Matthieu Vignes

Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.

The dynamics of root meristem distribution in the soil

Plants must develop efficient root architectures to secure access to nutrients and water in soil. This is achieved during plant development through a series of expansion and branching processes, mostly in the proximity of root apical meristems, where the plant senses the environment and explores immediate regions of the soil. We have developed a new approach to study the dynamics of root meristem distribution in soil, using the relationship between the increase in root length density and the root meristem density. Initiated at the seed, the location of root meristems in barley seedlings was shown to propagate, wave-like, through the soil, leaving behind a permanent network of roots for the plant to acquire water and nutrients. Data from observations on barley roots were used to construct mathematical models to describe the density of root meristems in space. These models suggested that the morphology of the waves of meristems was a function of specific root developmental processes. The waves of meristems observed in root systems of barley seedlings exploring the soil might represent a more general and fundamental aspect of plant rooting strategies for securing soil resources.

Gene Clustering via Integrated Markov Models Combining Individual and Pairwise Features

Clustering of genes into groups sharing common characteristics is a useful exploratory technique for a number of subsequent computational analysis. A wide range of clustering algorithms have been proposed in particular to analyze gene expression data, but most of them consider genes as independent entities or include relevant information on gene interactions in a suboptimal way. We propose a probabilistic model that has the advantage to account for individual data (e.g., expression) and pairwise data (e.g., interaction information coming from biological networks) simultaneously. Our model is based on hidden Markov random field models in which parametric probability distributions account for the distribution of individual data. Data on pairs, possibly reflecting distance or similarity measures between genes, are then included through a graph, where the nodes represent the genes, and the edges are weighted according to the available interaction information. As a probabilistic model, this model has many interesting theoretical features. In addition, preliminary experiments on simulated and real data show promising results and points out the gain in using such an approach. Availability: The software used in this work is written in C++ and is available with other supplementary material at http://mistis.inrialpes.fr/people/forbes/transparentia/supplementary.html.

A Model-Based Approach to Gene Clustering with Missing Observation Reconstruction in a Markov Random Field Framework

The different measurement techniques that interrogate biological systems provide means for monitoring the behavior of virtually all cell components at different scales and from complementary angles. However, data generated in these experiments are difficult to interpret. A first difficulty arises from high-dimensionality and inherent noise of such data. Organizing them into meaningful groups is then highly desirable to improve our knowledge of biological mechanisms. A more accurate picture can be obtained when accounting for dependencies between components (e.g., genes) under study. A second difficulty arises from the fact that biological experiments often produce missing values. When it is not ignored, the latter issue has been solved by imputing the expression matrix prior to applying traditional analysis methods. Although helpful, this practice can lead to unsound results. We propose in this paper a statistical methodology that integrates individual dependencies in a missing data framework. More explicitly, we present a clustering algorithm dealing with incomplete data in a Hidden Markov Random Field context. This tackles the missing value issue in a probabilistic framework and still allows us to reconstruct missing observations a posteriori without imposing any pre-processing of the data. Experiments on synthetic data validate the gain in using our method, and analysis of real biological data shows its potential to extract biological knowledge.

Bridging physiological and evolutionary time‐scales in a gene regulatory network

Gene regulatory networks (GRNs) govern phenotypic adaptations and reflect the trade-offs between physiological responses and evolutionary adaptation that act at different time-scales. To identify patterns of molecular function and genetic diversity in GRNs, we studied the drought response of the common sunflower, Helianthus annuus, and how the underlying GRN is related to its evolution. We examined the responses of 32,423 expressed sequences to drought and to abscisic acid (ABA) and selected 145 co-expressed transcripts. We characterized their regulatory relationships in nine kinetic studies based on different hormones. From this, we inferred a GRN by meta-analyses of a Gaussian graphical model and a random forest algorithm and studied the genetic differentiation among populations (FST ) at nodes. We identified two main hubs in the network that transport nitrate in guard cells. This suggests that nitrate transport is a critical aspect of the sunflower physiological response to drought. We observed that differentiation of the network genes in elite sunflower cultivars is correlated with their position and connectivity. This systems biology approach combined molecular data at different time-scales and identified important physiological processes. At the evolutionary level, we propose that network topology could influence responses to human selection and possibly adaptation to dry environments.

