Algorithms for Molecular Biology - Latest articles

On the optimality of the neighbor-joining algorithm

Kord Eickmeyer, Peter Huggins, Lior Pachter and Ruriko Yoshida — 2008-04-30

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps IR_{+}^{n \choose 2} to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n less than or equal to 8. A key requirement is the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. We show that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l2 radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.

Protein sequence and structure alignments within one framework

Gundolf Schenk, Thomas Margraf and Andrew E. Torda — 2008-04-01

Background: Protein structure alignments are usually based on very different techniques to sequence alignments. We propose a method which treats sequence, structure and even combined sequence + structure in a single framework. Using a probabilistic approach, we calculate a similarity measure which can be applied to fragments containing only protein sequence, structure or both simultaneously. Results: Proof-of-concept results are given for the different problems. For sequence alignments, the methodology is no better than conventional methods. For structure alignments, the techniques are very fast, reliable and tolerant of a range of alignment parameters. Combined sequence and structure alignments may provide a more reliable alignment for pairs of proteins where pure structural alignments can be misled by repetitive elements or apparent symmetries. Conclusions: The probabilistic framework has an elegance in principle, merging sequence and structure descriptors into a single framework. It has a practical use in fast structural alignments and a potential use in finding those examples where sequence and structural similarities apparently disagree.

A scoring matrix approach to detecting miRNA target sites

Simon Moxon, Vincent Moulton and Jan T Kim — 2008-03-31

Background: Experimental identification of microRNA (miRNA) targets is a difficult and time consuming process. As a consequence several computational prediction methods have been devised in order to predict targets for follow up experimental validation. Current computational target prediction methods use only the miRNA sequence as input. With an increasing number of experimentally validated targets becoming available, utilising this additional information in the search for further targets may help to improve the specificity of computational methods for target site prediction. Results: We introduce a generic target prediction method, the Stacking Binding Matrix (SBM) that uses both information about the miRNA as well as experimentally validated target sequences in the search for candidate target sequences. We demonstrate the utility of our method by applying it to both animal and plant data sets and compare it with miRanda, a commonly used target prediction method. Conclusion: We show that SBM can be applied to target prediction in both plants and animals and performs well in terms of sensitivity and specificity. Open source code implementing the SBM method, together with documentation and examples are freely available for download from the address in the Availability and Requirements section.

Learning from positive examples when the negative class is undetermined- microRNA gene identification

Malik Yousef, Segun Jung, Louise C Showe and Michael K Showe — 2008-01-28

Background: The application of machine learning to classification problems that depend only on positive examples is gaining attention in the computational biology community. We and others have described the use of two-class machine learning to identify novel miRNAs. These methods require the generation of an artificial negative class. However, designation of the negative class can be problematic and if it is not properly done can affect the performance of the classifier dramatically and/or yield a biased estimate of performance. We present a study using one-class machine learning for microRNA (miRNA) discovery and compare one-class to two-class approaches using naïve Bayes and Support Vector Machines. These results are compared to published two-class miRNA prediction approaches. We also examine the ability of the one-class and two-class techniques to identify miRNAs in newly sequenced species. Results: Of all methods tested, we found that 2-class naive Bayes and Support Vector Machines gave the best accuracy using our selected features and optimally chosen negative examples. One class methods showed average accuracies of 70–80% versus 90% for the two 2-class methods on the same feature sets. However, some one-class methods outperform some recently published two-class approaches with different selected features. Using the EBV genome as and external validation of the method we found one-class machine learning to work as well as or better than a two-class approach in identifying true miRNAs as well as predicting new miRNAs. Conclusion: One and two class methods can both give useful classification accuracies when the negative class is well characterized. The advantage of one class methods is that it eliminates guessing at the optimal features for the negative class when they are not well defined. In these cases one-class methods can be superior to two-class methods when the features which are chosen as representative of that positive class are well defined.AvailabilityThe OneClassmiRNA program is available at: 1

Reconstructing phylogenies from noisy quartets in polynomial time with a high success probability

