MOTIVATION: The Basic Local Alignment Search Tool, BLAST, is an indispensable tool for genomic research. BLAST has established itself as the canonical tool for sequence similarity search in large part thanks to its meaningful statistical analysis. Specifically, BLAST reports the E-value of each reported alignment, which is defined as the expected number of optimal local alignments that will score at least as high as the observed alignment score, assuming that the query and the database sequences are randomly generated. RESULTS: Here, we critically evaluate the E-values provided by the standard protein BLAST (blastp), showing that they can be at times significantly conservative while at others too liberal. We offer an alternative approach based on generating a small sample from the null distribution of random optimal alignments, and testing whether the observed alignment score is consistent with it. In contrast with blastp, our significance analysis seems valid, in the sense that it did not deliver inflated significance estimates in any of our extensive experiments. Moreover, although our method is slightly conservative, it is often significantly less so than the blastp E-value. Indeed, in cases where blastp's analysis is valid (i.e., not too liberal), our approach seems to deliver a greater number of correct alignments. One advantage of our approach is that it works with any reasonable choice of substitution matrix and gap penalties, avoiding blastp's limited options of matrices and penalties. In addition, we can formulate the problem using a canonical family-wise error rate control setup, thereby dispensing with E-values, which can at times be difficult to interpret. AVAILABILITY AND IMPLEMENTATION: The Apache licensed source code is available at https://github.com/batmen-lab/SGPvalue.

MOTIVATION: Target-decoy competition (TDC) is a commonly used method for false discovery rate (FDR) control in the analysis of tandem mass spectrometry data. This type of competition-based FDR control has recently gained significant popularity in other fields after Barber and Candès laid its theoretical foundation in a more general setting that included the feature selection problem. In both cases, the competition is based on a head-to-head comparison between an (observed) target score and a corresponding decoy (knockoff) score. However, the effectiveness of TDC depends on whether the data are homogeneous, which is often not the case: in many settings, the data consist of groups with different score profiles or different proportions of true nulls. In such cases, applying TDC while ignoring the group structure often yields imbalanced lists of discoveries, where some groups might include relatively many false discoveries and other groups include relatively very few. On the other hand, as we show, the alternative approach of applying TDC separately to each group does not rigorously control the FDR. RESULTS: We developed Group-walk, a procedure that controls the FDR in the target-decoy/knockoff setting while taking into account a given group structure. Group-walk is derived from the recently developed AdaPT-a general framework for controlling the FDR with side-information. We show using simulated and real datasets that when the data naturally divide into groups with different characteristics Group-walk can deliver consistent power gains that in some cases are substantial. These groupings include the precursor charge state (4% more discovered peptides at 1% FDR threshold), the peptide length (3.6% increase) and the mass difference due to modifications (26% increase). AVAILABILITY AND IMPLEMENTATION: Group-walk is available at https://cran.r-project.org/web/packages/groupwalk/index.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

MOTIVATION: With over 9000 unique users recorded in the first half of 2013, MEME is one of the most popular motif-finding tools available. Reliable estimates of the statistical significance of motifs can greatly increase the usefulness of any motif finder. By analogy, it is difficult to imagine evaluating a BLAST result without its accompanying E-value. Currently MEME evaluates its EM-generated candidate motifs using an extension of BLAST's E-value to the motif-finding context. Although we previously indicated the drawbacks of MEME's current significance evaluation, we did not offer a practical substitute suited for its needs, especially because MEME also relies on the E-value internally to rank competing candidate motifs. RESULTS: Here we offer a two-tiered significance analysis that can replace the E-value in selecting the best candidate motif and in evaluating its overall statistical significance. We show that our new approach could substantially improve MEME's motif-finding performance and would also provide the user with a reliable significance analysis. In addition, for large input sets, our new approach is in fact faster than the currently implemented E-value analysis.

MOTIVATION: A question that often comes up after applying a motif finder to a set of co-regulated DNA sequences is whether the reported putative motif is similar to any known motif. While several tools have been designed for this task, Habib et al. pointed out that the scores that are commonly used for measuring similarity between motifs do not distinguish between a good alignment of two informative columns (say, all-A) and one of two uninformative columns. This observation explains why tools such as Tomtom occasionally return an alignment of uninformative columns which is clearly spurious. To address this problem, Habib et al. suggested a new score [Bayesian Likelihood 2-Component (BLiC)] which uses a Bayesian information criterion to penalize matches that are also similar to the background distribution. RESULTS: We show that the BLiC score exhibits other, highly undesirable properties, and we offer instead a general approach to adjust any motif similarity score so as to reduce the number of reported spurious alignments of uninformative columns. We implement our method in Tomtom and show that, without significantly compromising Tomtom's retrieval accuracy or its runtime, we can drastically reduce the number of uninformative alignments. AVAILABILITY AND IMPLEMENTATION: The modified Tomtom is available as part of the MEME Suite at http://meme.nbcr.net.

SUMMARY: As was shown in Nagarajan et al. (2005), commonly used approximations for assessing the significance of multiple alignments can be be very inaccurate. To address this, we present here the FAST package, an open-source collection of programs and libraries for efficiently and reliably computing the significance of ungapped local alignments. We also describe other potential applications in Bioinformatics where these programs can be adapted for significance testing. AVAILABILITY: The FAST package includes C++ implementations of various algorithms that can be used as stand-alone programs or as a library of subroutines. The package and a web-server for some of the programs are available at www.cs.cornell.edu/~keich/FAST.

