This research work focus on the multiple sequence alignment, as developing an exact multiple sequence alignment for different protein sequences is a difficult computational task. In this research, a hybrid algorithm named Bacterial Foraging Optimization-Genetic Algorithm (BFO-GA) algorithm is aimed to improve the multi-objectives and carrying out measures of multiple sequence alignment. The proposed algorithm employs multi-objectives such as variable gap penalty minimization, maximization of similarity and non-gap percentage. The proposed BFO-GA algorithm is measured with various MSA methods such as T-Coffee, Clustal Omega, Muscle, K-Align, MAFFT, GA, ACO, ABC and PSO. The experiments were taken on four benchmark datasets such as BAliBASE 3.0, Prefab 4.0, SABmark 1.65 and Oxbench 1.3 databases and the outcomes prove that the proposed BFO-GA algorithm obtains better statistical significance results as compared with the other well-known methods. This research study also evaluates the practicability of the alignments of BFO-GA by applying the optimal sequence to predict the phylogenetic tree by using ClustalW2 Phylogeny tool and compare with the existing algorithms by using the Robinson-Foulds (RF) distance performance metric. Lastly, the statistical implication of the proposed algorithm is computed by using the Wilcoxon Matched-Pair Signed- Rank test and also it infers better results. Aligning refers to matching as many characters as possible from each sequence. Primarily, the sequence alignment is applied to infer functional, morphological and evolutionary relationship between the protein sequences. The alignment of the sequence is used to find similarity level between the query sequence and different database sequences.In Bioinformatics, the sequence alignments are used to show evolutionary relationships by constructing phylogenetic trees. Sequence alignment and phylogenetic analysis are strongly related due to measuring the relatedness of homologous sequence. Generally the protein sequence consists of amino acids, which are linked with each other. Sequence alignment describes the mode of arrangement of protein sequence, in order to distinguish the areas of similarity among them2. The multiple sequence alignment comes under the category of global alignment and it’s an adjacent of pairwise alignment to incorporate more than two sequences at a time. Various methods have been implemented on MSA, but these approaches add up under three major classes such as: dynamic programming, Progressive and Iterative methods. In this research work the proposed BFO-GA algorithm comes under the category of Iterative – Progressive method for incorporating the advantage of those methods. The remaining part of this research study is developed as follows: Section 2 illustrates the background field of several methods of solving multiple sequence alignment, Section 3 describes the methodology of MSA multi-objectives and optimization, Section 4 illuminates the proposed algorithm, Section 5 emphasizes the experimental outcomes for the benchmark databases and finally Section 6 spotlights the conclusion and turns over the range for further enhancement.Today, there are several sequence alignment techniques are available and this research study concentrates on the multiple sequence alignment. One of the fundamental problems in computational biology is the alignment of multiple sequences of DNA/Protein. The computational approaches which are used to align the Protein/DNA sequences generally falls into two categories: global and local alignments3. In theoretical, the dynamic programming is applicable to any number of sequences, simply it is computationally expensive in both memory and time. Later than a heuristic search known as progressive technique which is likewise identified as hierarchical or tree method is deployed for multiple sequence alignment4. Progressive alignment works by combining pairwise alignments beginning with the highest similar pair and progressing to the most distantly related. Efficient, and the resulting alignments may be reasonable are some of the advantages of the progressive alignment technique. Some of the tools which are developed by using the progressive technique are T-Coffee5 and different versions of Clustal. R-Coffee is a web server, which creates highly accurate multiple alignments of non-coding RNA sequences and it is founded on the principle of T-Coffee6. The major disadvantage of the progressive technique is the choice of selecting the “most related” sequences.The dynamic programming is the basic approach to solve multiple sequence alignment problems. Needleman-Wunsch algorithm is the foremost applications of dynamic programming, and it is applied to compare biological sequences7, focus on improving the accuracy of the initial pairwise alignments, which is the drawback of progressive technique. Now the developments of multiple sequence alignment methods have shifted to iterative algorithms with the progressive approach, such as ProbCons8, MAFFT9 and MUSCLE10. The iterative approach optimizes a scoring function that leads to exact biological alignment. Some more methods that employ progressive and iterative approaches are ClustalW11, Clustal Omega12, DIALIGN13, Match-Box14, M-Coffee15. COBALT tool incorporates constrains based methods into progressive method16. A few tools that based on consistency approaches are K-Align17 and Probalign18.To overcome the drawbacks of the progressive technique a new approach called Iterative approach, was developed by Gotoh. The iterative approach19, Simulated Annealing20, Gibbs Sampling21 and Hidden Markov Model22. Recently the combinations of iterative and stochastic methods are employed. The genetic algorithm is largely applied for multiple sequence alignment by applying the genetic operators. The approaches that are based on genetic algorithm are MSA-GA23, VDGA24, GAPAM23, RBT-GA25 and SAGA26. Evolutionary algorithms are also applied as a component for solving the multiple sequence alignment problems. The methods which illustrate the evolutionary algorithms are Particle Swarm Optimization (PSO)27, Ant colony optimization (ACO)28, Artificial Bee Colony (ABC)30, M-BPSO31, FTLPSO32 and Genetic algorithm with Ant Colony Optimization (GA-ACO)33. Most of the MSA methods are prepared utilizing a single objective to align the protein/DNA sequences. In recent times the methods which are developed for multiple sequence alignment problems are based on multi-objectives. The methods which are based on multi-objectives are NAGA II34, MSAGMOGA35 and MOMSA36.The iterative approach is too applied with the stochastic approach and examples of these advances is a Genetic Algorithms38. Hence the BFO-GA algorithm has been suggested for resolving the problem of MSA. And also in this research work, the combination of Similarity, Gap penalty and Non-Gap percentage is employed as the multi-objectives to obtain non-dominated optimal alignment by using the existing and the proposed BFO-GA algorithm.The Sum of Pairs (SP) and the Total Column Score (TCS) are used as performance measures to analyze the algorithms of multiple sequence alignment. Even though several algorithms have been trained for resolving the problem of multiple sequence alignment, but they do not promise to provide the global optimal solution39. Three or more primary sequences are used to perform the multiple sequence alignment. For a given family M =  of n sequences of fluctuating length L1 to Ln, the finite alphabet ∑ as,Normally, the multiple sequence alignments are performed from the primary sequence of a protein∑ consists of 4 characters {A, T, G, C} of nucleotides for DNA Sequences.35.∑ consists of 20 characters {A,R,N,D,C,E,Q,G,H,I,L,K,M,F,P,S,T,W,Y,V} of amino acids for protein sequences35.The major performance measure used for multiple sequence alignment is the Sum of Pairs (SP) and Total Column (TC) score. From the matched residues of Protein/DNA, the SP is calculated and the gap penalties are determined by mismatched residues or occurrences of gaps, whereas the similarity is assessed by the substitution matrix score. The similarity matrix score is constructed as 20 × 20 for protein sequences and 4 × 4 for DNA sequences, which represent entire possible transitions between the Protein/DNA sequences. There are two common substitution matrix are available such as Percent Accepted Mutation (PAM) and BLOcks Substitution Matrix (BLOSUM). There are different versions of substitution matrix such as BLOSUM 30, BLOSUM 45, BLOSUM 62, BLOSUM 80, PAM100 and PAM200. In this study, the similarity value is different from the substitution matrix which gives an arithmetical score for matches and mismatches of residuesMultiple sequence alignment is a complicated problem which consists of three distinct difficulties such as, choice of the sequences, choice of an objective function and optimization of a function. In the proposed BFO-GA algorithm the choice of the sequences is chosen based on the non-dominated optimal solution by using the crowding distance measure. And the optimization of the function is attained by using the BFO-GA algorithm.In this research work a multi-objective hybrid algorithm named Bacterial Foraging Optimization –Genetic Algorithm is proposed for multiple sequence alignment problems. Typically, the Sum of Pairs (SP) and the Total Column Score (TCS) performance measures are used to find the optimal solution for the MSA Problem. This research study concentrates on three objective functions to determine the optimal solution such as Maximization of Similarity, Minimization of Variable Gap Penalty and Maximization Non-Gap Percentage.The computation of position weight matrix for the alignment is generated from the resulted alignment solution. The dominance value (ce) of the leading amino acid or nucleotide in each column is set up as follows:The similarity of the alignment SM is defined as the average of dominant value of all columns in the position weight matrix and it is expressed in Eq. A gap is an artificial insertions and deletions (indel) into sequence to move similar segments of aligning residues into good alignment. A gap in same columns is not taken into account which has no substance. Different types of gap penalty scores are available such as Constant, Linear, Convex, Affine and profile based variable gap penalties. In this research work affine and variable gap penalty scoring is calculated for the existing and proposed algorithm such as the Genetic Algorithm, Ant Colony Optimization, Artificial Bee Colony, Particle Swarm Optimization and BFO-GA algorithm to anticipate better outcomes.40. The formula for calculating the affine gap penalty in the pairwise alignment of rows x and y is determined byInsertions and deletions are scored using an affine gap penalty that penalizes the gap once for opening and then proportionally to its length dependent. Two parameters are applied, namely gap opening and gap extensionopen → cost of opening a gapGapextend → cost of extending a gap by one more spaceGapg → length of gap stringThe optimization of affine gap is to group the gaps together, which will minimize the affine gap penalty.The general usage of affine gap penalty is not appropriate for multiple sequence alignment. The gap penalty values of affine are constant and applied equally in all positions, thus the value of gap penalty is determinant. A new position-specific gap penalty is used where the gap values vary according to the residues to find the optimal alignment. MAFFT and ClustalW tools adopted this type of gap penalty.The initial gap penalties are calculated based on the fixed values set by users. Mainly, there are two gap penalties are applied.Gap Opening Penalty (GOP): - indicates the cost of opening a new gap of any length.Gap Extension Penalty (GEP): - indicates the cost of every item in a gap.11: The gap opening penalties are recalculated based on the factors such as dependence on the weight matrix , depends on the similarity of the sequences (Percent identity of two sequences) and depending on the lengths of the sequences.Afterwards, the local gap opening and extension penalties are changed according to the following factorsR and T are a length of 2 sequences,n- Average of residue mismatch score,m- Percent identity scaling factorDepending on the difference in the lengths of the sequences.counting the frequency of each residue at either end of gaps in alignments, store in table)Position-specific gap penalties .Residue-specific penalties  → direction vector. dir (i) is a random number lying between .i,P+1,F,E → position of ith bacterium at a point in x1, x2, x3 coordinate system, in Pth Chemotaxis, Fth reproduction and Eth elimination and dispersal step.SC(i) → unit run-length of a bacteriumIn this proposed BFO-GA algorithm, the swimming length of the bacteria in multiple sequence alignment is randomly applied by the user. Only, in this research work the proposed algorithm gives better outcomes when the bacterium makes a motion in a forward direction with a swimming length of 5.In favor of the bacteria to pass at the highest food location, it is trusted that the optimum bacterium till a point of time in the search time should make an endeavor to draw in other bacteria so that together they unite at the desired location more quickly. To accomplish this, a penalty function based upon the degraded non-dominated sorting algorithm is executed to determine the fittest bacterium which has higher crowding distance and lower social status. The relative lengths of each bacterium from the fittest bacterium till that search duration are added to the original cost function. Figure The singular set of bacteria, after getting changed through several chemotactic stages reaches the breeding phase. At this stage, the best set of bacteria gets divided into two groups. The healthier half replaces with the other half of bacteria, which gets eliminated, due to their poorer foraging abilities. This formulates the population of bacteria constant in the development process. The reproduction of the initial population for the protein sequences is shown in Fig. 42. The choice of the best bacterium is done by crowded tournament selection. Based on the fitness value, every two best individuals are selected for crossover and it is shown in Fig. In selection phase, the sorting of individuals is done in the mating pool according to their fitness and then every two best individuals are selected for crossover. The best fitness bacterium is calculated by scoring each alignment according to the Multi-objectives , Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO) and existing online tools namely T-Coffee, Muscle, K-Align, MAFFT and Clustal Omega.This research focuses on the performance measures such as the ratio of pairs correctly aligned namely Sum of Pairs (SP), the ratio of the columns correctly aligned namely Total Column Score (TCS) and the multi-objectives such as maximization of similarity, gap penalty and Non-Gap percentage. The experiments are taken out in 2 X Intel Xenon E5-2670 V2 (2.5 GHz/10-core) CPU with 64 GB of memory, running Cent OS and the proposed BFO-GA algorithm was implemented in Java.th column in the alignment, The first performance standard used in this work named Sum-of pairs (SP) and it is set as the number of correctly aligned amino acids or residues with respect to the total number of residue pairs in the reference alignment. Consider the example test alignment of size R*T and a reference alignment of size R*Tr, where X is the number of sequences and T,Tr are the total number of columns in the test and reference alignment. Here th column in the reference alignment.Similarly The sum-of-pairs score for the test alignment is defined in Eq. And the second most common scoring scheme for Multiple Sequence Alignment is Total Column Score (TCS). Generally, TCS is defined as the number of correctly aligned columns with respect to the total number of columns in the reference alignment. Consider the example test alignment of size R × T and a reference alignment of size R × Tr, where R is the number of sequences and T, Tr are the total number of columns in the test and reference alignment. Here the score is defined as The total column score for test alignment is represented in Eq. 43, Prefab 4.010, SABmark 1.6544 and Oxbench 1.345 is used to examine and compare with various multiple sequence alignment methods. The BAliBASE 3.0 database contains 6255 protein sequences in total length. It includes five diverse reference sets, namely RV1, RV2, RV3, RV4 and RV5.In this work the universally known benchmark datasets such as Benchmark Alignment Database (BAliBASE 3.0)And the Sabmark database contains 3280 protein sequences in Twilight Zone families. That is the sequence similarity lies between 0–25% identity and common evolutionary origin cannot be established between most pairs of the sequences. The Prefab benchmark database contains 1682 reference alignments. Finally the Oxbench database consists of reference alignments in the master reference set and 605 sequences in the full reference set. Choosing of gap penalty for the benchmark datasets used in this study are keyed out based on the different gap penalty values such as 2%, 5%, 10%, 15% and 19%. It was found that 19% of gap value among various percentages gave better answers and hence it was specified.The Fig. From the Fig. The performance standards such as the Sum-of-Pairs (SP) and Total Column Score (TCS) for the proposed algorithm are compared with existing algorithms  and also with various online MSA tools such as T-Coffee, Muscle, K-Align, MAFFT and Clustal Omega. The Figs The final stage yields the statistical significance of the proposed algorithm which is estimated using non-parametric test, namely Wilcoxon Matched-Pair Signed-Rank test between each pair of methods by using significant confidence level of 5% . Each entry in the Table 46 to reconstruct the phylogenetic trees of the families. The Supplementary Fig. 47 is employed to assess the quality of the trees between the inferred trees and the acknowledgments.In this research four well-known benchmark datasets such as BAliBASE 3.0, Prefab 4.0, SABmark 1.65 and Oxbench 1.3 are used for comparing the proposed BFO-GA algorithm with the other existing algorithms. After performing the MSA, the resulting alignments are passed to the online tool ClustalW249. This study provides preliminary evidences that BFO-GA may be safer, and more broad subject is required.And also the RF distance is used to measure the smallest distance between trees to see the better inferred trees. Table The experiment has been carried out for 25 runs with 500 generations for 2%, 5%, 10%, 15% and 19% gap values respectively. Later all the iterations the average values are taken for 2,5,10, 15 and 19 percent gap values accordingly and the better values are identified at 19% gap. The results demonstrate that the proposed BFO-GA algorithm is more respectable among the other existing algorithms with respect to Affine and Variable Gap penalty Values. From these outcomes, it is understood that for the Similarity and Non-Gap Percentage objective values have been increased gradually, while the percentage of gap values have to increase. Accordingly the Gap penalties of Affine and Variable Gaps values have been decreased simultaneously when increasing the percentage of inserting gap value.The Sum of Pairs (SP) and the Total Column Score (TCS) are chosen as performance measure to compare the proposed algorithm with the existing algorithms. The mean value of 25 runs for 2%, 5%, 10%, 15% and 19% gap values indicates that the proposed algorithm provides better performance than the existing algorithms. In the beginning of the experiment iterations the SP and TCS value fluctuates in 5% and 10% and in later 15% and 19% iterations the SP and TCS values has increased. From all the iterations, it is noted that the proposed algorithm has best average results and it is found that for 19% gap penalty value better results are reached among all the iterations. For all the BAliBASE datasets the proposed algorithm provides more dependable outcomes with respect to affine and variable gap penalty values. Based on the experimental results and discussion, this research work concludes that the proposed BFO-GA algorithm can improve both the multi-objectives and performance measures than the existing algorithms.Today, the multiple sequence alignment problems are an unresolved issue for researchers. The alignment methods used to solve this problem should be habitually enhanced as they are important in the analysis of enormous data provided by next-generation sequencing and high-throughput experiments. The primary objective of this research study is to assess the evolutionary algorithms such as GA, ACO, ABC, PSO and exploring ways to further improve its execution to arrive at optimal solution. After careful analysis of the existing algorithms, this research work proposed BFO-GA algorithm to perform multiple sequence alignment and directs the result towards an optimal answer. The multi-objective optimization technique is used to resolve the problem which maximizes the similarity, non-gap percentage, and minimizes the value of gap penalty which goes to the Pareto - optimal result.The statistical significance is computed to compare the significance of the proposed algorithm with other existing methods by using the Wilcoxon Matched-Pair Signed-Rank test. From the experimental results, it is exposed that the proposed BFO-GA algorithm outperforms the other existing algorithm in terms of all Multi-objectives and performance measures. And besides the proposed algorithm achieves good outcomes yet for low similarity of the sequences. The conserved blocks are not received, while performing the multiple sequence alignment. Hence it is concluded that they are not homologous sequences. Ultimately, the phylogenetic tree is constructed for the RV3 reference family in BaliBASE 3.0 by using the resulting MSA alignments provided by the proposed BFO-GA algorithm. Based on the RF distance values, it is inferred that the proposed algorithm achieves better results than the other methods.In future the proposed algorithm can be blended or run with any other evolutionary algorithm to obtain the best optimal results. Different objectives may be innovated to find most excellent solutions of multiple sequence alignment and to get more conserved blocks. As well, this algorithm can be utilized for secondary and tertiary structure prediction of these successions.Supplementary Information


