Many Bioinformatics studies begin with a multiple sequence alignment as the foundation for their research. This is because multiple sequence alignment can be a useful technique for studying molecular evolution and analyzing sequence structure relationships.In this paper, we have proposed a Vertical Decomposition with Genetic Algorithm (VDGA) for Multiple Sequence Alignment (MSA). In VDGA, we divide the sequences vertically into two or more subsequences, and then solve them individually using a guide tree approach. Finally, we combine all the subsequences to generate a new multiple sequence alignment. This technique is applied on the solutions of the initial generation and of each child generation within VDGA. We have used two mechanisms to generate an initial population in this research: the first mechanism is to generate guide trees with randomly selected sequences and the second is shuffling the sequences inside such trees. Two different genetic operators have been implemented with VDGA. To test the performance of our algorithm, we have compared it with existing well-known methods, namely PRRP, CLUSTALX, DIALIGN, HMMT, SB_PIMA, ML_PIMA, MULTALIGN, and PILEUP8, and also other methods, based on Genetic Algorithms (GA), such as SAGA, MSA-GA and RBT-GA, by solving a number of benchmark datasets from BAliBase 2.0.The experimental results showed that the VDGA with three vertical divisions was the most successful variant for most of the test cases in comparison to other divisions considered with VDGA. The experimental results also confirmed that VDGA outperformed the other methods considered in this research. Multiple Sequence Alignment (MSA), the simultaneous alignment among three or more nucleotide or amino acid sequences, is one of the most essential tools in molecular biology. The goal of multiple sequence alignment is to align sequences according to their evolutionary relationships. For small lengths and small numbers of sequences, it is possible to create the alignment manually. However, efficient algorithms are essential for good alignments with more than eight sequences . The exiThe Dynamic Programming (exact method) approach  is good The progressive alignment algorithm , proposed by Feng and Doolittle  iterativThe iterative approach starts with an initial solution and then the current solution is improved using iterative steps. MUSCLE  is basedThere are some iterative and stochastic approaches for MSAs  based methods, such as SAGA , MSA-EC et al.,  proposedet al., , combineet al.,  from twoet al.,  dataset.et al., ,38. RBT et al.,  solved 3et al., -43 to enThe EAs have an important advantage over progressive methods in that the alignment component can be made independent of the objective function. This means that different fitness functions can be tested without making any adjustment to the alignment procedure, which makes them particularly attractive for testing new objective functions. Another useful advantage of these methods is that the computational duration can be compressed by parallelization. These advantages motivate us to apply EAs to solve MSA problems in this research. In this paper, we propose a new approach based on a genetic algorithm, namely VDGA, where we introduce a decomposition method to divide the sequences into smaller subsequences. These subsequences are then processed separately before being combined back into whole sequences. We have used the guide tree method to generate an initial population, in each separate part of the decomposition, and also during the mutation. The proposed method starts with the DP distance table. In the DP distance table, the distance between two sequences is calculated from a pairwise alignment using Dynamic Programming (DP). We have used this distance table to generate a guide tree. We have applied and analyzed two techniques on the guide tree so as to generate an initial population. In running the GA, we have considered the Weighted Sum of Pair score as the fitness measure, with the PAM250  score maThe performance of the proposed algorithm has been compared with the state of the art GA and non-GA based methods, namely SAGA, MSA-GA, RBT-GA, PRRP, CLUSTALX, Clustal W, DIALIGN, HMMT, SB_PIMA, ML_PIMA, MULTALIGN and PILEUP8. To allow us to compare with other methods, we have calculated the corresponding BAliscore of the best WSPM score. For comparison, the results of the 26 datasets solved by MSA-GA, and the alignment results of the 34 datasets solved by RBT-GA were taken from the published papers  respectiThis paper is organized as follows. After this background, the next section describes briefly the steps of a basic Genetic Algorithm and the details of the proposed VDGA method. The analyses of VDGA and comparisons with other well known methods have been discussed in the results and discussion section. Finally, we have summarised our work and planed for future work in the conclusions section.The general steps of the common GA can be summarized by the following pseudo-code:1. Initialisation: Generate Initial population2. Evaluation: Evaluate the individuals using a fitness function3. Select individuals (parents) and then4. Apply the genetic operators to them so as to create children5. New generation: Create new generation from some combination of old generation and new child generations..6. Go to 2 until it meets the stopping criteria7. End.The proposed Vertical Decomposition using Genetic Algorithm (VDGA) is a modification of the basic GA. Its steps are: generation of initial population, generation of child population by applying genetic operators, forming a new population for the next generation, Vertical Division, and the stopping criteria. The Vertical Division is the key concept of the proposed algorithm. This technique is applied after generating the first/initial generation and after generating child generation. To do this, inside the Vertical Division step, the alignment is separated into different parts, the null symbols are removed from each part and then the tree-base method is applied on each part. After applying the tree-base method, each part produces an alignment. The alignments of each part are then combined to create a new alignment. As the solution of the progressive alignment method (guide tree) usually converges to a local optimum, therefore in the initial generation stage, we use the guide tree method to find the local optima and its neighbouring points in two ways; randomly generated subtree and shuffling. With the genetic operator (mutation), we also use the guide tree method. To calculate the guide tree, we use both DP  and the For this, the DP distance of each pair is calculated using equation (1) from a pairwise alignment . To consS is computed by dividing the match score by the number of positions scored. Gap positions are ignored, and only exact matches contribute to the match score [Equation (2) is an alternate means to calculate the distance, and was developed based on the relationship between the observed amino acid substitutions and the actual (corrected) substitutions from PAM or BLOSUM . The match score .The flowchart of the proposed VDGA method is shown in Figure The aim of this step is to generate good initial solutions. The flowchart for generating the initial population is shown in Figure VDGA starts with a DP distance table. The guide tree is constructed from this table, which is referred to as TR1, and we generate a multiple sequence alignment (MSA1) from this guide tree.In the second stage, the distance table is calculated from the multiple sequence alignment (MSA1), which is called the Kimura distance table. The Kimura distances are calculated from the aligned sequences. The second tree, TR2, is constructed from the Kimura distance table, and we then produce MSA2 as shown in Figure In this stage, two mechanisms are implemented on the two trees (TR1 and TR2) to generate 100 different trees. The first mechanism is to generate guide trees with randomly selected sequences and the second is shuffling the sequences inside those trees. The initial population produced by this method contains a set of multiple sequence alignments. Therefore, after receiving the set of guide trees, it needs to make a set of multiple sequence alignments. The functions of these mechanisms are explained below.In this case, sequence numbers are selected randomly from one tree (either TR1 or TR2). The selected sequences then make a new sub-tree with the same branching orders as the original one, and the non-selected sequences make another new sub-tree. Lastly, these two sub-trees are connected together to make a new tree. Figure In this case, two sequence numbers are selected randomly from one tree (either TR1 or TR2). Then, these two sequences exchange their positions to make a new tree. Figure The Weighted Sum of Pair Method (WSPM) is commonly used as a fitness measure for MSAs. For it, each column in an alignment is scored by summing the product of the scores of each pair of symbols and their pair weight. The score of the entire alignment is then summed over all column scores by using equations (3) and (4).S is the cost of the multiple alignments. L is the length (columns) of the alignment; Sl is the cost of the l-th column of L length. N is the number of sequences, and Wij is the weight of sequence i and j. In CLUSTAL W, the weight is calculated for each sequence and the pair weight is the product of the two sequence weights. cost is the alignment score between the two aligned sequences Ai and Aj. When Ai ≠ '-' and Aj ≠ '-' then cost is determined either from the PAM (Percentage of Acceptable point Mutations) or BLOSUM [Ai = '-' and Aj = '-' then cost = 0. Finally, the cost function cost includes the sum of the substitution costs of the insertion/deletions when Ai ≠ '-' and Aj = '-' or Ai = '-' and Aj ≠ '-', using a model with affine gap penalties as shown in (4).Here, r BLOSUM  matrix. G is the gap penalty, g is the cost of opening a gap, x is the cost of extending the gap by one and n is the length of the gap.Here, In CLUSTAL W, the author used different weight matrices, which depend on the estimated divergence of the sequences to be aligned at each stage, and proposed dynamically changeable gap penalties to overcome the local minima issue. Therefore, in this research, the CLUSTAL W weighted scheme, the CLUSTAL W default gap penalties , and the PAM250 matrix, a mutation probability matrix, were considered for the WSPM fitness measure. Note that PAM250 is considered to be a good general matrix for protein database searching. Also, the PAM matrices have been developed based on global alignments. To calculate the weight of each sequence, we used the CLUSTAL W weight function.To optimize the VDGA, we have used both the sum of pair and the weighted sum of pair methods for the fitness function in our research. However, we have only reported the weighted sum of pair scores as the algorithm with this method performed better than with the sum of pair fitness function. This is because of the features (such as selection and crossover) and the parameters used in our algorithm.For each individual in