Clustering metagenomic sequences with interpolated Markov models
© Kelley and Salzberg; licensee BioMed Central Ltd. 2010
Received: 13 May 2010
Accepted: 2 November 2010
Published: 2 November 2010
Sequencing of environmental DNA (often called metagenomics) has shown tremendous potential to uncover the vast number of unknown microbes that cannot be cultured and sequenced by traditional methods. Because the output from metagenomic sequencing is a large set of reads of unknown origin, clustering reads together that were sequenced from the same species is a crucial analysis step. Many effective approaches to this task rely on sequenced genomes in public databases, but these genomes are a highly biased sample that is not necessarily representative of environments interesting to many metagenomics projects.
We present SCIMM (Sequence Clustering with Interpolated Markov Models), an unsupervised sequence clustering method. SCIMM achieves greater clustering accuracy than previous unsupervised approaches. We examine the limitations of unsupervised learning on complex datasets, and suggest a hybrid of SCIMM and supervised learning method Phymm called PHY SCIMM that performs better when evolutionarily close training genomes are available.
SCIMM and PHY SCIMM are highly accurate methods to cluster metagenomic sequences. SCIMM operates entirely unsupervised, making it ideal for environments containing mostly novel microbes. PHY SCIMM uses supervised learning to improve clustering in environments containing microbial strains from well-characterized genera. SCIMM and PHY SCIMM are available open source from http://www.cbcb.umd.edu/software/scimm.
Over the last 15 years, DNA sequencing technologies have advanced rapidly, allowing sequencing of over one thousand microbial genomes . Still, this accounts for only a sliver of the fantastic diversity of microbes on the planet . Sequencing of environmental DNA (often called metagenomics) has shown tremendous potential to drive the discovery and understanding of the "unculturable majority" of species -- the vast number of unknown microbes that cannot be cultured in the laboratory . Successful metagenomics projects have sequenced DNA from ocean water sampled from around the world , microbial communities in and on humans [5–8], and acid drainage from an abandoned mine . These and many other projects (e.g. [10–12]) promise to uncover the true extent of microbial diversity and give us a better understanding of how these unknown microbes live.
However, progress has been slowed by the difficulty of analysis of metagenomic data. The output from an environmental shotgun sequencing project is a large set of DNA sequence "reads" of unknown origin. Because these reads come from a diverse population of microbial strains, assembly produces a large collection of small contigs (contiguous stretches of unambiguously overlapping reads) [13, 14]. Two important goals of metagenomics are to determine what species are in the mixture in what proportions and to assemble substantial portions of individual genomes. A fragmented assembly of short sequences makes attaining these goals difficult. Advances in computational analysis techniques are essential to move the field forward.
To uncover what microbes are in a metagenomic sample, we must determine (1) which sequencing reads came from the same microbial strain, and (2) where those strains fit into the phylogenetic tree of life . Methods to solve these two problems are related. Clustering methods solve the former problem by binning sequences into clusters that represent a single taxonomic class. classification methods aim to solve the latter problem by assigning a specific taxonomic class to every sequence.
In some cases, the presence of marker genes like 16 S rRNA, which is very highly conserved across species but has variable regions, can be used to assign a taxonomic class to sequence fragments [16, 17], but this typically pertains to only a very small percentage of the reads. For example, ~0.1% of reads in a typical metagenomics project carry rRNA genes . More general sequence similarity-based methods align reads with BLAST  to known genomes deposited in public databases like GenBank  and use those alignments to assign a taxonomic classification [20–22]. However, sequence alignment can only classify reads from organisms with a close evolutionary relative that has already been sequenced . In most environments, this will not be the case for many of the reads; e.g. 70% of Sargasso Sea reads had a BLAST hit using "extremely lenient" search parameters, and only 30% aligned for nearly their whole length .
