A test for nucleotide sequence homology

Longest common subsequences of two random sequences

Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n –1 f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).

Longest common subsequences of two random sequences

Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n–1f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).

Statistical evaluation and comparison of a pairwise alignment algorithm that a priori assigns the number of gaps rather than employing gap penalties

MOTIVATION

Although pairwise sequence alignment is essential in comparative genomic sequence analysis, it has proven difficult to precisely determine the gap penalties for a given pair of sequences. A common practice is to employ default penalty values. However, there are a number of problems associated with using gap penalties. First, alignment results can vary depending on the gap penalties, making it difficult to explore appropriate parameters. Second, the statistical significance of an alignment score is typically based on a theoretical model of non-gapped alignments, which may be misleading. Finally, there is no way to control the number of gaps for a given pair of sequences, even if the number of gaps is known in advance.

RESULTS

In this paper, we develop and evaluate the performance of an alignment technique that allows the researcher to assign a priori set of the number of allowable gaps, rather than using gap penalties. We compare this approach with the Smith-Waterman and Needleman-Wunsch techniques on a set of structurally aligned protein sequences. We demonstrate that this approach outperforms the other techniques, especially for short sequences (56-133 residues) with low similarity (<25%). Further, by employing a statistical measure, we show that it can be used to assess the quality of the alignment in relation to the true alignment with the associated optimal number of gaps.

AVAILABILITY

The implementation of the described methods SANK_AL is available at http://cbbc.murdoch.edu.au/

CONTACT

matthew@cbbc.murdoch.edu.au.

Computational prediction of transcription-factor binding site locations

Various experimental and computational approaches have been used to identify genomic locations of transcription-factor binding sites; methods involving computational comparisons of related genomes have been particularly successful.

Identifying genomic locations of transcription-factor binding sites, particularly in higher eukaryotic genomes, has been an enormous challenge. Various experimental and computational approaches have been used to detect these sites; methods involving computational comparisons of related genomes have been particularly successful.

Human-mouse genome comparisons to locate regulatory sites

Elucidating the human transcriptional regulatory network is a challenge of the post-genomic era. Technical progress so far is impressive, including detailed understanding of regulatory mechanisms for at least a few genes in multicellular organisms, rapid and precise localization of regulatory regions within extensive regions of DNA by means of cross-species comparison, and de novo determination of transcription-factor binding specificities from large-scale yeast expression data. Here we address two problems involved in extending these results to the human genome: first, it has been unclear how many model organism genomes will be needed to delineate most regulatory regions; and second, the discovery of transcription-factor binding sites (response elements) from expression data has not yet been generalized from single-celled organisms to multicellular organisms. We found that 98% (74/75) of experimentally defined sequence-specific binding sites of skeletal-muscle-specific transcription factors are confined to the 19% of human sequences that are most conserved in the orthologous rodent sequences. Also we found that in using this restriction, the binding specificities of all three major muscle-specific transcription factors (MYF, SRF and MEF2) can be computationally identified.

The evolutionary relationships among known life forms

Sequences of small subunit (SSU) and large subunit (LSU) ribosomal RNA genes from archaebacteria, eubacteria, and the nucleus, chloroplasts, and mitochondria of eukaryotes have been compared in order to identify the most conservative positions. Aligned sets of these positions for both SSU and LSU rRNA have been used to generate tree diagrams relating the source organisms/organelles. Branching patterns were evaluated using the statistical bootstrapping technique. The resulting SSU and LSU trees are remarkably congruent and show a high degree of similarity with those based on alternative data sets and/or generated by different techniques. In addition to providing insights into the evolution of prokaryotic and eukaryotic (nuclear) lineages, the analysis reported here provides, for the first time, an extensive phylogeny of the mitochondrial lineage.

