Algorithms that compute directly on compressed genomic data allow analyses to keep pace with data generation.
In the past two decades, genomic sequencing capabilities have increased exponentially1,2,3, outstripping advances in computing power4,5,6,7,8. Extracting new insights from the data sets currently being generated will require not only faster computers, but also smarter algorithms. However, most genomes currently sequenced are highly similar to ones already collected9; thus, the amount of new sequence information is growing much more slowly.
Here we show that this redundancy can be exploited by compressing sequence data in such a way as to allow direct computation on the compressed data using methods we term 'compressive' algorithms. This approach reduces the task of computing on many similar genomes to only slightly more than that of operating on just one. Moreover, its relative advantage over existing algorithms will grow with the accumulation of genomic data. We demonstrate this approach by implementing compressive versions of both the Basic Local Alignment Search Tool (BLAST)10 and the BLAST-Like Alignment Tool (BLAT)11, and we emphasize how compressive genomics will enable biologists to keep pace with current data.
A changing environment
Successive generations of sequencing technologies have increased the availability of genomic data exponentially. In the decade since the publication of the first draft of the human genome (a 10-year, $400-million effort1,2), technologies3 have been developed that can be used to sequence a human genome in 1 week for less than $10,000, and the 1000 Genomes Project is well on its way to building a library of over 2,500 human genomes8.
These leaps in sequencing technology promise to enable corresponding advances in biology and medicine, but this will require more efficient ways to store, access and analyze large genomic data sets. Indeed, the scientific community is becoming aware of the fundamental challenges in analyzing such data4,5,6,7. Difficulties with large data sets arise in settings in which one analyzes genomic sequence libraries, including finding sequences similar to a given query (e.g., from environmental or medical samples) or finding signatures of selection in large sets of closely related genomes.
Currently, the total amount of available genomic data is increasing approximately tenfold every year, a rate much faster than Moore's Law for computational processing power (Fig. 1). Any computational analysis, such as sequence search, that runs on the full genomic library—or even a constant fraction thereof—scales at least linearly in time with respect to the size of the library and therefore effectively grows exponentially slower every year. If we wish to use the full power of these large genomic data sets, then we must develop new algorithms that scale sublinearly with data size (that is, those that reduce the effective size of the data set or do not operate on redundant data).
Sublinear analysis and compressed data
To achieve sublinear analysis, we must take advantage of redundancy inherent in the data. Intuitively, given two highly similar genomes, any analysis based on sequence similarity that is performed on one should have already done much of the work toward the same analysis on the other. We note that although efficient algorithms, such as BLAST10, have been developed for individual genomes, large genomic libraries have additional structure: they are highly redundant. For example, as human genomes differ on average by only 0.1% (ref. 2), 1,000 human genomes contain less than twice the unique information of one genome. Thus, although individual genomes are not very compressible12,13, collections of related genomes are extremely compressible14,15,16,17.
This redundancy among genomes can be translated into computational acceleration by storing genomes in a compressed format that respects the structure of similarities and differences important for analysis. Specifically, these differences are the nucleotide substitutions, insertions, deletions and rearrangements introduced by evolution. Once such a compressed library has been created, it can be analyzed in an amount of time proportional to its compressed size, rather than having to reconstruct the full data set every time one wishes to query it.
Many algorithms exist for the compression of genomic data sets purely to reduce the space required for storage and transmission12,13,14,15,17,18. Hsi-Yang Fritz et al.18 provide a particularly instructive discussion of the concerns involved. However, existing techniques require decompression before computational analysis. Thus, although these algorithms enable efficient data storage, they do not mitigate the computational bottleneck: the original uncompressed data set must be reconstructed before it can be analyzed.
There have been efforts to accelerate exact search through indexing techniques16,19,20. Although algorithms—such as Maq21, Burrows-Wheeler Aligner (BWA)22 and Bowtie23—already can map short resequencing reads to a few genomes quite well, compressive techniques will be extremely useful in the case of matching reads of unknown origin to a large database (say, in a medical or forensic context). Search acceleration becomes harder when one wishes to perform an inexact search (e.g., BLAST10 and BLAT11) because compression schemes in general do not allow efficient recovery of the similarity structure of the data set.
As proof of principle for the underlying idea of compressive genomics, we present model compressive algorithms that run BLAST and BLAT in time proportional to the size of the nonredundant data in a genomic library (Box 1, Fig. 2, Supplementary Methods, Supplementary Figs. 1–5 and Supplementary Software). We chose BLAST for a primary demonstration because it is widely used and also the principal means by which many other algorithms query large genomic data sets; thus any improvement to BLAST will immediately improve various analyses on large genomic data sets. Furthermore, the compressive architecture for sequence search we introduce here is tied not only to BLAST but also to many algorithms (particularly those based on sequence similarity).
Challenges of compressive algorithms
There are trade-offs to this approach. As more divergent genomes are added to a database, the computational acceleration resulting from compression decreases, although this is to be expected, as these data are less mutually informative. Although our compressive BLAST algorithm achieves over 99% sensitivity without substantial slowdown (Fig. 3 and Supplementary Figs. 6,7), improvements in sensitivity necessarily involve losses in speed.
There is also a trade-off between achieving optimal data compression and accuracy of analysis (Supplementary Fig. 6a). This trade-off is fundamental to the problem of compressive algorithms for biology: in genomic analysis, one is interested in the probability of similar sequences occurring by chance rather than because of common ancestry, whereas compression ratios depend only on the absolute sequence similarity. For example, two sequences of 50% identity for over 1,000 bases are a strong BLAST hit, but admit no useful compression because the overhead would outweigh the savings. Although these two measures of sequence similarity are closely related, the difference is at the root of these trade-offs. However, sacrificing some accuracy of distant matches helps to achieve a dramatic increase in speed from compression.
As computing moves toward distributed and multiprocessor architectures, one must consider the ability of new algorithms to run in parallel. Although we expect that the primary method of parallelizing compressive genomic search algorithms will be to run queries independently, truly massive data sets will require single queries to be executed in parallel as well. In the algorithms presented in Box 1, queries can be parallelized by dividing the compressed library and link table among computer processors, although the exact gains from doing so will depend on the topology of the link graph on the uncompressed database.
To the extent that researchers restrict their analyses to small data sets (e.g., what could be generated in a single laboratory as opposed to a large sequencing center), existing noncompressive custom pipelines may be sufficiently fast in the short term. However, if one wishes to extend an analysis to a much larger corpus of sequencing data (perhaps several terabytes of raw data), noncompressive approaches quickly become computationally impractical. This is where compressive algorithms are useful for smaller research groups in addition to large centers.
Compressive algorithms for genomics have the great advantage of becoming proportionately faster with the size of the available data. Although the compression schemes for BLAST and BLAT that we presented yield an increase in computational speed and, more importantly, in scaling, they are only a first step. Many enhancements of our proof-of-concept implementations are possible; for example, hierarchical compression structures, which respect the phylogeny underlying a set of sequences, may yield additional long-term performance gains. Moreover, analyses of such compressive structures will lead to insights as well. As sequencing technologies continue to improve, the compressive genomic paradigm will become critical to fully realizing the potential of large-scale genomics.
Software is available at http://cast.csail.mit.edu/.
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We thank J. Kelner, E. Demaine, G. Church, X.R. Bao, M. Schnall-Levin, Z. Albertyn, M. Lipson and E. Lieberman-Aiden for helpful discussions and comments, and L. Gaffney for assistance improving the figures. P.-R.L. acknowledges support from the National Defense Science and Engineering Graduate and US National Science Foundation Fellowships. M.B. acknowledges support from the Fannie and John Hertz Foundation and the National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.
The authors declare no competing financial interests.
Editor's note: This article has been peer-reviewed.
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Loh, PR., Baym, M. & Berger, B. Compressive genomics. Nat Biotechnol 30, 627–630 (2012). https://doi.org/10.1038/nbt.2241
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