Fixed-parameter algorithms for some combinatorial problems in bioinformatics

Fixed-parameterized algorithmics has been developed in 1990s as an approach to solve NP-hard problem optimally in a guaranteed running time. It offers a new opportunity to solve NP-hard problems exactly even on large problem instances. In this thesis, we apply fixed-parameter algorithms to cope with three NP-hard problems in bioinformatics: Flip Consensus Tree Problem is a combinatorial problem arising in computational phylogenetics. Using the formulation of the Flip Consensus Tree Problem as a graph-modification problem, we present a set of data reduction rules and two fixed-parameter algorithms with respect to the number of modifications. Additionally, we discuss several heuristic improvements to accelerate the running time of our algorithms in practice. We also report computational results on phylogenetic data. Weighted Cluster Editing Problem is a graph-modification problem, that arises in computational biology when clustering objects with respect to a given similarity or distance measure. We present one of our fixed-parameter algorithms with respect to the minimum modification cost and describe the idea of our fastest algorithm for this problem and its unweighted counterpart. Bond Order Assignment Problem asks for a bond order assignment of a molecule graph that minimizes a penalty function. We prove several complexity results on this problem and give two exact fixed-parameter algorithms for the problem. Our algorithms base on the dynamic programming approach on a tree decomposition of the molecule graph. Our algorithms are fixed-parameter with respect to the treewidth of the molecule graph and the maximum atom valence. We implemented one of our algorithms with several heuristic improvements and evaluate our algorithm on a set of real molecule graphs. It turns out that our algorithm is very fast on this dataset and even outperforms a heuristic algorithm that is usually used in practice

Novel approaches for bond order assignment and NMR shift prediction

Molecular modelling is one of the cornerstones of modern biological and pharmaceutical research. Accurate modelling approaches easily become computationally overwhelming and thus, different levels of approximations are typically employed. In this work, we develop such approximation approaches for problems arising in structural bioinformatics. A fundamental approximation of molecular physics is the classification of chemical bonds, usually in the form of integer bond orders. Many input data sets lack this information, but several problems render an automated bond order assignment highly challenging. For this task, we develop the BOA Constructor method which accounts for the non-uniqueness of solutions and allows simple extensibility. Testing our method on large evaluation sets, we demonstrate how it improves on the state of the art. Besides traditional applications, bond orders yield valuable input for the approximation of molecular quantities by statistical means. One such problem is the prediction of NMR chemical shifts of protein atoms. We present our pipeline NightShift for automated model generation, use it to create a new prediction model called Spinster, and demonstrate that it outperforms established, manually developed approaches. Combining Spinster and BOA Constructor, we create the Liops-model that for the first time allows to efficiently include the influence of non-protein atoms. Finally, we describe our work on manual modelling techniques, including molecular visualization and novel input paradigms.Methoden des molekularen Modellierens gehören zu den Grundpfeilern moderner biologischer und pharmazeutischer Forschung. Akkurate Modelling-Methoden erfordern jedoch enormen Rechenaufwand, weshalb üblicherweise verschiedene Näherungsverfahren eingesetzt werden. Im Promotionsvortrag werden solche im Rahmen der Promotion entwickelten Näherungen für verschiedene Probleme aus der strukturbasierten Bioinformatik vorgestellt. Eine fundamentale Näherung der molekularen Physik ist die Einteilung chemischer Bindungen in wenige Klassen, meist in Form ganzzahliger Bindungsordnungen. In vielen Datensätzen ist diese Information nicht enthalten und eine automatische Zuweisung ist hochgradig schwierig. Für diese Problemstellung wird die BOA Constructor-Methode vorgestellt, die sowohl mit uneindeutigen Lösungen umgehen kann als auch vom Benutzer leicht erweitert werden kann. In umfangreichen Tests zeigen wir, dass unsere Methode dem bisherigen Stand der Forschung überlegen ist. Neben klassischen Anwendungen liefern Bindungsordnungen wertvolle Informationen für die statistische Vorhersage molekularer Eigenschaften wie z.B. der chemischen Verschiebung von Proteinatomen. Mit der von uns entwickelten NightShift-Pipeline wird ein Verfahren zur automatischen Generierung von Vorhersagemodellen präsentiert, wie z.B. dem Spinster-Modell, das den bisherigen manuell entwickelten Verfahren überlegen ist. Die Kombination mit BOA Constructor führt zum sogenannten Liops-Modell, welches als erstes Modell die effiziente Berücksichtigung des Einflusses von nicht-Proteinatomen erlaubt