Composition-based methods for clustering and classification use properties of the DNA sequence such as oligonucleotide frequencies. These "genome signatures" are influenced by a variety of factors including codon usage, DNA structure, replication and repair processes, and evolutionary pressures [24–26]. They are fairly constant within a genome [27–29] and can be useful for inferring phylogenies . Crucially for the use of genome signatures for clustering and classification, they persist even in conserved  or horizontally transferred regions (after a sufficient period of time)  and remain diverse between species despite shared environmental pressures and interactions . Composition-based classification methods typically train on the oligonucleotide frequencies of all known genomes, and then classify sequences using supervised machine learning such as kernelized nearest neighbor , support vector machines , self-organizing maps , and naive Bayesian classifiers . Phymm, a recently developed composition-based approach developed in our group , trains interpolated Markov models (IMMs) on known genomes in order to classify sequences.
While supervised learning has proven useful in practice, shortcomings exist. Methods trained on the genomes in GenBank make an implicit assumption that those genomes are representative of microbes waiting to be found by metagenomics projects. This assumption is clearly violated by many if not most metagenomic samples. Supervised learning methods that tread carefully with respect to the potential biases caused by this assumption can still be useful analytical tools for many environments. Alternatively, genome signatures can be used for unsupervised clustering by learning the signatures from the set of sequences without the use of known genomes [33, 39–42]. Such approaches may be required when publicly available genomes are a poor fit to the data.
As an alternative to oligonucleotide frequencies, Markov chain models have shown great promise for characterizing genomic content , and have been implemented for both supervised classification  and unsupervised clustering  methods. In this paper, we cluster sequences using interpolated Markov models (IMMs), a type of Markov chain model that adapts the model complexity to take advantage of variable amounts of training data. This strategy is well suited to metagenomics clustering problems, where the amount of sequencing performed and the relative abundances of the species in the mix can vary widely. Our clustering framework proceeds similarly to one used to cluster sequences using hidden Markov models where optimization is performed iteratively by a relative of the k-means clustering algorithm . We refer to our method as SCIMM (Sequence Clustering with Interpolated Markov Models).
We test Scimm on simulated metagenomic datasets of fragments from mixtures of randomly selected known genomes and demonstrate improvement on the performance of the metagenomic sequence clustering programs CompostBin  and LikelyBin . We also assess the limitations of unsupervised learning on complex datasets, and describe how a combination of Scimm and Phymm, which we call PhyScimm, clusters more accurately when useful training data is available.
Markov models have proven to be an invaluable tool for sequence analysis , including capturing genome signatures . Here we present a clustering algorithm called SCIMM in which we use interpolated Markov models (IMMs) to model clusters of sequences. Clustering of sequences is performed using a variant of the k-means algorithm.
Interpolated Markov models
To train an IMM on a set of sequences, consider each w+1 sized window in the sequences and let the distribution of nucleotides at position i in the windows define random variable X i . Training creates a probabilistic decision tree using information gain as the splitting criteria where each node specifies certain nucleotides at a subset of the window positions and defines a probability distribution for the final nucleotide in the windows. To construct this tree, first, compute the mutual information I(X i ; X w+1 ) between the final position in the window and positions i ∈ 1..w. Define the initial split in the tree at the position with the greatest mutual information. Create branches to new nodes for all four nucleotides at this position. Next, perform a similar procedure for each branched node considering only windows containing the specific nucleotide at the position chosen. For these windows, compute the conditional mutual information of the remaining positions and choose the most informative position for the next split. Repeat this procedure to fill in the full decision tree, stopping early on paths where data becomes too sparse. At some point walking down each path, additional nucleotide positions may fail to be informative. We recognize this by computing a chi-square test between each node's distribution and its parent node's distribution. If the distributions are sufficiently similar, we stop branching and interpolate between the node and its parent's distributions, weighting each one based on the chi-square test result and the number of training windows mapped to the node.
To compute the likelihood that a novel sequence was generated by this IMM, consider each window of size w + 1 in the sequence as in Equation 1. For each window, follow a path through the decision tree to a leaf node according to the nucleotides at the positions defined by the nodes and branches. Score the next nucleotide in the novel sequence using the leaf node's interpolated probability distribution. More details of the training of IMMs and sequence likelihood computations can be found in the Glimmer descriptions [46, 47].