the initial population, the WSPM score is calculated, and the individuals are then sorted according to the descending order of their scores. To generate a child population of 100 individuals in any generation, the following three genetic operators are used.I. Single point crossover.II. Multiple point crossovers.III. Mutation.The following sub-section 'Selection of Parameters' considers the relative proportion of when these operators are used.a has the better score column, so that this parent is separated vertically into two pieces. The second parent b is also divided into two pieces in such a way that each row of the first piece  has the same number of elements as the first piece  of the first parent. These pieces of these two parents are then exchanged and merged together to generate two new individuals as shown in Figure In this crossover, one individual is selected from the top 50% and another from the bottom 50% of the parent generation. The single point crossover  is impleThe parents' selection process is the same as for the single point crossover. For multiple point crossovers, each parent is divided into three pieces. These pieces are then exchanged between the parents and are then merged together to generate two new individuals. However, only the best one will be taken as a child. The crossover is implemented in two steps as described below.To cut the first piece effectively, we compare the scores of the first 25% of columns for both parents. The parent having the better score is then divided vertically at that column. The other parent is also divided using the mechanism that was introduced in the single point crossover, as can be seen in Figure We now have two pieces of each parent from Step 1. To create another piece, we follow the same procedure of Step 1, but considering the last 25% of columns  are 10 and 12 respectively. The first 25% of the columns of the 1st parent are two and a half (2.5) columns. In that case, we considered 3 columns. In the first step, parent a has the better score in the first 25% columns. Therefore, Parent a is divided first and Parent b is tailored according to Parent a. After the division, we have two pieces from each parent . In the 2nd step, Parent b has the better score in the last 25% of columns. Therefore, Parent b is divided first and Parent a is tailored accordingly. This division provides two new pieces for each parent . Next, two new individuals are generated by connecting the pieces as (a1+b2'+a3) and (b1+a2'+b3). From these two individuals, the better one is selected as a child.In Figure One individual (MSA) is randomly selected from the whole population. From this MSA, the distance among sequences are calculated and stored in a distance table. The new guide tree is constructed from this calculated distance. In the new guide tree, the sequence numbers are shuffled to find a better guide tree and the MSA of the new guide tree is considered as a mutated child. This process is repeated until 50 sequential unsuccessful attempts occur. If this operator finds a better guide tree then it is considered as a new child, otherwise there is no effect on this generation. The procedure of mutation is shown in Figure This common GA approach is used, whereby the best solution is passed on unchanged to the next generation.For Vertical Division, we first separated (decomposed) each alignment vertically into two or more sub-alignments as shown in Figure Figure The Vertical Division step is applied in two places inside the proposed algorithm: once after the initial generation, and then after each child generation. We do this so we can apply the Vertical Division technique on aligned sequences. This is due to the fact that if the sequences are of different lengths, the Vertical decomposition of unaligned sequences may introduce either too many or too few residues in each decomposed part. Therefore, it could be difficult for the Vertical decomposition of an unaligned sequence to produce a good solution.It is known that smaller sequences can be aligned quickly with a high level of accuracy . This moTo form the new population, the best 50% of the combined parents and children are selected while ensuring that there is no duplication of the individuals. We must mention here that we have also studied other splits, such as 40-60 (parent-child) and 60-40. The study results showed that the 50-50 split outperforms the 40-60 and 60-40 splits with an average improvement of 4.38% and 7.66% respectively. Therefore, we have chosen the 50-50 mix with the proposed VDGA, which ensures a better balance between exploration and exploitation. The population size of 100 is chosen as it was used in SAGA . MoreoveThe best solution in each generation is recorded. If the best solution remains the same in 100 consecutive generations, the algorithm will be terminated. We have set this termination condition based on our experimental observations. We have tested our VDGA algorithm for up to 300 generations after getting the best solution, and we have observed that the best solution was hardly changed and that the variation of the average solution per generation was also insignificant.In order to evaluate our proposed approach, we have solved a good number of test datasets from the benchmark BAliBase alignment database. The original BAliBase version 1.0  consistsIn this section, we have first analyzed the performance of the vertical decompositions with both the guide tree and the genetic algorithm. From that, we have proposed the appropriate number of decompositions with the proposed GA method. Finally, we have compared our algorithm (VDGA) with other well-known methods. In this research, we have analyzed our results based on 10 independent runs. In comparison, MSA-GA and RBT-GA used 5 and 10 runs respectively.Initially, multiple sequence alignments were done without a GA but solely by the application of the guide tree method followed by the results of that being decomposed vertically into two, three and four parts, namely Decomp_2, Decomp_3 and Decomp_4 respectively with the null symbols ("-") being removed from each part. Then we again applied the guide tree methods in each part of the decomposition. These alignments were evaluated by WSPM and their corresponding BAliscore were also calculated. Both of these scores are reported in Table Comparing with the WSPM solutions of the guide tree, it is observed from Table On the other hand, comparing with the corresponding BAliscore solutions of the guide tree, Decomp_2 was better in 23 test cases and found the same best results in 5 test cases, Decomp_3 was better in 29 test cases and found the same bestn results in one test case, Decomp_4 was also better in 29 test cases and in three test cases it found the same best results out of 34 test cases. The non-parametric test also shows the significant advantage of these vertical decompositions with guide tree.From the experimental observation it is clear that the multiple sequence alignments using vertical decompositions perform better than that of the guide tree method in most of the test cases. In a very few cases, these techniques perform badly, or the same as, the guide tree. Although in general Decomp_3 performed best, sometimes the other decompositions performed better in some cases. After these experimental and statistical analyses with respect to the objective function and benchmark scores, we can safely conclude that the vertical decompositions can play an important role in improving existing solutions, and there is a possibility to find a better multiple sequence alignment if the vertical decompositions are used with an evolutionary approach .In this section, we have first analyzed the selection of parameters for VDGA and then discussed the appropriate number of decompositions. In some of the following analysis, the decomposition was kept inactive to judge the parameter's effect individually.rd mix) achieved an average improvement of 4.66% over the first mix, 0.421% over the second mix, 1.02% over the fourth mix and 4.93% over the fifth mix. From the experimental performance, we have decided to use 50% probabilities of crossover and mutation with VDGA. For the 50% crossovers, single point crossover is selected for half of them and double point crossover is used for the other half. These selections were also decided based on experimental analysis.In the proposed VDGA algorithm, we have used two basic search operators: crossover and mutation. In order to determine the probabilities of crossover and mutation, we have excluded the decompositions from GA and have carried out five different experiments , using ten randomly selected BaliBase datasets (version 2.0) . Our GA To form the child population from the parent population, we have divided the population into two groups based on their fitness values. Then one individual is selected from the top 50% and another from the bottom 50% for crossover. However, the new population is formed by taking the best individuals from the combined previous parents and children.We have chosen the population size of 100 as used in SAGA . Howeverrandomly generated initial population , and the second set used a hill climbing approach (for searching instead of our GA) starting from the improved initial population. WSPM was used as the fitness measure. Based on the corresponding BAliscore of the best found WSPM solution, the full algorithm achieved an average improvement of 8.43% compared to the same with the randomly generated initial population and 12.79% compared to the hill climbing approach. The first set of experiments thus proved the superiority of our proposed initial population, and the second set demonstrated the strength of our proposed genetic search operators.The proposed genetic algorithm, VDGA, uses an improved initial population and new genetic operators that contribute to it performing better than other algorithms. To analyze the effect of these two components on the algorithm's performance, we have excluded the decomposition part from our algorithm and tested two sets of new experiments. In the first set, GA was run with a To determine the appropriate stage for using decomposition inside VDGA, we have carried out experiments on eight datasets from BAliBase. We have tested our algorithm using decompositions in three cases. In the first case, the decompositions were used only after the initial generation, in the second case only after each child generation and finally after all generations. For Decomp_2, the VDGA with the third case improved the average solution by 1.74% better than the first case and 0.6% better than the second case. For Decomp_3, the VDGA with the third case improved the average solution of 2.91% compared to the first case and 0.87% compared to the second case. Moreover, Decomp_4 with the third case improved the average solution by 3.08% more than the first case but the second case performed better than the third case. Although VDGA with the third case for decomposition 4, did not perform better than with the second case, with other decompositions (Decomp_2 and Decomp_3) VDGA achieved much better