Paul E. Kearney

An information-based sequence distance and its application to whole mitochondrial genome phylogeny

MOTIVATION Traditional sequence distances require an alignment and therefore are not directly applicable to the problem of whole genome phylogeny where events such as rearrangements make full length alignments impossible. We present a sequence distance that works on unaligned sequences using the information theoretical concept of Kolmogorov complexity and a program to estimate this distance. RESULTS We establish the mathematical foundations of our distance and illustrate its use by constructing a phylogeny of the Eutherian orders using complete unaligned mitochondrial genomes. This phylogeny is consistent with the commonly accepted one for the Eutherians. A second, larger mammalian dataset is also analyzed, yielding a phylogeny generally consistent with the commonly accepted one for the mammals. AVAILABILITY The program to estimate our sequence distance, is available at http://www.cs.cityu.edu.hk/~cssamk/gencomp/GenCompress1.htm. The distance matrices used to generate our phylogenies are available at http://www.math.uwaterloo.ca/~mli/distance.html.

A Polynomial Time Approximation Scheme for Inferring Evolutionary Trees from Quartet Topologies and Its Application

Inferring evolutionary trees has long been a challenging problem for both biologists and computer scientists. In recent years research has concentrated on the quartet method paradigm for inferring evolutionary trees. Quartet methods proceed by first inferring the evolutionary history for every set of four species (resulting in a set Q of inferred quartet topologies) and then recombining these inferred quartet topologies to form an evolutionary tree. This paper presents two results on the quartet method paradigm. The first is a polynomial time approximation scheme (PTAS) for recombining the inferred quartet topologies optimally. This is an important result since, to date, there have been no polynomial time algorithms with performance guarantees for quartet methods. To achieve this result the natural denseness of the set Q is exploited. The second result is a new technique, called quartet cleaning, that detects and corrects errors in the set Q with performance guarantees. This result has particular significance since quartet methods are usually very sensitive to errors in the data. It is shown how quartet cleaning can dramatically increase the accuracy of quartet methods.

Phylogenetic k-Root and Steiner k-Root

Given a graph G = (V, E) and a positive integer k, the PHYLOGENETIC k-ROOT PROBLEM asks for a (unrooted) tree T without degree-2 nodes such that its leaves are labeled by V and (u, v) ∈ E if and only if dT (u, v) ≤ k. If the vertices in V are also allowed to be internal nodes in T, then we have the Steiner k-ROOT PROBLEM. Moreover, if a particular subset S of V are required to be internal nodes in T, then we have the RESTRICTED STEINER k-ROOT PROBLEM. Phylogenetic k-roots and Steiner k-roots extend the standard notion of GRAPH ROOTS and are motivated by applications in computational biology. In this paper, we first present O(n + e)-time algorithms to determine if a (not necessarily connected) graph G = (V, E) has an S-restricted 1-root Steiner tree for a given subset S ⊂ V , and to determine if a connected graph G = (V, E) has an S-restricted 2-root Steiner tree for a given subset S ⊂ V, where n = |V| and e = |E|. We then use these two algorithms as subroutines to design O(n + e)-time algorithms to determine if a given (not necessarily connected) graph G = (V, E) has a 3-root phylogeny and to determine if a given connected graph G = (V, E) has a 4-root phylogeny.

Orchestrating quartets: approximation and data correction

Inferring evolutionary trees has long been a challenging problem both for biologists and computer scientists. In recent years research has concentrated on the quartet method paradigm for inferring evolutionary trees. Quartet methods proceed by first inferring the evolutionary history for every set of four species (resulting in a set Q of inferred quarter topologies) and then recombining these inferred quarter topologies to form an evolutionary tree. This paper presents two results on the quartet method paradigm. The first is a polynomial time approximation scheme (PTAS) for recombining the inferred quartet topologies optimally. This is an important result since, to date, there have been no polynomial time algorithms with performance guarantees for quartet methods. In fact, this is the first known PTAS for inferring evolutionary trees under any paradigm. To achieve this result the natural denseness of the set Q is exploited. The second result is a new technique, called quartet cleaning, that detects and corrects errors in the set Q with performance guarantees. This result has particular significance since quartet methods are usually very sensitive to errors in the data. It is shown how quartet cleaning can dramatically increase the accuracy of quartet methods.

Probabilistic analysis indicates discordant gene trees in chloroplast evolution

Analyses of whole-genome data often reveal that some genes have evolutionary histories that diverge from the majority phylogeny estimated for the entire genome. We present a probabilistic model that deals with heterogeneity among gene trees, implement it via the Gibbs sampler, and apply it to the plastid genome. Plastids and their genomes are transmitted as a single block without recombination, hence homogeneity among gene trees within this genome is expected. Nevertheless, previous work has revealed clear heterogeneity among plastid genes (e.g., Delwiche and Palmer 1996). Other studies, using whole plastid genomes of various algae and land plants, found little additional heterogeneity (Martin et al. 1998; Adachi et al. 2000). We augment the earlier studies by using a data set of 14 taxa: 6 land plants, 2 green algae, a diatom, 2 red algae and a cryptophyte, the cyanelle of the glaucocystophyte Cyanophora, and the blue–green alga Synechocystis as an outgroup. Contrary to the earlier analyses, we cannot find even a single, dominant consensus tree. Therefore, we formulate a probabilistic model that divides the genes into two sets: those that follow the consensus tree and those that have independent gene trees. No particular tree is supported by more than three-fourths of the genes. But the set of genes that follows a certain tree is fairly independent of data processing and the method of analysis. With one possible exception, we find no evidence for collinear or functionally related genes to follow similar trees. The phylogenetic pattern also seems independent of bias in amino acid composition. Among possible explanations for the observed phenomenon, the hypothesis that different genes have different covarion structures is difficult to assess. But gene duplication may be possible through the inverted or direct repeat regions, while horizontal gene transfer seems less likely. In contrast to green algae and land plants, inverted repeat regions in red algae and in Cyanophora show abundant differences among the copies. Thus, genes may get duplicated when they are recruited into the inverted repeat region and one of the two copies may be lost after leaving the inverted repeat region.