Mono- through hexanucleotide composition of the Escherichia coli genome: a Markov chain analysis

Several statistical methods were tested for accuracy in predicting observed frequencies of di- through hexanucleotides in 74,444 bp of E. coli DNA. A Markov chain was most accurate overall, whereas other methods, including a random model based on mononucleotide frequencies, were very inaccurate. When ranked highest to lowest abundance, the observed frequencies of oligonucleotides up to six bases in length in E. coli DNA were highly asymmetric. All ordered abundance plots had a wide linear range containing the majority of the oligomers which deviated sharply at the high and low ends of the curves. In general, values predicted by a Markov chain closely followed the overall shape of the ordered abundance curves. A simple equation was derived by which the frequency of any nucleotide longer than four bases in the E. coli genome (or any genome) can be relatively accurately estimated from the nested set of component tri- and tetranucleotides by serial application of a 3rd order Markov chain. The equation yielded a mean ratio of 1.03 +/- 0.94 for the observed-to-expected frequencies of the 4,096 hexanucleotides. Hence, the method is a relatively accurate but not perfect predictor of the length in nucleotides between hexanucleotide sites. Higher accuracy can be achieved using a 4th order Markov chain and larger data sets. The high asymmetry in oligonucleotide abundance means that in the E. coli genome of 4.2 X 10(6) bp many relatively short sequences of 7-9 bp are very rare or absent.

A comprehensive package for DNA sequence analysis in FORTRAN IV for the PDP-11

A computer package written in Fortran-IV for the PDP-11 minicomputer is described. The package's novel features are: software for voice-entry of sequence data; a less memory intensive algorithm for optimal sequence alignment; and programs that fit statistical models to nucleic acid and protein sequences.

Rapid and sensitive protein similarity searches

An algorithm was developed which facilitates the search for similarities between newly determined amino acid sequences and sequences already available in databases. Because of the algorithm's efficiency on many microcomputers, sensitive protein database searches may now become a routine procedure for molecular biologists. The method efficiently identifies regions of similar sequence and then scores the aligned identical and differing residues in those regions by means of an amino acid replacability matrix. This matrix increases sensitivity by giving high scores to those amino acid replacements which occur frequently in evolution. The algorithm has been implemented in a computer program designed to search protein databases very rapidly. For example, comparison of a 200-amino-acid sequence to the 500,000 residues in the National Biomedical Research Foundation library would take less than 2 minutes on a minicomputer, and less than 10 minutes on a microcomputer (IBM PC).

On the statistical assessment of similarities in DNA sequences

The statistical behavior of the similarity score for unrelated DNA sequences calculated as letter-by-letter comparison or from various forms of optimal alignment was studied. It was found that natural DNA-sequences from a data base and true random sequences show the same statistical behavior in terms of such scores. This makes it possible to adopt a simple criterion for the rejection of fortuitous similarity. It is based on the mean and standard deviation of chance scores whose expected values, depending on chain length, gap penalty and probability of letter coincidence, may be calculated from formulae given in the paper.

Comparison of the nucleotide sequence of soybean 18S rRNA with the sequences of other small-subunit rRNAs

We present the sequence of the nuclear-encoded ribosomal small-subunit RNA from soybean. The soybean 18S rRNA sequence of 1807 nucleotides (nt) is contained in a gene family of approximately 800 closely related members per haploid genome. This sequence is compared with the ribosomal small-subunit RNAs of maize (1805 nt), yeast (1789 nt), Xenopus (1825 nt), rat (1869 nt), and Escherichia coli (1541 nt). Significant sequence homology is observed among the eukaryotic small-subunit rRNAs examined, and some sequence homology is observed between eukaryotic and prokaryotic small-subunit rRNAs. Conserved regions are found to be interspersed among highly diverged sequences. The significance of these comparisons is evaluated using computer simulation of a random sequence model. A tentative model of the secondary structure of soybean 18S rRNA is presented and discussed in the context of the functions of the various conserved regions within the sequence. On the basis of this model, the short base-paired sequences defining the four structural and functional domains of all 18S rRNAs are seen to be well conserved. The potential roles of other conserved soybean 18S rRNA sequences in protein synthesis are discussed.

Accelerated method for comparing amino acid sequences with allowance for possible gaps. Plotting optimum correspondence paths

An accelerated method is suggested which enables an effective comparison to be made of amino acid (nucleotide) sequences of great length with due regard to a large number of possible gaps. The method consists in limiting the area of complete similarity charts, calculated in accordance with the algorithm suggested by Sankoff (1972), by a certain specially selected diagonal band. The application of the Monte-Carlo method permits a statistical evaluation to be made of the certainty of the similarity of the compared sequences and to choose on such a "comparison band", an optimum "correspondence path" which can readily be transformed into sequence alignment. Using this approach, prolactin and somatotropin families of sequences were found to be homologous at a high level of significance and their optimum alignment with two gaps has been suggested. In contrast, two regions of assumed partial gene duplication in beta-galactosidase sequence, suggested by Hood et al. (1978), were found not to be statistically significantly similar.

The evolving tRNA molecule

The study of tRNA molecular evolution is crucial to understanding the origin and establishment of the genetic code as well as the differentiation and refinement of the machinery of protein synthesis in prokaryotes, eukaryotes, organelles, and phage systems. The small size of the molecule and its critical involvement in a multiplicity of roles distinguish its study from classical protein molecular evolution with respect to goals and methods. Here, the authors assess available and missing data, existing and needed methodology, and the impact of tRNA studies on current theories both of genetic code evolution and of the evolution of species. They analyze mutational "hot spots", the role of base modification, synthetase recognition, codon-anticodon interactions and the status of organelle tRNA.

A method for detecting distant evolutionary relationships between protein or nucleic acid sequences in the presence of deletions or insertions

A method for detecting homology between two protein or nucleic acid sequences which require insertions or deletions for optimum alignment has been devised for use with a computer. Sequences are assessed for possible relationship by Monte Carlo methods involving comparisons between the alignment of the real sequences and alignments of randomly scrambled sequences of the same composition as the real sequences, each alignment having the optimum number of gaps. As each gap is successively introduced into a comparison (real or random) a maximum score is determined from the similarity of the aligned residues. From the distribution of the maximum alignment scores of randomly scrambled sequences having the same number of gaps, the percentage of random comparisons having higher scores is determined, and the smallest of these percentage levels for each pair of sequences (real or random) indicates the optimum alignment. The fraction of the comparisons of random sequences having percentage levels at their optimum alignment below that of the real sequence comparison at its optimum estimates the probability that such an alignment might have arisen by chance. Related sequences are detected since their optimum alignment score, by virtue of a contribution from ancestral homology in addition to optimised random considerations, occupies a more extreme position in the appropriate frequency distribution of score than do the majority of optimum scores of randomly scrambled sequences in their appropriate distributions. Application of this 'optimum match' method of sequence comparison shows that the sensitivity of the 'maximum match' method of Needleman and Wunsch (1970) decreases quite dramatically with sequence comparisons which require only a few gaps for a reasonable alignment, or when sequences differ greatly in length. The 'maximum match' method as applied by Barker and Dayhoff (1972) has the additional disadvantage that deletions which have occurred in the longer of two homologous protein sequences further decrease the sensitivity of detection of relationship. The 'constrained match' method of Sankoff and Cedergren (1973) is seen to be misleading since large increments in the alignment score from added gaps do not necessarily result in a high total alignment score required to demonstrate sequence homology.

The evolution of histones

The amino acid sequences of bovine histones H2A, H2B, H3, and H4 and the first 107 residues of rabbit thymus histone H1 were examined using newly developed procedures designed to detect and evaluate weak similarities (de Haën et al., 1976). Using the McLachlan scoring system, regions of statistically significant similarity were found between several pairs of the four smallest histones. The probability that this set of similarities could result simply from chance was estimated to be less than 10(-5). No similarity was found between the H1 sequence and the other histones. The results are interpreted to indicate that at least the C-terminal portions of the core histones evolved from a common ancestral protein.

Frequency of insertion-deletion, transversion, and transition in the evolution of 5S ribosomal RNA

The problem of choosing an alignment of two or more nucleotide sequences is particularly difficult for nucleic acids, such as 5S ribosomal RNA, which do not code for protein and for which secondary structure is unknown. Given a set of 'costs' for the various types of replacement mutations and for base insertion or deletion, we present a dynamic programming algorithm which finds the optimal (least costly) alignment for a set of N sequences simultaneously, where each sequence is associated with one of the N tips of a given evolutionary tree. Concurrently, protosequences are constructed corresponding to the ancestral nodes of the tree. A version of this algorithm, modified to be computationally feasible, is implemented to align the sequences of 5S RNA from nine organisms. Complete sets of alignments and protosequence reconstructions are done for a large number of different configurations of mutation costs. Examination of the family of curbes of total replacements inferred versus the ratio of transitions/transversions inferred, each curve corresponding to a given number of insertions-deletions inferred, provides a method for estimating relative costs and relative frequencies for these different types of mutations.