average performance when the decompositions were used after all  generations, in comparison to the first and second cases. From these experimental observations, we have decided to use the decomposition technique after all generations.In order to judge the performance of the Vertical Division with GA, we have also performed experiments for 34 datasets from BAliBase 2.0, where we have considered the GA and also the VDGA  algorithms. The algorithms were each executed for 10 independent runs. For each dataset, the best and average WSPM scores out of the 10 runs were recorded, and the corresponding BAliscore of the best found WSPM solution was also calculated. The best and average WSPM scores and the corresponding BAliscore are reported in Table Z value (-3.189) and the significant test result (P = 0.001 < = 0.05) in Table Comparing with GA in terms of the best WSPM score, VDGA with Decomp_2 was better in 27, and worse in 7 test cases as shown in Table When considering the average WSPM score, the VDGA with all three decompositions  are significantly better than GA. In doing so VDGA with Decomp_2 was better in 22 test cases, Decomp_3 was better in 32 and Decomp_4 was in 24. In this comparison, VDGA with Decomp_3 successfully found better solutions in a maximum number of test cases in comparison to the other two decompositions. The statistical test results in Table Also comparing with the corresponding BAliscore of the best finding WSPM solution, VDGA with Decomp_2 was better in 22 test cases, Decomp_3 was in 24 and Decom_4 was in 23. The significance test in Table From the above experimental results and their statistical analyses, it is clear that VDGA with Decomp_3 found better solutions in more test cases than the other two decompositions and GA, and it is significantly better than GA and VDGA with the other two decompositions with respect to the best and average WSPM score and the corresponding BAliscore. As we have considered test sequences with length of up to 1000 in this research, we considered that the appropriate number of divisions for VDGA is 3 (Decomp_3) for sequences up to 1000 length. Further experiments would be required to determine the best setting for longer sequences.The computational time required for finding good multiple sequence alignments is dependent on the sequence length, the number of sequences, and the similarities of the sequences. In addition, the choice of algorithmic parameters also plays an important role. We have tried to develop a relationship between the computational time required  and the sequence length and sequence numbers. However, it is hard to make any firm conclusion based on linear/nonlinear regression analysis.To show the convergence behavior of our algorithm (VDGA with Decomp_3), we have plotted the best and the average WSPM scores against the number of generations. As examples, three such plots (for one specific run) for three datasets from reference 3 are presented in Figure To judge the quality of the solutions produced by our algorithm, we have considered only those benchmark datasets and algorithms that were considered in the papers reporting MSA-GA and RBT-GA, and that used BAliscore (an open source program of the BAliBase benchmark) to measure the accuracy of the solutions. The authors of MSA-GA considered the best solution of five runs for each dataset and reported the BAliscore. Moreover, the authors of RBT-GA also reported the best solution of ten runs with BAliscore. In our algorithm, we considered ten independent runs of each dataset and have used the corresponding BAliscore of the best found WSPM solution. BAliscore scores a solution  between 0.0 and 1.0. If the solution is identical with the corresponding manually created reference alignment then the score is 1.0. If nothing matches with the reference alignment then the score is 0.0. However, if some parts match with the reference alignment, then the score is in between 0.0 and 1.0.In MSA-GA, the authors considered 28 test datasets from references 1 to 5 and reference 8. Among them, 18 datasets were from reference 1 and two were from each of the other reference datasets. However, currently BAliscore does not work for reference set 8. This is because of insufficient information supplied either by the reference alignment file or by the annotation file. Therefore, we excluded the two datasets of reference 8, thus leaving 26 for comparison. In RBT-GA, the author considered all 23 test datasets of reference 2, and 11 out of 12 from reference 3. In total, we considered 56 test datasets, including 18 from reference 1, 23  from reference 2, 11 from reference 3, and 2 from each of references 4 and 5. All these datasets belong to the BAliBase 2.0 benchmark datasets.For each of the 56 datasets, we have executed our algorithm for 10 independent runs and recorded the best, worst, and average WSPM scores with standard deviation, and the corresponding BAliscore of the best WSPM score in Table For comparisons with other methods, we have taken from the published literature -36,51 thTo compare with the other methods, we have considered all three decompositions  with VDGA. The authors of MSA-GA  selectedIn Table Based on the average scores reported in the bottom row in Table We have also compared our results with RBT-GA. We have considered all of the 34 datasets and their approximate results as reported in the RBT-GA paper . The sumThe 23 datasets in this reference are significantly different in lengths and numbers of their sequences. They also contain what is called "orphan sequences". VDGA performed differently with different datasets. To judge the performance of VDGA with respect to BAliscore, we have compared with SAGA, RBT-GA, PRRP, CLUSTALX, DIALIGN, HMMT, SB_PIMA, ML_PIMA, MULTALIGN and PILEUP8. Table The average scores are also shown in Table Reference 3 contains sub-groups of sequences where the residue identities between groups are less than 25%. In this paper, we considered 11 test cases out of 12, and the experimental results that are presented in Table The overall performance of all the methods for this reference is presented in Figure t test, such as that the population should be normally distributed. The results based on the best found solutions of VDGA are presented in Table + or W-) is the sum of ranks based on the absolute value of the difference between two test variables. The sign of the difference between two independent samples is used to classify cases into one of two samples: differences below zero (negative rank W- ), or above zero (positive rank W+ ). As a null hypothesis, it is assumed that there is no significant difference between two samples. The alternative hypothesis is that there is a significant difference in the fitness values of the two samples. Hence, if the hypothesis test rejects the null hypothesis, then there is a significant difference, otherwise there is no significant difference. The number of test problems is N = 26 and 34 for MSA-GA and RBT-GA respectively, and we have used the 5% significance level. Based on the test results/rankings, we assigned two words ('yes' for P < = 0.05 or 'no' for P > 0.05 ) for the comparison of any two algorithms (as shown in the fifth column), where 'yes' means that the VDGA algorithm (with Decomp_3) is significantly different and better than the second, 'no' means that this is worse and there is no significant difference between the two algorithms, and 'same' means there is no significant difference and VDGA performed the same as the second. We tested for significant with the BAliscore corresponding to the best found WSPM scores produced by VDGA, in comparison to the published BAliscore results of the other methods.To study the difference between any two stochastic algorithms in a more meaningful way, we have performed statistical significant testing. We have chosen a non-parametric test, Wilcoxon Signed Rank test , as it aIn this comparison, we have considered only Decomp_3 with VDGA, as we have found from the preceding experiments that Decomp_3 is the best for VDGA. Therefore, to test the significance we have considered only VDGA_Decomp_3. In Table In this paper, a new GA based algorithm with Vertical Decomposition (VDGA) has been proposed to solve multiple sequence alignment problems. This approach works with the solution of a guide tree. To generate an initial population, two mechanisms are used. To assess the performance of the algorithm, a number of experiments were carried out for deciding the initial population, the genetic operator, an appropriate set of parameters for GA and of the suitable number of decompositions.An initial experiment was run to determine the parameters, and from the experimental results, the probability of crossover and mutation was set to 50%-50%. A simple hill climbing method with the standard VDGA initial population was performed to verify the performance of the genetic operators. Moreover, the VDGA method was also run with a randomly generated initial population to judge the performance of the initial generation. To test the performance of the decomposition, this technique was applied on the solution of the guide tree as well as inside the GA. The experimental results showed that the decomposition technique can successfully find better multiple sequence alignments, and also that the optimum number of decompositions for VDGA is 3 (i.e. Decomp_3).To evaluate our proposed approach, we considered a good number of benchmark datasets from BAliBase 2.0, so as to cover all the test sets of MSA-GA and RBT-GA. The proposed method was optimized based on the Weighted Sum of Pair score. Therefore, the BAliscore corresponds to the best WSPM score. This was used to compare with other methods, as the BAliscore is widely used as the measure of quality/accuracy of multiple sequence alignments. The experimental results showed that VDGA performed better for most of the test cases. Although the solution of VDGA was not the best for some test cases, it was close to the best for those cases. The overall behavior of our proposed method outperformed all of the other methods considered in this paper. VDGA performed better than the others mainly because of our proposed initial generation, the genetic operators, the operators setting, and most importantly its decomposition technique.After statistical and experimental analysis, we can safely conclude that the proposed method, VDGA with Decomp_3, can be considered as an effective method for solving multiple sequence alignment problems.Future studies intend to extend the experiments and to find a more efficient way for decomposition of longer and many sequences. We also want to optimize VDGA with different scoring schemes, such as the recent Log Expectation scoring function , as wellFN was responsible for conception, design, implementation, testing and drafting of the VDGA. RS and DE were responsible for revising this proposed concept critically and hence for important intellectual content. All authors have read and approved the final manuscript. The first author contributed 50 percent of this work. The other authors contributed 25 percent each.