The ordinal quartet method

The utility of ordinal assertions for infer&g evolutionary trees from sequence data is examined. If M is a difference matrix derived from a set of sequences then “M(s,z) 5 M(s, y)” is an ordinal assertion supported by .&l where s, x and g( are sequences. Ordinal assertions are shown to be an accurate and robust source of evolutionary information. The following results are presentedz A method for inf&g @et topology, the Ordinal Quartet iVethod, is introduced Siulations are reported which demonstrate that the Ordkal Quartet Method is signiEcs&ly more accurate and robust than the popular We& Pour-Point Condition Method. This improvement drastically increases the accuracy of quartet recomb&&on methods, such as the Short Quartet Method [lo] and the Q’ Method [S] whose accuracy is critidy dependent upon the ability to infer quartet topology accurately. It is also demonstrated that, unlike other quartet inference methods sudh as the Weak FoePoint Condition Method, the Orwet Method does not require data correction. The first convergence rate analysis for methods utili&g ordinal assertions is presented. The results obtained are notable in that they apply to any method that utilize ordid assertions. ‘The author gratefully acknowledges the support of NSERC and OGS. *Department of Compnter Science, University of Waterloo, Waterloo ON, CANADA N3L 3G1, pkwuneyemath.aoatooo.ca Permission to m&e digital/bard copies of all or part of this matenal for personal or classroomuseegranteduithoutfeeprovidedthatthe copies are not made or distributed for profit or commercial advantage, the copyriEhtnoh‘ce,thetitleofthepubliutionanditsdateappear.andnoticris given that copyright is by penmss *on ofthe ACM, Inc. To copy otherwise, torepublish to post on servers or to rediiiute to lists, requires specik permission andfor fee. RECOhB 9s New York NY USA Copyright 199s o-s9791-9769/9sl3..s5.00

Methods for reconstructing the history of tandem repeats and their application to the human genome

The genomes of many species are dominated by short sequences repeated consecutively called tandem repeats. An understanding of the biological mechanisms that create and extend tandem repeats would be facilitated by reconstructing the history of duplication events that generated the tandem repeats. This paper explores the computational problem of reconstructing the duplication history of a tandem repeat. Specifically, the problem of reconstructing the minimum-cost duplication history is proved to be NP-hard even if the lengths and boundaries for the duplication events are fixed. When the lengths and boundaries are fixed, the minimum-cost duplication history can actually be represented by a tree. A non-trivial extension of the tree-alignment algorithms from [Wang et al. (Algorithmica 16 (1996) 302; SIAM J. Comput. 30 (1) (2000) 283)] gives a polynomial time approximation scheme (PTAS) for this special case. Experiments on more than 9000 tandem repeats from human chromosomes 1 and 22 demonstrate that our PTAS generates less costly histories in acceptable time than other heuristic methods. We also note that our PTAS works for any metric space. Therefore, our algorithm is also a PTAS for constructing a minimum Steiner tree (MST) when the order of all the regular nodes on the output Steiner tree is known.Assigned to patriarchal poetry too sue sue sue sue shall sue sell and magnificent can as coming let the same shall shall shall shall let it share is share is share shall shall shall shall shell shell shall share is share shell can shell be shell be shell moving in in in inner moving move inner in in inner in meant meant might might may collect collected recollected to refuse what it is is it.

The use of functional domains to improve transmembrane protein topology prediction.

Transmembrane proteins affect vital cellular functions and pathogenesis, and are a focus of drug design. It is difficult to obtain diffraction quality crystals to study transmembrane protein structure. Computational tools for transmembrane protein topology prediction fill in the gap between the abundance of transmembrane proteins and the scarcity of known membrane protein structures. Their prediction accuracy is still inadequate: TMHMM, the current state-of-the-art method, has less than 52% accuracy in topology prediction on one set of transmembrane proteins of known topology. Based on the observation that there are functional domains that occur preferentially internal or external to the membrane, we have extended the model of TMHMM to incorporate functional domains, using a probabilistic approach originally developed for computational gene finding. Our extension is better than TMHMM in predicting the topology of transmembrane proteins. As prediction of functional domain improves, our systems prediction accuracy will likely improve as well.

NeST graphs

We establish results on NeST graphs (intersection tolerance graphs of neighborhood subtrees of a tree) and several subclasses. In particular, we show the equivalence of proper NeST graphs and unit NeST graphs, the equivalence of fixed distance NeST graphs and threshold tolerance graphs, and the proper containment of NeST graphs in weakly chordal graphs. The latter two results answer questions of Monma, Reed and Trotter, and Bibelnieks and Dearing.

Selecting the branches for an evolutionary tree: a polynomial time approximation scheme

Many fundamental questions in evolution remain unresolved despite the abundance of genetic sequence data that is now available. This state of affairs is partly due to the lack of simultaneously efficient and accurate computational methods for inferring evolutionary trees. Efficient methods are critical since the abundance of sequence data has resulted in the need to analyze large datasets. Methods with guaranteed accuracy are important since biologists require proof that results are meaningful. In this paper the first polynomial time approximation scheme (PTAS) for selecting the branches of an evolutionary trees from a list of candidate branches is presented. PTASs are highly desirable since they allow the approximation of an optimal solution with arbitrary precision in polynomial time. This PTAS is based upon recent advances in the approximation of smooth polynomial integer programs.