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Methods for measuring genetic distances in phylogenetics are known to be sensitive to the evolutionary model assumed. However, there is a lack of established methodology to accommodate the trade-off between incorporating sufficient biological reality and avoiding model overfitting. In addition, as traditional methods measure distances based on the observed number of substitutions, their tend to underestimate distances between diverged sequences due to backward and parallel substitutions. Various techniques were proposed to correct this, but they lack the robustness against sequences that are distantly related and of unequal base frequencies. In this article, we present a novel genetic distance estimate based on information theory that overcomes the above two hurdles. Instead of examining the observed number of substitutions, this method estimates genetic distances using Shannon's mutual information. This naturally provides an effective framework for balancing model complexity and goodness of fit. Our distance estimate is shown to be approximately linear to elapsed time and hence is less sensitive to the divergence of sequence data and compositional biased sequences. Using extensive simulation data, we show that our method 1) consistently reconstructs more accurate phylogeny topologies than existing methods, 2) is robust in extreme conditions such as diverged phylogenies, unequal base frequencies data, and heterogeneous mutation patterns, and 3) scales well with large phylogenies., (© The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

A biological compression model, expert model, is presented which is superior to existing compression algorithms in both compression performance and speed. The model is able to compress whole eukaryotic genomes. Most importantly, the model provides a framework for knowledge discovery from biological data. It can be used for repeat element discovery, sequence alignment and phylogenetic analysis. We demonstrate that the model can handle statistically biased sequences and distantly related sequences where conventional knowledge discovery tools often fail.

Background: Traditional genome alignment methods consider sequence alignment as a variation of the string edit distance problem, and perform alignment by matching characters of the two sequences. They are often computationally expensive and unable to deal with low information regions. Furthermore, they lack a well-principled objective function to measure the performance of sets of parameters. Since genomic sequences carry genetic information, this article proposes that the information content of each nucleotide in a position should be considered in sequence alignment. An information-theoretic approach for pairwise genome local alignment, namely XMAligner, is presented. Instead of comparing sequences at the character level, XMAligner considers a pair of nucleotides from two sequences to be related if their mutual information in context is significant. The information content of nucleotides in sequences is measured by a lossless compression technique., Results: Experiments on both simulated data and real data show that XMAligner is superior to conventional methods especially on distantly related sequences and statistically biased data. XMAligner can align sequences of eukaryote genome size with only a modest hardware requirement. Importantly, the method has an objective function which can obviate the need to choose parameter values for high quality alignment. The alignment results from XMAligner can be integrated into a visualisation tool for viewing purpose., Conclusions: The information-theoretic approach for sequence alignment is shown to overcome the mentioned problems of conventional character matching alignment methods. The article shows that, as genomic sequences are meant to carry information, considering the information content of nucleotides is helpful for genomic sequence alignment., Availability: Downloadable binaries, documentation and data can be found at ftp://ftp.infotech.monash.edu.au/software/DNAcompress-XM/XMAligner/.

Background: Features of a DNA sequence can be found by compressing the sequence under a suitable model; good compression implies low information content. Good DNA compression models consider repetition, differences between repeats, and base distributions. From a linear DNA sequence, a compression model can produce a linear information sequence. Linear space complexity is important when exploring long DNA sequences of the order of millions of bases. Compressing a sequence in isolation will include information on self-repetition. Whereas compressing a sequence Y in the context of another X can find what new information X gives about Y. This paper presents a methodology for performing comparative analysis to find features exposed by such models., Results: We apply such a model to find features across chromosomes of Cyanidioschyzon merolae. We present a tool that provides useful linear transformations to investigate and save new sequences. Various examples illustrate the methodology, finding features for sequences alone and in different contexts. We also show how to highlight all sets of self-repetition features, in this case within Plasmodium falciparum chromosome 2., Conclusion: The methodology finds features that are significant and that biologists confirm. The exploration of long information sequences in linear time and space is fast and the saved results are self documenting.

A method has been developed for discovering patterns in DNA sequences. Loosely based on the well-known Lempel Ziv model for text compression, the model detects repeated sequences in DNA. The repeats can be forward or inverted, and they need not be exact. The method is particularly useful for detecting distantly related sequences, and for finding patterns in sequences of biased nucleotide composition, where spurious patterns are often observed because the bias leads to coincidental nucleotide matches. We show here the utility of the method by applying it to genomic sequences of Plasmodium falciparum. A single scan of chromosomes 2 and 3 of P. falciparum, using our method and no other a priori information about the sequences, reveals regions of low complexity in both telomeric and central regions, long repeats in the subtelomeric regions, and shorter repeat areas in dense coding regions. Application of the method to a recently sequenced contig of chromosome 10 that has a particularly biased base composition detects a long internal repeat more readily than does the conventional dot matrix plot. Space requirements are linear, so the method can be used on large sequences. The observed repeat patterns may be related to large-scale chromosomal organization and control of gene expression. The method has general application in detecting patterns of potential interest in newly sequenced genomic material.

Alignment algorithms can be used to infer a relationship between sequences when the true relationship is unknown. Simple alignment algorithms use a cost function that gives a fixed cost to each possible point mutation-mismatch, deletion, insertion. These algorithms tend to find optimal alignments that have many small gaps. It is more biologically plausible to have fewer longer gaps rather than many small gaps in an alignment. To address this issue, linear gap cost algorithms are in common use for aligning biological sequence data. More reliable inferences are obtained by aligning more than two sequences at a time. The obvious dynamic programming algorithm for optimally aligning k sequences of length n runs in O(n(k)) time. This is impractical if k>/=3 and n is of any reasonable length. Thus, for this problem there are many heuristics for aligning k sequences, however, they are not guaranteed to find an optimal alignment. In this paper, we present a new algorithm guaranteed to find the optimal alignment for three sequences using linear gap costs. This gives the same results as the dynamic programming algorithm for three sequences, but typically does so much more quickly. It is particularly fast when the (three-way) edit distance is small. Our algorithm uses a speed-up technique based on Ukkonen's greedy algorithm (Ukkonen, 1983) which he presented for two sequences and simple costs., (Copyright 2000 Academic Press.)

A new statistical model for DNA considers a sequence to be a mixture of regions with little structure and regions that are approximate repeats of other subsequences, i.e. instances of repeats do not need to match each other exactly. Both forward- and reverse-complementary repeats are allowed. The model has a small number of parameters which are fitted to the data. In general there are many explanations for a given sequence and how to compute the total probability of the data given the model is shown. Computer algorithms are described for these tasks. The model can be used to compute the information content of a sequence, either in total or base by base. This amounts to looking at sequences from a data-compression point of view and it is argued that this is a good way to tackle intelligent sequence analysis in general.

We describe a model for strings of characters that is loosely based on the Lempel Ziv model with the addition that a repeated substring can be an approximate match to the original substring; this is close to the situation of DNA, for example. Typically there are many explanations for a given string under the model, some optimal and many suboptimal. Rather than commit to one optimal explanation, we sum the probabilities over all explanations under the model because this gives the probability of the data under the model. The model has a small number of parameters and these can be estimated from the given string by an expectation-maximization (EM) algorithm. Each iteration of the EM algorithm takes O(n2) time and a few iterations are typically sufficient. O(n2) complexity is impractical for strings of more than a few tens of thousands of characters and a faster approximation algorithm is also given. The model is further extended to include approximate reverse complementary repeats when analyzing DNA strings. Tests include the recovery of parameter estimates from known sources and applications to real DNA strings.

An information-theoretic DNA compression scheme devised by Milosavljevic and Jurka (1993) has been used in many places in the literature for both the discovery of new genes and the compression of DNA. Their compression method applies an encoding of previously occurring runs. They use 5 different code-words: four being the DNA bases, A, C, G and T, and the other being a pointer to a previously occurring run. They advocate a code-word of length log2 5 for each of these and then encoding a run by a code-word of length 2 x log2 n, where n is the length of the sequence. This scheme encodes the start of the sequence with a code-word of length log2 n and likewise encodes the end of the sequence with a code-word of length log2 n. In this paper, we show the above coding scheme to be inefficient in various ways and improve upon it so that it can compress DNA. We discuss our implementation of various schemes some of which run in linear time.

In this paper, a number of existing and novel techniques are considered for ordering cloned extracts from the genome of an organism based on fingerprinting data. A metric is defined for comparing the quality of the clone order for each technique. Simulated annealing is used in combination with several different objective functions. Empirical results with many simulated data sets for which the correct solution is known indicate that a simple greedy algorithm with some subsequent stochastic shuffling provides the best solution. Other techniques that attempt to weight comparisons between nonadjacent clones bias the ordering and give worse results. We show that this finding is not surprising since without detailed attempts to reconcile the data into a detailed map, only approximate maps can be obtained. Making N2 pieces of data from measurements of N clones cannot improve the situation.

Early work on proteins identified the existence of helices and extended sheets in protein secondary structures, a high-level classification which remains popular today. Using the Snob program for information-theoretic Minimum Message Length (MML) classification, we are able to take the protein dihedral angles as determined by X-ray crystallography, and cluster sets of dihedral angles into groups. Previous work by Hunter and States has applied a similar Bayesian classification method, AutoClass, to protein data with site position represented by 3 Cartesian co-ordinates for each of the alpha-Carbon, beta-Carbon and Nitrogen, totalling 9 co-ordinates. By using the von Mises circular distribution in the Snob program, we are instead able to represent local site properties by the two dihedral angles, phi and psi. Since each site can be modelled as having 2 degrees of freedom, this orientation-invariant dihedral angle representation of the data is more compact than that of nine highly-correlated Cartesian co-ordinates. Using the information-theoretic message length concepts discussed in the paper, such a more concise model is more likely to represent the underlying generating process from which the data came. We report on the results of our classification, plotting the classes in (phi, psi) space; and introducing a symmetric information-theoretic distance measure to build a minimum spanning tree between the classes. We also give a transition matrix between the classes and note the existence of three classes in the region phi approximately -1.09 rad and psi approximately -0.75 rad which are close on the spanning tree and have high inter-transition probabilities. This gives rise to a tight, abundant and self-perpetuating structure.

Restriction mapping generally requires the application of information from various digestions by restriction enzymes to find solution sets. We use both the predicate calculus and constraint solving capabilities of CLP(R) to develop an engine for restriction mapping. Many of the techniques employed by biologists to manually find solutions are supported by the engine in a consistent manner. We provide generalized pipeline and cross-multiply operators for combining sub-maps. Our approach encourages the building of maps iteratively. We show how other techniques can be readily incorporated.

Restriction site mapping programs construct maps by generating permutations of fragments and checking for consistency. Unfortunately many consistent maps often are obtained within the experimental error bounds, even though there is only one actual map. A particularly efficient algorithm is presented that aims to minimize error bounds between restriction sites. The method is generalized for linear and circular maps. The time complexity is derived and execution times are given for multiple enzymes and a range of error bounds.