Determination of bias in the relative abundance of oligonucleotides in DNA sequences.

Different statistical measures of bias of oligonucleotide sequences in DNA sequences were compared, both by theoretical analysis and according to their abilities to predict the relative abundances of oligonucleotides in the genome of Escherichia coli. The expected frequency of an oligonucleotide calculated from a maximal order Markov model was shown to be a degenerate case of the expected frequency calculated from biases of all subwords arising when noncontiguous subwords exhibit no bias. Since (at least in E. coli) noncontiguous sequences exhibit significant bias, the total compositional bias approach is expected to represent biases in genomic sequences more faithfully than Markov approaches. In fact, the efficacy of statistics based on Markov analysis even at the highest order were inferior in predicting actual frequencies of oligonucleotides to methods that factored out biases of internal subwords with gaps. Using total compositional bias as a measure of relative abundance, tetranucleotide and hexanucleotide palindromes were found to be distributed differently from nonpalindromic sequences, with their means shifted somewhat towards underrepresentation. A subpopulation of palindromic hexanucleotides, however, was highly underrepresented, and this group consisted almost entirely of targets for Type II restriction enzymes found within strains of E. coli. Sites recognized by Type I endonucleases from related strains were not markedly biased, and with pentanucleotides, palindromic and nonpalindromic sequences had nearly identical distributions. The loss of restriction sites may be explained by the free transfer of plasmids encoding restriction enzymes and episodic selection for the presence of the enzymes.     

Tsukuba BB: a branch and bound algorithm for local multiple alignment of DNA and protein sequences.

In this paper we present a branch and bound algorithm for local gapless multiple sequence alignment (motif alignment) and its implementation. The algorithm uses both score-based bounding and a novel bounding technique based on the "consistency" of the alignment. A sequence order independent search tree is used in conjunction with a technique for avoiding redundant calculations inherent in the structure of the tree. This is the first program to exploit the fact that the motif alignment problem is easier for short motifs. Indeed, for a short fixed motif width, the running time of the algorithm is asymptotically linear in the size of the input. We tested the performance of the program on a dataset of 300 E. coli promoter sequences and a dataset of 85 lipocalin protein sequences. For a motif width of 4, the optimal alignment of the entire set of sequences can be found. For the more natural motif width of 6, the program can align 21 sequences of length 100, more than twice the number of sequences which can be aligned by the best previous exact algorithm. The algorithm can relax the constraint of requiring each sequence to be aligned, and align 105 of the 300 promoter sequences with a motif width of 6. For the lipocalin dataset, we introduce a technique for reducing the effective alphabet size with a minimal loss of useful information. With this technique, we show that the program can find meaningful motifs in a reasonable amount of time by optimizing the score over three motif positions.     

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs may be described as an ordered collection of p > or = 1 "boxes" (each box corresponding to one part of the structured motif), p substitution rates (one for each box) and p - 1 intervals of distance (one for each pair of successive boxes in the collection). The contents of the boxes--that is, the motifs themselves--are unknown at the start of the algorithm. This is precisely what the algorithms are meant to find. A suffix tree is used for finding such motifs. The algorithms are efficient enough to be able to infer site consensi, such as, for instance, promoter sequences or regulatory sites, from a set of unaligned sequences corresponding to the noncoding regions upstream from all genes of a genome. In particular, both algorithms time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application to the identification of promoter and regulatory consensus sequences in bacterial genomes is shown.     

Sequence alignment with an appropriate substitution matrix.

A widely used algorithm for computing an optimal local alignment between two sequences requires a parameter set with a substitution matrix and gap penalties. It is recognized that a proper parameter set should be selected to suit the level of conservation between sequences. We describe an algorithm for selecting an appropriate substitution matrix at given gap penalties for computing an optimal local alignment between two sequences. In the algorithm, a substitution matrix that leads to the maximum alignment similarity score is selected among substitution matrices at various evolutionary distances. The evolutionary distance of the selected substitution matrix is defined as the distance of the computed alignment. To show the effects of gap penalties on alignments and their distances and help select appropriate gap penalties, alignments and their distances are computed at various gap penalties. The algorithm has been implemented as a computer program named SimDist. The SimDist program was compared with an existing local alignment program named SIM for finding reciprocally best-matching pairs (RBPs) of sequences in each of 100 protein families, where RBPs are commonly used as an operational definition of orthologous sequences. SimDist produced more accurate results than SIM on 50 of the 100 families, whereas both programs produced the same results on the other 50 families. SimDist was also used to compare three types of substitution matrices in scoring 444,461 pairs of homologous sequences from the 100 families.     

