An ant colony optimization approach for phylogenetic tree reconstruction problem

Vietnam National University, Hanoi College of Technology Huy Quang D inh A n A nt Colony O p tim izatio n A p p ro ach for P hylogenetic Tree R eco n stru ctio n P ro b le m M ajor : Information Technology Code : 1.01.10 M ASTER THESIS Advisor : Prof A rndt von Haeseler Co-Advisor : Dr Hoang Xuan Huan Hanoi - December, 2006 C o n te n ts A b s tr a c t *ii D e c la tio n IV A c k n o w le d g e m e n ts v In tr o d u c tio n 1.1 M o tivation 1.2 1.1.1 Com putational B iology 1.1.2 Phytogeny R e c o n stru c tio n Thesis Works and S t r u c t u r e P h y lo g e n e tic T re e R e c o n s tru c tio n 2.1 Phylogenetic T r e e s 2.2 Sequence Alignment 2.2.1 Biological D a t a 2.2.2 Pairwise and Multiple sequence a lig n m e n t 2.3 Approaches for phylogeny re c o n stru ctio n 11 2.4 Maximum Parsimony Principle 11 2.4.1 Parsimony C o n c e p t 11 2.4.2 Counting evolutionary changes 12 2.4.3 Remarks on Maximum Parsimony A p p ro a ch e s 14 2.5 Finding the best tree by heuristic searches 15 2.5.1 Sequential Addition Methods 15 2.5.2 Tree Arrangement M e th o d s 16 vi C ontents _ _ 2.5.3 3.2 The Ant Algorithms 20 20 3.1.1 Double bridge experim ents 20 3.1.2 Ant S y s te m 22 3.1.3 Ant Colony S y s te m 24 3.1.4 Max-Min Ant S ystem 25 Ant Colony Optimization M eta-h eu ristic 27 3.2.1 Problem R e p re se n ta tio n 27 3.2.2 Artificial A n ts 28 3.2.3 Meta-heuristic S c h e m e 29 3.3 Remarks on ACO A p p licatio n 30 3.4 ACO approaches in phylogenetics 31 P hylogenetic Inference w ith Ant Colony O ptim ization 33 4.1 Related W orks 33 4.2 Tree Graph D escription 34 4.3 4.4 4.5 19 A n t C olony O p tim iz a tio n 3.1 Other heuristic search m e t h o d s 4.2.1 BD Tree C o d e 34 4.2.2 State Graph D e sc rip tio n .38 Our ACO-applicd A p p ro a c h 39 4.3.1 Pheromoue Trail and Heuristic Information 4.3.2 Solution Construction Procedure 4.3.3 Pheromonc Update Chosen Procedure Simulation Results 40 40 42 42 4.4.1 Simulated Data 43 4.4.2 Real D a t a 44 D iscussion 46 C onclusion a n d O u tlo o k 48 B ibliography 50 C o n te n ts viii A p p e n d ix Probabilistic Decision R u le 57 Tree encoding from a BD tree c o d e BD tree code Decoding a lg o rith m .58 ACC) Solution Construction P ro c e d u re 58 Pltcromone Trails Update P r o c e d u re 59 Algorithm for calculating evolutionary changes 60 57 57 List of Figures 1.1 The exponentially growth of nucleotide d a ta b a s e s 2.1 A looted tree of life 2.2 Unrooted tree representation of annelid relationships 2.3 Three possible topologies of unrooted tree for four t a x a 2.4 An example of four types of nucleotide mutations (Nei and Kumar, 0 ) 2.5 Multiple Sequence Alignment E x a m p le 10 2.6 An example for Fitch a lg o rith m 13 2.7 An example of sequential addition m e th o d 16 2.8 An example of Nearest-Neighbor Interchange O p eratio n 17 2.9 An example of Subtree Pruning and Regrafting Operation 18 2.10 An example of Tree Bisection and Rcconnncction O p e r a t io n 18 3.1 Experimental setup for the double bridge e x p e rim e n t 21 3.2 Results gained in the double bridge experiment 4.1 22 Example of encoding a tree from a given BD tree code 36 4.2 Graph structure description with a*,iV p la n e 38 4.3 An example of tree building on the a, N p la n e .39 4.4 A found tree with 17 real species ix .45 List of T ables 2.1 Twenty different types of amino acids with corresponding codc 4.1 The number of instances for which the reconstructed tree and the generated true tree arc identical in the simulated data instances 4.2 Simulation results with real data of our proposed a p p ro a c h 44 x 43 C h a p te r I n t r o d u c t io n 1.1 1.1.1 M o tiv a tio n C o m p u ta tio n a l B iology Nowadays, based on the modern com puter technologies and the development of efficient sequencing technologies, a huge am ount of genetic d a ta is collected in many genome projects including GenBank(USA), EM BL-Bank(Europe), and DNA D atabase of Japan (DDBJ) (see Figure 1.1) The size of the GenBank database is extrem ely large: over 65 billion DNA ba.se pairs in 61 million molecular sequences J This drastic growth of biological d a ta requires com putational tools for biological data (.so-called bioinformatics tools) being capable of handing a large-scale analysis The term s bioinformatics and com putational biology are often used interchange­ ably It is further emphasized th a t there is a tight coupling of developments and knowledge between the more hypothesis-driven research in com putational biology and technique-driven research in bioinformatics A lot of approaches in com puter science have been applied to solve more and more complex problems in com putational biology (Baldi and Brunak, 2000); unfortunately almost, all such problems are N P-hard or NP-complctc Therefore, heuristic search m ethods play an im portant role in tackling the com binatorial optim ization problems 1htt p: / / www n cb i.n lm nih.gov / G e n b a n k / 2h