The identification of reference genomes and taxonomic labels from metagenome data underlies many microbiome studies. Here we describe two algorithms for compositional analysis of metagenome sequencing data. We first investigate the FracMinHash sketching technique, a derivative of modulo hash that supports Jaccard containment estimation between sets of different sizes. We implement FracMinHash in the sourmash software, evaluate its accuracy, and demonstrate large-scale containment searches of metagenomes using 700,000 microbial reference genomes. We next frame shotgun metagenome compositional analysis as the problem of finding a minimum collection of reference genomes that "cover" the known k-mers in a metagenome, a minimum set cover problem. We implement a greedy approximate solution using FracMinHash sketches, and evaluate its accuracy for taxonomic assignment using a CAMI community benchmark. Finally, we show that the minimum metagenome cover can be used to guide the selection of reference genomes for read mapping. sourmash is available as open source software under the BSD 3-Clause license at github.com/dib-lab/sourmash/.

Sketching methods offer computational biologists scalable techniques to analyze data sets that continue to grow in size. MinHash is one such technique that has enjoyed recent broad application. However, traditional MinHash has previously been shown to perform poorly when applied to sets of very dissimilar sizes. FracMinHash was recently introduced as a modification of MinHash to compensate for this lack of performance when set sizes differ. While experimental evidence has been encouraging, FracMinHash has not yet been analyzed from a theoretical perspective. In this paper, we perform such an analysis and prove that while FracMinHash is not unbiased, this bias is easily corrected. Next, we detail how a simple mutation model interacts with FracMinHash and are able to derive confidence intervals for evolutionary mutation distances between pairs of sequences as well as hypothesis tests for FracMinHash. We find that FracMinHash estimates the containment of a genome in a large metagenome more accurately and more precisely when compared to traditional MinHash, and the confidence interval performs significantly better in estimating mutation distances. A python-based implementation of the theorems we derive is freely available at https://github.com/KoslickiLab/mutation-rate-ci-calculator. The results presented in this paper can be reproduced using the code at https://github.com/KoslickiLab/ScaledMinHash-reproducibles.

Sketching methods offer computational biologists scalable techniques to analyze data sets that continue to grow in size. MinHash is one such technique to estimate set similarity that has enjoyed recent broad application. However, traditional MinHash has previously been shown to perform poorly when applied to sets of very dissimilar sizes. FracMinHash was recently introduced as a modification of MinHash to compensate for this lack of performance when set sizes differ. This approach has been successfully applied to metagenomic taxonomic profiling in the widely used tool sourmash gather. While experimental evidence has been encouraging, FracMinHash has not yet been analyzed from a theoretical perspective. In this paper, we perform such an analysis to derive various statistics of FracMinHash, and prove that while FracMinHash is not unbiased (in the sense that its expected value is not equal to the quantity it attempts to estimate), this bias is easily corrected for both the containment and Jaccard index versions. Next, we show how FracMinHash can be used to compute point estimates as well as confidence intervals for evolutionary mutation distance between a pair of sequences by assuming a simple mutation model. We also investigate edge cases where these analyses may fail, to effectively warn the users of FracMinHash indicating the likelihood of such cases. Our analyses show that FracMinHash estimates the containment of a genome in a large metagenome more accurately and more precisely when compared to traditional MinHash, and the point estimates and confidence intervals perform significantly better in estimating mutation distances.

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Genome editing using the CRISPR/Cas9 system requires designing guide RNAs (sgRNA) that are efficient and specific. Guide RNAs are usually designed using reference genomes which limits their use in organisms with no or incomplete reference genomes. Here, we present kRISP-meR, a reference free method to design sgRNAs for CRISPR/Cas9 system. kRISP-meR takes as input a target region and sequenced reads from the organism to be edited and generates sgRNAs that are likely to minimize off-target effects. Our analysis indicates that kRISP-meR is able to identify majority of the guides identified by a widely used sgRNA designing tool, without any knowledge of the reference, while retaining specificity.