The diversity of microbiota is best explored by understanding the phylogenetic structure of the microbial communities. Traditionally, sequence alignment has been used for phylogenetic inference. However, alignment-based approaches come with significant challenges and limitations when massive amounts of data are analyzed. In the recent decade, alignment-free approaches have enabled genome-scale phylogenetic inference. Here we evaluate three alignment-free methods: ACS, CVTree, and Kr for phylogenetic inference with 16s rRNA gene data. We use a taxonomic gold standard to compare the accuracy of alignment-free phylogenetic inference with that of common microbiome-wide phylogenetic inference pipelines based on PyNAST and MUSCLE alignments with FastTree and RAxML. We re-simulate fecal communities from Human Microbiome Project data to evaluate the performance of the methods on datasets with properties of real data. Our comparisons show that alignment-free methods are not inferior to alignment-based methods in giving accurate and robust phylogenic trees. Moreover, consensus ensembles of alignment-free phylogenies are superior to those built from alignment-based methods in their ability to highlight community differences in low power settings. In addition, the overall running times of alignment-based and alignment-free phylogenetic inference are comparable. Taken together our empirical results suggest that alignment-free methods provide a viable approach for microbiome-wide phylogenetic inference. Historically, bacterial systematics has been a difficult problem because bacteria lack morphological features, which would be easy to characterize. However, after Carl Woese and collaborators started creating phylogenies based on small subunit (SSU) ribosomal RNA (rRNA) sequences, sequencThe overwhelming explosion in the amount of genetic sequence data available for research has been brought about in the last decade by advances in molecular sequencing technologies. Traditional analysis pipelines for such data involve alignment-based methods such as BLAST , PyNAST k-mer words, which are treated as unitary traits. The idea of k-mer, or perfectly matched strings of selected length, have been used by groups such as Blasdell and Gibbs et al in tree inferences for proteins and nucleotides . The average length of these longest common substrings is calculated as a reflection of similarity between X and Y. For example, given two sequences X = ‘TCTGA’ and Y = ‘CCTGT’, the length would be 3. ACS is normalized to account for the sequence lengths, resulting in a similarity measure between X and Y. To convert it to a distance, the inverse is taken and a correction term is subtracted to ensure that the distance between identical sequences is 0. The running time of ACS distance computation algorithm is linear in the length of the longest sequence. The efficiency of the algorithm allows pairwise distance computation for a moderate to large number of sequences.Average common substring approach (ACS)  is basedl, it finds the frequency of appearance of overlapping strings of a fixed length k in the sequence. The frequency can also be divided by the total number (l-k+1) of k-strings to obtain the probability of that string appearing in the protein. The collection of frequencies and probabilities can be thought of as the result of mutations and selection forces with each k-string as a unit. While mutations happen randomly at the molecular level, selections are the forces that drive evolution. Neutral mutations account for some randomness found in the k-string composition. They are referred to as the random background and must be subtracted from the simple counting results to find the selective changes. After counting for all strings of k-1 mers and k-2 mers, the probability of appearance of k-string can be predicted using a Markov assumption. The difference between the actual counts and predicted counts is then used as the component of a new “normalized” CV, and pairwise distances between the new CVs are computed to generate a dissimilarity matrix.CVTree  uses a cX = ‘TCTGA’ and Y = ‘TCGGT’, at every position i along the sequence X, we find the shortest substring starting at i that is not found in Y. In this case, ‘TCT’ is the shortest string starting at position 1 that is absent from Y. The average length of these absent substrings is calculated to infer similarity between the two sequences. Because this method is based on a mathematical model of DNA sequence evolution, it is restricted to DNA sequences. However, this method is reported to be more accurate than model-free approaches [Kr method  attemptsproaches .Fig 1. We evaluate the alignment-free methods relative to the common alignment-based inference approaches on re-simulated stool communities.A general outline of the methods used in the comparisons is provided in S1 Text.After we filtered the OTUs from the HMP dataset, the taxonomic identity of these OTUs have been used to generate the gold standard, with their respective reference sequences used for tree inference. The obtained trees are then compared using PHYLIP program TREEDIST. The parameters used for running individual programs can be found in To compare the alignment-free methods to the state-of-the-art methods in microbiome community, we have included trees obtained from alignment-based methods. Specifically, for alignment method, we used PyNAST  and MUSCIn the second comparison, we created consensus trees of each group to compare the accuracy of alignment-free and alignment-based trees as a whole. We used the same re-simulation strategy as in the first comparison. The PHYLIP program CONSENSE is used to create consensus trees from individual trees. We first computed the consensus tree of the alignment-free trees using CONSENSE. After resolving multifurcations in the consensus tree by adding zero-length branches, we next used FITCH to estimate the branch lengths of the consensus tree under the three alignment free alternatives. The final branch lengths have been computed as the average branch length for ACS, Kr and CVTree. Similarly, we also obtained consensus trees for the alignment-based methods. We created a consensus for each alignment method  and for each tree inference . We also created a consensus tree of all alignment-based trees. The consensus trees have been included in the tree distance computation as in the other comparisons.Taxonomic tree generator algorithm. To establish a taxonomic tree, we created a “tree generator” program that generates the tree based on the taxonomy information provided by Greengenes, which would serve as the “gold standard” in evaluating the accuracy of the trees. The program does so by first storing the taxonomy information in the form of a matrix, which includes the name of each sequence and its taxonomy information. It then goes through the taxonomy information level by level  and compares the sequences to one another at each level. The resulting comparison results are written in the required tree structure.http://www.nyuinformatics.org).All experiments presented in this manuscript were run on the Asclepius Compute Cluster at the Center for Health Informatics and Bioinformatics (CHIBI) at New York University Langone Medical Center . This discordance suggests that the distance metrics capture different aspects of the evolutionary process.First, we evaluate the relative performance of the three alignment-free methods in recovering the taxonomic tree. On average, all three methods perform comparably with no clear winner. Interestingly, even though the overall similarity of the alignment-free trees to the taxonomic tree is comparable, there is a lot of discordance among the trees inferred by the three alignment-free methods  to up to 28 hours (MUSCLE/RAxML).For alignment-free methods, the timing is composed of initially building distance matrices, and then building trees from the distances matrices using NEIGHBOR. Building the distance matrices with CVTree took approximately 5 minutes, while building the distance matrices for ACS and Kr took approximately 5 hours. Neighbor took on average 1 to 2 hours to build a tree for each of these methods. The total time varied from a little over 1 hour (CVTree/Neighbor) to 7 hours (ACS/Neighbor and Kr/Neighbor).Building the consensus tree from individual trees took approximately 3 minutes regardless of the tree types.A commonly adopted approach for analysis of microbiome data is to perform permutational multivatiate analysis of variance analysis (PERMANOVA) to associate the microbial communities with experimental variables . This anTable 1 summarizes the estimated effect sizes and significance values for this analysis. We note that the estimated effect size based on FastTree weighted Unifrac distances is higher than for any of the alignment-free methods or their consensus. However, when the treatment effect is considered, the estimated effect is larger for the alignment-free methods, and largest for the alignment-free consensus. This results holds regardless of which effect size measurement is used—the coefficient of determination (R2) or omega squared (ω2), which has been shown to be superior for microbiome studies [Fig 4).We re-analyze the data from a recent study of the effect of sub-therapeutic antibiotic treatment (STAT) on the microbiota . In this studies . All of Fig 5). We note that when effect sizes are large , the inference obtained with both trees are almost identical. However, in the cases with small effect sizes, we note that the p-values obtained with alignment-free phylogenies tend to be lower, indicating a higher power to detect small effects .We have further explored the question of whether alignment-free consensus tree helps to distinguish small effect sizes in PERMANOVA analysis of the weighted Unifrac distances. Here we considered the control fecal specimens from the STAT dataset and simulated additional datasets for comparison by permuting a prescribed number of OTU labels . This allowed us to obtain datasets with varying effect sizes without affecting the underlying phylogenetic structure between OTUs. We have analyzed the resulting simulated datasets for differences from the original data using PERMANOVA with weighted Unifrac distances based on the alignment-free consensus and PyNAST with FastTree phylogeny  is significantly longer than for PyNAST/FastTree, the accuracy achieved may make it a worthwhile endeavor. It is also worth noting that while PyNAST and FastTree were considerably faster than the alignment-free methods, the other combinations took significantly longer times. In particular, MUSCLE took about three hours longer than PyNAST and RAxML, averaging about 24 hours (versus only an hour for FastTree). The result of PyNAST/FastTree, as noted above, was also better than any other alignment-based combination.Although alignment-free methods are able to overcome the limitations of alignment-based methods as discussed previously, they are often passed over because of the presumed compromise in accuracy. However, our study showed that while individual tree may have decreased accuracy, their consensus trees may actually achieve greater accuracy. Most importantly as demonstrated by our re-analysis of the sub-therapeutic antibiotic treatment dataset, some studies may benefit from utilization of alignment-free trees, which may help to bring out important smaller effects.S1 Fig(PDF)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


The recent advancement of whole genome alignment software has made it possible to align two genomes very efficiently and with only a small sacrifice in sensitivity. Yet it becomes very slow if the extra sensitivity is needed. This paper proposes a simple but effective method to improve the sensitivity of existing whole-genome alignment software without paying much extra running time.We have applied our method to a popular whole genome alignment tool LAST, and we called the resulting tool LASTM. Experimental results showed that LASTM could find more high quality alignments with a little extra running time. For example, when comparing human and mouse genomes, to produce the similar number of alignments with similar average length and similarity, LASTM was about three times faster than LAST. We conclude that our method can be used to improve the sensitivity, and the extra time it takes is small, and thus it is worthwhile to be implemented in existing tools. Because of the recent advances in sequencing technology and genome assembly software, it is now feasible to sequence the whole genome of many species in nature. To elicit useful information from these multi-gigabase long sequences of As, Cs, Gs and Ts, one common approach is to make connections by comparing them to each other. Whole genome alignment is the computational problem of finding similar regions between two different genomes.Current genome alignment software tools are able to align two genomes very efficiently and with only a small sacrifice in sensitivity –9. Yet, A[1..n] and B[1..m], and it asks for finding those pairs of subsequences A[i..j] and B[k..ℓ] such that A[i..j] and B[k..ℓ] are similar. We use the alignment of A[i..j] and B[k..ℓ] to measure their similarity. To get an alignment of A[i..j] and B[k..