A novel algorithm for finding interspersed repeat regions

The analysis of repeats in the DNA sequences is an important subject in bioinformatics. In this paper, we propose a novel projection-assemble algorithm to find unknown interspersed repeats in DNA sequences. The algorithm employs random projection algorithm to obtain a candidate fragment set, and exhaustive search algorithm to search each pair of fragments from the candidate fragment set to find potential linkage, and then assemble them together. The complexity of our projection-assemble algorithm is nearly linear to the length of the genome sequence, and its memory usage is limited by the hardware. We tested our algorithm with both simulated data and real biology data, and the results show that our projection-assemble algorithm is efficient. By means of this algorithm, we found an un-labeled repeat region that occurs five times in Escherichia coil genome, with its length more than 5,000 bp, and a mismatch probability less than 4%.     

Efficient optimal decomposition of a sequence into disjoint regions, each matched to some template in an inventory.

Given an amino acid sequence, we discuss how to find efficiently an optimal set of disjoint regions (substrings, domains, modules, etc.), each of which can be matched to some element of a predefined inventory containing, for example, consensus sequences, protosequences, or protein family profiles. A two-stage approach to sequence decomposition, consisting of the detection of all acceptable matches followed by the construction of an optimal subset of compatible matches, leads to computational difficulties. When the problem is reformulated in terms of network comparisons, it can be solved in time quadratic in the length of the sequence and linear with the number of templates in the inventory, by a single pass of a dynamic programming algorithm. This method has the advantage that the criterion for acceptable matches can be relaxed without materially affecting computing time. Except under special conditions it is more efficient than previous segmentation methods based on dynamic programming.     

Codon Size Reduction as the Origin of the Triplet Genetic Code

The genetic code appears to be optimized in its robustness to missense errors and frameshift errors. In addition, the genetic code is near-optimal in terms of its ability to carry information in addition to the sequences of encoded proteins. As evolution has no foresight, optimality of the modern genetic code suggests that it evolved from less optimal code variants. The length of codons in the genetic code is also optimal, as three is the minimal nucleotide combination that can encode the twenty standard amino acids. The apparent impossibility of transitions between codon sizes in a discontinuous manner during evolution has resulted in an unbending view that the genetic code was always triplet. Yet, recent experimental evidence on quadruplet decoding, as well as the discovery of organisms with ambiguous and dual decoding, suggest that the possibility of the evolution of triplet decoding from living systems with non-triplet decoding merits reconsideration and further exploration. To explore this possibility we designed a mathematical model of the evolution of primitive digital coding systems which can decode nucleotide sequences into protein sequences. These coding systems can evolve their nucleotide sequences via genetic events of Darwinian evolution, such as point-mutations. The replication rates of such coding systems depend on the accuracy of the generated protein sequences. Computer simulations based on our model show that decoding systems with codons of length greater than three spontaneously evolve into predominantly triplet decoding systems. Our findings suggest a plausible scenario for the evolution of the triplet genetic code in a continuous manner. This scenario suggests an explanation of how protein synthesis could be accomplished by means of long RNA-RNA interactions prior to the emergence of the complex decoding machinery, such as the ribosome, that is required for stabilization and discrimination of otherwise weak triplet codon-anticodon interactions.     

