Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

De Novo Assembly of Nucleotide Sequences in a Compressed Feature Space

Sequencing technologies allow for an in-depth analysis of biological species but the size of the generated datasets introduce a number of analytical challenges. Recently, we demonstrated the application of numerical sequence representations and data transformations for the alignment of short reads to a reference genome. Here, we expand out approach for de novo assembly of short reads. Our results demonstrate that highly compressed data can encapsulate the signal suffi- ciently to accurately assemble reads to big contigs or complete genomes

Learning Character Strings via Mastermind Queries, with a Case Study Involving mtDNA

We study the degree to which a character string, $Q$, leaks details about itself any time it engages in comparison protocols with a strings provided by a querier, Bob, even if those protocols are cryptographically guaranteed to produce no additional information other than the scores that assess the degree to which $Q$ matches strings offered by Bob. We show that such scenarios allow Bob to play variants of the game of Mastermind with $Q$ so as to learn the complete identity of $Q$. We show that there are a number of efficient implementations for Bob to employ in these Mastermind attacks, depending on knowledge he has about the structure of $Q$, which show how quickly he can determine $Q$. Indeed, we show that Bob can discover $Q$ using a number of rounds of test comparisons that is much smaller than the length of $Q$, under reasonable assumptions regarding the types of scores that are returned by the cryptographic protocols and whether he can use knowledge about the distribution that $Q$ comes from. We also provide the results of a case study we performed on a database of mitochondrial DNA, showing the vulnerability of existing real-world DNA data to the Mastermind attack.Comment: Full version of related paper appearing in IEEE Symposium on Security and Privacy 2009, "The Mastermind Attack on Genomic Data." This version corrects the proofs of what are now Theorems 2 and 4

Searching and Indexing Genomic Databases via Kernelization

The rapid advance of DNA sequencing technologies has yielded databases of thousands of genomes. To search and index these databases effectively, it is important that we take advantage of the similarity between those genomes. Several authors have recently suggested searching or indexing only one reference genome and the parts of the other genomes where they differ. In this paper we survey the twenty-year history of this idea and discuss its relation to kernelization in parameterized complexity

Distributed hybrid-indexing of compressed pan-genomes for scalable and fast sequence alignment

Computational pan-genomics utilizes information from multiple individual genomes in large-scale comparative analysis. Genetic variation between case-controls, ethnic groups, or species can be discovered thoroughly using pan-genomes of such subpopulations. Whole-genome sequencing (WGS) data volumes are growing rapidly, making genomic data compression and indexing methods very important. Despite current space-efficient repetitive sequence compression and indexing methods, the deployed compression methods are often sequential, computationally time-consuming, and do not provide efficient sequence alignment performance on vast collections of genomes such as pan-genomes. For performing rapid analytics with the ever-growing genomics data, data compression and indexing methods have to exploit distributed and parallel computing more efficiently. Instead of strict genome data compression methods, we will focus on the efficient construction of a compressed index for pan-genomes. Compressed hybrid-index enables fast sequence alignments to several genomes at once while shrinking the index size significantly compared to traditional indexes. We propose a scalable distributed compressed hybrid-indexing method for large genomic data sets enabling pan-genome-based sequence search and read alignment capabilities. We show the scalability of our tool, DHPGIndex, by executing experiments in a distributed Apache Spark-based computing cluster comprising 448 cores distributed over 26 nodes. The experiments have been performed both with human and bacterial genomes. DHPGIndex built a BLAST index for n = 250 human pan-genome with an 870:1 compression ratio (CR) in 342 minutes and a Bowtie2 index with 157:1 CR in 397 minutes. For n = 1,000 human pan-genome, the BLAST index was built in 1520 minutes with 532:1 CR and the Bowtie2 index in 1938 minutes with 76:1 CR. Bowtie2 aligned 14.6 GB of paired-end reads to the compressed (n = 1,000) index in 31.7 minutes on a single node. Compressing n = 13,375,031 (488 GB) GenBank database to BLAST index resulted in CR of 62:1 in 575 minutes. BLASTing 189,864 Crispr-Cas9 gRNA target sequences (23 MB in total) to the compressed index of human pan-genome (n = 1,000) finished in 45 minutes on a single node. 30 MB mixed bacterial sequences were (n = 599) were blasted to the compressed index of 488 GB GenBank database (n = 13,375,031) in 26 minutes on 25 nodes. 78 MB mixed sequences (n = 4,167) were blasted to the compressed index of 18 GB E. coli sequence database (n = 745,409) in 5.4 minutes on a single node.Peer reviewe