ℓ], we insert spaces into the two subsequences to make their length equal, and put one subsequence on top of the other. We assign a score to each column of the alignment depending on whether the characters in that column are match, mismatch, or any of them is space, and the score of an alignment is the sum of the scores assigned to its columns. The similarity of A[i..j] and B[k..ℓ] is measured by the highest score given by their best alignment. Our task is to find all subsequences of A and B whose alignment scores are no less than some score threshold.The input of the whole genome alignment problem is two multi-gigabase long DNA sequences A[1..n] and B[1..m] is to use dynamic programming to find, for each positions 1≤i≤n and 1≤j≤m, whether there is an alignment around A[i] and B[j] with score no less than the score threshold. Obviously, this approach is too slow. The idea of the “seed-and-extend” heuristic is to use an efficient method to find a set of promising position pairs such that for those not in this set, it is very likely that there are no similar regions around them. Then, it uses dynamic programming to find, for each promising position pair, whether there is an alignment around them with high enough score. Below, we briefly describe the basic steps of “seed-and-extend”. (i)Index building: We distinguish the two input sequences such that one is the reference sequence and the other is the query sequence. We first build an indexing structure such as suffix array, hash table or BWT  for the (ii)A and B. These matching pairs, which we called seeds, suggest a much smaller set of positions from which we find the promising positions. Gapless extension: The set of seeds found in the previous step suggests a much smaller set of positions for us to find similar regions. However, they are still too large for us to handle each of them using dynamic programming. This step further reduces its size as follows: for each seed, we extend it at both ends by repeatedly adding the next characters in both sequences to the alignment. Note that we will not introduce any gap in the extension, and thus this step is very fast. During the extension process, we will remember the maximum score seen so far, and if the current score is much lower than this maximum score, it means that we have gone too far, and we stop and return the alignment with the maximum score seen so far.D.To reduce the number of promising positions, we examine the set of gapless alignments returned by this step, and discard those whose score are smaller than some pre-defined threshold (iv)Gap extension: For each of the remaining gapless alignment, we use dynamic programming to find whether there is an alignment around its starting positions with high enough scores.Most existing software tools for whole genome alignment use the "seed-and-extend" heuristic . To explD has critical effect on the efficiency and sensitivity: a low threshold allows more promising position pairs to be checked, and thus it is likely to find more similar regions, but we will also waste more time in checking more gapless alignments that do not lead to any similar regions. To demonstrate this effect, we have used the popular whole-genome alignment tool LAST  and B[k..ℓ]. We use LAST as an example. We will insert the following filtering step between LAST’s gapless extension step and gap extension step, and run LAST using a lower threshold εD, where 0<ε<1 and D is LAST’s default threshold: S be the set of gapless alignments with score between εD and D. For each alignment ∈S, we will remove it from S if (i) there is no following gapless alignment within a distance of d from it  following with i−jo≤d and k−ℓo≤d), and (ii) there is no preceding alignment within a distance of d from it  preceding with io−j≤d and ko−ℓ≤d).Let We now explain how to make use of this idea to increase the sensitivity without much extra processing time. Let D, together with those still in S will be passed to the gap extension step.Then, those gapless alignments with threshold no less than D, and our method will not introduce any error because all gapless alignment will be further checked by the gap extension step. As shown below, the filtering step of our method is efficient and easy to implement. So of gapless alignments with score greater than or equal to D, and select the set S of gapless alignments with score between εD and D.Step 1:  Select the set A[i..j],B[k..ℓ])∈So∪S in ascending order of i, the starting position of A[i..j].Step 2:  Radix sort the gapless alignments ∈S scanned, check if there is any gapless alignment So∪S following in the list within distance d, and if yes, move it to So.  can stop as soon as we reach an alignment  with i′>j+d.)Step 3:  Scanned the sorted list, and for each alignment ∈So∪S in descending order of j, the ending position of A[i..j].Step 4:  Radix sort the gapless alignments ∈S scanned, check if there is any gapless alignment So∪S following in the list within distance d, and if yes, move it to So.Step 5:  Scanned the sorted list, and for each alignment  to the genome of mouse (≈2.8G), of dog (≈2.4G), of cat (≈2.5G), of cow (≈2.7G), and of rat (≈2.8G). We use the human genome as the reference, and LAST will build an index for it. These genomes were all downloaded from [To justify our method, we have modified LAST as described in the previous section, and used it to align the human genome  and our modification LASTM, we compared the number of alignments produced by each software and measured their quality based on the length and similarity. We suppose that the more alignments with similar quality produced, the higher the sensitivity.D, and the distance d for the filtering step is set to 2000. The table shows that our method runs in time similar to that of LAST with threshold D, but the number of alignments reported is significantly larger, which is close to that reported by LAST with threshold 0.85D. Also, the table shows that the quality of the alignments returned by our method is similar to that returned by LAST; they have similar average length, and similar average similarity .Table Furthermore, Table This paper proposes a method to increase the sensitivity of whole genome alignment tools that use the "seed-and-extend" heuristic. Our method is simple and easy to implement, and the extra time it takes is small, and thus it is worthwhile to be implemented in existing tools.


The increasing application of next generation sequencing technologies has led to the availability of thousands of reference genomes, often providing multiple genomes for the same or closely related species. The current approach to represent a species or a population with a single reference sequence and a set of variations cannot represent their full diversity and introduces bias towards the chosen reference. There is a need for the representation of multiple sequences in a composite way that is compatible with existing data sources for annotation and suitable for established sequence analysis methods. At the same time, this representation needs to be easily accessible and extendable to account for the constant change of available genomes.We introduce seq-seq-pan, a framework that provides methods for adding or removing new genomes from a set of aligned genomes and uses these to construct a whole genome alignment. Throughout the sequential workflow the alignment is optimized for generating a representative linear presentation of the aligned set of genomes, that enables its usage for annotation and in downstream analyses.By providing dynamic updates and optimized processing, our approach enables the usage of whole genome alignment in the field of pan-genomics. In addition, the sequential workflow can be used as a fast alternative to existing whole genome aligners for aligning closely related genomes.https://gitlab.com/rki_bioinformaticsseq-seq-pan is freely available at The online version of this article (doi:10.1186/s12864-017-4401-3) contains supplementary material, which is available to authorized users. Thanks to the continuous advances in next generation sequencing (NGS) technologies the number of sequenced whole genomes is also continuously increasing. This has led to a 10,000 fold increase in available bacterial genomes over the past 20 years . This prInitially defined to be the sum of core and dispensable genes of all strains of one bacterial organism , the terWe assessed a collection of tools applied for the analysis of multiple sequences Table . Many ofWhile four of the analyzed tools - JST , MHC-PRGAnother (well-established) representation of sets of genomes is their alignment. Whole genome alignments (WGA) implicitly provide a coordinate system that allows the translation between pan-genome and strain genome position, enabling annotation of the alignment with biological features of the individual genomes. Due to the extensive research on whole genome alignment –28, stanIn summary, WGA structures presently fulfill most of the desirable properties of a pan-genome, but a severe drawback of existing methods is their final, non-updatable alignment result.We here present seq-seq-pan, a framework that enables the usage of WGA as a pan-genome data structure. We provide methods for adding additional genomes or removing them from a set of aligned sequences and use them to sequentially align whole genome sequences. Throughout the sequential process we take measures to optimize the resulting whole genome alignment and provide a linear representation that can be used in place of a reference genome with established methods for subsequent analyses such as read mapping and variant detection.The key notion of seq-seq-pan is to use and optimize fast, well established whole genome alignment methods to construct a pan-genome from an a priori indefinite set of genomes. For this part, we use progressiveMauve , a fast Below we describe all steps of the whole workflow in detail. The details of implementation and consecutive order of individual steps are depicted in Additional file LCBs are combined into a consensus genome by concatenating the consensus sequence of each block. At each position within the LCB, all aligned sequences are compared and the most abundant base is chosen for the consensus sequence. In case of ties, the base is drawn randomly from the available choices. To prevent alignments across block borders when the consensus genome is used for alignment, we integrate a sequence of 1000 ’N’ (undefined nucleic acid) between the consensus sequence blocks into the final sequence. In addition to the consensus genome, two accompanying index files are created. One contains the start positions of all delimiter sequences within the consensus genome and therefore enables the reconstruction of the alignment of all genomes from the alignment of the consensus genome with an additional sequence (referred to as “consensus index file”). The second index file contains the coordinates of all gaps of all sequences per block in the consensus genome, improving the performance of the reconstruction step and the mapping of coordinates between genomes. Furthermore, we make note of the sequence identifier and the description of all genomes and chromosomes, as this information is not contained in the final output of progressiveMauve.When aligning two sequences with progressiveMauve , the aliSequences specific for one of the genomes are also reported as LCBs, but these only contain parts of this one genome. LCBs containing only a single unaligned sequence are typically moved to the end of the alignment file. They are created to ensure collinearity within blocks and can sometimes be of small length. When used in a sequential workflow, it can be advisable to avoid assembling short one-sequence-LCBs and attaching all of them to the end of the consensus genome. We prevent the accumulation of small blocks by merging short one-sequence-LCBs with their neighboring blocks within the genome and realigning consecutive gap stretches see “” sectionAlignment