BackgroundMost statistical methods for phylogenetic estimation in use today treat a gap  within the input sequence alignment as missing data. However, the statistical properties of this treatment of indels have not been fully investigated.ResultsWe prove that maximum likelihood phylogeny estimation, treating indels as missing data, can be statistically inconsistent for a general (and rather simple) model of sequence evolution, even when given the true alignment. Therefore, accurate phylogeny estimation cannot be guaranteed for maximum likelihood analyses, even given arbitrarily long sequences, when indels are present and treated as missing data.ConclusionsOur result shows that the standard statistical techniques used to estimate phylogenies from sequence alignments may have unfavorable statistical properties, even when the sequence alignment is accurate and the assumed substitution model matches the generation model. This suggests that the recent research focus on developing statistical methods that treat indel events properly is an important direction for phylogeny estimation. Theoretically, we now know a great deal about phylogenetic estimation.  We know, for example, that when sequences evolve with only substitutions (but no indels) under models such as the General Time Reversible (GTR) model, then accurate estimation of trees (with high probability) is guaranteed, provided that appropriate methods (such as maximum likelihood) are used and the sequences are “long enough” However, sequence evolution includes indels, and so typically a phylogenetic analysis begins with a set of sequences of different lengths.  A phylogenetic analysis of such a dataset, therefore, must either first align these sequences before applying a phylogenetic estimation method or it must co-estimate the alignment and tree at the same time.  In this paper, we discuss theoretical and empirical aspects of phylogeny estimation in the presence of indels, focusing on two-phase methods using maximum likelihood (henceforth referred to as "ML").  We include, for completeness sake, a discussion of co-estimation methods. Methods that estimate trees and alignments from unaligned sequences  have also been developed, including POY Despite the progress in co-estimation methods, most phylogenies are estimated in two phases: first an alignment is estimated, and then a tree is computed on the alignment. Once the sequences are aligned, a decision must be made about how to  treat the gaps in the alignment. In current practice, the following are the dominant gap-treatments:    • Remove all sites in which any gap appears, thus reducing to a gap-free alignment with fewer sites,     • Assign an additional “fictitious” state for each gap,     • Code all the gaps in the alignment, and treat the presence/absence of gaps as a binary character , and    • Treat the gaps as missing data. In parsimony analyses, this is often treated by finding the best nucleotide to replace the gap, but in likelihood-based analyses, this is often treated by summing the likelihood over all possible nucleotides for each gap.The first option of removing all sites with gaps has the advantage of being statistically consistent for models in which the substitution process and the mechanism producing  insertions and deletions are independent, but it has the disadvantage of removing data – and could result in sequence alignments that have so few sites as to be phylogenetically  uninformative. Indeed, while this may not happen on small datasets, on large nucleotide datasets, this could lead to empty alignments.The second option of assigning an additional state for each gap presents other challenges. By definition, the true alignment represents positional homology, and hence two positions that have a nucleotide in a site constrain all nodes on the evolutionary path between them to also have a nucleotide in that position. In other words, ensuring that the model makes phylogenetic sense is rather complicated. Therefore, the substitution process must be extended carefully to handle an additional fictitious state properly. Finally, when the indel process can insert and delete several nucleotides at a time, the sites within the alignment no longer evolve independently, making this treatment invalid. The third option, of coding each gap  in the alignment, includes a collection of techniques, ranging  from extremely simple (create a single binary presence/absence character for each position that contains any gap) to very complex techniques. Software to automatically produce these additional binary characters encoding the gaps in a given alignment includes GapCoder We begin with the Jukes-Cantor (JC) model of DNA sequence evolution JC  := supθ P). That is, MLJC is the supremum of all likelihood scores obtained for JC model trees with the same fixed tree topology T . Although the likelihood is continuous, the supremum may not actually be achieved for some θ because the range of values allowed for this parameter is not a closed set; that is, the supremum may be approached by parameter values θ for which some of the p(e) are arbitrarily close to the boundary values 0 or 3/4. Finally, we can talk about the JC ML tree for a fixed gap-free alignment A, as the tree T such that the likelihood MLJC is maximized over all trees.Letting the tree topology T and alignment A be fixed, we define MLMaximum likelihood (ML) inference of the parameter T under the JC model is defined as follows:    • Input: sequence alignment A containing no gapsJC is maximized    • Output: all model trees T such that MLAlgorithmically, ML phylogeny estimation typically operates by searching through the space of all binary trees, estimating  parameters of the model  on each tree so as to maximize likelihood on that tree, and then returns the tree and its model parameters that return the highest likelihood.  We now discuss ML analysis when the input sequence alignment contains gaps, and gaps are treated as missing data.  The same algorithmic approach is used as when the input alignment does not contain gaps, except that the likelihood calculation must also be able to work with gapped sequences. As discussed above, there are several different ways of treating gaps, but the standard technique treats gaps as missing data.   It is well known that ML is statistically consistent for the GTR model , when the data are generated by the GTR model and the optimization problem is solved exactly. However, we will show that ML, treating gaps as missing data,  can be inconsistent under these conditions, when the input sequence alignments contain gaps. In other words, we will prove that ML can produce the wrong tree, under some conditions on the input sequence alignment.  Let S be a set of DNA sequences in an alignment A. We will say that the alignment A is "monotypic" if for each site in A, there is exactly one nucleotide type . In particular, we do not allow any site to be entirely gapped. For example, the following is a monotypic alignment:    s1 =  A − −    s2 =  − C −    s3 =  A − −    s4 =  − − −    s5 =  − − −    s6 =  − − T    s7=  A − −The following results were established in JC =(1/4)R, where R is the number of sites in the alignment A.Lemma 1. Let A be a monotypic alignment for the set S of sequences, and let T be an arbitrary tree on S. If gaps are treated as missing data, then MLJC  is realized by a sequence of parameter values in which all the p(e) converge to 0). For this setting of the substitution parameters, the probability of the data is just the probability of picking the correct state for that site, which is 1/4 under the JC model. Hence, the ML score of the alignment, given the tree T, is (1/4)R, where R is the number of sites in A.Proof. This result follows from Lemma 1 in Theorem 1. Let A be a monotypic alignment for set S. Then all trees on S are optimal solutions for ML under Jukes-Cantor, if gaps are treated as missing data.Proof. This result follows from Theorem 2 in This theorem indicates a potential problem with treating gaps as missing data. If the mechanism generating the data has a high probability of producing aligned sequences that are monotypic for some parameter values, then it will be difficult to reliably infer the underlying phylogenetic tree if the gaps are treated merely as missing data rather than features of the data  that are informative about the path that evolution has taken. More specifically, for those models of evolution for which monotypic alignments have non-zero probability, ML, treating gaps as missing data, may not be statistically consistent.treating gaps as missing data in a ML analysis is statistically inconsistent.  Theorem 1 shows that treating gaps as missing data has the potential to result in meaningless phylogenetic estimations, even when analyzed under maximum likelihood (ML) for the correct model, since - under an extreme case in which the substitution probabilities are all zero - all trees are equally good solutions to maximum likelihood.  In other words, what this theoretical result shows is that under an extreme condition in which substitution probabilities are zero, not treated as missing data. Therefore, monotypic alignments are not phylogenetically uninformative if the alignments contain indels. This should be contrasted to monotypic alignments without indels: these are phylogenetically uninformative because no changes of any type -- substitution or indel - occur on any branch of the tree.  In other words, the usual way of thinking about sequence evolution in which sites evolve only with substitutions would lead one to think of monotypic alignments as arising only when all branch lengths are zero.  This is not the case when indels as well as substitutions can occur since they each have their own evolutionary parameters, because then evolution can occur with indels but without substitutions, and produce monotypic alignments.  As this discussion shows, such model conditions are still identifiable because of the results from is phylogenetic signal in an alignment that contains gaps even for the case of monotypic alignments, and this signal can be used to estimate the true tree, provided that appropriate methods are used.  The point to be taken is that treating gaps as missing data within a standard ML analysis is not an appropriate method. We now compare this observation from In contrast to this theoretical result, we consider the performance in practice of statistically-based methods such as ML and Bayesian MCMC. Simulation studies when sequences evolve without indels have shown that these statistically-based methods produce highly accurate trees, typically better than trees estimated using maximum parsimony or distance-based methods , and it is certainly possible for other methods to be developed that would be statistically consistent.  The point we make here is only that the standard ML analysis, treating gaps as missing data, does not have that guarantee.The  theorem in this paper holds under the assumption of all substitution probabilities being zero (the case where only indels but no substitutions occur).  Thus, this theoretical result can be criticized as being applicable only to a biologically unrealistic case.   A careful reader could therefore ask "Is maximum likelihood, treating gaps as missing data, provably statistically consistent for model conditions with substitutions and not just indels?" The answer is that there are no published theoretical results establishing statistical consistency for maximum likelihood when gaps are treated as missing data.  However, as was shown in These results add to the growing literature about theoretical guarantees (or lack thereof) in phylogenetic analysis. Unfortunately, what we now know is that theoretical guarantees for phylogeny estimation have only been established for very restrictive conditions: indel-free evolution  with well-behaved site substitution models. This raises the real possibility that the standard likelihood-based methods of analysis . Guarantees of statistical consistency do not necessarily yield good performance in practice, but they can lead to methods with good empirical performance . Therefore, an effort should be made to develop such methods, and to test these methods on both biological and simulated data, in order to evaluate their accuracy under realistic conditions. Until then, phylogenetic analyses can certainly be based upon standard two-phase approaches, but biologists should use these standard methods with caution - realizing that even the best of the current two-phase methods do not have statistical guarantees.The author thanks Steve N. Evans for stimulating and helpful discussions, and the two anonymous referees for their comments.This research was supported by two grants from the NSF (ATOL grant DEB 0733029 The author has declared that no competing interests exist.


