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Inferring Genomic Duplication Events

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Inferring Genomic Duplication Events University of Warsaw Faculty of Mathematics, Informatics and Mechanics Jarosław Paszek Student no. 209217 Inferring genomic duplication events PhD’s dissertation in COMPUTER SCIENCE Supervisor: dr hab. Paweł Górecki Institute of Informatics, University of Warsaw May 2018 Supervisor’s statement Hereby I confirm that the presented thesis was prepared under my supervision and that it fulfills the requirements for the degree of PhD of Computer Science. Date Supervisor’s signature Author’s statement Hereby I declare that the presented thesis was prepared by me and none of its contents was obtained by means that are against the law. The thesis has never before been a subject of any procedure of obtaining an academic degree. Moreover, I declare that the present version of the thesis is identical to the attached electronic version. Date Author’s signature Abstract Inferring genomic duplication events One of evolutionary molecular biology fundamental problems is to discover ge- nomic duplication events and their locations in the species tree. Such events can be reconstructed by clustering single gene duplications inferred by reconciling a set of gene trees with a species tree. Existing reconciliation based approaches vary in the two fundamental aspects: (a) the choice of evolutionary scenarios that model al- lowed locations of duplications in the species tree, and (b) the rules of clustering gene duplications from gene trees into a single multiple duplication event, i.e., episode clustering (EC) or minimum episodes (ME) methods. There are several mod- els in the literature that specify how gene duplications from gene families can be interpreted as one duplication episode. However, in all duplication episode problems gene trees are rooted. This restriction limits the applicability, since unrooted gene family trees are frequently inferred by phylogenetic methods. In this dissertation, we propose a model of evolutionary scenarios that preserves the minimal number of gene duplications. We study the RME problem, that is, ME method of clustering when input gene trees are rooted. Our analysis concerns several models of allowed evolutionary scenarios with a focus on interval models in which every gene duplication has an interval consisting of allowed locations in the species tree and fulfills some additional requirements like monotonicity. We present math- ematical foundations for general genomic duplication problems. Next, we propose the first linear time and space algorithm for RME jointly for any interval model and the algorithm for the most general model in which every evolutionary scenario is allowed. We also present a comparative study of different models of genomic du- plication based on simulated and empirical datasets. We provide algorithms and tools that can be applied to solve efficiently RME problems for various models. Our comparative study helps to identify which model is the most reasonable choice in inferring genomic duplication events. This dissertation proposes the first solutions to the open problems of UEC (un- rooted episode clustering) and UME (unrooted minimum episodes) in which every reconciliation with the minimal number of single gene duplications is allowed and under the assumption that input gene trees are unrooted. In particular, we show new theoretical properties of unrooted reconciliation for the duplication cost and apply them to design several exact and heuristic algorithms for solving the genomic duplication problems. Our comparative study shows that we can improve known results on genomic duplication inference from rooted trees. Moreover, our evaluation on empirical datasets confirms several genomic duplication events from the litera- ture and demonstrates that the proposed algorithms can be successfully applied in practice. Streszczenie Studium zdarzeń duplikacji w genomie Jednym z fundamentalnych zagadnień w molekularnej biologii obliczeniowej jest wykrywanie zdarzeń duplikacji w genomie oraz określenie ich położenia w drzewie gatunków. Rekonstrukcja tych zdarzeń jest możliwa poprzez klastrowanie poje- dynczych duplikacji genu, wyznaczonych przez uzgadnianie zbioru drzew genów ze zbiorem gatunków. Istniejące metody różnią się w dwóch zasadniczych kwestiach: (a) wyboru scenariuszy ewolucyjnych, które modelują dopuszczalne lokalizacje dup- likacji w drzewie gatunków oraz (b) określenia zasad klastrowania duplikacji genów z drzew genów w jedno zdarzenie wielokrotnej duplikacji, metod jak np. episode clustering (EC) lub minimum episodes (ME). Analizując literaturę można wyróżnić kilka modeli opisujących jak duplikacje genów z drzew rodzin genów in- terpretować jako jedno zdarzenie, jednak wszystkie one dotyczą przypadku, gdy drzewa genów są