Self-similar Analysis of Plant Architecture Reveals Hierarchical Classes of Meristem States

International audienceApical meristems are small embryogenic regions, located at the tip of plant axes, that build up plant organs by cellular division. The production of the meristems depends on their internal physical, physiological and genetic state and is controled by contextual factors (like micro-environment, availability of nutrients, etc.). In principle, the number of variables that may be used to define the state of a meristem, taking account the nature and the concentrations of molecules in each cell, their position, the physical stresses at each point, the geometry of cells, their genetic contents, etc., is infinitely large. Due to this intrinsic complexity, and to the current lack of hindsight on processes at such small scales, the connection between a meristem state, its micro-environment and what it produces at varying time scales seems until now largely out of reach

An edit distance between quotiented trees

International audienceIn this paper we propose a dynamic programming algorithm to compare two quotiented trees using a constrained edit distance. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on an adaptation of an algorithm recently proposed by Zhang for comparing unordered rooted trees. This method is currently being used in plant architecture modelling to quantify different types of variability between plants represented by quotiented trees

Quantifying the degree of self-nestedness of trees. Application to the structural analysis of plants

17 pagesInternational audienceIn this paper we are interested in the problem of approximating trees by trees with a particular self-nested structure. Self-nested trees are such that all their subtrees of a given height are isomorphic. We show that these trees present remarkable compression properties, with high compression rates. In order to measure how far a tree is from being a self-nested tree, we then study how to quantify the degree of self-nestedness of any tree. For this, we define a measure of the self-nestedness of a tree by constructing a self-nested tree that minimizes the distance of the original tree to the set of self-nested trees that embed the initial tree. We show that this measure can be computed in polynomial time and depict the corresponding algorithm. The distance to this nearest embedding self-nested tree (NEST) is then used to define compression coefficients that reflect the compressibility of a tree. To illustrate this approach, we then apply these notions to the analysis of plant branching structures. Based on a database of simulated theoretical plants in which different levels of noise have been introduced, we evaluate the method and show that the NESTs of such branching structures restore partly or completely the original, noiseless, branching structures. The whole approach is then applied to the analysis of a real plant (a rice panicle) whose topological structure was completely measured. We show that the NEST of this plant may be interpreted in biological terms and may be used to reveal important aspects of the plant growth

A constrained edit distance algorithm between semi-ordered trees

AbstractIn this paper, we propose a formal definition of a new class of trees called semi-ordered trees and a polynomial dynamic programming algorithm to compute a constrained edit distance between such trees. The core of the method relies on a similar approach to compare unordered [Kaizhong Zhang, A constrained edit distance between unordered labeled trees, Algorithmica 15 (1996) 205–222] and ordered trees [Kaizhong Zhang, Algorithms for the constrained editing distance between ordered labeled trees and related problems, Pattern Recognition 28 (3) (1995) 463–474]. The method is currently applied to evaluate the similarity between architectures of apple trees [Vincent Segura, Aida Ouangraoua, Pascal Ferraro, Evelyne Costes, Comparison of tree architecture using tree edit distances: Application to two-year-old apple tree, Euphytica 161 (2007) 155–164]

A structural method for assessing self-similarity in plants

International audienceThe important rôle of architecture in the understanding of plants [8, 12, 23] generates a need for investigational tools. Generic tools have already been developed to vizualize plant architecture in three dimensions [20], to model the development of plant structure [6, 20], to measure plant architecture [24] , and to analyze and quantify relations between plant components [11]

Toward a quantification of self-similarity in plants

International audienceSelf-similarity of plants has attracted the attention of biologists for at least 50 years, yet its formal treatment is rare, and no measure for quantifying the degree of self-similarity currently exists. We propose a formal definition and measures of self-similarity, tailored to branching plant structures. To evaluate self-similarity, we make use of an algorithm for computing topological distances between branching systems, developed in computer science. The formalism is illustrated using theoretical branching systems, and applied to analyze self-similarity in two sample plant structures: inflorescences of Syringa vulgaris (lilac) and shoots of Oryza sativa (rice