K -means clustering framework
The k-means algorithm is a widely used, simple and effective method for clustering data points. We review that algorithm before introducing our own approach to clustering sequences. Points are modeled as having come from k sources, each represented by a cluster mean. The algorithm begins by initializing these cluster means, e.g. by randomly choosing k data points. Next, one repeats the following steps. First, compute the distance between all points and the k cluster means. Second, assign each point to its nearest cluster.
Finally, recompute the cluster means using the current assignment of points to clusters. After a number of iterations, one arrives at a stable partitioning of data points that approximates the minimum sum of squared distances between data points and their assigned cluster means.
Using CEM, the CML criterion converges to a local maximum .
Because the Maximization step is not straightforward maximum likelihood estimation (instead using IMM training's highly effective heuristics to choose a model order and interpolate between models), we lose the theoretical guarantee of CML convergence . In practice, we did not find this to be a problem as the algorithm converged in all experiments. However, SCIMM halts when fewer than 0.1% of the sequences change clusters in order to reduce computation time because the last few stages of this procedure tend to shuffle a small number of sequences with a negligible effect on clustering accuracy.
SCIMM inherits the simplicity and effectiveness of the k-means algorithm, but also its sensitivity to initial conditions. We found that the likelihood landscape is riddled with local maxima from which the optimization cannot escape. Initially partitioning the sequences by very simple clustering algorithms yielded insufficient results.
To improve performance, we tried using previous methods for unsupervised clustering of metagenomic sequences to initialize the IMMs. We focused on two particularly successful approaches, LikelyBin and CompostBin. LikelyBin models sequences using k fixed 2nd-4th order Markov models learned by counting oligonucleotides . Because LikelyBin uses simpler models with far fewer parameters than IMMs, a Markov chain Monte Carlo algorithm is used to search the parameter space for the parameters that maximize the likelihood of generating the sequences. LikelyBin is publicly available at http://ecotheory.biology.gatech.edu/downloads/likelybin. The second approach, CompostBin , works as follows. For each sequence, count oligonucleotide frequencies and project the frequency vectors into three dimensions using principal component analysis. Next, create a graph where each sequence is represented by a vertex and edges are placed between a sequence and its six nearest neighbors. Finally, split the sequences into two partitions by finding a minimum normalized cut in this graph across which few edges exist . This process is repeated until the desired number of clusters is reached. Though CompostBin is publicly available from http://bobcat.genomecenter.ucdavis.edu/souravc/compostbin, we re-implemented the main unsupervised ideas of the algorithm to better fit in our pipeline and refer to our version as CBCBCompostBin. One notable adjustment to the method was to make the number of nearest neighbors with which to build the graph a function of the number of sequences, because fewer sequences required a less connected graph for good performance. Choosing the number of nearest neighbors is a difficult subproblem of the normalized cut clustering method upon which CompostBin is based . We found that the function , where f returns the number of nearest neighbors and n is the number of input sequences, worked well in practice, but did not address this problem in depth because experimental results demonstrated that SCIMM's accuracy did not depend significantly on the parameter choice.
To initialize the IMMs for SCIMM, we can run either LikelyBin or CBCBCompostBin on a random subset of the sequences with a user-specified number of clusters k and train an IMM on every cluster returned. We used a random subset because both algorithms can be slow for large data sets, and 2-3 Mb of sequence was sufficient to train the IMMs to begin the iterative clustering procedure. Because the two programs approach sequence clustering differently, they tend to succeed on different datasets -- e.g. for mixtures of 10 genomes, the standard deviation of the difference between LikelyBin's and CBCBCompostBin's precision (defined below) is 8.3% and recall is 6.5%. Therefore, we initially partition the sequences with both LikelyBin and CBCBCompostBin and perform one iteration of Scimm on each. For each partitioning, we compute the CML criterion and continue iterating on only the partitioning with the greater value.
Supervised initial partitioning
As we will show, unsupervised clustering methods are very effective on low complexity datasets, but less accurate on metagenomic samples with many (e.g. >20) microbial strains. With more strains, the genome signatures may blend together and become difficult to properly discern. Alternatively, classification methods like Phymm are immune to the complexity of the dataset because each sequence is classified independently of the others . Sequence classifications can be interpreted as implying a clustering, for instance by forming clusters from all sequences classified to the same genus. Therefore, a classification method can also be used to obtain an initial partitioning for SCIMM.
We considered a hybrid of supervised and unsupervised learning referred to as PHY SCIMM where we obtained an initial partitioning of the sequences with Phymm. First, we randomly chose a subset of sequences (again due to computation time concerns and the sufficiency of a subset), classified the sequences, and clustered at a certain taxonomic level (family in our tests). Due to misclassification noise, Phymm will usually return too many clusters. To filter out clusters of misclassified sequences, we found only keeping clusters containing of the sequenced bases where k is the number of genomes in the mixture (e.g. > 1% for 20 genomes) to be a useful heuristic. Note that Phymm is not limited to returning k clusters, and the number of clusters returned depends on the strictness of filtering, which the user would need to specify in a novel environment. After filtering clusters, we moved all unclustered sequences to an additional cluster, otherwise SCIMM tended to incorrectly force these sequences into the generally high quality clusters from Phymm classifications. Finally, we iterated IMM clustering as in the standard SCIMM algorithm. SCIMM and PHY SCIMM are available open source from http://www.cbcb.umd.edu/software/scimm under the Perl Artistic License http://www.perl.com/pub/a/language/misc/Artistic.html.
Results and Discussion
To assess the performance of SCIMM and PHY SCIMM, we simulated sequencing reads from mixtures of 1028 sequenced genomes in GenBank  as of 2009 and clustered the reads with each method. The degree to which the diversity of a random mixture of these genomes is representative of a real metagenomic environment has not been explored in depth. We make two points in support of this experimental setup. First, because certain model and disease-related organisms are of particular interest to researchers, GenBank contains many clusters of extremely closely-related genomes that make clustering difficult and may be representative of a heterogeneous species population from a real metagenomic environment; for example, 29 Escherichia coli, 16 Salmonella enterica, and 15 Staphylococcus aureus genomes were included. Second, while the expected clustering accuracy of any single method on a novel metagenomic environment may not exactly match the statistics reported in our tests, the simulations still serve to rank SCIMM and previous unsupervised approaches based on clustering accuracy.
For each test, we randomly chose k genomes and k corresponding uniformly distributed random numbers in the interval (0,1). We simulated 30000 reads of length 800 base pairs (bp) so that the percentage of reads from each genome in the sample was proportional to that genome's random number. We clustered the reads with SCIMM, LikelyBin, and CBCBCompostBin. LikelyBin runs used 2 MCMC start points and a 3rd order Markov model. CBCBCompostBin runs used 5-mers.
In order to obtain global performance statistics, precision and recall were combined across clusters and genomes by weighting each term by the number of sequenced nucleotides from the cluster or genome. We also measured accuracy using the adjusted Rand index. The Rand index is the proportion of pairs of data points that are correctly placed together or apart, and the adjusted Rand index modifies this statistic based on the sizes of the clusters .
Varying read length
Varying error rate
Experiments clustering single datasets can teach us about specific strengths and weaknesses of the methods and how they can be applied most effectively. To use more realistic data, we clustered the Arachne-assembled contigs from the FAMeS simulated metagenomic datasets of low (simLC) and medium (simMC) complexity . These were created by mixing real reads from the original sequencing projects of 113 organisms. The contigs are dominated by a few species, but have a long tail of very low abundance species. We clustered with SCIMM using k = 2-6 clusters and with PHY SCIMM initializing clusters from genus level classifications assigned to >1% of the total bp. Because Phymm has trained IMMs for these publicly available genomes, we held out IMMs similar to organisms in the mixture at the strain and species levels. In a noisy dataset with many organisms like this one, sequences from different strains of the same species are effectively indistinguishable. Thus, we computed accuracy at the species level for the tests that follow.
