The goal of metagenomics is to study the composition of microbial communities, typically using high-throughput shotgun sequencing. In the metagenomic binning problem, we observe random substrings (called contigs) from a mixture of genomes and want to cluster them according to their genome of origin. Based on the empirical observation that genomes of different bacterial species can be distinguished based on their tetranucleotide frequencies, we model this task as the problem of clustering N sequences generated by M distinct Markov processes, where M N . Utilizing the large-deviation principle for Markov processes, we establish the information-theoretic limit for perfect binning. Specifically, we show that the length of the contigs must scale with the inverse of the Chernoff Information between the two most similar species. Our result also implies that contigs should be binned using the conditional relative entropy as a measure of distance, as opposed to the Euclidean distance often used in practice.

The complexity of genome assembly is due in large part to the presence of repeats. In particular, large reverse-complemented repeats can lead to incorrect inversions of large segments of the genome. To detect and correct such inversions in finished bacterial genomes, we propose a statistical test based on tetranucleotide frequency (TNF), which determines whether two segments from the same genome are of the same or opposite orientation. In most cases, the test neatly partitions the genome into two segments of roughly equal length with seemingly opposite orientations. This corresponds to the segments between the DNA replication origin and terminus, which were previously known to have distinct nucleotide compositions. We show that, in several cases where this balanced partition is not observed, the test identifies a potential inverted misassembly, which is validated by the presence of a reverse-complemented repeat at the boundaries of the inversion. After inverting the sequence between the repeat, the balance of the misassembled genome is restored. Our method identifies 31 potential misassemblies in the NCBI database, several of which are further supported by a reassembly of the read data.

Summary The complexity of genome assembly is due in large part to the presence of repeats. In particular, large reverse-complemented repeats can lead to incorrect inversions of large segments of the genome. To detect and correct such inversions in finished bacterial genomes, we propose a statistical test based on tetranucleotide frequency (TNF), which determines whether two segments from the same genome are of the same or opposite orientation. In most cases, the test neatly partitions the genome into two segments of roughly equal length with seemingly opposite orientations. This corresponds to the segments between the DNA replication origin and terminus, which were previously known to have distinct nucleotide compositions. We show that, in several cases where this balanced partition is not observed, the test identifies a potential inverted misassembly, which is validated by the presence of a reverse-complemented repeat at the boundaries of the inversion. After inverting the sequence between the repeat, the balance of the misassembled genome is restored. Our method identifies 31 potential misassemblies in the NCBI database, several of which are further supported by a reassembly of the read data. Availability and implementation A github repository is available at https://github.com/gcgreenberg/Oriented-TNF.git. Supplementary information Supplementary data are available at Bioinformatics online.

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