BACKGROUND: Hidden Markov models and hidden Boltzmann models are employed in computational biology and a variety of other scientific fields for a variety of analyses of sequential data. Whether the associated algorithms are used to compute an actual probability or, more generally, an odds ratio or some other score, a frequent requirement is that the error statistics of a given score be known. What is the chance that random data would achieve that score or better? What is the chance that a real signal would achieve a given score threshold? RESULTS: Here we present a novel general approach to estimating these false positive and true positive rates that is significantly more efficient than are existing general approaches. We validate the technique via an implementation within the HMMER 3.0 package, which scans DNA or protein sequence databases for patterns of interest, using a profile-HMM. CONCLUSION: The new approach is faster than general naïve sampling approaches, and more general than other current approaches. It provides an efficient mechanism by which to estimate error statistics for hidden Markov model and hidden Boltzmann model results.

MOTIVATION: A backtrace through a dynamic programming algorithm's intermediate results in search of an optimal path, or to sample paths according to an implied probability distribution, or as the second stage of a forward-backward algorithm, is a task of fundamental importance in computational biology. When there is insufficient space to store all intermediate results in high-speed memory (e.g. cache) existing approaches store selected stages of the computation, and recompute missing values from these checkpoints on an as-needed basis. RESULTS: Here we present an optimal checkpointing strategy, and demonstrate its utility with pairwise local sequence alignment of sequences of length 10,000. AVAILABILITY: Sample C++-code for optimal backtrace is available in the Supplementary Materials. SUPPLEMENTARY INFORMATION: Supplementary data is available at Bioinformatics online.

MOTIVATION: Identification of functionally conserved regulatory elements in sequence data from closely related organisms is becoming feasible, due to the rapid growth of public sequence databases. Closely related organisms are most likely to have common regulatory motifs; however, the recent speciation of such organisms results in the high degree of correlation in their genome sequences, confounding the detection of functional elements. Additionally, alignment algorithms that use optimization techniques are limited to the detection of a single alignment that may not be representative. Comparative-genomics studies must be able to address the phylogenetic correlation in the data and efficiently explore the alignment space, in order to make specific and biologically relevant predictions. RESULTS: We describe here a Gibbs sampler that employs a full phylogenetic model and reports an ensemble centroid solution. We describe regulatory motif detection using both simulated and real data, and demonstrate that this approach achieves improved specificity, sensitivity, and positive predictive value over non-phylogenetic algorithms, and over phylogenetic algorithms that report a maximum likelihood solution. AVAILABILITY: The software is freely available at http://bayesweb.wadsworth.org/gibbs/gibbs.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A partial digestion of DNA (e.g. cosmid. Lambda, YAC, chromosome) is performed and the lengths of thoses fragments which hybridize to a labeled probe are measured using gel electrophoresis. We give an efficient algorithm that takes as input this experimental data and proposes one or more candidate solutions. Each solution designates the location of each restriction site and specifies the endpoints of each fragment. (Further experiments can then be designed to select the correct solution from this small set of candidates.) The algorithm works well even when the experiment gives inexact values for the lengths.