Gang Wu, Ming-Yang Kao, Guohui Lin and Jia-Huai You — 2008-01-24

Background: In recent years, quartet-based phylogeny reconstruction methods have received considerable attentions in the computational biology community. Traditionally, the accuracy of a phylogeny reconstruction method is measured by simulations on synthetic datasets with known "true" phylogenies, while little theoretical analysis has been done. In this paper, we present a new model-based approach to measuring the accuracy of a quartet-based phylogeny reconstruction method. Under this model, we propose three efficient algorithms to reconstruct the "true" phylogeny with a high success probability. Results: The first algorithm can reconstruct the "true" phylogeny from the input quartet topology set without quartet errors in O(n2) time by querying at most (n - 4) log(n - 1) quartet topologies, where n is the number of the taxa. When the input quartet topology set contains errors, the second algorithm can reconstruct the "true" phylogeny with a probability approximately 1 - p in O(n4 log n) time, where p is the probability for a quartet topology being an error. This probability is improved by the third algorithm to approximately 11+q2+12q4+116q5 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIXaqmaeaacqaIXaqmcqGHRaWkcqWGXbqCdaahaaqabeaacqaIYaGmaaGaey4kaSYaaSaaaeaacqaIXaqmaeaacqaIYaGmaaGaemyCae3aaWbaaeqabaGaeGinaqdaaiabgUcaRmaalaaabaGaeGymaedabaGaeGymaeJaeGOnaydaaiabdghaXnaaCaaabeqaaiabiwda1aaaaaaaaa@3D5A@, where q=p1−p MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemyCaeNaeyypa0tcfa4aaSaaaeaacqWGWbaCaeaacqaIXaqmcqGHsislcqWGWbaCaaaaaa@3391@, with running time of O(n5), which is at least 0.984 when p < 0.05. Conclusion: The three proposed algorithms are mathematically guaranteed to reconstruct the "true" phylogeny with a high success probability. The experimental results showed that the third algorithm produced phylogenies with a higher probability than its aforementioned theoretical lower bound and outperformed some existing phylogeny reconstruction methods in both speed and accuracy.

Evaluating deterministic motif significance measures in protein databases

Pedro Gabriel Ferreira and Paulo J Azevedo — 2007-12-24

Background: Assessing the outcome of motif mining algorithms is an essential task, as the number of reported motifs can be very large. Significance measures play a central role in automatically ranking those motifs, and therefore alleviating the analysis work. Spotting the most interesting and relevant motifs is then dependent on the choice of the right measures. The combined use of several measures may provide more robust results. However caution has to be taken in order to avoid spurious evaluations. Results: From the set of conducted experiments, it was verified that several of the selected significance measures show a very similar behavior in a wide range of situations therefore providing redundant information. Some measures have proved to be more appropriate to rank highly conserved motifs, while others are more appropriate for weakly conserved ones. Support appears as a very important feature to be considered for correct motif ranking. We observed that not all the measures are suitable for situations with poorly balanced class information, like for instance, when positive data is significantly less than negative data. Finally, a visualization scheme was proposed that, when several measures are applied, enables an easy identification of high scoring motifs. Conclusion: In this work we have surveyed and categorized 14 significance measures for pattern evaluation. Their ability to rank three types of deterministic motifs was evaluated. Measures were applied in different testing conditions, where relations were identified. This study provides some pertinent insights on the choice of the right set of significance measures for the evaluation of deterministic motifs extracted from protein databases.