The former option is a basic one and applicable only to full-length sequences, whereas the latter option is applicable even when the unaligned sequences are short and fragmentary. These methods internally infer the phylogenetic relationship among the sequences in the existing alignment and the phylogenetic positions of unaligned sequences. Benchmarks based on two independent simulations consistently suggest that the “–addfragments” option outperforms recent methods, PaPaRa and PAGAN, in accuracy for difficult problems and that these three methods appropriately handle easy problems.Two methods to add unaligned sequences into an existing multiple sequence alignment have been implemented as the ‘Availability:http://mafft.cbrc.jp/alignment/software/Contact:katoh@ifrec.osaka-u.ac.jpSupplementary information:Supplementary data are available at Bioinformatics online Recent advances of sequencing technologies produce a large amount of sequence data. A relatively small number of sequences are carefully aligned and annotated in databases, for example, –add and –addfragments, which are different combinations of existing routines in the MAFFT package and a rapid local alignment method, LAST 2 elements, of the sequences in the existing alignment and the new sequences. The distance can be computed by several different methods, including that based on the local pairwise alignment scores by dynamic programming (DP) [indicated as –add (DP) in Tables below] and that based on the number of shared 6mers [indicated as –add (6mer)]. Global alignment can also be selected here, but we did not test this option. In all cases, a similarity score is converted to a distance as in Compute a distance matrix, with (N + n) tips from the distance matrix.Build a guide tree with  as in Compute a distance matrix of the existing alignment consisting of N × n pairwise local alignments between the N sequences in the existing alignment and the n new sequences. Only the best alignment is used per sequence pair. If no alignment is found, the distance is set to 1. By default, the Smith–Waterman algorithm (–addfragments (DP) in Tables below]. It can be replaced by LAST for faster computation [indicated as –addfragments (LAST)] for nucleotide data.Compute lgorithm  is used n new sequences, the same calculation as in the –add option is repeated independently. That is,N + 1 tips, using the distances calculated in steps 1 and 2.Build a guide tree consisting of N + 1 sequences using the guide tree computed at the previous step.Compute a multiple alignment consisting of For each of the n different MSAs, calculated in step 3, into one MSA, inserting gaps as necessary. For each of the n MSAs,If no gap was inserted into the existing alignment in step 3, then no new gap is necessary in this step.If gaps were inserted into the existing alignment to align the new sequence in step 3, then corresponding gaps are inserted in the other new sequences in this step.Combine For handling short unaligned sequences, another option, If different new sequences create gaps in the same position in the existing alignment, then the inserted new sequences are aligned to each other.Each of steps 1–3 runs in parallel, on a multi-core PC.We implemented the aforementioned options in MAFFT version 6.927. To test their performance, we used the same datasets as those used in the PAGAN article , the difference among these three methods was small, but a slight tendency was observed that PAGAN performed better for easy cases and that –addfragments performed better for difficult cases.The N, in the existing alignment is large. Our method computes and stores O(N2) distances, whereas tree information needs only O(N) space. We are planning to try more approximate methods to overcome this limitation in the future. On the other hand, the –addfragments option is scalable to the number of new sequences, n.Our approach differs from PaPaRa and PAGAN, in that it internally infers a tree of the existing alignment and the phylogenetic positions of new sequences in the tree. Thus, it can be applied even when we have no sound phylogenetic information of the existing alignment. This feature can be a disadvantage, when the number of sequences, We had to use simulation because there is no established benchmark dataset based on actual sequences for this purpose. Thus, the assessment here is still insufficient, especially for comparing methods with different scoring systems. We cannot completely exclude the possibility that the observations just reflect the fitness of the parameter set to the simulation setting. However, we can safely compare different MAFFT options that use the same parameter set. They behaved similarly for the two independent datasets, generated by different programs, INDElible and ROSE. Thus, it is unlikely that the results are artificial because of simulation settings. In the future, benchmark datasets of actual sequences should be established for this type of problem.We did not assess the accuracy of phylogenetic placement of the fragmentary sequences. As noted previously, MAFFT does not use a user-defined tree of the existing alignment, unlike PaPaRa and PAGAN. MAFFT calculates the phylogenetic positions of new sequences in an internally constructed tree, instead of a user-defined tree. Thus, it is difficult to make straightforward assessments about the correctness of the phylogenetic position in a given tree. Tests of phylogenetic placement using alignments by different methods, including that described here, are being performed by Tandy Warnow’s group .mafft–addfragments showed high performance for problems that were previously used for assessing this type of method. It can be a basis for extensions in several directions, such as specific support for NGS data, and faster and more scalable calculation.The present results suggest the usefulness of a simple and natural algorithm for adding new sequences into an alignment. The straightforward strategy implemented as


Hepatitis C virus (HCV) is one of the leading causes of viral hepatitis worldwide and its genotype 3a is predominant in vast areas of Pakistan.The present study reports the first full sequence of HCV 3a isolate PK-1 from Pakistan. This nucleotide sequence was compared with six other HCV genotype 3a full length sequences from different regions of the world by using statistical methods of phylogenetic analysis.The nucleotide difference of these seven sequences shows that HCV genotype 3a of phylogenetically distinct origin is circulating in Pakistan. Flaviviridae 7] and JaButt and colleagues  showed tet al [Phylogenetic analysis of the isolate PK-1 and all the full length HCV genotype 3a genomes (n = 7) in the GenBank database (Table et al .The full length genomic sequences of HCV 3a reported from USA, New Zealand, Italy and Australia were clustered together while Pakistani isolate is shown phylogenetically distinct by 500 replicates bootstrap analysis Figure . EstimatThe authors declare that they have no competing interests.MI conceived of the study. IR, SB, SA, HA and AH performed the sequencing studies. MA and IR organized the data and drafted the manuscript. SB, LA and AH helped MA in sequence alignment and evolutionary analysis. All the authors read and approved the final manuscript.


Accurate and efficient structural alignment of non-coding RNAs (ncRNAs) has grasped more and more attentions as recent studies unveiled the significance of ncRNAs in living organisms. While the Sankoff style structural alignment algorithms cannot efficiently serve for multiple sequences, mostly progressive schemes are used to reduce the complexity. However, this idea tends to propagate the early stage errors throughout the entire process, thereby degrading the quality of the final alignment. For multiple protein sequence alignment, we have recently proposed PicXAA which constructs an accurate alignment in a non-progressive fashion.Here, we propose PicXAA-R as an extension to PicXAA for greedy structural alignment of ncRNAs. PicXAA-R efficiently grasps both folding information within each sequence and local similarities between sequences. It uses a set of probabilistic consistency transformations to improve the posterior base-pairing and base alignment probabilities using the information of all sequences in the alignment. Using a graph-based scheme, we greedily build up the structural alignment from sequence regions with high base-pairing and base alignment probabilities.http://www.ece.tamu.edu/~bjyoon/picxaa/.Several experiments on datasets with different characteristics confirm that PicXAA-R is one of the fastest algorithms for structural alignment of multiple RNAs and it consistently yields accurate alignment results, especially for datasets with locally similar sequences. PicXAA-R source code is freely available at:  Increasing number of newly discovered non-coding RNAs (ncRNAs) with huge functional variety has revealed the substantial role that RNAs play in living organisms -3. The fL3N) in time and O(L2N) in memory for N sequences of length L makes this algorithm impractical even for a small number of sequences. Hence, several studies have proposed various approximations to the Sankoff algorithm  is a weight parameter between the target sequence x and rest of sequences. This transformation assumes that all sequences y ∈ S – {x} are homologous to the given sequence x. However, when we have a set of distantly related sequences in S, this assumption does not necessarily hold. To address this problem, here, we modify this transformation by improving the base-pairing probability using the information just from the closely related sequences to the given sequence x. Therefore, like the inter-sequence consistency transformation, we explicitly consider the relative significance of each sequence y ∈ S – {x} in improving the base-pairing probabilities in x.where Z = {y ∈ S – {x}|x ◊ y} be the set of sequences in S – {x} that are homologous to x. The notation x ◊ y means x and y are homologous and functionally related to each other. Using only the relevant sequences, which are included in