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2 Mash: fast genome and metagenome distance estimation Don L Armstrong Institute for Genomic Biology, Computing Genomes for Reproductive Health, University of Illinois, Urbana-Champaign June 23, 2016 Code and slides are here:
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4 The Problem Don Armstrong (IGB) MASH June 23, / 13
5 MinHash Algorithm Decompose dataset into k-mers Hash k-mers (32/64bit) Estimate Jaccard Index J(A, B) Don Armstrong (IGB) MASH June 23, / 13
6 MinHash Algorithm What about strandedness Take lexically lowest sequence Given 7-mers 5 -ACTGCAC-3 and its reverse complement, 5 -GTGCAGT-3 Decompose dataset into k-mers A G Hash k-mers (32/64bit) Use ACTGCAC Estimate Jaccard Index J(A, B) Because S(A B) is a random sample of A B the fraction of elements in S(A B) which are shared by S(A) and S(B) is an unbiased estimate of J(A, B) J(A, B) S(A B) S(A) (B) S(A B) Don Armstrong (IGB) MASH June 23, / 13
7 MinHash Algorithm Decompose dataset into k-mers Hash k-mers (32/64bit) Estimate Jaccard Index J(A, B) Don Armstrong (IGB) MASH June 23, / 13
8 MinHash Algorithm Estimating Jaccard Index J(A, B) = A B A B Sample randomly from A and B Because S(A Decompose B) is a random dataset into k-mers sample of A BHash the fraction k-mers of (32/64bit) elements in S(A Estimate B) which Jaccard are Index J(A, B) shared by S(A) and S(B) is an How can we randomly sample? unbiased estimate of J(A, B) Properties of the hash! J(A, B) S(A B) S(A) (B) S(A B) Don Armstrong (IGB) MASH June 23, / 13
9 Hash functions and their properties A function which can map arbitrary sized data to output of fixed size They re used everywhere: caches, duplicate filtering, cryptography, finding similar substrings, finding similar records, etc Good hash functions are deterministic, uniform, and rarely produce collisions Cryptographic hash functions are non-invertible (SHA-512, etc) Other hash functions may have continuity (IE, AAAB and AAAC will hash to nearby values) for example, the MD5 of DON is 78ed35b3eb1f21c6179d824610d6d5c9 while DO is f0994cd6244c f3ff Don Armstrong (IGB) MASH June 23, / 13
10 MurmurHash3 properties Simple Good distribution Good collision resistance Good avalanche properties (single bit in the input changes the output significantly) Don Armstrong (IGB) MASH June 23, / 13
11 MurmurHash3 properties Simple Good distribution Good collision resistance Good avalanche properties (single bit in the input changes the output significantly) 0 -> 25dd8f d5e42427eff1c d63d15 1 -> 6c30934a0ea2c0473d37b6d8bb5b955b435a8bc1 2 -> 315a5aa84aa6cfa4f3fb4b652a596770be0365e8 Don Armstrong (IGB) MASH June 23, / 13
12 MurmurHash3 properties Simple Good distribution Good collision resistance Good avalanche properties (single bit in the input changes the output significantly) Fast Key questions: 1 Does it map DNA and protein sequences uniformly into output? 2 Does the non-random input distribution of DNA/protein sequences expose pathologic behavior of the hash function? Partially answered by the smhasher test suite which exposed issues with MurmurHash2 (which is ideally the DieHarder of hash testing) Don Armstrong (IGB) MASH June 23, / 13
13 Why is this quick Hashing is relatively fast Only read the data once Can be trivially parallized Only need to keep the k lowest hash values for each dataset Much faster than string alignment Don Armstrong (IGB) MASH June 23, / 13
14 How does it stack up against ANI? Sketch size s k-mer size k Mash D is the mash distance ANI is the average nucleotide identity between genomes Increasing s improves match; k seems to max near 27 ANI only considers core genome, so at some point ANI and Mash will diverge Don Armstrong (IGB) MASH June 23, / 13
15 Mash error bounds with k = 21 Don Armstrong (IGB) MASH June 23, / 13
16 De novo clustering of all RefSeq genomes Each node is a genome Nodes are connected if Mash distance 005 and p Don Armstrong (IGB) MASH June 23, / 13
17 Primate species trees calculated by mash (right) in comparison to UCSC genome browser trees (left) Don Armstrong (IGB) MASH June 23, / 13
18 Comparison between mash and COMMET using Global ocean survey clustering Mostly reproduces the clusters seen in the original study Don Armstrong (IGB) MASH June 23, / 13
19 Comparison of sequences and assemblies from 888 sequencing runs and 879 assemblies from MHP and MetaHit projects Mostly reproduces the clusters seen in the original study COMMET would have required 140,000 hours to run this analysis; mash did it in 25 hours or so Don Armstrong (IGB) MASH June 23, / 13
20 Conclusions Compare genomes on a massive scale which would be impossible for typical techniques Good for rapid triaging of sequencing data to identify outliers Metagenomics and identification of samples Caveats Based on k-mer sketch; possibility of batch effects Phylogeny reconstructions are approximate, and do not track mutation rates, etc What about deconvolution of mixed samples? Probably need different techniques Don Armstrong (IGB) MASH June 23, / 13
21 References
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