Efficient and accurate P-value computation for Position Weight Matrices

Hélène Touzet and Jean-Stéphane Varré — 2007-12-11

Background: Position Weight Matrices (PWMs) are probabilistic representations of signals in sequences. They are widely used to model approximate patterns in DNA or in protein sequences. The usage of PWMs needs as a prerequisite to knowing the statistical significance of a word according to its score. This is done by defining the P-value of a score, which is the probability that the background model can achieve a score larger than or equal to the observed value. This gives rise to the following problem: Given a P-value, find the corresponding score threshold. Existing methods rely on dynamic programming or probability generating functions. For many examples of PWMs, they fail to give accurate results in a reasonable amount of time. Results: The contribution of this paper is two fold. First, we study the theoretical complexity of the problem, and we prove that it is NP-hard. Then, we describe a novel algorithm that solves the P-value problem efficiently. The main idea is to use a series of discretized score distributions that improves the final result step by step until some convergence criterion is met. Moreover, the algorithm is capable of calculating the exact P-value without any error, even for matrices with non-integer coefficient values. The same approach is also used to devise an accurate algorithm for the reverse problem: finding the P-value for a given score. Both methods are implemented in a software called TFM-PVALUE, that is freely available. Conclusion: We have tested TFM-PVALUE on a large set of PWMs representing transcription factor binding sites. Experimental results show that it achieves better performance in terms of computational time and precision than existing tools.

Review of "Reconstructing Evolution: New mathematical and computational advances" edited by Olivier Gascuel and Mike Steel

Andreas Spillner — 2007-11-06

no abstract for this type of article

Exact p-value calculation for heterotypic clusters of regulatory motifs and its application in computational annotation of cis-regulatory modules

2007-10-10

Background: cis-Regulatory modules (CRMs) of eukaryotic genes often contain multiple binding sites for transcription factors. The phenomenon that binding sites form clusters in CRMs is exploited in many algorithms to locate CRMs in a genome. This gives rise to the problem of calculating the statistical significance of the event that multiple sites, recognized by different factors, would be found simultaneously in a text of a fixed length. The main difficulty comes from overlapping occurrences of motifs. So far, no tools have been developed allowing the computation of p-values for simultaneous occurrences of different motifs which can overlap. Results: We developed and implemented an algorithm computing the p-value that s different motifs occur respectively k1, ..., ks or more times, possibly overlapping, in a random text. Motifs can be represented with a majority of popular motif models, but in all cases, without indels. Zero or first order Markov chains can be adopted as a model for the random text. The computational tool was tested on the set of cis-regulatory modules involved in D. melanogaster early development, for which there exists an annotation of binding sites for transcription factors. Our test allowed us to correctly identify transcription factors cooperatively/competitively binding to DNA.MethodThe algorithm that precisely computes the probability of simultaneous motif occurrences is inspired by the Aho-Corasick automaton and employs a prefix tree together with a transition function. The algorithm runs with the O(n|Σ|(m|ℋ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFlecsaaa@3762@| + K|σ|K) ∏i ki) time complexity, where n is the length of the text, |Σ| is the alphabet size, m is the maximal motif length, |ℋ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFlecsaaa@3762@| is the total number of words in motifs, K is the order of Markov model, and ki is the number of occurrences of the ith motif. Conclusion: The primary objective of the program is to assess the likelihood that a given DNA segment is CRM regulated with a known set of regulatory factors. In addition, the program can also be used to select the appropriate threshold for PWM scanning. Another application is assessing similarity of different motifs.AvailabilityProject web page, stand-alone version and documentation can be found at http://bioinform.genetika.ru/AhoPro/

Finding coevolving amino acid residues using row and column weighting of mutual information and multi-dimensional amino acid representation

Rodrigo Gouveia-Oliveira and Anders G Pedersen — 2007-10-03

Background: Some amino acid residues functionally interact with each other. This interaction will result in an evolutionary co-variation between these residues – coevolution. Our goal is to find these coevolving residues. Results: We present six new methods for detecting coevolving residues. Among other things, we suggest measures that are variants of Mutual Information, and measures that use a multidimensional representation of each residue in order to capture the physico-chemical similarities between amino acids. We created a benchmarking system, in silico, able to evaluate these methods through a wide range of realistic conditions. Finally, we use the combination of different methods as a way of improving performance. Conclusion: Our best method (Row and Column Weighed Mutual Information) has an estimated accuracy increase of 63% over Mutual Information. Furthermore, we show that the combination of different methods is efficient, and that the methods are quite sensitive to the different conditions tested.