Nucleotide bias observed with a short SELEX RNA aptamer library

Systematic evolution of ligands by exponential enrichment (SELEX) is a powerful in vitro selection process used for over 2 decades to identify oligonucleotide sequences (aptamers) with desired properties (usually high affinity for a protein target) from randomized nucleic acid libraries. In the case of RNA aptamers, several highly complex RNA libraries have been described with RNA sequences ranging from 71 to 81 nucleotides (nt) in length. In this study, we used high-throughput sequencing combined with bioinformatics analysis to thoroughly examine the nucleotide composition of the sequence pools derived from several selections that employed an RNA library (Sel2N20) with an abbreviated variable region. The Sel2N20 yields RNAs 51?nt in length, which unlike longer RNAs, are more amenable to large-scale chemical synthesis for therapeutic development. Our analysis revealed a consistent and early bias against inclusion of adenine, resulting in aptamers with lower predicted minimum free energies (ΔG) (higher structural stability). This bias was also observed in control, "nontargeted" selections in which the partition step (against the target) was omitted, suggesting that the bias occurred in 1 or more of the amplification and propagation steps of the SELEX process.     

An exact parallel algorithm to compare very long biological sequences in clusters of workstations

Biological Sequence Comparison is one of the most important operations in Computational Biology since it is used to determine how similar two sequences are. Smith and Waterman proposed an exact algorithm (SW), based on dynamic programming, that is able to obtain the best local alignment between two sequences in quadratic time and space. In order to compare long biological sequences, SW is rarely used since the computation time and the amount of memory required becomes prohibitive. For this reason, heuristic methods like BLAST are widely used. Although faster, these heuristic methods do not guarantee that the best result will be produced. In this paper, we propose an exact parallel variant of the SW algorithm that obtains the best local alignments in quadratic time and reduced space. The results obtained in two clusters (8-machine and 16-machine) for DNA sequences longer than 32 KBP (kilo base-pairs) were very close to linear and, in some cases, superlinear. For very long DNA sequences (1.6 MBP), we were able to reduce execution time from 12.25 hours to 1.54 hours, in our 8-machine cluster. As far as we know, this is the first time 1.6 MBP sequences are compared with an exact SW variant. In this case, 30240 best local alignments were obtained.

Phylogenetic invariants for genome rearrangements.

We review the combinatorial optimization problems in calculating edit distances between genomes and phylogenetic inference based on minimizing gene order changes. With a view to avoiding the computational cost and the "long branches attract" artifact of some tree-building methods, we explore the probabilization of genome rearrangement models prior to developing a methodology based on branch-length invariants. We characterize probabilistically the evolution of the structure of the gene adjacency set for reversals on unsigned circular genomes and, using a nontrivial recurrence relation, reversals on signed genomes. Concepts from the theory of invariants developed for the phylogenetics of homologous gene sequences can be used to derive a complete set of linear invariants for unsigned reversals, as well as for a mixed rearrangement model for signed genomes, though not for pure transposition or pure signed reversal models. The invariants are based on an extended Jukes-Cantor semigroup. We illustrate the use of these invariants to relate mitochondrial genomes from a number of invertebrate animals.     

Sequence complexity profiles of prokaryotic genomic sequences: a fast algorithm for calculating linguistic complexity

MOTIVATION: One of the major features of genomic DNA sequences, distinguishing them from texts in most spoken or artificial languages, is their high repetitiveness. Variation in the repetitiveness of genomic texts reflects the presence and density of different biologically important messages. Thus, deviation from an expected number of repeats in both directions indicates a possible presence of a biological signal. Linguistic complexity corresponds to repetitiveness of a genomic text, and potential regulatory sites may be discovered through construction of typical patterns of complexity distribution. RESULTS: We developed software for fast calculation of linguistic sequence complexity of DNA sequences. Our program utilizes suffix trees to compute the number of subwords present in genomic sequences, thereby allowing calculation of linguistic complexity in time linear in genome size. The measure of linguistic complexity was applied to the complete genome of Haemophilus influenzae. Maps of complexity along the entire genome were obtained using sliding windows of 40, 100, and 2000 nucleotides. This approach provided an efficient way to detect simple sequence repeats in this genome. In addition, local profiles of complexity distribution around the starts of translation were constructed for 21 complete prokaryotic genomes. We hypothesize that complexity profiles correspond to evolutionary relationships between organisms. We found principal differences in profiles of the GC-rich and other (non-GC-rich) genomes. We also found characteristic differences in profiles of AT genomes, which probably reflect individual species variations in translational regulation. AVAILABILITY: The program is available upon request from Alexander Bolshoy or at http://csweb.haifa.ac.il/library/#complex.     