ukorzenione. Warunek ten ogranicza możliwości zastosowań, gdyż to nieukorzenione drzewa genów są wynikiem popularnych metod filogenetycznych. W niniejszej rozprawie, proponujemy model scenariuszy ewolucyjnych, który za- chowuje minimalną liczbę duplikacji genów. Badamy problem RME, czyli klastrowa- nia metodą ME w przypadku, gdy wejściowe drzewa genów są ukorzenione. Przeana- lizowaliśmy kilka modeli dopuszczalnych scenariuszy ewolucyjnych, ze szczególnym uwzględnieniem modeli interwałowych, w których każda duplikacja genu ma przy- pisany interwał dopuszczalnych lokalizacji w drzewie gatunków, oraz nakładają- cych dodatkowe ograniczenia jak monotoniczność. Przedstawiamy matematyczne podstawy dla ogólnych problemów duplikacji genomowych. Następnie, dla prob- lemu RME proponujemy pierwszy liniowy algorytm uniwersalny dla modeli inter- wałowych oraz algorytm dla najbardziej ogólnego modelu, w którym każdy scenariusz ewolucyjny jest dopuszczalny. Dodatkowo przedstawiamy studium porównawcze dla różnych modeli duplikacji genomowych, które bazuje na danych symulowanych i empirycznych. Dostarczamy algorytmów i narzędzi do efektywnego rozwiązywa- nia problemów RME dla różnych modeli. Nasze studium porównawcze pozwala na zidentyfikowanie, który model stanowi najrozsądniejszy wybór przy wnioskowaniu zdarzeń duplikacji genomu. Niniejsza rozprawa przedstawia pierwsze rozwiązania dla otwartych problemów UEC (episode clustering) i UME (minimum episodes), w których każdy scenariusz implikujący minimalną liczbę pojedynczych duplikacji genu jest dopuszczalny oraz przyjmujemy założenie, że wejściowe drzewa genów są nieukorzenione. W szczegól- ności prezentujemy nowe teoretyczne własności nieukorzenionego uzgadniania dla kosztu duplikacyjnego i wykorzystujemy je do zaprojektowania dokładnych i heurysty- cznych algorytmów rozwiązujących problemy duplikacji genomowych. Nasza ewalu- acja eksperymentalna pokazuje, że potrafimy ulepszyć znane wyniki dla wnioskowa- nia duplikacji genomowych z ukorzenionych drzew. Dodatkowo nasza analiza na empirycznych danych potwierdziła kilka zdarzeń duplikacji genomowych z literatury demonstrując, że proponowane algorytmy można z sukcesem wykorzystywać w prak- tyce. Keywords genomic duplication, duplication episode, reconciliation, minimum episodes problem, episode clustering problem, unrooted gene tree, gene tree, species tree Thesis domain (Socrates-Erasmus subject area codes) 11.3 Informatyka Subject classification Applied computing ! Life and medical sciences ! ! Genomics ! Bioinformatics ! Computational biology ! Computational genomics Mathematics of computing ! Discrete mathematics ! ! Graph theory ! Trees ! Graph theory ! Graph algorithms Tytuł pracy w języku polskim Studium zdarzeń duplikacji w genomie List of publications of major results from the thesis: Paszek, J. and Górecki, P. (2016). Genomic duplication problems for unrooted gene trees. BMC Genomics, 17(1):165–175. doi: 10.1186/s12864-015-2308-4. Paszek, J. and Górecki, P. (2017a). Efficient algorithms for genomic duplica- tion models. IEEE/ACM Transactions on Computational Biology and Bioin- formatics. doi: 10.1109/TCBB.2017.2706679. Paszek, J. and Górecki, P. (2017b). New algorithms for the genomic dupli- cation problem. In: Meidanis J., Nakhleh L. (eds) Comparative Genomics. RECOMB-CG 2017. Lecture Notes in Computer Science, 10562:101–115. Springer, Cham. Paszek, J. and Górecki, P. (2018). Inferring duplication episodes from unrooted gene trees. BMC Genomics, 19(5):288. doi: 10.1186/s12864-018-4623-z. List of selected publications in phylogenetics: Górecki, P., Paszek, J., and Eulenstein, O. (2017). Unconstrained Diameters for Deep Coalescence. IEEE/ACM Transactions on Computational Biology and Bioin- formatics, 14(5):1002–1012. doi: 10.1109/TCBB.2016.2520937. Górecki, P., Markin, A., Mykowiecka, A., Paszek, J., and Eulenstein, O. (2017). Phy- logenetic tree reconciliation: Mean values for fixed gene trees. LNCS, 10330:234–245. Górecki, P., Paszek, J., and Mykowiecka, A. (2016). Mean values of gene dupli- cation and loss cost functions. LNCS, 9683:189–199. Górecki, P., Paszek, J., and Eulenstein, O. (2014). Duplication Cost Diameters. LNCS, 8492:212–223. Górecki, P., Paszek, J., and Eulenstein, O. (2014). Unconstrained gene tree di- ameters for deep coalescence. In Proceedings of the 5th ACM Conference on Bioin- formatics, Computational Biology, and Health Informatics, BCB ’14, pages 114–121. (ACM SIGBio best paper award in 2014) Selected other publications: Gambin, T., Startek, M., Walczak, K., Paszek, J., Grzebelus, D., and Gambin, A. (2013). Tirfinder: A web tool for mining class ii transposons carrying terminal in- verted repeats. Evolutionary Bioinformatics, 9:17–27. Huczko, A., Lange, H., Paszek, J., Bystrzejewski, M., Cudziło, S., Gachet, S., Mon- thioux, M., Zhu, Y. Q., Kroto, H. W., and Walton,
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