A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Biological Sequence Simulation for Testing Complex Evolutionary Hypotheses: indel-Seq-Gen Version 2.0

Sequence simulation is an important tool in validating biological hypotheses as well as testing various bioinformatics and molecular evolutionary methods. Hypothesis testing relies on the representational ability of the sequence simulation method. Simple hypotheses are testable through simulation of random, homogeneously evolving sequence sets. However, testing complex hypotheses, for example, local similarities, requires simulation of sequence evolution under heterogeneous models. To this end, we previously introduced indel-Seq-Gen version 1.0 (iSGv1.0; indel, insertion/deletion). iSGv1.0 allowed heterogeneous protein evolution and motif conservation as well as insertion and deletion constraints in subsequences. Despite these advances, for complex hypothesis testing, neither iSGv1.0 nor other currently available sequence simulation methods is sufficient. indel-Seq-Gen version 2.0 (iSGv2.0) aims at simulating evolution of highly divergent DNA sequences and protein superfamilies. iSGv2.0 improves upon iSGv1.0 through the addition of lineage-specific evolution, motif conservation using PROSITE-like regular expressions, indel tracking, subsequence-length constraints, as well as coding and noncoding DNA evolution. Furthermore, we formalize the sequence representation used for iSGv2.0 and uncover a flaw in the modeling of indels used in current state of the art methods, which biases simulation results for hypotheses involving indels. We fix this flaw in iSGv2.0 by using a novel discrete stepping procedure. Finally, we present an example simulation of the calycin-superfamily sequences and compare the performance of iSGv2.0 with iSGv1.0 and random model of sequence evolution

Louse (Insecta : Phthiraptera) mitochondrial 12S rRNA secondary structure is highly variable

Lice are ectoparasitic insects hosted by birds and mammals. Mitochondrial 12S rRNA sequences obtained from lice show considerable length variation and are very difficult to align. We show that the louse 12S rRNA domain III secondary structure displays considerable variation compared to other insects, in both the shape and number of stems and loops. Phylogenetic trees constructed from tree edit distances between louse 12S rRNA structures do not closely resemble trees constructed from sequence data, suggesting that at least some of this structural variation has arisen independently in different louse lineages. Taken together with previous work on mitochondrial gene order and elevated rates of substitution in louse mitochondrial sequences, the structural variation in louse 12S rRNA confirms the highly distinctive nature of molecular evolution in these insects

GUIDANCE: a web server for assessing alignment confidence scores

Evaluating the accuracy of multiple sequence alignment (MSA) is critical for virtually every comparative sequence analysis that uses an MSA as input. Here we present the GUIDANCE web-server, a user-friendly, open access tool for the identification of unreliable alignment regions. The web-server accepts as input a set of unaligned sequences. The server aligns the sequences and provides a simple graphic visualization of the confidence score of each column, residue and sequence of an alignment, using a color-coding scheme. The method is generic and the user is allowed to choose the alignment algorithm (ClustalW, MAFFT and PRANK are supported) as well as any type of molecular sequences (nucleotide, protein or codon sequences). The server implements two different algorithms for evaluating confidence scores: (i) the heads-or-tails (HoT) method, which measures alignment uncertainty due to co-optimal solutions; (ii) the GUIDANCE method, which measures the robustness of the alignment to guide-tree uncertainty. The server projects the confidence scores onto the MSA and points to columns and sequences that are unreliably aligned. These can be automatically removed in preparation for downstream analyses. GUIDANCE is freely available for use at http://guidance.tau.ac.il