the set Z, we define this transformation as:Let The second term in the right hand side of the above equation can be also written as:I{·}, where I{x ◊ y} = 1 if y is homologous to x, and I{x ◊ y} = 0 otherwise. In practice, we cannot judge with certainty whether two sequences are homologous or not. Thus, we describe this relationship probabilistically, using the expectation as: E [I{x ◊ y}] = P(x ◊ y), where P(x ◊ y) is the homology probability and can be estimated as described in the previous subsection. By replacing the identity functions with their expected values in the previous equation, we propose the following enhanced intra-sequence probabilistic consistency transformation as:using the identity function intra-sequence consistency transformation; that is, the pairwise base alignments induced from a given structural alignment should be consistent with the base-pairings in the corresponding pair sequence. However, this time, we utilize the base-pairing information to improve the x – y alignment.In the third consistency transformation, we incorporate the structural information to the pairwise alignments. This transformation is based on the same observation that motivated the Based on this motivation, Katoh and Toh introduced the four-way consistency transformation in  which waβ ∈  is a weight parameter.where inter-sequence consistency transformation has a complexity of O(µ2Lm3), the intra-sequence transformation has a complexity of O(µ3Lm2), and the four-way consistency transformation has a computational complexity of O(µ4Lm2), where µ is the average number of non-zero elements per row , m is the number of sequences, and L is the length of each sequence.Using the sparsity of alignment and pairing probability matrices, we can efficiently implement these three transformations successively. The intra-sequence consistency transformation and four-way consistency transformation, described in the previous subsection, helps PicXAA-R to effectively integrate both sequence and structural similarities to construct the final alignment. The proposed structural alignment approach is described in the following.To find a valid structural alignment of a set of RNA sequences, we propose a two-step greedy approach that builds up the alignment starting from those regions with higher base-pairing and base alignment probabilities. The proposed greedy scheme extends the idea of PicXAA  to multiThe greedy alignment approach we proposed in PicXAA  is conceG =  where, V is the set of vertices and E is the set of directed edges. Each vertex c(i) ∈ V corresponds to a column in the final alignment, and each directed edge e = (c(i), c(j)) ∈ E implies that column c(i) precedes column c(j) in the given alignment. Each column c(i) ∈ V consists of positions from different sequences that will appear in the same column in the final alignment.We represent the structural alignment as a directed acyclic graph When inserting a new pairwise base alignment, we should consider the following requirements to obtain a legitimate multiple RNA alignment:G should remain acyclic.• (Avoid Cycles) The alignment graph c, c′), if column c appears in the left part of the stem in the final structure, then for each base ix ∈ c that pairs with some xi′ ∈ c′ of the same sequence x, we should have i <i′.• (Left-Right Compatibility) In the first greedy step where we use structural information, we should consider left-right compatibility. That is, for any paired columns  from B. For a selected base-pair, we look for the best match among the members of B. That is, we seek for a pair  ∈ B which belongs to another sequence y and satisfies the two compatibility conditions above in G while maximizing the following probability:Here, jy, yj′), we insert two pairwise alignments (ix ~ jy) and (xi′ ~ yj′) into the alignment graph G. Figure For this pair  to G, three scenarios may occur: (1) New column addition; (2) Extension of an existing column; or (3) Merging of two columns. The detailed description of the procedures needed for each case can be found in [Upon inserting a new pair found in . Later iix, jy) according to their transformed alignment probability A. We greedily build up G by repeatedly picking the most probable pair in A, which is not processed yet, provided that it is compatible with the current alignment. Again, insertion of any pair p* =  to G will result in one of the scenarios of new column addition, extension of an existing column, or merging of two columns.In this step, we update the skeleton alignment obtained in the previous step by successively inserting the most probable pairwise base alignments into the multiple structural alignment, as in PicXAA . Thus, wHere, we briefly discuss these three cases (For detailed description see ):New column addition: We insert a new compatible vertex c* = {ix, jy} in G if neither ix nor jy belongs to some existing column in G. Figure 1. Extending an existing column: If only one of the bases in p*, let say ix, belongs to some vertex c ∈ V, we should add the other base jy to the same vertex c. Figure 2. Merging two vertices: When ix ∈ c1 and jy ∈ c2 belong to two different vertices c1, c2 ∈ V, we merge the vertices c1 and c2. Figure 3. G to avoid redundant edges, thereby improving the computational efficiency of the construction process.After updating the graph as described above, we prune G to find the multiple alignment. We use the depth-first search algorithm to order the vertices in V in an ordered set A =  such that there is no path from iv to jv in G for any i > j. In the resulted ordered set A, each member corresponds to a column in the alignment, and putting them together gives the alignment. Further details of the graph construction and alignment process can be found in [Upon finishing the two-step graph construction, we use the obtained alignment graph found in . An illuA = v1, v, ⋯ , vn x ∈ S:As the final step, we apply a refinement step to improve the alignment quality in sequence regions with low alignment probability. We employ the iterative refinement strategy based on the discriminative-split-and-realignment technique that was introduced in PicXAA . We repexS ⊂ S, the set of similar sequences to x using the k-means clustering.1. Find x with the profile of sequences in xS.2. Align S – xS.3. Perform the profile-profile alignment of This refinement strategy takes advantage of both the intra-family similarity as well as the inter-family similarity, thereby improving the alignment quality in low similarity regions without breaking the confidently aligned bases.We use four different benchmark datasets: BRAliBase 2.1 , Murlet We compared PicXAA-R with several well-known RNA sequence alignment algorithms:ProbConsRNA 1.10 , MXSCARNsum-of-pairs score (SPS), which represents the percentage of correctly aligned bases; (2) structure conservation index (SCI) [AE is the minimum free energy of the consensus MSA as computed by RNAalifod [All the experiments have been performed on a 2.2GHz Intel Core2Duo system with 4GB memory. On all datasets we use two measurements to evaluate the performance of each alignment scheme: (1) ex (SCI)  that meaNAalifod  and Ē isNAalifod ./(TP + FN), Positive Predictive Value PPV = TP/(TP + FP), and Matthews correlation coefficient (MCC):On Murlet dataset, in addition to the SPS and SCI scores, we measure sensitivity SEN = TPwhere true positive (TP) indicates the number of correctly predicted base-pairs, true negative (TN) is the number of base-pairs correctly predicted as unpaired, false negative (FN) is the number of not predicted true base-pairs, and false positive (FP) is the number of incorrectly predicted base-pairs.In each table the total computational time for each algorithm is also reported in seconds.α = 0.4, β = 0.1, and bT = 0.5. These parameters are optimized manually using small datasets. Besides, we use McCaskill algorithm [Throughout the experiment we use the parameter setting of lgorithm  to compulgorithm  to find et al.[First, we evaluated the accuracy of PicXAA-R using the BRAliBase 2.1 alignment benchmark. Wilm et al. has deveet al.. BRAliBaTable To more clearly compare these techniques, we provide the average SPS and SCI scores as a function of the average percent identity on k5, k7, k10, and k15 reference sets in Figure et al.[The BraliBase 2.1 benchmark is not designed for local alignment testing and has reference alignments with just up to 15 sequences. Thus, Wang et al. designedTables These results confirm that PicXAA-R can efficiently yield an accurate structural alignment for a set of large number of locally similar RNAs.Murlet dataset  consistsFigure intra-sequence consistency transformation, we incorporate the folding and alignment information of all sequences to enhance both the posterior base-pairing and base alignment probabilities. We utilize these enhanced probabilities as the building blocks of the two-step greedy scheme which builds up the alignment starting from sequence regions with high local similarity and high base-pairing probability. As shown in several experiments, PicXAA-R can efficiently yield highly accurate structural alignment of ncRNAs. This performance is more vivid for datasets consisting sequences with local similarities and low pairwise identities. To the best of our knowledge, PicXAA-R is the fastest structural alignment algorithm after MXSCARNA among all the current RNA aligners while it significantly outperforms MXSCARNA on local datasets like BraliSub and LocExtR. High speed implementation of PicXAA-R as well as its accuracy makes it a practical tool for structural alignment of large number of ncRNAs with low sequence identity which is very helpful for novel ncRNA prediction.In this paper, we proposed PicXAA-R, a probabilistic structural RNA alignment technique based on a greedy algorithm. Using a set of probabilistic consistency transformations, including a novel Conceived the algorithm: SMES, BJY. Implemented the algorithm and performed the experiments: SMES. Analyzed the results: SMES, BJY. Wrote the paper: SMES, BJY.The authors declare that they have no competing interests.