An algorithm for the simulation of the growth of root systems on deformable domains

Models of root systems are essential tools to understand how crops access and use soil resources during their development. However, scaling up such models to field scale remains a great challenge. In this paper, we detail a new approach to compute the growth of root systems based on density distribution functions. Growth was modelled as the dynamics of root apical meristems, using Partial Differential Equations. Trajectories of root apical meristems were used to deform root domains, the bounded support of root density functions, and update density distributions at each time increment of the simulation. Our results demonstrate that it is possible to predict the growth of root domains, by including developmentally meaningful parameters such as root elongation rate, gravitropic rate and branching rate. Models of this type are computationally more efficient than state-of-the-art finite volume methods. At a given prediction accuracy, computational time is over 10 times quicker; it allowed deformable models to be used to simulate ensembles of interacting plants. Application to root competition in crop-weed systems is demonstrated. The models presented in this study indicate that similar approaches could be developed to model shoot or whole plant processes with potential applications in crop and ecological modelling.

Inferring Networks from Multiple Samples with Consensus LASSO

Abstract Networks are very useful tools to decipher complex regulatory relationships between genes in an organism. Most work address this issue in the context of i.i.d., treated vs. control or time-series samples. However, many data sets include expression obtained for the same cell type of an organism, but in several conditions. We introduce a novel method for inferring networks from samples obtained in various but related experimental conditions. This approach is based on a double penalization: a first penalty aims at controlling the global sparsity of the solution whilst a second penalty is used to make condition-specific networks consistent with a consensual network. This “consensual network” is introduced to represent the dependency structure between genes, which is shared by all conditions. We show that different “consensus” penalties can be used, some integrating prior (e.g., bibliographic) knowledge and others that are adapted along the optimization scheme. In all situations, the proposed double penalty can be expressed in terms of a LASSO problem and hence, solved using standard approaches which address quadratic problems with L1 -regularization. This approach is combined with a bootstrap approach and is made available in the R package therese1. Our proposal is illustrated on simulated datasets and compared with independent estimations and alternative methods. It is also applied to a real dataset to emphasize the differences in regulatory networks before and after a low-calorie diet.

Combined expression data with missing values and gene interaction network analysis: a Markovian integrated approach

DNA microarray technologies provide means for monitoring in the order of tens of thousands of gene expression levels quantitatively and simultaneously. However data generated in these experiments can be noisy and have missing values. When it is not ignored, the last issue has been solved by imputing the expression matrix in order to keep going with traditional analysis method. Although it was a first useful step, it is not recommended to use value imputation to deal with missing data. Moreover, appropriate tools are needed to cope with noisy background in expression levels and to take into account a dependency structure among genes under study. Alternative approaches have been proposed but to our knowledge none of them has the ability to fulfil all these features. We therefore propose a clustering algorithm that explicitely accounts for dependencies within a biological network and for missing value mechanism to analyze microarray data. In experiments on synthetic and real biological data, our method demonstrates enhanced results over existing approaches.

Inférence de réseaux de régulation de gènes au travers de scores étendus dans les réseaux bayésiens

L’inference de reseaux de regulation de genes s’oriente actuellement vers l’utilisation conjointe d’informations biologiques complementaires. Nous utilisons ici des donnees de marqueurs genetiques en plus des classiques donnees d’expression dans le cadre des reseaux bayesiens statiques discrets. Nous comparons les qualites de differents scores ainsi que l’impact d’un a priori lie a la connectivite des reseaux. Nous proposons et comparons deux modelisations aux approches existantes pour l’inference de reseaux de regulation. Sur des donnees simulees, l’un de nos modeles obtient les meilleurs resultats dans le cas d’echantillons de petites tailles. Nous utilisons ce meme modele sur des donnees reelles d’Arabidopsis thaliana.

SpaCEM3: a software for biological module detection when data is incomplete, high dimensional and dependent

Summary: Among classical methods for module detection, SpaCEM3 provides ad hoc algorithms that were shown to be particularly well adapted to specific features of biological data: high-dimensionality, interactions between components (genes) and integrated treatment of missingness in observations. The software, currently in its version 2.0, is developed in C++ and can be used either via command line or with the GUI under Linux and Windows environments. Availability: The SpaCEM3 software, a documentation and datasets are available from http://spacem3.gforge.inria.fr/. Contact: matthieu.vignes@toulouse.inra.fr; SpaCEM3-help@lists.gforge.inria.fr