The Treeterbi and Parallel Treeterbi algorithms: efficient, optimal decoding for ordinary, generalized and pair HMMs

MOTIVATION: Hidden Markov models (HMMs) and generalized HMMs been successfully applied to many problems, but the standard Viterbi algorithm for computing the most probable interpretation of an input sequence (known as decoding) requires memory proportional to the length of the sequence, which can be prohibitive. Existing approaches to reducing memory usage either sacrifice optimality or trade increased running time for reduced memory. RESULTS: We developed two novel decoding algorithms, Treeterbi and Parallel Treeterbi, and implemented them in the TWINSCAN/N-SCAN gene-prediction system. The worst case asymptotic space and time are the same as for standard Viterbi, but in practice, Treeterbi optimally decodes arbitrarily long sequences with generalized HMMs in bounded memory without increasing running time. Parallel Treeterbi uses the same ideas to split optimal decoding across processors, dividing latency to completion by approximately the number of available processors with constant average overhead per processor. Using these algorithms, we were able to optimally decode all human chromosomes with N-SCAN, which increased its accuracy relative to heuristic solutions. We also implemented Treeterbi for Pairagon, our pair HMM based cDNA-to-genome aligner. AVAILABILITY: The TWINSCAN/N-SCAN/PAIRAGON open source software package is available from http://genes.cse.wustl.edu.     

一种有效的重复序列识别算法

重复序列的分析是基因组研究中的一个重要课题,进行这一研究的基础则是从基因组序列中快速有效地找出其中的重复序列。一种投影拼接算法,即利用随机投影获得候选片断集合,利用片断拼接对候选片断进行拼接,以发现基因组中的重复序列。分析了算法的计算复杂度,构造了半仿真测试数据,对算法的测试结果表明了其有效性。     

Signal sequences. The limits of variation

Variations in length and composition of the charged N-terminal, central hydrophobic and polar C-terminal regions in a large sample of signal sequences have been mapped, both as a function of the overall length of the sequence, and in an absolute sense, i.e. various "extremes" have been sought. The results show subtle differences between eukaryotic and prokaryotic sequences, but the general impression of signal sequences as being highly variable is reinforced. Criteria for a "minimal" signal sequence are suggested and discussed.     

New bounds and tractable instances for the transposition distance

The problem of sorting by transpositions asks for a sequence of adjacent interval exchanges that sorts a permutation and is of the shortest possible length. The distance of the permutation is defined as the length of such a sequence. Despite the apparently intuitive nature of this problem, introduced in 1995 by Bafna and Pevzner, the complexity of both finding an optimal sequence and computing the distance remains open today. In this paper, we establish connections between two different graph representations of permutations, which allows us to compute the distance of a few nontrivial classes of permutations in linear time and space, bypassing the use of any graph structure. By showing that every permutation can be obtained from one of these classes, we prove a new tight upper bound on the transposition distance. Finally, we give improved bounds on some other families of permutations and prove formulas for computing the exact distance of other classes of permutations, again in polynomial time     

Introns Form Compositional Clusters in Parallel with the Compositional Clusters of the Coding Sequences to Which they Pertain

This report deals with the study of compositional properties of human gene sequences evaluating similarities and differences among functionally distinct sectors of the gene independently of the reading frame. To retrieve the compositional information of DNA, we present a neighbor base dependent coding system in which the alphabet of 64 letters (DNA triplets) is compressed to an alphabet of 14 letters here termed triplet composons. The triplets containing the same set of distinct bases in whatever order and number form a triplet composon. The reading of the DNA sequence is performed starting at any letter of the initial triplet and then moving, triplet-to-triplet, until the end of the sequence. The readings were made in an overlapping way along the length of the sequences. The analysis of the compositional content in terms of the composon usage frequencies of the gene sequences shows that: (i) the compositional content of the sequences is far from that of random sequences, even in the case of non-protein coding sequences; (ii) coding sequences can be classified as components of compositional clusters; and (iii) intron sequences in a cluster have the same composon usage frequencies, even as their base composition differs notably from that of their home coding sequences. A comparison of the composon usage frequencies between human and mouse homologous genes indicated that two clusters found in humans do not have their counterpart in mouse whereas the others clusters are stable in both species with respect to their composon usage frequencies in both coding and noncoding sequences.     

Rfold: an exact algorithm for computing local base pairing probabilities

MOTIVATION: Base pairing probability matrices have been frequently used for the analyses of structural RNA sequences. Recently, there has been a growing need for computing these probabilities for long DNA sequences by constraining the maximal span of base pairs to a limited value. However, none of the existing programs can exactly compute the base pairing probabilities associated with the energy model of secondary structures under such a constraint. RESULTS: We present an algorithm that exactly computes the base pairing probabilities associated with the energy model under the constraint on the maximal span W of base pairs. The complexity of our algorithm is given by O(NW2) in time and O(N+W2) in memory, where N is the sequence length. We show that our algorithm has a higher sensitivity to the true base pairs as compared to that of RNAplfold. We also present an algorithm that predicts a mutually consistent set of local secondary structures by maximizing the expected accuracy function. The comparison of the local secondary structure predictions with those of RNALfold indicates that our algorithm is more accurate. Our algorithms are implemented in the software named 'Rfold.' AVAILABILITY: The C++ source code of the Rfold software and the test dataset used in this study are available at http://www.ncrna.org/software/Rfold/.     

Rapid and sensitive dot-matrix methods for genome analysis

MOTIVATION: Dot-matrix plots are widely used for similarity analysis of biological sequences. Many algorithms and computer software tools have been developed for this purpose. Though some of these tools have been reported to handle sequences of a few 100 kb, analysis of genome sequences with a length of >10 Mb on a microcomputer is still impractical due to long execution time and computer memory requirement. RESULTS: Two dot-matrix comparison methods have been developed for analysis of large sequences. The methods initially locate similarity regions between two sequences using a fast word search algorithm, followed with an explicit comparison on these regions. Since the initial screening removes most of random matches, the computing time is substantially reduced. The methods produce high quality dot-matrix plots with low background noise. Space requirements are linear, so the algorithms can be used for comparison of genome size sequences. Computing speed may be affected by highly repetitive sequence structures of eukaryote genomes. A dot-matrix plot of Yeast genome (12 Mb) with both strands was generated in 80 s with a 1 GHz personal computer.     

Local combinational variables: an approach used in DNA-binding helix-turn-helix motif prediction with sequence information

Sequence-based approach for motif prediction is of great interest and remains a challenge. In this work, we develop a local combinational variable approach for sequence-based helix-turn-helix (HTH) motif prediction. First we choose a sequence data set for 88 proteins of 22 amino acids in length to launch an optimized traversal for extracting local combinational segments (LCS) from the data set. Then after LCS refinement, local combinational variables (LCV) are generated to construct prediction models for HTH motifs. Prediction ability of LCV sets at different thresholds is calculated to settle a moderate threshold. The large data set we used comprises 13 HTH families, with 17 455 sequences in total. Our approach predicts HTH motifs more precisely using only primary protein sequence information, with 93.29% accuracy, 93.93% sensitivity and 92.66% specificity. Prediction results of newly reported HTH-containing proteins compared with other prediction web service presents a good prediction model derived from the LCV approach. Comparisons with profile-HMM models from the Pfam protein families database show that the LCV approach maintains a good balance while dealing with HTH-containing proteins and non-HTH proteins at the same time. The LCV approach is to some extent a complementary to the profile-HMM models for its better identification of false-positive data. Furthermore, genome-wide predictions detect new HTH proteins in both Homo sapiens and Escherichia coli organisms, which enlarge applications of the LCV approach. Software for mining LCVs from sequence data set can be obtained from anonymous ftp site ftp://cheminfo.tongji.edu.cn/LCV/freely.