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Ratings and Reviews Write a review. Most relevant reviews. When included in the clustering, these samples were the only ones that failed to cluster by body site Additional file 1 : Figure S7. However, because the Mash distance is based on simple k-mer sets, it may be more prone to batch effects from sequencing or sample preparation methods. For example, Mash does not cluster MetaHIT samples by health status, as previously reported [ 37 ], and MetaHIT samples appear to preferentially cluster with one another.

Mash enables the comparison and clustering of whole genomes and metagenomes on a massive scale. Potential applications include the rapid triage and clustering of sequence data, for example, to quickly select the most appropriate reference genome for read mapping or to identify mis-tracked or low quality samples that fail to cluster as expected. Strong correlation between the Mash distance and sequence mutation rate enables approximate phylogeny construction, which could be used to rapidly determine outbreak clusters for thousands of genomes in real time.

Additionally, because the Mash distance is based upon simple set intersections, it can be computed using homomorphic encryption schemes [ 38 ], enabling privacy-preserving genomic tests [ 39 ].

Future applications of Mash could include read mapping and metagenomic sequence classification via windowed sketches or a containment score to test for the presence of one sequence within another [ 4 ]. However, both of these approaches would require additional sketch overhead to achieve acceptable sensitivity.

Improvements in database construction are also expected. For example, rather than storing a single sketch per sequence or window , similar sketches could be merged to further reduce space and improve search times.

Obvious strategies include choosing a representative sketch per cluster or hierarchically merging sketches via a Bloom tree [ 40 ]. Finally, both the sketch and dist functions are designed as online algorithms, enabling, for example, dist to continually update a sketch from a streaming input.

The program could then be modified to terminate when enough data have been collected to make a species identification at a predefined significance threshold. This functionality is designed to support the analysis of real-time data streams, as is expected from nanopore-based sequencing sensors [ 24 ].

To construct a MinHash sketch, Mash first determines the set of constituent k-mers by sliding a window of length k across the sequence. Mash supports arbitrary alphabets e. Depending on the alphabet size and choice of k , each k-mer is hashed to either a bit or bit value via a hash function, h. For nucleotide sequence, Mash uses canonical k-mers by default to allow strand-neutral comparisons.

In this case, only the lexicographically smaller of the forward and reverse complement representations of a k-mer is hashed. For a given sketch size s , Mash returns the s smallest hashes output by h over all k-mers in the sequence Fig.

For a sketch size s and genome size n , a bottom sketch can be efficiently computed in O n log s time by maintaining a sorted list of size s and updating the current sketch only when a new hash is smaller than the current sketch maximum. As demonstrated by Fig. With these parameters, the resulting sketch size equals 1. For large genomes, this represents an enormous lossy compression e.

However, the probability of a given k-mer K appearing in a random genome X of size n is:. This will skew any k-mer based distance and make distantly related genomes appear more similar than reality.

To avoid this phenomenon, it is sufficient to choose a value of k that minimizes the probability of observing a random k-mer. Given a known genome size n and the desired probability q of observing a random k-mer e. The small k also improves sensitivity, which helps when comparing noisy data like single-molecule sequencing Additional file 1 : Figures S2 and S3.

Lastly, for sketching raw sequencing reads, Mash provides both a two-stage MinHash and Bloom filter strategy to remove erroneous k-mers. These approaches assume that redundancy in the data e. Given a coverage threshold c , Mash can optionally ignore such low-abundance k-mers with counts less than c. By default, the coverage threshold is set to one and all k-mers are considered for the sketch.

Increasing this threshold enables the two-stage MinHash filter strategy, which is based on tracking both the k-mer hashes in the current sketch and a secondary set of candidate hashes. At any time, the current sketch contains the s smallest hashes of all k-mers that have been observed at least c times and the candidate set contains hashes that are smaller than the largest value in the sketch sketch max , but have been observed less than c times.

When processing new k-mers, those with a hash greater than the sketch max are immediately discarded, as usual. However, if a new hash is smaller than the current sketch max, it is checked against the candidate set. If absent, it is added to this set. If present with a count less than c — 1, its counter is incremented. If present with a count of c — 1 or greater, it is removed from the candidate set and added to the sketch.

At this point, the sketch max has changed and the candidate set can be pruned to contain only values less than the new sketch maximum. The result of this online method is equivalent to running the MinHash algorithm on only those k-mers that occur c or more times in the input. However, in the worst case, if all k-mers in the input occur less than the coverage threshold c , no hashes would escape the candidate set and memory use would increase with each new k-mer processed.