is improved by realigning genomes at sites where a gap ends in one sequence and starts in the other (referred to as “consecutive gaps”). We scan through the whole alignment and identify all positions with consecutive gaps. Then we extend the interval to the sequence on both sides of the gap sequences by the length of the longer sequence or up to block borders and align these sequences again.Aligning a genome with a consensus genome can result in alignments that span the borders of the LCBs making up the consensus genome. We identify these blocks using the consensus index file. Then, we split them at the start and end of the delimiter sequence. If the alignment spans a complete delimiter sequence the separation results in three new blocks: the first and third one contain the aligned sequences of the two genomes. The second one includes only the sequence of the new genome that was aligned to the delimiter sequence. All gaps contained in this block are removed. In cases where the delimiter sequence is matched with a gap sequence only, we discard the complete block.We take the forward representation of all one-sequence-blocks per genome and sort them. We concatenate the sequences, again integrating stretches of 1000 ’N’, ending up with one sequence for each of the genomes. These sequences are then aligned using the same process as with the full genomes. Alignment with progressiveMauve, the optional Merging Step and the Realignment Step, are followed by a two-step Resolving and Reconstruction process using each of the initially concatenated sequences as “consensus sequence”  as the origin of the evolution simulation. For the evolution parameters we adapted the example provided by the EVOLVER team. We fit the parameters to the smaller size of the E. coli genome by changing the probabilities of large insertion and deletion events and setting the maximum size of these events to 7000 – roughly the size of the longest E. coli gene. We simulated twelve genomes without using mutation acceptance constraints with the phylogeny depicted in Fig. Accuracy of alignment was tested on a simulated dataset of 13 genomes. For the simulation of genomes with a known true alignment we used the EVOLVER software  and the M. tuberculosis we choose the alignment of the other aligners to act as the true alignment and our results as the prediction in each comparison. Here, we use the F-score to assess the similarity of the alignments. As in this case there is no ground truth to compare our results to we derive the accuracy of our alignment method from comparison to four other alignment tools.We use an alignment comparison method to compare our results with the results of other whole-genome aligners: the tool mafComparator from the mafTools collection . To compDue to the sequential nature of our workflow, the order in which genomes are added to the pan-genome might influence the resulting alignment. When additional genomes are added to existing alignments, they can not be set in relation to the genomes that are part of the alignment, but have to be added “on top” of them. Therefore, the alignment process should yield similar alignments irrespective of the order of genomes. To investigate the effect of sorting we arrange the genomes by similarity and by consecutive dissimilarity and compare the results. To sort the input genome sequences by similarity we apply the D2z score  on all pAs an alternative, to obtain a series of strongly differing genomes, we sort them as follows: we again start with the genome with the smallest distance from all others. Then we choose the one with the lowest similarity score as second and the genome most similar to the first for the third position and continue to alternate genomes in this manner throughout the complete set .M.tuberculosis dataset a hundred times and the larger datasets (S. aureus and E. coli) 10 times with randomly sorted genomes and compare them to the alignment using genomes sorted by similarity. We also compare alignments that were created with and without using the merging steps  genomes. TBA requires pairwise alignments for all genomes in the dataset and builds the alignment on top of these. Table M. tuberculosis dataset, Table The memory requirements during the alignment construction are correlated with the elapsed time in most cases and are therefore lowest for seq-seq-pan, except for TBA. However, memory consumption of TBA will increase with the level of parallelization.M. tuberculosis genomes, the construction of In addition to the set of reference genomes, PanCake requires pairwise alignments of all genomes to construct a pan-genome. In the case of our experiments with 43 h nucmer  separatementclass2pt{minimh nucmer . Due to h nucmer  can be uIn this contribution, we introduced seq-seq-pan which enhances whole genome alignments by adding critical features for pan-genome data structures e.g. updating the set of genomes within the pan-genome. It provides a fast and simple construction process for whole genome alignments while optimizing the results for usage in subsequent analyses. The continuous merging of small unaligned blocks prevents the accumulation of sequences without context or position within the alignment and preserves the synteny of the original genomes, while the realignment of pairwise alignments avoids the introduction of additional repeats into the linear pan-genome representation. Both steps influence the composition of the linear consensus sequence and support its usage with mapping based methods such as read alignment.The whole genome alignment format that we use as representation of a pan-genome in seq-seq-pan retains the full sequences and gaps for all aligned genomes in addition to meta-information about block borders. Therefore, it is not suitable to store the pan-genome efficiently. However, this format ensures loss-less and faster handling of the data. Further, it is thereby accessible by currently available downstream analysis tools without requiring subsequent novel tool implementations.We demonstrate that the sort order of genomes does not substantially influence the result despite the sequential nature of our approach.We compared seq-seq-pan with four whole genome aligners that offer alignment of non-collinear sequences. These tools use sophisticated methods for the identification of ortho- and even paralogs and conserved sequences. With these features, they identify similar but unrelated sequences within genomes, an aspect that is not considered in the field of pan-genomics. As we do not take such measures, we did not expect very high concordance between our results and the whole genome alignments. However, our comparison shows that our alignment differs as much from the results of progressiveMauve, progressiveCactus, Mugsy and TBA as their results differ among each other. Our approach is able to align a set of genomes much faster and with less memory usage than these whole genome alignment tools. Due to the focus on highly conserved sequences, some of these tools also provide a very fragmented alignment with many small blocks, which is prevented by the merge step in seq-seq-pan.We compare our approach with currently available methods in terms of applicability and needed prerequisites (input data). For a detailed comparison, we chose PanCake as an approach by which a pan-genome can be constructed from a large set of genomes. We show that the construction of the pan-genome and using the structure for basic tasks requires substantially less time with seq-seq-pan than with PanCake. Some features, such as removing a genome from the pan-genome and the construction of a linear presentation of the pan-genome in the form of a consensus sequence, are not directly available in any other pan-genomics tool. For instance, the authors of PanCake focused on the analysis of core and accessory gene sets and therefore provide different functionalities.M. tuberculosis genomes became available in the NCBI Ref-Seq database. This already highlights the importance of having the ability to extend a pan-genome structure. Methods such as the investigated whole genome alignment tools that constrain the user to start the alignment afresh with the increased number of genomes are at risk of reaching computational limits  which is mitigated by our iterative approach which quickly adds new sequences without having to rebuild previously calculated results. Furthermore, publicly available sets of genomes, such as the collection of “Complete Genomes” in the NCBI RefSeq database, are subject to change due to altered quality standards or the redefinition of reference genomes, such as the commonly used M. tuberculosis H37Rv strain. Therefore, it is essential that pan-genome representations also provide the feature to easily remove genomes from the initial set without impacting the remaining genomes. Most of the evaluated tools do not provide methods for updating a constructed pan-genome. Particularly research like molecular surveillance, where new data is continuously analyzed and incorporated, depends on data structures that allow the integration of an up-to-date set of genomes.In the time between November 30th, 2016 and January 20th, 2017 eight new In summary, we present a data structure for the representation of pan-genomes that provides a unique set of features needed for efficiently working with collections of related sequences and that can be integrated with existing methods for visualization and subsequent analyses.Additional file 1Supplementary Information for “seq-seq-pan”: Building a computational pan-genome data structure on whole genome alignment”. Additional file Additional file 2Supplementary Tables for “seq-seq-pan: Building a computational pan-genome data structure on whole genome alignment”. Additional file


BarraCUDA is an open source C program which uses the BWA algorithm in parallel with nVidia CUDA to align short next generation DNA sequences against a reference genome. Recently its source code was optimised using “Genetic Improvement”.The genetically improved (GI) code is up to three times faster on short paired end reads from The 1000 Genomes Project and 60% more accurate on a short BioPlanet.com GCAT alignment benchmark. GPGPU BarraCUDA running on a single K80 Tesla GPU can align short paired end nextGen sequences up to ten times faster than bwa on a 12 core server.The speed up was such that the GI version was adopted and has been regularly downloaded from SourceForge for more than 12 months. Bioinformaticians have seized the advantages of using computer graphics hardware (GPUs) , particuRecently  we preseBoth version of BarraCUDA and bwa use the Burrows-Wheeler algorithm. This requires the reference genome to be converted offline into an index file. The whole of the index must be kept in memory. Fortunately modern GPUs have high capacity and high bandwidth to their on-board memory Highnam et al.  report tLuo et al.  compare https://nvlabs.github.io/nvbio/nvbowtie_page.html was written by nVidia on top of their nvbio CUDA templates to emulate Bowtie2 on their GPUs. They claim similar accuracy and on real 100 bp paired end NGS data they claim a single dual K80 Tesla gives a 2.1 speed up compared to Bowtie2 using 20 threads on an Intel Xeon E5-2690 v2 CPU.nvBowtie n bp) takes O(n) time.  Arioc [The above tools are based on compressing the reference genome into a prefix index using the Burrows-Wheeler transform (which gives bwa its name). This has the advantage that typically, e.g. for human data, the whole index can be fitted into a GPU’s memory or indeed into many laptops and personal computers. However it means at best finding each NGS short read (of .) Arioc  takes a O(1)) access but in practise search is complicated by the need to deal with inexact matches and the size of the hash table. Wilton et al. [http://nvlabs.github.io/nvbio/) Wilton et al. [Arioc  uses hasn et al.  say for n et al.  run the n et al. , Fig. 8)n et al. , Fig. 8)n et al. .Typically next generation sequencing (NGS) alignment tools  have a start up overhead. Once started, data are often processed at a constant rate. (I.e. run time is linear in number of NGS DNA sequences.) However speed may be dramatically affected by user selected options and the quality of the data. For example, some tools allow the user to force all potential matches to be reported. Naturally this can considerably reduce the aligner’s speed. Similarly poor data can force the aligner to do more internal back tracking, which can similarly reduce the alignment rate (particularly if the user changes parameters to compensate for the noisy data).1 (previous section), GPU based aligners usually copy large data structures onto the GPU only once when they start. For BarraCUDA and similar aligners this means for human data the GPU must have at least 4GB of on board RAM.In many cases the aligners have strict memory requirements. Typically the computing hardware must have sufficient RAM to hold one or more large indexes. The size of the index typically depends upon the reference genome. Once this requirement is met, there is often little additional advantage if the size of RAM is increased. With CPU based aligners, Lenis and Senar  showed pGPU based aligners (such as BarraCUDA) typically get their speed by using a GPU thread per sequence. This works well where DNA strings map directly and uniquely to the reference genome. However, e.g. when data are noisy, there may be a need for the search to backtrack. Since when backtracking is invoked is different for each query, this means each GPU thread behaves differently, which means in turn that they diverge. Modern GPUs support thread divergence transparently, however divergent threads impact the GPU’s speed. In the case of the GI version of BarraCUDA we deal with this by inserting a non-divergent high speed pre-pass. This handles most cases. DNA strings which do not map simply, fall back to the slower divergent code. Thus, as with other tools, mentioned above, in practise speed will depend upon how noisy the DNA strings are. Although thread divergence is particularly a problems with GPU based aligners, the problem of noisy data needing more complex handling affects all NGS aligners and their speed can always be adversely affected by poor quality DNA sequence data.Genetic improvement is the process of applying search based optimisation techniques, such as genetic programming , directlDarwinian evolution is applied inside the computer ) was down loaded from GitHub and compiled with default settings (i.e. including support for multi-threading).bwa  .http://sourceforge.net/projects/seqbarracuda/files/latest/download). Again it was built with default setting (including support for multi-threading). However a second version was built specifically for the GT 730 which was compiled with -arch 2.1 to support compute level 2.1 (the default is now 3.5 or higher).BarraCUDA (0.7.107), was down loaded from SourceForge (The reference human genome  was down2). It contains 14 102 867 sequences. Approximately 5.7% of sequences occur more than once.One of The 1000 Genomes Project ’s normalhttp://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/gp-code/www.bioplanet.com/gcat/gcat_set_037). It contains 5 972 625 paired end (100 base) sequences. (Less than 0.1% of sequences were repeated.) Example bash command line using process substitution, pipes and input-output redirection to run two “aln” processes (one per paired end) in parallel with “sampe”, thus avoiding use of intermediate disk files.$exe1, $hg19, $seq1, $seq2 and $sam are the names of bash environment variables. $exe1 is the program, , $hg19 is the location of the reference genome index, $seq1 and $seq2 are the files holding the pairs of DNA sequences and $sam is the output. See also Fig. bwa, the original BarraCUDA (i.e. version 0.6.2) and the GI version of BarraCUDA i.e. 0.7.107) were each run five times on both the fourteen million real world paired end DNA sequences from The 1000 Genomes Project “” section07 were eApart from the low end GT 730, BarraCUDA is typically between two and ten times faster than bwa on a 12 core compute server. Table bwa “aln” (via pthreads) uses multiple threads. However bwa “sampe” does not support multiple host threads. This may explain why bwa performs relatively badly on the short 36 bp 1000 Genomes Project data.We have used large real world and benchmark sequences. However both bwa and BarraCUDA are sensitive not only to the length of the DNA sequences but also how noisy they are. Resolving ambiguous matches caused by noise slows them down.Depending upon examples, even a £50 GPU running BarraCUDA can be faster than bwa on a twelve core 2.60 GHz server. With a top end nVidia Tesla GPU, BarraCUDA can be more than ten times faster than bwa on a 12 core server.1 Arioc’s index considerably exceeds current GPU memories and care must be taken to try and limit the volume of re-loaded data.2 ERR001270 is available from The 1000 Genome Project’s FTP site. Additionally a copy can be down loaded from http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/gp-code/barracuda_0.7.105/1000.


In the case of eukaryotes, the selection of only one protein isoform per genomic locus is mandatory to avoid biases linked to redundancy. Here, we present IsoSel, a tool devoted to the selection of alternative isoforms in the context of phylogenetic reconstruction. It provides a better alternative to the widely used approach consisting in the selection of the longest isoforms and it performs better than Guidance, its only available counterpart. IsoSel is publicly available at  The alternative splicing, a process by which a single coding gene may lead to different transcripts and thus to different protein isoforms, is common in Eukaryotes. For instance, about 20% of plant genes  and 90% It is therefore absolutely necessary to select a unique sequence per genomic locus before reconstructing a phylogeny. Although manual selection provides usually the best results, this becomes tedious when the number of sequences and/or of homologous families is large. Two simple automated approaches are therefore commonly used: the random selection of one isoform , 7 or thIn that context, we developed IsoSel (Isoform Selector), a tool designed to the selection of protein isoforms specifically designed for phylogenetic reconstruction. IsoSel is based on the same approach as the one used by Guidance , a tool The first step of an IsoSel run consists in the alignment of an input protein dataset, using either CLUSTALO , MAFFT  or MUSCLa be the reference alignment obtained during step 1, ℓ the length of this alignment and n the number of bootstrap replicates set by the user. First, n alignment replicates are generated by the standard bootstrap procedure . For each bootstrap replicate, a distance matrix is then computed by IsoSel, this using one of the amino acid substitution models implemented in the program: Poisson (with or without Gamma correction), PAM (or its Kimura approximation), JTT (or its Gamma-corrected Poisson approximation), BLOSUM62, WAG or LG. From this distance matrix, the BioNJ [n resulting realignments of a represent the perturbed alignments.The second step is the generation of a set of perturbed alignments through a bootstrap approach. Let he BioNJ  algorithThe third and final step is the computation of the Sum-of-Pairs (SP) score  using thm be the number of sequences of the input dataset and b (1 ≤ b ≤ n) one of the n perturbed alignments generated during the second step. For each sequence i (1 ≤ i ≤ m) of length li from b, the pair score of the amino acid at position k (1 ≤ k ≤ li) is computed as:pijk is equal to 1 or 0 whether or not the amino acid at position k of sequence i is facing the same amino acid at the position k′ (1 ≤ k′ ≤ lj) of sequence j in the reference and perturbed alignment  at this position in a. If there no other residue at this position , Let lignment . Also, mSi for sequence i is calculated by averaging the residues scores:Si ≤ 1. The higher its value, the better the alignment of the isoform with the other sequences. For each genomic locus, the isoform with the best score is kept.From IsoSel comes with a lot of available options and parameters  and we will not list them all. But some of those options are of special interest as they can allow to improve greatly the results depending on the dataset contents. Below is a short description of those key options and in which context they should be used.a. For that purpose, we have implemented an option (-gap) which penalizes the sequences introducing gaps in the reference alignment. With this option, pijk is weighted by the number of gaps present at position k in a:mg = m − mk is the number of gaps at this position in a. If there is no gap, then mg = 1. Here, pijk is the same as before excepted that it is fixed at −1 if there is no other residue at this position in the reference alignment. By construction, Si values are computed using the same equation as before but they are much smaller. Nevertheless the alternative transcript selected is always the one with the highest score. This option is suited for datasets containing alternative isoforms resulting from intron retention or exon skipping events that are restricted to a reduced set of taxonomic groups.The standard SP score described in the previous section does not take into account the number of gaps present at a given site of -gap penalizes too long isoforms, the option -short was designed to penalize short isoforms, even if they are well aligned. In this case, Si is no longer calculated by dividing the sum of residue scores by the length of the sequence, but by the length of the reference alignment:-gap option, the Si values obtained are, by construction, smaller. This option is suited for datasets with isoforms corresponding to partial sequences or when a very short isoform is specific to a given taxonomic group.If the option -DS option (for “Distance Scores”) approximates the SP score by the mean of observed divergence (p-distance) between sequence i and the other input dataset sequences. Unlike the other scoring schemes, there is no bootstrap resampling procedure and the isoform selected is the one with the smallest distance .The bootstrap approach, with the computation of a set of perturbed alignments, is very time consuming when the number and/or the length of the sequences increase. To allow a faster approach, the -DS option uses a modified p-distance in which a gap is considered as a supplementary character state. In that way, considering two isoforms that only differs by an exon skipping event, their modified p-distance will not be near to one as it is with the standard p-distance. A bias towards the systematic selection of smaller isoform is thus avoided.In order to take into account the difference of lengths between isoforms, the dij be the modified p-distance between sequences i and j . The score Si corresponding to the sequence i is then computed as:ms its cardinal. The higher Si, the more distant to the other sequences of the input dataset is the sequence i.Let -DS option, the -WOT option (for “With Other Transcripts”) computes the mean of distances on the entire input dataset. Then In combination to the -auto) allowing to estimate them. Under this mode, if the reference alignment has > 35% of sites containing > 80% gaps, the Si scores are computed with the -gap option. If there are > 600 sequences in the input dataset or if the alignment length is > 10000 AA, then the option -DS is selected. In all other cases, the default parameters are used.Best options for IsoSel are dataset dependent, therefore we have implemented an automated mode .IsoSel minimal input requirement is an unaligned set of protein sequences in Fasta format. The output is a text file containing the scores for each input sequence . Optionaexample.fasta, contains 58 homologs of the human AKTS1 protein taken from Ensembl and