SimMC has 7307 contigs of mean size 2332 bp from 51 microbial strains. These contigs are distributed among the strains slightly more uniformly, but still only six species account for 99.0% of the nucleotides. These six include two strains each from the species Rhodopseudomonas palustris and Xylella fastidiosa. Bradyrhizobium sp. BTAi1 also appears and presents a challenge similar to that described above for simLC. For k = 2 and 3, SCIMM formed strong clusters for the the Xylella fastidiosa strains and the Bradyrhizobiaceae strains, leading to very high recall. As we increased k, these strains were split among the clusters, significantly decreasing the recall (see Figure 5). From this experiment and the last one, we see that clustering performance is best when k is set to the number of dominant phylogenetic sources. Increased values of k risk splitting a dominant species into multiple clusters rather than effectively clustering a far less abundant species. Precision did not increase with more clusters because when the Bradyrhizobiaceae strains split into multiple clusters, each one contained a mixture of both species. When IMMs from the same species were available, PHY SCIMM produced much better clusters with 90% precision and 85% recall. But, accuracy dropped precipitously when IMMs were held out at the species level. Thus, we see again that PHY SCIMM clusters more accurately if very related genomes are available for training, but pure unsupervised clustering is preferable for a metagenome containing organisms whose taxa are unsequenced.
Instead of computing accuracy at the species level, we could consider a higher level in the hierarchy of taxonomic classification, such as the family level. By doing so, we reward the clustering algorithm for clustering together two sequences that originated from different strains in the same family, such as Bradyrhizobium sp. BTAi1 and the Rhodopseudomonas palustris strains. Family level precision is >97% in all tests, meaning that generally when SCIMM is merging two separate species into a cluster, they are phylogenetically related.
In vitro-simulated metagenome
To further explore the effectiveness of SCIMM and PHY SCIMM on more realistic data, we clustered sequencing reads from an in vitro-simulated microbial community . Here, ten microbes were mixed into a simulated metagenome and sequenced using a number of different protocols and sequencing techniques. These ten were chosen to cover a wide range of microbial diversity, but also to include closely related species, specifically two Lactobacillus strains and two Lactococcus strains. The resulting reads were then assigned to their source genome via BLAST  alignments to a database of the ten microbes' genomes. After combining classified reads from all non-454 datasets, we obtained 24410 mated reads and 3285 singleton reads.
We clustered the reads with SCIMM into 8 clusters for the 8 species in the data and computed 87% recall and 88% precision at the species level. As expected, the Lactobacillus and Lactococcus strains each clustered together well. High quality clusters formed around the medium abundance strains Shewanella amazonensis SB2B and Myxococcus xanthus DK 1622, but SCIMM split reads from the most abundant strain Acidothermus cellulolyticus 11B into mainly two clusters. Meanwhile, low abundance strains Pediococcus pentosaceus ATCC 25745 and Halobacterium sp. NRC-1 lacked the data to form their own pure clusters and co-clustered with the Lactococcus strains and Acidothermus cellulolyticus 11B respectively. Knowing that SCIMM can struggle with low abundance species and seeing that 2 of the 8 clusters were effectively unused and contained far fewer reads than the rest, we reduced the number of clusters to 6. Doing so brought the two Acidothermus cellulolyticus 11B clusters together and increased the recall to 94%.
Clustering the reads with PHY SCIMM led to further insight. The level at which IMMs were held out did not have a significant impact on clustering accuracy for this dataset, so we discuss the results from holding out IMMs from the same genus as the strains in the simulated metagenome. We initially clustered sequences using family classifications that were assigned to >3% of the sequences. Performance was considerably worse than unsupervised SCIMM with a 79% recall and 83% precision on the 7 clusters.
PHY SCIMM struggled with Acidothermus cellulolyticus 11B because there are no other trained IMMs in its family Acidothermaceae. Instead, Phymm assigned its reads to the families Mycobacteriaceae, Microbacteriaceae, and Propionibacteriaceae. Each of these families belong to the order Actinomycetales, and so PHY SCIMM performed far better when initialized using order classifications (6 clusters with 88% recall and 92% precision). Interestingly, Phymm misclassifies many reads from the Lactococcus strains, the Lactobacillus strains, and Shewanella amazonensis SB2B to the order Enterobacteriales, but iterative IMM clustering is able to effectively separate these species despite a poor initialization.
Determining the relationships between sequences is a crucial step in metagenomics analysis. In this paper, we introduce SCIMM, an unsupervised sequence clustering method based on interpolated Markov models (IMMs). Our experiments show that SCIMM clusters sequences more accurately than previous unsupervised algorithms.