tt p: / / www.b is ti.nill gov/ C om puB ioD ef pdf 1.1 M o tiv a tio n Figure 1.1: The exponentially growth of nucleotide databases Growth of the International Nucleotide Sequence Database Collaboration B.IS« P & rs by 'S H n fla rk ii— ** t M S i — OOBJ —• http://w w w ncbi.nlm.nih.gov/Genbank/ Recently, Ant Colony Optimization (Dorigo 1992) has been proposed and shortly afterwards has been recognized as one efficient method for finding an approximate solution for NP-hard problems The first application is traveling salesman problem by inspiring by the real ants’s behavior when traveling from the colony to the food resource and transporting the food back ACO technique is widely used in various types of combinatorial optimization problems including in bioinformatics (Dorigo and Stutzle, 2004) 1.1.2 P hylogeny R eco n stru ctio n Since the t ime of Charles Darwin, evolutionary biology has been a main focus among biologists to understand the evolutionary history of all organisms Where the re­ lationship of the structure of the organisms is often expressed as a phylogenetic tree (Haeckel 1866) Since the mid of twentieth century, the emergence of rnolec- 1.2 T h e sis W o rk s an d S tr u c tu r e ul,u biology has given rise to a new branch ot study based on inolccular scqucnce (e.g DNA or protein) Moreover, phylogenetic analysis helps not only elucidate the evolutionary pattern but also understand the process of adaptive evolution at the molecular level (Nei and Kumar 2000) In molecular phylogenetics, the sequences of the contemporary species arc given and one asks for the tree topology (including the branch lengths) which explains the data It is commonly accepted that phytogenies arc rooted bifurcating trees, where the root is the most common ancestor of the contemporary species The leaves represent contemporary species, and the internal nodes stand for spéciation events Among plenty of approaches to rcconstruc phylogenetic trees, the statistic-based methods have been recognized as sound and accurate methods Determining the best phylogénies based on optimality critcrions such as maximum parsimony, mini­ mum evolution and maximum likelihood was proved as NP-hard and NP-completc problems (Graham and Foulds, 1982; Day and Sankoff, 1986; Chor and Tullcr, 2005) 1.2 T hesis W orks and Structure In this thesis, we will build a general framework to apply ACO principle into phylo­ genetics and mainly deal with maximum parsimony However, such approach can be easily adapted to any objective function Our contribution is the formal description of framework to apply ACO mctaheuristics to solve the phylogcny reconstruction problem Attempts to solve the phylogenetic reconstruction problem using ACO gained only a poor results partly because of the poor construction graph (Ando and lba, 2002: Kumnorkacw et a l, 2004; Perrctto and Lopes, 2005) We proposed a mure general graph representation to overcome this problem Except the introduction and conclusion, the thesis is organized into chapters The first chapter sketches the major problem of reconstructing phylogenetic trees from given biological sequences The second chapter will show the general building block of ACO technique and application for solving the combinatorial optimization problems The third chapter describes the main outcome of the thesis It will de­ scribe our approach and some initial experiences to employ ACO into phylogenetics C h a p te r P h y lo g e n e tic T ree R e c o n s tru c tio n The goal of the phylogenetic tree reconstruction problem is to assemble a tree rep­ resenting a hypothesis about the evolutionary relationship among a set of genes, species, or other taxa In this chapter, we will briefly introduce the main concept of phylogenetics and the state-of-the-art methods In particular, we will concen­ trate on the maximum parsimony principle used as an objective function for our optimization approach discussed in chapter 2.1 P h y lo g en etic Trees According to Charles Darwin’s evolution theory, all species have evolved from an­ cestors under the pressure of natural selection (Darwin, 1872) Evolutionary trees or phylogenetic trees in phylogenetics terminology arc the one way to display the evolu­ tionary relationships among species A phylogenetic tree, also called an evolutionary tree , or a phytogeny is a graph-theoretic tree representing the evolutionary relation­ ships among a number of species having a common ancestor Figure 2.1 depicts the phylogenetic tree of life consisting of three domains of all existing species: Bacte­ ria Archaea, and Eukarya In a phylogenetic: tree, each internal node represents ¿in unknown common ancestor th at split into two or more species, its descendants Each external node or leaf represents a living spec ies, each branch has a length cor­ responding to the time between two splitting events or to the amount of changes that accumulated between two splits 46 4.5 Discussion is wrv meaningful in which we can see that some pairs whose the elose relationship