where Sw) is now the sum over the xα of all the alignment segments that occur in Sw.where P(c) PhyloGibbs uses the same priors (60) as for configurations over single sequences. PhyloGibbs uses Markov chain Monte-Carlo sampling to sample the space of all binding site configurations. The move-set employed when sampling binding site configurations in multiple alignments is essentially the same as the move-set for binding site configurations in single sequences illustrated in Fig. c* that maximizes the posterior probability P(c|D). Finally, a further sampling run is used to calculate the posterior probabilities of the sites in configuration c*. PhyloGibbs reports both the configuration c* and the inferred WMs of the motifs in c*, as well as posterior probabilities for all sites occurring in c*. In [For the prior over configurations n c*. In  we demonn c*. In . These tad hoc algorithms that use comparative genomic information in various ways in motif finding. This includes for example methods that simply identify significantly conserved sequence segments in multiple alignments, [l segments that occur in all orthologous sequences, such that the minimal number of mutations necessary to relate the length-l segments, i.e. the parsimony score, is under some prespecified cut-off. Another approach is to first search for significantly conserved segments in orthologous intergenic regions, and to then multiply align conserved segments from the upstream regions of co-regulated genes. This approach is taken by the PhyloCon algorithm [Finally, it is important to distinguish the motif finding methods that rigorously incorporate phylogeny by probabilistically modeling the evolution of binding sites, such as the PhyME and PhyloGibbs algorithms just discussed, from more gnments, -32. Thesgnments, ,53, orthgnments, ,55 one olgorithm  which, iThe biggest challenge for incorporating comparative genomic information in motif finding that is currently outstanding is the treatment of the multiple alignment. It is clear that errors in the multiple alignment can have very deleterious effects on the performance of algorithms such as PhyME, PhyloGibbs, and MotEvo. Ideally one would simultaneously search the space of all multiple alignments and all binding site configurations. However, this space is very large and it is currently unclear if and how it can be effectively searched, especially for large data-sets.