The analysis of RNA sequences, once a small niche field for a small collection of scientists whose primary emphasis was the structure and function of a few RNA molecules, has grown most significantly with the realizations that 1) RNA is implicated in many more functions within the cell, and 2) the analysis of ribosomal RNA sequences is revealing more about the microbial ecology within all biological and environmental systems. The accurate and rapid alignment of these RNA sequences is essential to decipher the maximum amount of information from this data.Two computer systems that utilize the Gutell lab's RNA Comparative Analysis Database (rCAD) were developed to align sequences to an existing template alignment available at the Gutell lab's Comparative RNA Web (CRW) Site. Multiple dimensions of cross-indexed information are contained within the relational database - rCAD, including sequence alignments, the NCBI phylogenetic tree, and comparative secondary structure information for each aligned sequence. The first program, CRWAlign-1 creates a phylogenetic-based sequence profile for each column in the alignment. The second program, CRWAlign-2 creates a profile based on phylogenetic, secondary structure, and sequence information. Both programs utilize their profiles to align new sequences into the template alignment.de-novo alignment programs. We have compared our programs with a total of eight alternative alignment methods on different sets of 16S rRNA alignments with sequence percent identities ranging from 50% to 100%. Both CRWAlign programs were superior to these other programs in accuracy and speed.The accuracies of the two CRWAlign programs were compared with the best template-based rRNA alignment programs and the best Both CRWAlign programs can be used to align the very extensive amount of RNA sequencing that is generated due to the rapid next-generation sequencing technology. This latter technology is augmenting the new paradigm that RNA is intimately implicated in a significant number of functions within the cell. In addition, the use of bacterial 16S rRNA sequencing in the identification of the microbiome in many different environmental systems creates a need for rapid and highly accurate alignment of bacterial 16S rRNA sequences. The first three RNAs identified - messenger RNA (mRNA), ribosomal RNA (rRNA) and transfer RNA (tRNA) were associated with the translation of RNA to proteins - protein synthesis. While DNA is known to carry genetic information from one generation to the next, and proteins are capable of forming three-dimensional structures that catalyze chemical reactions, the function of RNA was perceived as the carrier of the information to code for amino acids in a protein, serve as a scaffold for proteins in the ribosome, and attach amino acids to the growing protein chain during protein synthesis. All three of these RNA functions were considered to be labile and passive. However this simple perspective of RNA has been undergoing a major transformation. RNA is capable of forming complex three-dimensional structure like proteins. And like proteins these higher-order structures catalyze reactions. Now hundreds, if not thousands, of different RNA families are being identified and characterized. And RNA is being associated with many previously known functions in the cell, and equally if not more significant, RNA is being associated with many newly identified functions. This major paradigm shift in molecular and cellular biology is dramatically changing our appreciation of the machinery, mechanisms, and regulation within cells, and providing a better understanding for the normal and aberrant physiological conditions in biological organisms -4.The identification and characterization of macromolecular sequences and their higher-order structures have utilized a very important principle in molecular and evolutionary biology. Different primary structures (or sequences) can form the same higher-order structure for different RNAs and proteins . This coThe analysis of these alignments are used to discover patterns of structural variation and conservation, secondary and higher-order structure, phylogenetic relationships and associate function to the RNA's structure. A few of the significant discoveries made from this type of analysis include: the determination of the phylogenetic relationships for organisms that encompass all branches of the tree of life and the identification of the third domain of life - the Archaea , the accDe novo alignment, and template-based alignment. De novo sequence alignment programs  geneTemplate-based sequence alignment programs utilize an alignment that is usually manually curated to optimize its accurate juxtaposition of nucleotides. This alignment serves as the reference to facilitate the alignment of new sequences. Several automated template-based sequence alignment services for different RNAs are available on the web: Silva  . In particular, while the program RNAMotif can search a structural model with a maximum of 100 structural elements, 16S rRNA contains over 400 structural elements. Second, these programs are also unable to encapsulate all possible variations in the RNA molecule and search candidates with acceptable performance. And third, these programs require structural descriptor to be generated manually, a process that requires a substantial amount of effort for RNA. While some of these programs have some provisions to align sequences based on similar primary and secondary structure characteristics, their performance are not adequate for aligning large numbers of large RNA sequences with great specificity.A variation on this approach uses a seed alignment with the correct secondary structure for that RNA family to generate a descriptor that defines the primary and secondary structure constraints. Sequences that satisfy the conditions of this descriptor are identified. Several programs that use this procedure have been developed. RNAMOT ,29, one de novo alignment algorithms have difficulty placing the nucleotides sharing common structural/functional features within each sequence into the correct columns of the alignment. In contrast, the previously determined seed alignment used in the template-based alignment algorithms has been refined to maximize the correct juxtaposition of structural, functional, and evolutionary relationships of the sequences. Thus the template-based alignment algorithms will be more accurate in the generation of new multiple sequence alignments.When sequences have minimal pairwise identity with one another, Here we present two template-based alignment programs: CRWAlign-1  and CRWAhttp://www.rna.icmb.utexas.edu/) [http://www.ncbi.nlm.nih.gov/-Taxonomy/taxonomyhome.html/). Both CRWAlign-1 and CRWAlign-2 can be used to align any type of RNA molecule that has an existing high quality alignment and for CRWAlign-2 has an accurate secondary structure model. The size of the template alignment is limited only by the number of columns and phylogenetic groups in the alignment and the size of available memory. The Gutell lab used CRWAlign-1 and CRWAlign-2 on a 16S rRNA bacteria alignment that is 10,000 columns wide and contains more than 100,000 sequences.The CRWAlign-2 program automatically generates the structural profiles containing sophisticated constraints, searches for and creates structural models satisfying this profile, and aligns the sequences against the template. The structural information used in CRWAlign-2 is obtained from rCAD and the CRW Site (as.edu/) . The phyde novo alignment programs (SATe and MAFFT) in our comparison. For a rigorous assessment across all alignment programs, the bacterial 16S rRNA is selected as the test set, which have at least 1,400 nucleotides per sequence in length. The results reveal that both CRWAlign-1 and CRWAlign-2 align new sequences more accurately than these other methods.Our primary objective is to measure the performance of CRWAlign-1 and CRWAlign-2, and compare these performances with the most widely-used template-based alignment programs including three web-based alignment systems  and three stand-alone alignment programs . Our analysis also included two CRWAlign-1 consists of two steps: 1) generate the alignment statistics of the template alignment sequences for each taxonomic group; and 2) align new sequences iteratively guided by the generated alignment statistics.The alignment statistics are generated from the template alignment. An example of the process of generating these statistics for a template alignment consisting of 10 sequences is shown in Figure Definition 1: For column i, the conservation value (Ci) is the number of sequences with a nucleotide in this column divided by the total number of sequences in the taxonomic node. The partial sequence starting after or ending before column i is excluded from the calculation.i.e. the entire alignment). Columns with conservation values greater than 80% are considered highly-conserved. The alignment is then divided into blocks that each contains the same number of highly conserved columns. The last block could have fewer columns that are highly-conserved  for each column, measured as the ratio of the number of sequences with each nucleotide divided by the total number of sequences with a nucleotide. This value is calculated with the equation:ip Nis the nucleotide composition value for the ith column, p∈{A, C, G, U}, and SCp(i) is the number of sequences with nucleotide p in column i. An example for the yellow highlighted nucleotides in the conserved column 3, block 2 in Figure where In addition to the conservation value (a measure of the percentage of the sequences that contain a nucleotide at a column) and the composition value (a measure of the frequency for each nucleotide type at a column), a metric is required that captures both of these measures - the conservation and nucleotide composition values for the columns within each block (Def. 3). An average is computed for the set of scores determined for each sequence within each block.Definition 3: For each block in the specified taxonomic node and subsequence S, Y is the number of conserved columns, and Z is the number of non-gap conserved columns. The equation for SC(b) - the score for each subsequence within block b is:i is the percentage of sequences with a nucleotide at the ith column in subsequence S (see Definition 1), and Nj(Sj) is the nucleotide composition value at non-gapped conserved column j in subsequence S (see Definition 2). The value 0.8 in the second component is the weight that was determined heuristically. The SC(b) values for different blocks in Figure where the conservation value CFigure • For the first - conservation value component of the equation:○ The conservation value for column 1 is 0.86 (6/7) since six of the seven sequences have a nucleotide in this column.○ The conservation value for columns 2, 3, 4, and 5 is 1.0 (7/7) since all seven of the sequences have a nucleotide in these columns.