from a local database of complete eukaryotic proteomes. Among those 59 sequences, 26 correspond to alternative isoforms whose genomic origin is indicated in the second file, named isoforms_locus_tag.txt. The first column of this second file corresponds to the sequence names (the same as those in the example.fasta file) and the second column to an identifier allowing associating a set of isoforms to a given gene. For example, the three lines below:An example dataset containing two files is included in the program distribution. The first one, named >ENSP00000375710|Homo_sapiens ENSG00000204673>ENSP00000375711|Homo_sapiens ENSG00000204673>ENSP00000375706|Homo_sapiens ENSG00000204673allows to specify that sequences ENSP00000375710, ENSP00000375711 and ENSP00000375706 are isoforms that originate from a single gene, identified as ENSG00000204673.E ≤ 10−30. The first collection corresponded to a subset of Ensembl release 80 containing 32 species while the second was made of 84 complete eukaryotic proteomes taken from GenBank release 70 . From each MSA, two trees were inferred to compute the tree length and the DL score. The first tree was inferred by SeaView  using th4 [Among the 154 sets, we used the one built with the human protein WDR18 (UniProtKB accession number Q9BV38) as a case study. For this sequence, the BLASTP search in the two collections led to a set of 73 homologous protein sequences. Among them, fourteen (19.2%) resulted from alternative splicing events . Selecti4 . The res4 .There is presently no gold standard to evaluate the quality of a MSA relatively to a phylogenetic criterion. However, Rzhetsky and Nei , stated -auto option led to shorter trees than the random and the longest isoform selections, respectively. A Wilcoxon paired test showed that these results are highly significant (both P < 2.2 × 10−16). In 119 cases (78.8%), one of the IsoSel options led to a shorter tree than the Guidance selection, which is also highly significant (P < 5.27 × 10−12).The longest and the random isoforms selections led to the smallest trees in only three and five cases, respectively. Moreover, for 129 and 127 of the 154 datasets , using IsoSel with the Another criterion of gene tree quality is its congruence to a reference species tree, especially in the case of eukaryotic species where horizontal gene transfers are rare events. We therefore performed a tree reconciliation for each of our datasets using Notung. The DL score provided by this program is proportional to the minimum number of duplications and losses needed to reconcile a gene tree with a species tree. Therefore, the lower the score is, the closer the gene tree is to the species tree.P < 10−8). Globally, for 63.5% of the datasets, the use of IsoSel led to equal or less discordant gene trees than those obtained using the other approaches , one of the IsoSel options allowed to obtain a tree with an equal (20 cases) or better (102 cases) DL score than the one inferred after the selection of the longest isoform. The comparison with the random selection gave similar results as IsoSel was better in 117 cases and equal in seven . Finally, in 128 cases (84.7%), IsoSel gave better results than the Guidance selection and performed equally in thirteen cases (8.6%). All those results are highly significants  is misplaced, this erroneous placement being probably linked to the long branch generated  procedures are shown in enerated . SaccoglIsoSel is a command line software designed for the automatic selection of protein isoforms in the framework of phylogenetic analyses. Based on the SP score, it allows to obtain datasets that are optimized for tree reconstruction. The only other software that can be compared to IsoSel is Guidance but this program presents some limitations. First, it requires the independent installation of a broad range of tools  while IsoSel is self-sufficient and is distributed with all the binaries required for its functioning. Then, it can only be run with the JTT substitution model while IsoSel allows the use of all standard site-homogeneous models. On a practical point of view, Guidance is usually slower than IsoSel when multithreading is enabled (data not shown). This point is probably linked to the fact that Guidance was not designed for alternative isoforms selection but rather as a general tool for assessing MSA quality. With this broader purpose, Guidance has to compute many scores in addition to SP, which lower its performances in terms of speed.Globally, it appears that, compared to the other available approaches, IsoSel allows selecting most frequently the sequences leading to gene trees that are shorter and closer to the species tree. It is thus more suited for phylogenetic reconstructions. IsoSel is implemented in C/C++, is optimized for multithreading and is available under the CeCILL license.S1 TableNumber of protein sequences available in Ensembl for each of the 32 selected species.(PDF)Click here for additional data file.S2 TableNumber of protein sequences for each selected eukaryotic complete genomes. The selected species are different from the ones from Ensembl.(PDF)Click here for additional data file.S3 TableFor each of the randomly selected human protein, the number of homologous sequences detected using BLASTP is indicated in the third column. The fourth and fifth columns give the gene number and percentage of alternative isoforms, respectively. Alignment length and different statistics about the detected homologs are listed in the last columns. ORFans, datasets containing less than 20 homologs or with only one gene generating alternative isoforms are highlighted in light grey, blue and yellow, respectively.(PDF)Click here for additional data file.S4 TableFor each of the 154 used datasets, the tree length obtained with each method is listed. The shortest are highlighted in blue. For three datasets , the selection with Guidance failed due to program crash. They are highlighted in light orange.(PDF)Click here for additional data file.S5 TableFor each of the 154 used datasets, the DL score computed by Notung with each isoform selection strategy is listed. The most consistent are highlighted in blue. For three datasets , the selection with Guidance failed due to program crash. They are highlighted in light orange.(PDF)Click here for additional data file.S1 FigThis tree was built according to Lecointre and Le Guyader book , the Ens(PDF)Click here for additional data file.


Recently the study of the complex system of connections in neural systems, i.e. the connectome, has gained a central role in neurosciences. The modeling and analysis of connectomes are therefore a growing area. Here we focus on the representation of connectomes by using graph theory formalisms. Macroscopic human brain connectomes are usually derived from neuroimages; the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network - this process is referred to as parcellation. The atlas-based parcellations present some known limitations in cases of early brain development and abnormal anatomy. Consequently, it has been recently proposed to perform atlas-free random brain parcellation into nodes and align brains in the network space instead of the anatomical image space, as a way to deal with the unknown correspondences of the parcels. Such process requires modeling of the brain using graph theory and the subsequent comparison of the structure of graphs. The latter step may be modeled as a network alignment (NA) problem.In this work, we first define the problem formally, then we test six existing state of the art of network aligners on diffusion MRI-derived brain networks. We compare the performances of algorithms by assessing six topological measures. We also evaluated the robustness of algorithms to alterations of the dataset.The results confirm that NA algorithms may be applied in cases of atlas-free parcellation for a fully network-driven comparison of connectomes. The analysis shows MAGNA++ is the best global alignment algorithm. The paper presented a new analysis methodology that uses network alignment for validating atlas-free parcellation brain connectomes. The methodology has been experimented on several brain datasets. The brain is a complex organ of vertebrates and it is composed of single specialized cells called neurons. Neurons are connected among them by synapses forming a complex network of connections. Connections among neurons carry signal pulses that carry information . The actRecent studies have demonstrated in an independent way a strict relation among the set of connections, the functions of the brains and the relations among the insurgence of neurological diseases and the variations of mechanims of connections with respect to healthy people . For exaconnectome referred to as the set of elements and interactions 13] the aSuch work, demonstrates the possibility to use NA into the atlas-free parcellation workflow and it poses to the research community the challenge to systematically explore the performance of different NA algorithms since different NA approaches are widely applied in molecular biology analysis, but they have not been explored yet in relation to MRI connectomics.The techniques for the alignment of biological networks fall into two categories: (i) the local network alignment searches relatively small similar subnetworks that are likely to represent conserved functional structures, (ii) the global network alignment looks for the best superimposition of the whole input networks. However, these approaches can not be easily applied in the connectome alignment problem. The reason is related to the strategy underlying methodology of alignment. For example, the local network aligners, widely used to build the alignment of protein interaction networks (PINs) , take asIn this paper we selected six existing state of the art global alignment algorithms and we tested these aligners on diffusion MRI-derived brain networks. The algorithms tested here are MAGNA++ , NETAL , GHOST , GEDEVO anatomical connectivity consisting of axonal fibers connecting cortical and subcortical regions inferred from diffusion imaging  signal between brain regions.An essential step in the analysis and macroscopic mapping of brain network is the subdivision of the brain into large-scale regions, also known as “parcellation process”. The brain parcellation consists of dividing the brain into a set of macroscopic, homogeneous and non-overlapping regions with respect to information provided, generally, by techniques based on magnetic resonance imaging (MRI) . Especiapredefined anatomical templates. This approach consists of the registration of the structural images from MRI to anatomical atlas based on the Brodmann areas )|.where However, ICS fails in the penalization of misaligning edges in the smaller network because it takes into account the target network.S3[Finally, the Symmetric Substructure Score, S3, takes iS3 has been shown to be superior to existing measures since it penalizes both alignments from sparse graph regions to dense graph regions and alignments from dense graph regions to sparse graph regions.Node Similarity: Such function considers the similarity among mapped nodes. Nodes of the aligned graphs can be more or less similar to each other. Thus the alignment should align each node of one graph to the most similar node of the other one given a node similarity functions, s→R, v1∈V1, v2∈V2. The overall objective is to maximize the sum of scores considering aligned nodes. Hybrid approaches: Some recent formulations of Q take into account of both of the approaches by linear combination.The network alignment problem can be formulated in various ways. In general, the network alignment can be classified as local alignment or global alignment.local alignment aims to find multiple and unrelated regions of isomorphism, i.e. same graph structure, between the input networks, where each region implies a mapping independently of other regions. The