UNLABELLED: We present GIMSAN (GIbbsMarkov with Significance ANalysis): a novel tool for de novo motif finding. GIMSAN combines GibbsMarkov, our variant of the Gibbs Sampler, described here for the first time, with our recently introduced significance analysis. AVAILABILITY: GIMSAN is currently available as a web application and a stand-alone application on Unix and PBS (Portable Batch System) cluster through links from http://www.cs.cornell.edu/~keich.

BACKGROUND: In analyzing the stability of DNA replication origins in Saccharomyces cerevisiae we faced the question whether one set of sequences is significantly enriched in the number and/or the quality of the matches of a particular position weight matrix relative to another set. RESULTS: We present SADMAMA, a computational solution to a address this problem. SADMAMA implements two types of statistical tests to answer this question: one type is based on simplified models, while the other relies on bootstrapping, and as such might be preferable to users who are averse to such models. The bootstrap approach incorporates a novel "site-protected" resampling procedure which solves a problem we identify with naive resampling. CONCLUSION: SADMAMA's utility is demonstrated here by offering a plausible explanation to the differential ARS activity observed in our previous mcm1-1 mutant experiments 1, by suggesting the relevance of multiple weak ACS matches to efficient replication origin function in Saccharomyces cerevisiae, and by suggesting an explanation to the observed negative effect FKH2 has on chromatin silencing 2. SADMAMA is available for download from http://www.cs.cornell.edu/~keich/.

Accurate base-assignment in repeat regions of a whole genome shotgun assembly is an unsolved problem. Since reads in repeat regions cannot be easily attributed to a unique location in the genome, current assemblers may place these reads arbitrarily. As a result, the base-assignment error rate in repeats is likely to be much higher than that in the rest of the genome. We developed an iterative algorithm, EULER-AIR, that is able to correct base-assignment errors in finished genome sequences in public databases. The Wolbachia genome is among the best finished genomes. Using this genome project as an example, we demonstrated that EULER-AIR can 1) discover and correct base-assignment errors, 2) provide accurate read assignments, 3) utilize finishing reads for accurate base-assignment, and 4) provide guidance for designing finishing experiments. In the genome of Wolbachia, EULER-AIR found 16 positions with ambiguous base-assignment and two positions with erroneous bases. Besides Wolbachia, many other genome sequencing projects have significantly fewer finishing reads and, hence, are likely to contain more base-assignment errors in repeats. We demonstrate that EULER-AIR is a software tool that can be used to find and correct base-assignment errors in a genome assembly project.

Large-scale comparison of genomic DNA is of fundamental importance in annotating functional elements of genomes. To perform large comparisons e.ciently, BLAST [3, 2] and other widely used tools use seeded alignment, which compares only sequences that can be shown to share a common pattern or "seed" of matching bases. The literature suggests that the choice of seed substantially affects the sensitivity of seeded alignment, but designing and evaluating seeds is computationally challenging. This work addresses problems arising in seed design. We give the fastest known algorithm for evaluating the sensitivity of a seed in a Markov model of ungapped alignments, as well as theoretical results on which seeds are good choices. We also describe Mandala, a software tool for seed design, and show that it can be used to improve the sensitivity of alignment in practice.

We introduce the notion of a multiprofile and use it for finding subtle motifs in DNA sequences. Multiprofiles generalize the notion of a profile and allow one to detect subtle consensus sequences that escape detection by the standard profiles. Our MULTIPROFILER algorithm outperforms other leading motif finding algorithms in a number of synthetic models. Moreover, it can be shown that in some previously studied motif models, MULTIPROFILER is capable of pushing the performance envelope to its theoretical limits.

MOTIVATION: Gene activity is often affected by binding transcription factors to short fragments in DNA sequences called motifs. Identification of subtle regulatory motifs in a DNA sequence is a difficult pattern recognition problem. In this paper we design a new motif finding algorithm that can detect very subtle motifs. RESULTS: We introduce the notion of a multiprofile and use it for finding subtle motifs in DNA sequences. Multiprofiles generalize the notion of a profile and allow one to detect subtle patterns that escape detection by the standard profiles. Our MULTIPROFILER algorithm outperforms other leading motif finding algorithms in a number of synthetic models. Moreover, it can be shown that in some previously studied motif models, MULTIPROFILER is capable of pushing the performance envelope to its theoretical limits. AVAILABILITY: http://www-cse.ucsd.edu/groups/bioinformatics/software.html

MOTIVATION: What constitutes a subtle motif? Intuitively, it is a motif that is almost indistinguishable, in the statistical sense, from random motifs. This question has important practical consequences: consider, for example, a biologist that is generating a sample of upstream regulatory sequences with the goal of finding a regulatory pattern that is shared by these sequences. If the sequences are too short then one risks losing some of the regulatory patterns that are located further upstream. Conversely, if the sequences are too long, the motif becomes too subtle and one is then likely to encounter random motifs which are at least as significant statistically as the regulatory pattern itself. In practical terms one would like to recognize the sequence length threshold, or the twilight zone, beyond which the motifs are in some sense too subtle. RESULTS: The paper defines the motif twilight zone where every motif finding algorithm would be exposed to random motifs which are as significant as the one which is sought. We also propose an objective tool for evaluating the performance of subtle motif finding algorithms. Finally we apply these tools to evaluate the success of our MULTIPROFILER algorithm to detect subtle motifs.