○ The Y value is the set of highly conserved columns defined operationally as the columns that have a nucleotide in more than 80% of their sequences within a block. As noted earlier a block is usually created with 15 - 20 highly conserved columns. For the examples in Figures • For the second composition component of the equation:○ The composition value for the individual sequences in Figure ○ In contrast, column 2 has four A's and three G's. Those sequences with an A at column 2 have 4/7 in the second column of numbers (for the second component) in Figure ○ The Z value - non-gapped conservation values is five for the first six sequences, and four for the seventh sequence.The procedure to align sequences with information from a template alignment utilizes these scores that are determined for each block and for each specific phylogenetic/taxonomic node and its parent's nodes. A description of the general strategy mimics the iterative procedure used by the Gutell lab to manually align rRNA sequences, starting in the early 1980s ,35. This1. Determine the phylogenetic group that the query sequence is most likely a member of.Phylogenetic information is known: The first step selects the most closely related phylogenetic/taxonomic group when an exact match occurs between a genus name in the template alignment and the sequence to be aligned The NCBI taxonomic information within rCAD is utilized. CRWAlign-1 selects the lowest taxon with existing alignment statistics.a. Phylogenetic information is not known: If no phylogenetic information is known, the CRWAlign-1 will align the new sequence superficially against each taxon at a predefined leaf level, which is six in our experiments. The node that aligns the most nucleotides in the first stage will be used for the remainder of the alignment process for the sequence. Since the sequence to be aligned :  Divide and conquer approach, align the block with the highest SC(b) score for specific taxonomic nodes, then sequentially select blocks with lower scores.i.e. the block having an average score higher than 90% of the highest allowed: 1.8 * 0.9 = 1.62). To insure the greatest accuracy at this stage, no deletion of conserved columns is allowed, and only a very limited number of insertions between conserved columns are acceptable. Aligning the most highly-conserved blocks with stringent criteria at the early stage assures that the aligned block has a high probability of being correct, reduces the complexity of the problem, and increases the speed.a. With the lowest taxon selected (or predetermined), CRWAlign-1 attempts to align the most highly-conserved blocks with a high average score , which is 3' of the previously aligned block 4. The 5' end of block 5 - GGGUC Figure  does not3. Align sequences against highly conserved blocks in the parent node:a. Once the alignment against the most conserved blocks at the lowest taxon  is complete, the CRWAlign-1 program will attempt to align sequences to the highly conserved blocks obtained with a set of sequences in the parent taxon (i.e. bacilli). Figure b. While blocks 2, 4, and 5 have been aligned  are described more accurately and assigned with a weight score indicating its frequency; b) a weight score cutoff section defines the lowest score of an elongating structural model (to significantly reduce the running time of structure identification process); and c) a phylogeny section describes the most relevant constraints applying on various phylogenetic groups.The structural profile contains information describing various constraints applied to the canonical, regular, or standard RNA secondary structure and relevant taxonomy. The syntax of the profile is based on the original RNAMotif program  but enhai.e. seq1-2 under node 1, seq3-4 under node 2, and seq5-7 under node 3. For each of the three nodes, variation in nucleotide composition is shown in the secondary structure diagram and in the alignment. The first sequence in each node is shown in black, with variations within each node shown in blue  and the descriptor that was generated in Stage 1.The program attempts to identify the structural elements within the descriptor in a sequence. As shown in Figure e.g. a helix) or an unpaired region . When the attempted extension is successful, then this larger extended structure becomes the seed for the next round. This extension of the structural model iterates either to a complete structural model, as defined by the identification of all of the structural elements in the descriptor. Or when the extension on the 5' and/or 3' ends of the seeds cannot be extended, and then the process is terminated, resulting in a partial structure model.The next step prioritizes or ranks the structural elements in the descriptor by their stringency, as measured with a probability score for each structural element. The more stringent, the less likely it will occur by chance, and thus has a lower probability score. The identification of the structural model starts with the structural elements with the lowest probability scores, which serve as the initial seed or nucleation points. The program then attempts to identify the structural elements that are adjacent to these initial seeds. A structural element can be either a base paired region , regardless of sequence conservation. In contrast, sequence conservation in the unpaired regions is the primary factor in the juxtaposition of sequences.As noted earlier, our version of the enhanced RNAMotif program is capable of aligning sequences based on a common secondary structure. With the complete structural models determined in stage 2, the sequence to be aligned is split into multiple fragments. Each fragment represents a specific structural element in the secondary structure. After the fragments are generated, this alignment program identifies the previously aligned template sequence that is most similar to the sequence to be aligned, based on the length of the fragment and the sequence conservation. The alignment of the new sequence against the template will first attempt to juxtapose the pairing regions . Silva, RDP and Greengenes are only available as web-servers and able to only align 16S rRNA while the remaining seven programs (either template-based or de novo) are capable of aligning any type of RNA sequences. Our analysis of these programs and web sites used the default parameters.There are eight alignment programs included in the comparison with CRWAlign-1 and CRWAlign-2: ssu-align, infernal, HMMER, MAFFT, SATe, RDP, Silva, and GreenGenes. Six are template-based programs: ssu-align, infernal, HMMER, Silva, RDP, and GreenGenes while the other two (MAFFT and SATe) align sequences from scratch. Among the six template-based programs, ssu-align, Innfernal and HMMER are stand-alone and available for download at Both test and template data sets are random subsets of the bacterial 16S rRNA alignment available at the Comparative RNA Web (CRW) Site  of sequence i is stacked with nucleotide 63 (C) of sequence j in the correct alignment, then the test alignment must have nucleotide 55 (sequence i) only stacked with nucleotide 63 (sequence j).where Several alignment programs have limitations in the type of sequence to be aligned. Since the bacterial 16S rRNA is the only RNA that can be aligned by all ten programs, it is used in this study. A test set consisting of 1000 bacterial 16S rRNA sequences was aligned by each alignment program. The accuracies of the generated alignments were calculated based upon the pairwise sequence identity ranges Figure . The foude novo programs  were able to align sequences as well as the template-based programs in the high sequence identity range (80-90% and 90-100%), their accuracies were remarkably lower than the template-based accuracies for sequences with low pairwise identity.All 10 programs achieved high accuracy in the 90-100% pairwise sequence identity range. CRWAlign-1, CRWAlign-2 and Silva outperformed the other programs with ~99.25% accuracy, which was 0.2%  to 1.0% (for GreenGenes) higher than the other seven programs. In the 80-90% identity range, CRWAlign-1 (98.9%) and CRWAlign-2 (98.8%) were superior to the other eight programs, including Silva, by 0.5% (Silva) to 2.7% (GreenGenes). In the 70-80% sequence identity range, CRWAlign-1 achieved ~99% accuracy, 1% above the second best program. CRWAlign-2 and ssu-align followed with 97.9% accuracy. The other seven programs varied from 1.8% (Silva) to 5.7% (Mafft) less than the top three programs. In 60-70% and 50-60% sequence identity ranges, both CRWAlign-1 and CRWAlign-2 beat every other program in accuracy, while CRWAlign-1 achieved higher accuracy scores than CRWAlign-2. While the e.g. helix, unpaired region) in the reference sequences. A significant percentage of the unaligned sequences are not complete. Thus it is anticipated that the CRWAlign-2 will align complete sequences with higher accuracy.The structure-based alignment program, CRWAlign-2, identified the complete secondary structural models in the unaligned sequences and used the structural model to align the sequences. This required the unaligned sequence to be "complete": it should contain every structural element  into the program. Due to platform requirements and software dependencies, CRWAlign-1 and CRWAlign-2 were tested on Windows Server 2008 R2 Enterprise (64 bit) with an Intel Xeon x7550 @ 2 GHz. HMMER and Infernal were run on a Linux platform  with an Intel Core i7 920 @2.67 GHz. The ssu-align program was run on Solaris 10.0 with an Intel Xeon processor 5400. These three server configurations have very comparable speeds. Figure CRWAlign-1 consists of two phases: 1) analyzing the template alignment to generate statistics, and 2) aligning sequences. The CRWAlign-2 programconsists of three phases: 1) the generation of structural descriptor, 2) the identification of complete structural models for each sequence, and 3) aligning sequences. The total run time of both CRWAlign-1 and CRWAlign-2 is expected to be sensitive to the template size as well as the number of sequences to be aligned.The execution time of CRWAlign-1 and CRWAlign2 for aligning two test sets with varying size using three different template alignments  were determined and shown in Figure Similar results were observed in CRWAlign-2 Figure . The comWhile manual curation has been used to create the optimal juxtaposition of similar structural elements in the sequence alignments available at the Comparative RNA Web (CRW) Site , this prIn addition to CRWAlign-1 that aligns sequences , we havede novo RNA sequence alignment programs . The structure information created from CRWAlign-2 can be converted into different formats, such as bpseq, alden, rnaml, ct, and bracket , furtheThe execution time of the CRWAlign-1 program is significantly less than the three programs available for download, ssu-align, HMMER, and Infernal Figure . CRWAligSince the rate of sequence data generated with next-gen sequencing is increasing faster than Moore's law, it is essential that more accurate and fast automatic alignment methods be developed. And given that multiple-dimensions of information are available in systems like rCAD , we haveMicrosoft Research provided an external research grant to RRG. Although one of the authors, SO, is employed by Microsoft, no one else at Microsoft or Microsoft Research have any competing interests with any aspect of this manuscript. The other authors have declared that no competing interests exist.Lei Shang:• Project design and contributed to the preparation of the manuscript• Developed computer programs• Analysed the dataDavid P. Gardner:• Project design and contributed to the preparation of the manuscript• Developed computer programs• Analysed the dataWeijia Xu:• Project design and contributed to the preparation of the manuscript• Analysed the dataJamie J. Cannone:• Prepared data for project• Consulted on program development, general comments about the study, and revised the manuscriptDaniel P. Miranker:• Consulted on program development, general comments about the study, and revised the manuscriptStuart Ozer:• Consulted on program development, general comments about the study, and revised the manuscriptRobin R. Gutell:• Project design and contributed to the preparation of the manuscript• Analysed the data