Local Similarity Between Quotiented Ordered Trees

International audienceIn this paper we propose a dynamic programming algorithm to evaluate local similarity between ordered quotiented trees using a constrained edit scoring scheme. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on two adaptations of an algorithm proposed by Zhang et al. [K. Zhang, D. Shasha, Simple fast algorithms for the editing distance between trees and related problems (1989) 1245-1262] for comparing ordered rooted trees. After some preliminary definitions and the description of this tree edit algorithm, we propose extensions to globally and locally compare two quotiented trees. This last method allows to find the region in each tree with the highest similarity. Algorithms are currently being used in genomic analysis to evaluate variability between RNA secondary structures

Lossy compression of plant architectures

International audiencePlants usually show intricate structures whose representation and management are an important source of complexity of models. Yet plant structures are also repetitive: although not identical, the organs, axes, and branches at different positions are often highly similar. From a formal perspective, this repetitive character of plant structures was first exploited in fractal-based plant models (Barnsley, 2000; Ferraro et al., 2005; Prusinkiewicz and Hanan, 1989; Smith, 1984). In particular, L-systems have extensively been used in the last two decades to amplify parsimonious rule-based models into complex branching structures by specifying how fundamental units are repeatedly duplicated and modified in space and over time (Prusinkiewicz et al., 2001). However, the inverse problem of finding a compact representation of a branching structure has remained largely opened, and is now becoming a key issue in modeling applications as it needs to be solved to both get insight into the complex organization of plants and to decrease time and space complexity of simulation algorithms. The idea is that a compressed version of a plant structure might be much more efficient to manipulate than the original extensive branching structure. For instance, Soler et al. (2003) have shown that the complexity of radiation simulation can be drastically reduced if self-similar representations of plants are used. Unfor- tunately, strict self-similarity has a limited range of applications, because neither real plants nor more sophisticated plant models are exactly self-similar. Consequently, we propose in this paper an algorithm that exploit approximate self-similarity to compress plant structures to various degrees, representing a tradeoff between compression rate and accuracy. This new compression method aims at making possible to efficiently model, simulate and analyze plants using these compressed representations

Identification de motifs au sein des structures biologiques arborescentes

Avec l explosion de la quantité de données biologiques disponible, développer de nouvelles méthodes de traitements efficaces est une problématique majeure en bioinformatique. De nombreuses structures biologiques sont modélisées par des structures arborescentes telles que les structures secondaires d ARN et l architecture des plantes. Ces structures contiennent des motifs répétés au sein même de leur structure mais également d une structure à l autre. Nous proposons d exploiter cette propriété fondamentale afin d améliorer le stockage et le traitement de tels objets.En nous inspirant du principe de filtres sur les séquences, nous définissons dans cette thèse une méthode de filtrage sur les arborescences ordonnées permettant de rechercher efficacement dans une base de données un ensemble d arborescences ordonnées proches d une arborescence requête. La méthode se base sur un découpage de l arborescence en graines et sur une recherche de graines communes entre les structures. Nous définissons et résolvons le problème de chainage maximum sur des arborescences. Nous proposons dans le cas des structures secondaires d ARN une définition de graines (l d) centrées.Dans un second temps, en nous basant sur des techniques d instanciations utilisées, par exemple, en infographie et sur la connaissance des propriétés de redondances au sein des structures biologiques, nous présentons une méthode de compression permettant de réduire l espace mémoire nécessaire pour le stockage d arborescences non-ordonnées. Après une détermination des redondances nous utilisons une structure de données plus compacte pour représenter notamment l architecture de la plante, celle-ci pouvant contenir des informations topologiques mais également géométriques.The explosion of available biological data urges the need for bioinformatics methods. Manybiological structures are modeled by tree structures such as RNA secondary structure and plantsarchitecture. These structures contain repeating units within their structure, but also betweendifferent structures. We propose to exploit this fundamental property to improve storage andtreatment of such objects.Following the principle of sequence filtering, we define a filtering method on ordered treesto efficiently retrieve in a database a set of ordered trees close from a query. The method isbased on a decomposition of the tree into seeds and the detection of shared seeds between thesestructures. We define and solve the maximum chaining problem on trees. We propose for RNAsecondary structure applications a definition of (l d) centered seed.Based on instantiation techniques used for instance in computer graphics and the repetitivenessof biological structures, we present a compression method which reduces the memoryspace required for plant architecture storage. A more compact data structure is used in order torepresent plant architecture. The construction of this data structure require the identification ofinternal redundancies and taking into account both topological and geometrical informations.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF