Sampling solution traces for the problem of sorting permutations by signed reversals

International audienceBackgroundTraditional algorithms to solve the problem of sorting by signed reversals output just one optimal solution while the space of all optimal solutions can be huge. A so-called trace represents a group of solutions which share the same set of reversals that must be applied to sort the original permutation following a partial ordering. By using traces, we therefore can represent the set of optimal solutions in a more compact way. Algorithms for enumerating the complete set of traces of solutions were developed. However, due to their exponential complexity, their practical use is limited to small permutations. A partial enumeration of traces is a sampling of the complete set of traces and can be an alternative for the study of distinct evolutionary scenarios of big permutations. Ideally, the sampling should be done uniformly from the space of all optimal solutions. This is however conjectured to be ♯P-complete.ResultsWe propose and evaluate three algorithms for producing a sampling of the complete set of traces that instead can be shown in practice to preserve some of the characteristics of the space of all solutions. The first algorithm (RA) performs the construction of traces through a random selection of reversals on the list of optimal 1-sequences. The second algorithm (DFALT) consists in a slight modification of an algorithm that performs the complete enumeration of traces. Finally, the third algorithm (SWA) is based on a sliding window strategy to improve the enumeration of traces. All proposed algorithms were able to enumerate traces for permutations with up to 200 elements.ConclusionsWe analysed the distribution of the enumerated traces with respect to their height and average reversal length. Various works indicate that the reversal length can be an important aspect in genome rearrangements. The algorithms RA and SWA show a tendency to lose traces with high average reversal length. Such traces are however rare, and qualitatively our results show that, for testable-sized permutations, the algorithms DFALT and SWA produce distributions which approximate the reversal length distributions observed with a complete enumeration of the set of traces

Sampling and counting genome rearrangement scenarios

Even for moderate size inputs, there are a tremendous number of optimal rearrangement scenarios, regardless what the model is and which specific question is to be answered. Therefore giving one optimal solution might be misleading and cannot be used for statistical inferring. Statistically well funded methods are necessary to sample uniformly from the solution space and then a small number of samples are sufficient for statistical inferring

Gene order rearrangement methods for the reconstruction of phylogeny

The study of phylogeny, i.e. the evolutionary history of species, is a central problem in biology and a key for understanding characteristics of contemporary species. Many problems in this area can be formulated as combinatorial optimisation problems which makes it particularly interesting for computer scientists. The reconstruction of the phylogeny of species can be based on various kinds of data, e.g. morphological properties or characteristics of the genetic information of the species. Maximum parsimony is a popular and widely used method for phylogenetic reconstruction aiming for an explanation of the observed data requiring the least evolutionary changes. A certain property of the genetic information gained much interest for the reconstruction of phylogeny in recent time: the organisation of the genomes of species, i.e. the arrangement of the genes on the chromosomes. But the idea to reconstruct phylogenetic information from gene arrangements has a long history. In Dobzhansky and Sturtevant (1938) it was already pointed out that “a comparison of the different gene arrangements in the same chromosome may, in certain cases, throw light on the historical relationships of these structures, and consequently on the history of the species as a whole”. This kind of data is promising for the study of deep evolutionary relationships because gene arrangements are believed to evolve slowly (Rokas and Holland, 2000). This seems to be the case especially for mitochondrial genomes which are available for a wide range of species (Boore, 1999). The development of methods for the reconstruction of phylogeny from gene arrangement data has made considerable progress during the last years. Prominent examples are the computation of parsimonious evolutionary scenarios, i.e. a shortest sequence of rearrangements transforming one arrangement of genes into another or the length of such a minimal scenario (Hannenhalli and Pevzner, 1995b; Sankoff, 1992; Watterson et al., 1982); the reconstruction of parsimonious phylogenetic trees from gene arrangement data (Bader et al., 2008; Bernt et al., 2007b; Bourque and Pevzner, 2002; Moret et al., 2002a); or the computation of the similarities of gene arrangements (Bergeron et al., 2008a; Heber et al., 2009). 1 1 Introduction The central theme of this work is to provide efficient algorithms for modified versions of fundamental genome rearrangement problems using more plausible rearrangement models. Two types of modified rearrangement models are explored. The first type is to restrict the set of allowed rearrangements as follows. It can be observed that certain groups of genes are preserved during evolution. This may be caused by functional constraints which prevented the destruction (Lathe et al., 2000; Sémon and Duret, 2006; Xie et al., 2003), certain properties of the rearrangements which shaped the gene orders (Eisen et al., 2000; Sankoff, 2002; Tillier and Collins, 2000), or just because no destructive rearrangement happened since the speciation of the gene orders. It can be assumed that gene groups, found in all studied gene orders, are not acquired independently. Accordingly, these gene groups should be preserved in plausible reconstructions of the course of evolution, in particular the gene groups should be present in the reconstructed putative ancestral gene orders. This can be achieved by restricting the set of rearrangements, which are allowed for the reconstruction, to those which preserve the gene groups of the given gene orders. Since it is difficult to determine functionally what a gene group is, it has been proposed to consider common combinatorial structures of the gene orders as gene groups (Marcotte et al., 1999; Overbeek et al., 1999). The second considered modification of the rearrangement model is extending the set of allowed rearrangement types. Different types of rearrangement operations have shuffled the gene orders during evolution. It should be attempted to use the same set of rearrangement operations for the reconstruction otherwise distorted or even wrong phylogenetic conclusions may be obtained in the worst case. Both possibilities have been considered for certain rearrangement problems before. Restricted sets of allowed rearrangements have been used successfully for the computation of parsimonious rearrangement scenarios consisting of inversions only where the gene groups are identified as common intervals (Bérard et al., 2007; Figeac and Varré, 2004). Extending the set of allowed rearrangement operations is a delicate task. On the one hand it is unknown which rearrangements have to be regarded because this is part of the phylogeny to be discovered. On the other hand, efficient exact rearrangement methods including several operations are still rare, in particular when transpositions should be included. For example, the problem to compute shortest rearrangement scenarios including transpositions is still of unknown computational complexity. Currently, only efficient approximation algorithms are known (e.g. Bader and Ohlebusch, 2007; Elias and Hartman, 2006). Two problems have been studied with respect to one or even both of these possibilities in the scope of this work. The first one is the inversion median problem. Given the gene orders of some taxa, this problem asks for potential ancestral gene orders such that the corresponding inversion scenario is parsimonious, i.e. has a minimum length. Solving this problem is an essential component 2 of algorithms for computing phylogenetic trees from gene arrangements (Bourque and Pevzner, 2002; Moret et al., 2002a, 2001). The unconstrained inversion median problem is NP-hard (Caprara, 2003). In Chapter 3 the inversion median problem is studied under the additional constraint to preserve gene groups of the input gene orders. Common intervals, i.e. sets of genes that appear consecutively in the gene orders, are used for modelling gene groups. The problem of finding such ancestral gene orders is called the preserving inversion median problem. Already the problem of finding a shortest inversion scenario for two gene orders is NP-hard (Figeac and Varré, 2004). Mitochondrial gene orders are a rich source for phylogenetic investigations because they are known for more than 1 000 species. Four rearrangement operations are reported at least in the literature to be relevant for the study of mitochondrial gene order evolution (Boore, 1999): That is inversions, transpositions, inverse transpositions, and tandem duplication random loss (TDRL). Efficient methods for a plausible reconstruction of genome rearrangements for mitochondrial gene orders using all four operations are presented in Chapter 4. An important rearrangement operation, in particular for the study of mitochondrial gene orders, is the tandem duplication random loss operation (e.g. Boore, 2000; Mauro et al., 2006). This rearrangement duplicates a part of a gene order followed by the random loss of one of the redundant copies of each gene. The gene order is rearranged depending on which copy is lost. This rearrangement should be regarded for reconstructing phylogeny from gene order data. But the properties of this rearrangement operation have rarely been studied (Bouvel and Rossin, 2009; Chaudhuri et al., 2006). The combinatorial properties of the TDRL operation are studied in Chapter 5. The enumeration and counting of sorting TDRLs, that is TDRL operations reducing the distance, is studied in particular. Closed formulas for computing the number of sorting TDRLs and methods for the enumeration are presented. Furthermore, TDRLs are one of the operations considered in Chapter 4. An interesting property of this rearrangement, distinguishing it from other rearrangements, is its asymmetry. That is the effects of a single TDRL can (in the most cases) not be reversed with a single TDRL. The use of this property for phylogeny reconstruction is studied in Section 4.3. This thesis is structured as follows. The existing approaches obeying similar types of modified rearrangement models as well as important concepts and computational methods to related problems are reviewed in Chapter 2. The combinatorial structures of gene orders that have been proposed for identifying gene groups, in particular common intervals, as well as the computational approaches for their computation are reviewed in Section 2.2. Approaches for computing parsimonious pairwise rearrangement scenarios are outlined in Section 2.3. Methods for the computation genome rearrangement scenarios obeying biologically motivated constraints, as introduced above, are detailed in Section 2.4. The approaches for the inversion median problem are covered in Section 2.5. Methods for the reconstruction of phylogenetic trees from gene arrangement data are briefly outlined in Section 2.6.3 1 Introduction Chapter 3 introduces the new algorithms CIP, ECIP, and TCIP for solving the preserving inversion median problem. The efficiency of the algorithm is empirically studied for simulated as well as mitochondrial data. The description of algorithms CIP and ECIP is based on Bernt et al. (2006b). TCIP has been described in Bernt et al. (2007a, 2008b). But the theoretical foundation of TCIP is extended significantly within this work in order to allow for more than three input permutations. Gene order rearrangement methods that have been developed for the reconstruction of the phylogeny of mitochondrial gene orders are presented in the fourth chapter. The presented algorithm CREx computes rearrangement scenarios for pairs of gene orders. CREx regards the four types of rearrangement operations which are important for mitochondrial gene orders. Based on CREx the algorithm TreeREx for assigning rearrangement events to a given tree is developed. The quality of the CREx reconstructions is analysed in a large empirical study for simulated gene orders. The results of TreeREx are analysed for several mitochondrial data sets. Algorithms CREx and TreeREx have been published in Bernt et al. (2008a, 2007c). The analysis of the mitochondrial gene orders of Echinodermata was included in Perseke et al. (2008). Additionally, a new and simple method is presented to explore the potential of the CREx method. The new method is applied to the complete mitochondrial data set. The problem of enumerating and counting sorting TDRLs is studied in Chapter 5. The theoretical results are covered to a large extent by Bernt et al. (2009b). The missing combinatorial explanation for some of the presented formulas is given here for the first time. Therefor, a new method for the enumeration and counting of sorting TDRLs has been developed (Bernt et al., 2009a)