strategy consists of the mapping or set of mappings between subsets of nodes such that their similarity is maximal over all possible subsets. These subnetworks correspond to conserved patterns of interaction that can represent a conserved motif or pattern of activities . The glIn this work, six global alignment algorithms were chosen to built the global alignment of brain networks. We give hereafter a short conceptual description.A popular existing method of global alignment is MAGNA . MAGNA iThe second aligner is NETAL , an algoThe third algorithm, GHOST , is a glThe fourth global aligner is GEDEVO , a novelUnderlying the GEDEVO method is the Graph Edit Distance model (GED), where a graph is transferred into another one with a minimal number of edge insertions and deletions. Thus, GEDEVO uses the GED as optimization model for finding the best alignments.The fifth algorithm is WAVE  a generaThe last algorithm is Natalie2.0 , a netwoSection for a complete description.The dataset consisted of 24 diffusion MRI-derived structural networks of human brain: 12 networks with a number of nodes equal to 95 and the 12 networks with a number of nodes equal to 1000. The brain networks are related to three different stages of development by including newborns (NE), six-month-old infants (6M), and adults (AD). See networks95 and networks1000) related to same growth stages  by applying MAGNA++, NETAL, GHOST, GEDEVO, WAVE and Natalie2.0 algorithms. Initially, we aligned each network with itself. We executed this stage in order to test if the algorithm is able to build the alignment . However, among the selected algorithm, MAGNA++ is the unique tool that enables to compute all quality measures, NC, EC, ICS and S3. For this reason, we computed the quality of built alignments by using the software for NA evaluation proposed in [S3 (G S3), and NCV combined with G S3 (NCV-G S3). P-NC evaluates the the precision of the alignment i.e. the percentage of the aligned node pairs that are also present in the true node mapping. P-NC is defined as: Here, we aim to evaluate the quality of the alignments built with MAGNA++, NETAL, GHOST, GEDEVO, WAVE, Natalie2.0 NA algorithms. The topological quality is related to two alignment algorithm capability as the reconstruction of the true node mapping and the conservation of as much as possible edges. Typically, the Node Correctness (NC) is the measure widely used to evaluate how an alignment reconstructs the true node mapping correctly. Instead, different measures are used to evaluate how well the edges are conserved on an alignment, such as EC, ICS or posed in . The soff.were M is the set of node pairs that are mapped under the true node mapping and N be the set of node pairs that are aligned under f and it is defined as: R-NC evaluates the percentage of all node pairs from the true node mapping that are aligned under S3 is the percentage of conserved edges Nc out of the total of both conserved and non-conserved edges Nn: G NCV is the percentage of nodes from G1 and G2 that are also in G’1 and G’2 subgraphs:S3 is the geometric mean of the NCV and G S3 measures. These six measures evaluate alignment quality from different aspects and they can be divided in two groups, the first one composed by P-NC, R-NC and F-N measures that estimate how well the alignment captures the true node mapping, and the second one formed by NCV, G S3 and NCV-G S3 measures that capture the size of the alignment. We computed P-NC, R-NC, F-NC, NCV, G S3 and NCV-G S3 for each alignment built with MAGNA++, NETAL, GHOST, GEDEVO, WAVE, Natalie2.0. Then, we compared these measures in order to analyze which algorithm ensures a higher alignment quality. However, we focus on F-NC and NCV-GS3 as the most representative non-redundant measures because these are both a combination of two individual measures.Finally, NCV-G networks95 whereas Figs. networks1000.Figures networks95 and networks1000. We also note that values of NCV-G S3 for networks95 are higher than NCV-G S3 for networks1000.We note that the best results in terms of edge conservation were obtained when applying MAGNA++ as global aligner both on networks95, with exception of the quality of 12 alignments built with MAGNA++ that was better than other algorithms. For the networks1000, the F-NC values are higher for the alignment built with WAVE with exception of the alignments built with NETAL.Regarding the reconstruction of the true node mapping we note that the quality of alignment is homogeneous among We analyzed the robustness of the different algorithms to various levels of graph alteration . We generated a series of altered networks derived from the high-confidence brain network. We built the synthetic counterparts with 5, 10, 15, 20 and 25% of added noise. We obtained 60 synthetic networks with 95 nodes and 60 synthetic networks with 1000 nodes. To measure the performance of MAGNA++, NETAL, GHOST, GEDEVO, WAVE, Natalie2.0, we aligned the high-confidence brain network with its noisy counterparts obtained by random removal of edges from the network. Since all networks contain the same nodes, we know the true node mapping. The high-confidence network is an exact subgraph of each noisy network. Exploiting randomness, we ran each experiment 30 times and averaged results over the 30 runs . The aimUnderstanding brain connectivity can shed light on the brain cognitive functioning that occurs via the connections and interaction between neurons. The term brain connectivity refers to different aspects of brain organization including anatomical connectivity consisting of axonal fibers across cortical regions and functional connectivity defined as the observed statistical correlations of the BOLD signal between regions of interest. A powerful formalism to represent the brain connectivity derives from graph theory. The graph theoretical modeling of the human connectome has already enabled important discoveries and will most likely continue to do this in the future. In this study we proposed to apply classical global alignment algorithms such as MAGNA++, NETAL, GHOST, GEDEVO, WAVE, Natalie2.0, to align atlas-free human brain networks at three developmental stages. We analyzed the alignment results in term of topological quality measures and performance. According to these analyses, MAGNA++ resulted the best alignment algorithm. Our ongoing study is focused on the implementation of an ad hoc algorithm for connectome alignment. Since there are many conditions in which the classical parcellation is not useful, we retain that this seminal work may open the way for the use of network alignment in atlas-free parcellation.networks95. Table networks1000 even though the nodes number is different from 1000. Table The dataset consisted of diffusion MRI-derived structural networks of human brain at different stages of development, starting with newborns . AcquisiIn this section we describe in detail the global alignment algorithm selected to align the diffusion brain networks.V1|<|V2|) and builds the final global alignment. Moreover, to build the alignment MAGNA requires several parameters such as the type of initial population, population size, maximum number of generations , and optimization function . Furthermore, MAGNA introduces new and superior alignment quality measure that takes the best from each existing measure, The Symmetric Substructure Score (S3) [MAGNA  is a glore (S3) . that taS3 has been shown to be superior to existing measure, see [ure, see  for moreThere exists a MAGNA extension, named MAGNA++ , that inS3) and any desired node conservation measure. Let us define SN and SE, as node and edge conservation measures, then MAGNA++ maximizes the following measure: While MAGNA maximizes edge conservation during the alignment, MAGNA++ enables both the maximization of any different measures of edge conservation  that computes the difference in neighboring topologies of two nodes within a distance equal to 4. Afterward, the mapping f is partitioned into two sets of pairs with low and hight scores. The high scoring pairs are swapped randomly, whereas a number of randomly chosen bad pairs in the mapping are swap with directed mutations. After each swap, the scores among the new pairs are recomputed. This operation enables to keep good pairs and to swap a bad pair more often with another bad pair. At the end, the one swap that induces the best score is kept. In this way, the final score of the mapping results improved.GEDEVO is a global network aligner based on an evolutionary algorithm that uses the Graph Edit Distance (GED) as optimization model for finding the best alignments. The GED is a general model for the Graph Matching problem and it is defined as the minimal modifications required to transfer a graph into another graph. So, lets one-to-one mapping Weighted Alignment VotEr (WAVE) is a novel algorithm which builds an alignment by maximizing both node and edge conservation. When WAVE is used on top of well-established node cost functions, the alignment results improved with respect to different methods that optimize only node or edge conservation or treat each conserved edge the same. The reason consists of the capability of WAVE to favor conserved edges with similar NCF end nodes over those with dissimilar NCF end nodes. Furthermore, WAVE introduces a novel measure of edge conservation denoted as weighted edge conservation (WEC). WEC measure counts the number of conserved edges and weights each conserved edge by the node cost function based similarity of its end nodes. Thus, the edges with highly similar end nodes are preferred to be aligned over the edges with dissimilar end nodes. Starting from an empty alignment, WAVE calculates the marginal gain of adding an available node pair to the alignment. The marginal gain depends on the Alignment Quality that is based on a combination of weighted edge conservation and weighted node conservation measures. Thus, the pair with the highest marginal gain is aligned. Furthermore, when a pair of nodes is aligned, this node pair has a chance to give a weighted vote to their neighbors, where weighted vote for the initial vote of each node pair derives from a node conservation measures. At each step WAVE aligns each node pair with the highest vote and votes for all the pairs of neighbors. Finally, the vote that a node pair gets from its aligned neighbors is the marginal gain to the objective function of aligning them.Natalie 2.0 is an open source software for global network alignment which supports different scoring schemes taking into account both node-to-node correspondences and network topologies. By formulating the global network alignment as a mathematical program, this can be considered as a special case of the well-studied quadratic assignment problem. Natalie 2.0 focuses on sparse network alignment, where each node can be mapped only to a typically small subset of nodes in the other network. This corresponds to a quadratic assignment problem instance with a symmetric and sparse weight matrix. Thus, Natalie 2.0 obtains strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach.S3 (G S3), and NCV combined with G S3 (NCV-G S3) can be selected. To compute topological evaluation with P-NC, R-NC, and F-NC, the true node mapping between the aligned networks as additional input must be provided. For the topological measures NCV, GS3 and NCV-GS3, the two aligned networks are required as additional input. The biological evaluation is allowed by selecting four measures, GO correctness (GC), Precision of known protein function prediction (P-PF), Recall of known protein function prediction (R-PF) and F-score of known protein function prediction (F-PF). For the calculation of these biological measures, GO data of both aligned networks are required as input. The run time to compute the evaluation measures is few seconds.To compute the quality of built alignments we used the software for fairly evaluating a NA method proposed by . The sof