in nature such as (chicken duck), {mount, rat), (sheep, cow), and ( rabbit, hare) have the same evolutionary father while hamster is closer mouse than pig and marsupial in evolut ionarv relationship The experimental results with some real data sets proved that our method can he considered as the useful effective in phylogenetics under maximum parsimony criterion It cm be easily applied with other optimality criterion such as maximum likelihood Ibr gaining the "true” tree Adjusting the parameters in ACO application is very difficult due to we have to observe the increasing and decreasing of both the optimal result and the pheromonc t rails in each iteration lor possible changes Therefore, we run each instance 25 times for obtaining the average result In ACO it is very important, factor besides the best result gained (Dorigo and Stutzle, 2004) Anyway, we overcame the limitations of the previous ACO approach for phylogenetic tree reconstruction problem Wc can deal wit h the large data with any objective function with the acceptable results Due to the limited time, the thesis failed to show the better experimental results However, we believe that this results is enough good to show the efficiency of our ACO approac h 4.5 Discussion This chapter showed our main contribution in the thesis, the general ACO framework for phylogenetic reconstruction We proposed the construction graph based on BD tree code (Bandclt and Dress, 1986) Thanks to the way to construct tree according to stepwise addition, we found a successful way to map the path of ant on the graph to the solution as the phylogenetic tree Based on that, we can search and move in tree space quickly and efficiently without too much memory requirement It will provide the ACO application in phylogenetics many interesting suggestions Our simulations and the analysis on both the simulated data and real data showed that our method works However, more investigations arc necessary to fully exploit, the properties of ACO in phylogenetics Besides that, wc have the 4.5 Discussion 47 disadvantage that, it is poor heuristic information The better heuristic information can gain the better experimental results Chousing the suitable and efficient heuristic information that can express the phylogenetic information for each so-called state node or partial tree is really dif­ ficult In ca.se of not good heuristic information, the searching process of ACO approach is bias to random search The scope of this thesis did not focus on that, t lit: m.tin goal is building the general state graph and proving the efficiency of that graph by computer simulations in some typical data in both simulated cases and real ins!antes C h a p te r C onclusion and O utlook In conclusion our work provides a new AGO framework for solving phylogenetic: tree reconstruction problem thanks to the efficient construction graph The initially experimental results proved the efficiency of the proposed framework in both terms of accuracy and openness feature We believe that it is deserved to be considered by the phylogenetic community • C o n stru c tio n G p h We have built the construction graph successfully described in the chapter Thanks to BD tree code, we represented the phylogenetic tree as the path of ants according to sequential addition strategy Our graph with only n points where 11 is the number of given species is more general and efficient compared to the existed graph reviewed in the last sect ion of chapter With the proposed graph, we can deal with any objective fund ion in phylogenetics such as : maximum parsimony as our work, distance* based and maximum likelihood Then, it can be considered by both ACO and pliyli«genetics community • S im ulation P erform ance In this thesis, we built the computer simulation with many experimental data and showed both best and average results for consideration Although it is the general approach, the experimental results still are comparable with one of the most well-known parsimony methods, PhyLip version 3.5c (Fclsenstcin, 1993) in small data sets Therefore, our preliminary results motivate for further improvements C h a p te r Conclusion and O utlook 49 Outlook • in the lullin', we will try more adjusting experimental parameters As well known, ilie experimental parameters (initial and boundary pheromone values, the coefficient a i the number of ants, the pheromone evaporation parame­ ter the number of iterations) play a very important role in ACO application (Dorigo and St utzle, 2004) They arc totally different for each type of problem Due' to i he limited time, we paused in some initial experimental results showed in chapter We believe that under the detail observing mechanism for the pur«meters, we can adjust them more efficiently Besides that, other ACO ap­ proaches such as ACS multi-level ant system including some another efficient local searching strategies such as SPR, TBR (reviewed in chapter 2) will be considered as the 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