Evolution of whole genomes through inversions:models and algorithms for duplicates, ancestors, and edit scenarios

Advances in sequencing technology are yielding DNA sequence data at an alarming rate – a rate reminiscent of Moore's law. Biologists' abilities to analyze this data, however, have not kept pace. On the other hand, the discrete and mechanical nature of the cell life-cycle has been tantalizing to computer scientists. Thus in the 1980s, pioneers of the field now called Computational Biology began to uncover a wealth of computer science problems, some confronting modern Biologists and some hidden in the annals of the biological literature. In particular, many interesting twists were introduced to classical string matching, sorting, and graph problems. One such problem, first posed in 1941 but rediscovered in the early 1980s, is that of sorting by inversions (also called reversals): given two permutations, find the minimum number of inversions required to transform one into the other, where an inversion inverts the order of a subpermutation. Indeed, many genomes have evolved mostly or only through inversions. Thus it becomes possible to trace evolutionary histories by inferring sequences of such inversions that led to today's genomes from a distant common ancestor. But unlike the classic edit distance problem where string editing was relatively simple, editing permutation in this way has proved to be more complex. In this dissertation, we extend the theory so as to make these edit distances more broadly applicable and faster to compute, and work towards more powerful tools that can accurately infer evolutionary histories. In particular, we present work that for the first time considers genomic distances between any pair of genomes, with no limitation on the number of occurrences of a gene. Next we show that there are conditions under which an ancestral genome (or one close to the true ancestor) can be reliably reconstructed. Finally we present new methodology that computes a minimum-length sequence of inversions to transform one permutation into another in, on average, O(n log n) steps, whereas the best worst-case algorithm to compute such a sequence uses O(n√n log n) steps

