A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics

International audienceIn this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold. We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n 2)-space, O(n 2ρ+2.5)-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n ρ+1)-space, O(n ρ+2)-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [20]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph. We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n ρ+2) for the energy barrier problem, improving upon a partial O(n 2ρ+2.5) algorithm for the problem

Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw\u27. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^{O(tw)}n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw\u27 or tw-tw\u27 is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics

Magneto-transport Subbands Spectroscopy in InAs Nanowires

We report on magneto-transport measurements in InAs nanowires under large magnetic field (up to 55T), providing a direct spectroscopy of the 1D electronic band structure. Large modulations of the magneto-conductance mediated by an accurate control of the Fermi energy reveal the Landau fragmentation, carrying the fingerprints of the confined InAs material. Our numerical simulations of the magnetic band structure consistently support the experimental results and reveal key parameters of the electronic confinement.Comment: 13 Pages, 5 figure

Morphological, ecological and genetic aspects associated with endemism in the Fly Orchid group

The European genus Ophrys (Orchidaceae) is famous for its insect-like floral morphology, an adaptation for a pseudocopulatory pollination strategy involving Hymenoptera males. A large number of endemic Ophrys species have recently been described, especially within the Mediterranean Basin, which is one of the major species diversity hotspots. Subtle morphological variation and specific pollinator dependence are the two main perceptible criteria for describing numerous endemic taxa. However, the degree to which endemics differ genetically remains a challenging question. Additionally, knowledge regarding the factors underlying the emergence of such endemic entities is limited. To achieve new insights regarding speciation processes in Ophrys, we have investigated species boundaries in the Fly Orchid group (Ophrys insectifera sensu lato) by examining morphological, ecological and genetic evidence. Classically, authors have recognized one widespread taxon (O. insectifera) and two endemics (O. aymoninii from France and O. subinsectifera from Spain). Our research has identified clear morphological and ecological factors segregating among these taxa; however, genetic differences were more ambiguous. Insights from cpDNA sequencing and amplified fragment length polymorphisms genotyping indicated a recent diversification in the three extant Fly Orchid species, which may have been further obscured by active migration and admixture across the European continent. Our genetic results still indicate weak but noticeable phylogeographic clustering that partially correlates with the described species. Particularly, we report several isolated haplotypes and genetic clusters in central and southeastern Europe. With regard to the morphological, ecological and genetic aspects, we discuss the endemism status within the Fly Orchid group from evolutionary, taxonomical and conservation perspectives

Why is lateral root growth so variable? A framework to analyze growth variability among lateral roots and the possible roles of auxin and carbon

International audienceLateral root (LR) development is a major component of the efficiency of a plant to capture soil resources. A remarkable facet of lateral root behavior is stochasticity affecting the different stages of LR growth, leading to a large range of lateral root lengths along the primary root. It has been argued that such variability among LR could be an adaptive trait enabling a greater plasticity and efficiency of the root system in front of the spatial and temporal heterogeneity of soil resources (Forde, 2009). In order to characterize variability in LR growth and evaluate the role of hormonal and biochemical signals that might influence it, we analyzed the patterns of development of hundreds of lateral roots in a set of maize seedlings grown in rhizotrons. The SmartRoot toolbox was used to provide a comprehensive recording of individual root growth dynamics. Using a clustering method based on growth variables such as elongation rate and growth duration, we could identify 3 main different elongation patterns in maize LRs composed of accelerating, slowly decelerating and rapidly arrested LRs, as found in other species (Pagès, 1995). The molecular and cellular characterization of these root types revealed differences in meristem size, apical diameters as well as apical diameter variation. Moreover, fast growing roots showed increased sugar content along their tips. Finally, by affecting either the sugar or the auxin status (by pruning seminal roots or using auxin transport mutants) we differentially altered the proportion of the different root types, suggesting that both signals contribute to shape the root system in response to variations of environmental conditions.FORDE, B. (2009), J. Exp. Bot. 60 (14): 3989-4002PAGES, L. (1995), New Phytologist, 130: 503–50

Automated Design of Dynamic Programming Schemes for RNA Folding with Pseudoknots

Despite being a textbook application of dynamic programming (DP) and routine task in RNA structure analysis, RNA secondary structure prediction remains challenging whenever pseudoknots come into play. To circumvent the NP-hardness of energy minimization in realistic energy models, specialized algorithms have been proposed for restricted conformation classes that capture the most frequently observed configurations. While these methods rely on hand-crafted DP schemes, we generalize and fully automatize the design of DP pseudoknot prediction algorithms. We formalize the problem of designing DP algorithms for an (infinite) class of conformations, modeled by (a finite number of) fatgraphs, and automatically build DP schemes minimizing their algorithmic complexity. We propose an algorithm for the problem, based on the tree-decomposition of a well-chosen representative structure, which we simplify and reinterpret as a DP scheme. The algorithm is fixed-parameter tractable for the tree-width tw of the fatgraph, and its output represents a ?(n^{tw+1}) algorithm for predicting the MFE folding of an RNA of length n. Our general framework supports general energy models, partition function computations, recursive substructures and partial folding, and could pave the way for algebraic dynamic programming beyond the context-free case

Investigating the role of the Melanocortin-1 Receptor gene in an extreme case of microgeographical variation in the pattern of melanin-based plumage pigmentation

Received: August 23, 2012; Accepted: October 26, 2012; Published: December 5, 2012The Réunion grey white-eye (Zosterops borbonicus) is a single-island endemic passerine bird that exhibits striking geographically structured melanic polymorphism at a very small spatial scale. We investigated the genetic basis of this color polymorphism by testing whether the melanocortin-1 receptor (MC1R), a gene often involved in natural melanic polymorphism in birds, was associated with the observed plumage variation. Although we found three non-synonymous mutations, we detected no association between MC1R variants and color morphs, and the main amino-acid variant found in the Réunion grey white-eye was also present at high frequency in the Mauritius grey white-eye (Zosterops mauritianus), its sister species which shows no melanic polymorphism. In addition, neutrality tests and analysis of population structure did not reveal any obvious pattern of positive or balancing selection acting on MC1R. Altogether these results indicate that MC1R does not play a role in explaining the melanic variation observed in the Réunion grey white-eye. We propose that other genes such as POMC, Agouti or any other genes involved in pigment synthesis will need to be investigated in future studies if we are to understand how selection shapes complex patterns of melanin-based plumage pigmentation.Peer reviewe