Nathalie Villa-Vialaneix

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.

1HNMR-Based metabolomic profiling method to develop plasma biomarkers for sensitivity to chronic heat stress in growing pigs

The negative impact of heat stress (HS) on the production performances in pig faming is of particular concern. Novel diagnostic methods are needed to predict the robustness of pigs to HS. Our study aimed to assess the reliability of blood metabolome to predict the sensitivity to chronic HS of 10 F1 (Large White × Creole) sire families (SF) reared in temperate (TEMP) and in tropical (TROP) regions (n = 56±5 offsprings/region/SF). Live body weight (BW) and rectal temperature (RT) were recorded at 23 weeks of age. Average daily feed intake (AFDI) and average daily gain were calculated from weeks 11 to 23 of age, together with feed conversion ratio. Plasma blood metabolome profiles were obtained by Nuclear Magnetic Resonance spectroscopy (1HNMR) from blood samples collected at week 23 in TEMP. The sensitivity to hot climatic conditions of each SF was estimated by computing a composite index of sensitivity (Isens) derived from a linear combination of t statistics applied to familial BW, ADFI and RT in TEMP and TROP climates. A model of prediction of sensitivity was established with sparse Partial Least Square Discriminant Analysis (sPLS-DA) between the two most robust SF (n = 102) and the two most sensitive ones (n = 121) using individual metabolomic profiles measured in TEMP. The sPLS-DA selected 29 buckets that enabled 78% of prediction accuracy by cross-validation. On the basis of this training, we predicted the proportion of sensitive pigs within the 6 remaining families (n = 337). This proportion was defined as the predicted membership of families to the sensitive category. The positive correlation between this proportion and Isens (r = 0.97, P < 0.01) suggests that plasma metabolome can be used to predict the sensitivity of pigs to hot climate.

What is a good (gene) network

We are fashion victims. Networking is fashionable so we decided last year that it was time to start to work on networks. In the last years, biology has evolved to understand how the relationships between a large number of elements (genes, proteins, ...) can influence the way a living organism functions. This question is well modelled by the use of biological networks that are a huge topic of interest in recent literature. As an example, the Leipzig WCGALP included several articles about biological networks (e.g. Tesson et al.; Jager et al.; Kadarmideen et al.; Reverter et al.). One of those was our work (Liaubet et al.) which, at the end of the talk, gave rise to THE question: ‘What is a good network?’ This innocent and apparently simple question has haunted us ever since. The answer is complex, much too complex for a short editorial, but we can draw some evidence from our experience. When working with biological networks, we are dealing with many different underlying questions: gene networks, protein networks or when speaking about the kind of relationships that they model, transcriptomic networks, regulation networks and interaction networks. We may consider the particular case of a gene co-expression network based on high throughput transcriptomic data. Usually, in this field, very limited prior biological knowledge is available as well as a frustrating annotation level (usually, in that kind of experiment in livestock species, about half of the genes have no functional or ontological annotation). With that restricted background, the use of a network model can help to improve the knowledge about the way genes interact and to emphasize key genes implicated in a given process. In Leipzig, we admired Trudy Mackay’s talk because the Drosophila model is so powerful. However, network inference with that kind of data has to be handled with care. For example, our first attempt was to build co-expression networks of differential genes (genes whose expression varies according to a phenotype of interest) for a developmental trait, between species. The results were very disappointing because networks were unstable, had similar structure, whatever the kind of genes considered (differential or chosen at random), and no pertinent biological conclusion could be drawn. This was the perfect example of a bad network! In that first experiment, the main problem was the too low number (about five) of observations available for each species. However, it was the starting point to understand the key features needed to obtain a good network. Now note that the question ‘What is a good network?’ can be divided into two sub-questions: What is a good network for biologists? What is a good network for statisticians? Statisticians like robustness. The number of observations used to define the network is never large enough. A simple simulation study can illustrate the fact that at least 20–30 observations are needed to accurately estimate a correlation coefficient, and even more to infer a medium size network (Schäfer and Strimmer, 2005a, Bioinformatics 21, 754–764). Furthermore, methods designed to deal with ‘small’ sample sizes and a large number of variables are required: When using the common Graphical Gaussian Models, this can consist of regularization (Dobra et al., 2004, J. Multiv. Anal. 90, 196–212; Mainshausen and Bühlmann, 2006, Ann. Stat. 34, 3), shrinkage (Schäfer and Strimmer, 2005b, Stat. Appl. Genet. Mol. Biol. 4, 32), bootstrap (Schäfer and Strimmer, 2005a), etc. But once the strength of the relations between two genes has been inferred by the chosen method, the subsequent question is: What are the important interactions? No other processing could be performed (e.g., keeping the complete network with edges weighted by the partial correlations), but use of ad hoc or significant thresholds can be beneficial for the readability and further interpretability of the network. Biologists like simple outputs to understand the data and recognize biological processes and molecular pathways. Moreover, they are on a quest for the ‘Grail of causality’, with the help of statistical models (Schadt et al., 2005, Nat. Genet. 37, 710–717; the Leipzig WCGALP papers by Rosa et al.; Tesson et al.; Mackay), or based on the properties of a gene network. In a good network, one should be able to emphasize the key genes in the biological process: For instance, hubs [nodes (genes) that are connected with a large number of genes] are straightforward candidates for being interesting genes but they can sometimes be disappointing because they are much J. Anim. Breed. Genet. ISSN 0931-2668