Algorithmes pour la reconstruction de génomes ancestraux

L’inférence de génomes ancestraux est une étape essentielle pour l’étude de l’évolution des génomes. Connaissant les génomes d’espèces éteintes, on peut proposer des mécanismes biologiques expliquant les divergences entre les génomes des espèces modernes. Diverses méthodes visant à résoudre ce problème existent, se classant parmis deux grandes catégories : les méthodes de distance et les méthodes de synténie. L’état de l’art des distances génomiques ne permettant qu’un certain répertoire de réarrangements pour le moment, les méthodes de synténie sont donc plus appropriées en pratique. Nous proposons une méthode de synténie pour la reconstruction de génomes ancestraux basée sur une définition relaxée d’adjacences de gènes, permettant un contenu en gène inégal dans les génomes modernes causé par des pertes de gènes de même que des duplications de génomes entiers (DGE). Des simulations sont effectuées, démontrant une capacité de former une solution assemblée en un nombre réduit de régions ancestrales contigües par rapport à d’autres méthodes tout en gardant une bonne fiabilité. Des applications sur des données de levures et de plantes céréalières montrent des résultats en accord avec d’autres publications, notamment la présence de fusion imbriquée de chromosomes pendant l’évolution des céréales.Ancestral genome inference is a decisive step for studying genome evolution. Knowing genomes from extinct species, one can propose biological mecanisms explaining divergences between extant species genomes. Various methods classified in two categories have been developped : distance based methods and synteny based methods. The state of the art of distance based methods only permit a certain repertoire of genomic rearrangements, thus synteny based methods are more appropriate in practice for the time being. We propose a synteny method for ancestral genome reconstruction based on a relaxed defenition of gene adjacencies, permitting unequal gene content in extant genomes caused by gene losses and whole genome duplications (WGD). Simulations results demonstrate our method’s ability to form a more assembled solution rather than a collection of contiguous ancestral regions (CAR) with respect to other methods, while maintaining a good reliability. Applications on data sets from yeasts and cereal species show results agreeing with other publications, notably the existence of nested chromosome fusion during the evolution of cereals

Mathematical models for evolution of genome structure

The structure of a genome can be characterized by its gene content. Evolution of genome structure in closely related species can be studied by examining their synteny or conserved gene order and content. A variety of evolutionary rearrangements like polyploidy, inversions, transpositions, translocations, gene duplication and gene loss degrade synteny over time. In this dissertation, I approach the problem of understanding synteny in genomes and how far back its evolutionary history can be traced in multiple ways. First, I present a probabilistic model of the rearrangements gene loss and transposition (gain) and apply it to the problem of estimating the relative contribution of these rearrangements within a set of syntenic genome segments. This model can be used to predict gene content in syntenic regions of unsequenced genomes. Next, I use optimization methods to recover syntenic segments between genomes based on reconstructions of their parent ancestry. I examine how these reconstructions can be used as input to programs that identify syntenic regions in genomes to reveal more synteny than was previously detected. I use simulations that incorporate each of the evolutionary rearrangements described above to evaluate the models presented in this dissertation. Finally, I apply these models to genomic data from yeast and flowering plants, two eukaryotic systems that are known to have experienced polyploidy. This application is of particular relevance in flowering plants, in which a lot of economically and scientifically important polyploid species have incompletely sequenced genomes

Sound processing in the mouse auditory cortex: organization, modulation, and transformation