By demonstrating the ability of IMMs to successfully cluster sequences, we add to the growing evidence of the effectiveness of IMMs for modeling DNA sequences [38, 53]. Markov chain models have proven to be useful sequence modeling tools for many bioinformatics applications . The increased modeling sophistication and ability to handle varying amounts of training data make IMMs preferable for many of these applications.
We compared two variations of clustering with IMMs. SCIMM is purely unsupervised and makes use of the previously published methods LikelyBin and CompostBin to initially partition the sequences. PHY SCIMM partitions the sequences using supervised Phymm classifications before the unsupervised iterative IMM clustering stage. Supervised learning proved to be a valuable addition to the pipeline when genomes were available to train on from the same genus as the microbes in the mixture. Pure unsupervised learning is preferable when the available genomes to train on are not representative of those from which the sequencing reads originated. Because the classification accuracy of Phymm is independent of the complexity of the mixture, supervised learning also improves clustering of complex mixtures of twenty or more microbes. Developing more sophisticated combinations of classification and clustering methods may prove to be a fruitful line of research.
We believe SCIMM and PHY SCIMM will be valuable tools for researchers seeking to determine the relationships between sequencing reads from a metagenomics project. For environments with ten or fewer species, unsupervised clustering with SCIMM finds accurate clusters. However, the number of clusters k must be chosen carefully by the user. Specific knowledge about the environment, especially regarding the number of dominant microbes and their relationships to each other, can inform the choice of k and impact the utility of a clustering of the environment's sequences. Nevertheless, tests on the FAMeS dataset showed that various values of k can produce useful clusters. Lesser values of k tend to provide greater recall with lower precision. Greater values of k may decrease recall by dividing a particularly dominant species into more than one cluster but will usually improve precision.
When the microbes in an environment are thoroughly represented in public databases, PHY SCIMM finds even more accurate clusters. PHY SCIMM is also more effective for mixtures of twenty or more strains. The user does not need to choose the number of clusters with PHY SCIMM, but must choose the classification level and minimum support to initialize a cluster. The simulated read experiments offer guidelines for how to set these parameters effectively. Tests with the FAMeS and in vitro-simulated metagenome datasets demonstrated that incorporating knowledge about the dominant organisms in the environment can have a significant positive impact on the clusters.
Metagenomics projects are increasingly turning to less expensive and higher throughput second generation sequencing technologies such as those from Roche/454 and Illumina. Clustering of 400 bp read lengths is still reasonably effective for mixtures of five or fewer strains. Shorter reads, such as the 100-125 bp lengths currently available from Illumina, cannot be accurately clustered by our methods for environments with realistic complexity. However, if these reads can be assembled into larger contigs, then effective clustering of the contigs is possible.
A number of avenues appear worthwhile for further research. A principled method for setting parameters that affect the number of clusters would certainly aid researchers using the method. Preliminary sequencing of 16 S rRNA or other marker genes followed by clustering may effectively achieve this goal [17, 54]. The k-means iterative clustering framework used by SCIMM works well with a good initial partitioning of the sequences, but other optimization methods might prove more robust to the initial conditions and less prone to getting stuck in local maxima. Because SCIMM nearly always improves on the clustering results of LikelyBin and CBCBCompostBin, there is reason to believe that it would also improve on initial clusters from more accurate future methods. We excluded an interesting feature from the original CompostBin in our experiments whereby reads containing informative marker genes were identified and classified using AMPHORA  and the classifications were used to add supplemental edges to the nearest neighbor graph. A similar semi-supervised scheme could be implemented in SCIMM as well. Finally, assembly and clustering are both important steps in metagenomics pipelines, and further exploration of the relationship between the two has the potential to improve both tasks.
We thank Arthur Brady, Art Delcher, Mihai Pop, Carl Kingsford, Saket Navlakha, James White, and Adam Phillippy for valuable discussions on the method and the manuscript.
This work was supported in part by the National Institutes of Health grants R01-LM006845 and R01-LM083873 to SLS.
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