Alternatively, a Bloom filter can be used to probabilistically exclude single-copy k-mers using a fixed amount of memory. In this approach, a Bloom filter is maintained instead of a candidate list and new hashes are inserted into the sketch only if they are less than sketch max and found in the Bloom filter. If a new hash would have otherwise been inserted in the sketch but was not found in the Bloom filter, it is inserted into the Bloom filter so that subsequent appearances of the hash will pass.

This effectively excludes many single-copy k-mers from the sketch, but does not guarantee that all will be filtered. With this approach, filtering k-mers with a copy number greater than one would also be possible using a counting Bloom filter, but this has not been implemented since the exact method typically outperforms the Bloom method in practice, both in terms of accuracy and memory usage.

Because the sketches are stored in sorted order, this requires only O s time and effectively computes:. Specific confidence bounds are given below and in Additional file 1 : Figure S1. Note, however, that the relative error can grow quite large for very small Jaccard values i.

In these cases, a larger sketch size or smaller k is needed to compensate. The Jaccard index is a useful measure of global sequence similarity because it correlates with ANI, a common measure of global sequence similarity. However, like the MUM index [ 19 ], J is sensitive to genome size and simultaneously captures both point mutations and gene content differences. This can be a useful metric for clustering, but is non-linear in terms of the sequence mutation rate.

In contrast, the Mash distance D seeks to directly estimate a mutation rate under a simple Poisson process of random site mutation.

As noted by Fan et al. To account for two genomes of different sizes, Fan et al. In contrast, Mash sets t to the average genome size n , thereby penalizing for genome size differences and measuring resemblance e. Equation 4 carries many assumptions and does not attempt to model more complex evolutionary processes, but closely approximates the divergence of real genomes Fig.

With appropriate choices of s and k , it can be used as a replacement for costly ANI computations. Table 1 and Additional file 1 : Figure S2 give error bounds on the Mash distance for various sketch sizes and Additional file 1 : Figure S3 illustrates the relationship between the Jaccard index, Mash distance, k-mer size, and genome size. In the case of distantly related genomes it can be difficult to judge the significance of a given Jaccard index or Mash distance.

As illustrated by Eq. How many k-mers then are expected to match between the sketches of two unrelated genomes? This depends on the sketch size and the probability of a random k-mer appearing in the genome, where the expected Jaccard index r between two random genomes X and Y is given by:.

From Eq. For the population size m of all distinct k-mers in X and Y and the number of shared k-mers w , where:. For the sketch size s , shared size w , and population size m :. Mash uses Eq. This equation does not account for compositional characteristics like GC bias, but it is useful in practice for ruling out clearly insignificant results especially for small values of k and j.

Interestingly, past work suggests that a random model of k-mer occurrence is not entirely unreasonable [ 41 ]. Note, this P value only describes the significance of a single comparison and multiple testing must be considered when searching against a large database.

While not ideal for large genomes due to the small k or highly divergent genomes due to the small sketch , these parameters are well suited for determining species-level relationships between the microbial genomes that currently constitute the majority of RefSeq. For similar genomes e. As ANI drops further, the Jaccard index rapidly becomes very small and larger sketches are required for accurate estimates. Confidence bounds for the Jaccard estimate can be computed using the inverse cumulative distribution function for the hypergeometric or binomial distributions Additional file 1 : Figure S1.

For example, with a sketch size of , two genomes with a true Jaccard index of 0. In rare cases this strategy resulted in over-separation due to database mislabeling. Plasmids and organelles were grouped with their corresponding nuclear genomes when available; otherwise they were kept as separate entries.

Each chunk was sketched with:. This required Note: option -f is not required in Mash v1. Each chunked sketch file was then compared against the combined sketch file, again in parallel, using:.

This required 6. For the ANI comparison, a subset of Escherichia genomes was selected to present a range of distances yet bound the runtime of the comparatively expensive ANI computation. The corresponding Mash distances were taken from the all-vs-all distance table as described above. For the primate phylogeny, the FASTA files were sketched separately, in parallel, taking an average time of 8. The sketches were combined with Mash paste and the combined sketch given to dist.

Accessions for all genomes used are given in Additional file 1 : Table S1. The UCSC tree was downloaded from [ 51 ]. Each dataset listed in Table 3 was compared against the full RefSeq Mash database using the following command for assemblies:. Note: option -u was replaced by -b in Mash v1. The RefSeq genome with the smallest significant distance, with ties broken by P value, was also reported.

The full dataset was split into 44 samples corresponding to Table 1 in Rusch et al.