The auditory system begins with the cochlea, a frequency analyzer and signal amplifier with exquisite precision. As neural information travels towards higher brain regions, the encoding becomes less faithful to the sound waveform itself and more influenced by non-sensory factors such as top-down attentional modulation, local feedback modulation, and long-term changes caused by experience. At the level of auditory cortex (ACtx), such influences exhibit at multiple scales from single neurons to cortical columns to topographic maps, and are known to be linked with critical processes such as auditory perception, learning, and memory. How the ACtx integrates a wealth of diverse inputs while supporting adaptive and reliable sound representations is an important unsolved question in auditory neuroscience. This dissertation tackles this question using the mouse as an animal model. We begin by describing a detailed functional map of receptive fields within the mouse ACtx. Focusing on the frequency tuning properties, we demonstrated a robust tonotopic organization in the core ACtx fields (A1 and AAF) across cortical layers, neural signal types, and anesthetic states, confirming the columnar organization of basic sound processing in ACtx. We then studied the bottom-up input to ACtx columns by optogenetically activating the inferior colliculus (IC), and observed feedforward neuronal activity in the frequency-matched column, which also induced clear auditory percepts in behaving mice. Next, we used optogenetics to study layer 6 corticothalamic neurons (L6CT) that project heavily to the thalamus and upper layers of ACtx. We found that L6CT activation biases sound perception towards either enhanced detection or discrimination depending on its relative timing with respect to the sound, a process that may support dynamic filtering of auditory information. Finally, we optogenetically isolated cholinergic neurons in the basal forebrain (BF) that project to ACtx and studied their involvement in columnar ACtx plasticity during associative learning. In contrast to previous notions that BF just encodes reward and punishment, we observed clear auditory responses from the cholinergic neurons, which exhibited rapid learning-induced plasticity, suggesting that BF may provide a key instructive signal to drive adaptive plasticity in ACtx

Memory-based preferential choice in large option spaces

Whether adding songs to a playlist or groceries to a shopping basket, everyday decisions often require us to choose between an innumerable set of options. Laboratory studies of preferential choice have made considerable progress in describing how people navigate fixed sets of options. Yet, questions remain about how well this generalises to more complex, everyday choices. In this thesis, I ask how people navigate large option spaces, focusing particularly on how long-term memory supports decisions. In the first project, I explore how large option spaces are structured in the mind. A topic model trained on the purchasing patterns of consumers uncovered an intuitive set of themes that centred primarily around goals (e.g., tomatoes go well in a salad), suggesting that representations are geared to support action. In the second project, I explore how such representations are queried during memory-based decisions, where options must be retrieved from memory. Using a large dataset of over 100,000 online grocery shops, results revealed that consumers query multiple systems of associative memory when determining what choose next. Attending to certain knowledge sources, as estimated by a cognitive model, predicted important retrieval errors, such as the propensity to forget or add unwanted products. In the final project, I ask how preferences could be learned and represented in large option spaces, where most options are untried. A cognitive model of sequential decision making is proposed, which learns preferences over choice attributes, allowing for the generalisation of preferences to unseen options, by virtue of their similarity to previous choices. This model explains reduced exploration patterns behaviour observed in the supermarket and preferential choices in more controlled laboratory settings. Overall, this suggests that consumers depend on associative systems in long-term memory when navigating large spaces of options, enabling inferences about the conceptual properties and subjective value of novel options

Contextual signals in visual cortex:How sounds, state, and task setting shape how we see

What we see is not always what we get. Even though the light that hits the retina might convey the same images, how visual information is processed and what we eventually do with it depend on many contextual factors. In this thesis, we show in a series of experiments how the sensory processing of the same visual input in the visual cortex of mice is affected by our internal state, movements, other senses and any task we are performing. We found that recurrent activity originating within higher visual areas modulates activity in the primary visual cortex (V1) and selectivity amplifies weak compared to strong sensory-evoked responses. Second, visual stimuli evoked similar early activity in V1, but later activity strongly depended on whether mice were trained to report the visual stimuli, and on the specific task. Specifically, adding a second modality to the task demands extended the temporal window during which V1 was causally involved in visual perception. Third, we report that not only visual stimuli but also sounds led to strong responses in V1, composed of distinct auditory-related and motor-related activity. Finally, we studied the role of Posterior Parietal Cortex in an audiovisual change detection task. Despite extensive single-neuron and population-level encoding of task-relevant visual and auditory stimuli, as well as upcoming behavioral responses, optogenetic inactivation did not affect task performance. Whereas these contextual factors have previously been studied in isolation, we obtain a more integrated understanding of how factors beyond visual information determine what we actually see