BACKGROUND: As biological networks often show complex topological features, mathematical methods are required to extract meaningful information. Clustering methods are useful in this setting, as they allow the summary of the network's topology into a small number of relevant classes. Different strategies are possible for clustering, and in this article we focus on a model-based strategy that aims at clustering nodes based on their connectivity profiles. RESULTS: We present MixNet, the first publicly available computer software that analyzes biological networks using mixture models. We apply this method to various networks such as the E. coli transcriptional regulatory network, the macaque cortex network, a foodweb network and the Buchnera aphidicola metabolic network. This method is also compared with other approaches such as module identification or hierarchical clustering. CONCLUSION: We show how MixNet can be used to extract meaningful biological information, and to give a summary of the networks topology that highlights important biological features. This approach is powerful as MixNet is adaptive to the network under study, and finds structural information without any a priori on the structure that is investigated. This makes MixNet a very powerful tool to summarize and decipher the connectivity structure of biological networks.

This book is a set of 11 chapters written by different authors. Most of the authors are academic researchers from medicine, genetics, bioinformatics or computer science departments and some of them work for private corporations (Affymetrix, Agilent and GeneGo). As usual with this type of book with many authors, the orientation, level and content of the chapters are very different. Some aim at presenting the state-of-the-art of the normalization procedures for a given type of microarray, others attempt to study the impact of the pretreatment step on the results of the analysis, and others are restricted to a presentation of a new normalization procedure. However, an effort at global presentation has been made with a summary of the chapters at the beginning of the book and a general index table at the end. This book is clearly not made for complete reading from the beginning to the end, but rather for picking the information useful for each reader. There are two chapters about the normalization procedures for cDNA microarrays, three for Affymetrix arrays, three for specific microarrays (CGH, Exons and SNP) and three about general analysis describing the consequences of the normalization step on the biological findings. The normalization and more generally the preprocessing steps of cDNA microarray data are presented (Chapter 5), with a comparison between 14 preprocessing steps for the correction of the intensity dependent and the spatial bias. Although the content has already been presented in a bioinformatics journal, this presentation is useful and shows that the choice of a normalization procedure has important consequences on the classification of biological samples. Chapter 4, about the spatial normalization for cDNA microarrays, shows impressive images of this bias but lacks general coverage as it is too much focused on one specific method proposed by the authors. The preprocessing steps for Affymetrix arrays (RMA, GCRMA and MAS5.0) are clearly described in Chapter 3, with a short case study. A cross-normalization comparisons experiment for Affymetrix arrays is described in Chapter 7. It shows that the normalization not only changes the actual value of the individual probes but also the order of these values which is drastically modified. For example, there are only 26 common probes declared differentially expressed, using three different normalization methods (GC-RMA, MAS5.0 and PLIER), after keeping the 1000 probes most differentially expressed for each method, for a comparison between two conditions (lung and spleen). In the same experiment, 903 probes pertain to the set of the first 1000 probes for GC-RMA and are not in the corresponding sets for PLIER and MAS5.0. Moreover, the authors show that the GO interpretation of the results and the ratios of the housekeeping genes are also strongly modified by the normalization method. The authors propose to use successively several normalization methods and to look for a consensus between them in terms of GO classes or in terms of pathways. The experiment compares three very different conditions (liver, spleen, lung), so that many probes are expected to be differentially expressed, a fact which may explain that the lists of the first 1000 probes are different for different normalization methods. This perhaps explains that the conclusion of the chapter is strangely much more positive about the quality of microarray experiments than the content of the chapter. A similar study is described in Chapter 1 about a systematic and comprehensive analysis of all the data preprocessing stages on differentially expressed gene selection on multiple human data sets. The conclusion is that, even using a single platform and the same statistical selection method, there are substantial discrepancies between the results. Therefore, ‘statistical analysis techniques and inter-laboratory experiment protocols are not the causes of cross-platform disparities’. The authors claim, and I agree with them, that ‘just developing new algorithms for data preprocessing, without addressing the reasons why the current method fail, will not solve the problems … efforts should be directed to improved chip design, large sample sizes, evaluation of tools on real-life data sets (and not only calibration ones) and standardization of evaluation techniques and laboratory protocols’. However, there are some contradictions between chapters, for Chapter 2 is especially devoted to presenting one more new statistical method for the normalization of microarrays. Chapter 6 is about cross-laboratory expression array concordance and a modeling of the sources of variation in microarray experiments. It provides a guide to the analysis of reproducibility, like the MAQC (microarray quality control) project. This is a very good idea. Unfortunately, this chapter is not very well written so that, at the end of the chapter, the reader is not in position to make his own reproducibility study. The last three chapters are devoted to the normalization of specific arrays (exon arrays, array CGH and SNP). Chapter 9 contains a detailed analysis of the Affymetrix exon arrays with a clear and valuable workflow for the analysis of such data. There is already a large set of publications about CGH arrays, but Chapter 10 describes a specific part of the normalization step, which is called centralization. Chapter 11 describes methods for estimating copy number and loss of heterozygosity for Affymetrix GenChip human mapping arrays. The last cover page of the book claims that it ‘provides scientists with a complete resource on the most effective tools available for microarray data’. This is only partially true because this task is clearly impossible. The scientist who wants to know how to normalize his own microarray data will find more precise and specific information in the bioinformatics journals. The same page claims that it ‘reviews the latest advances in peptide, glycol, antibody expression and SNP microarrays’, but there is very little information about the first three topics which are not in the index. Moreover the content is uneven: some chapters are very clear and well written and give important messages, but others are not at the same level of quality. Overall this book is an interesting contribution to the topic of the normalization of microarrays. Preprocessing and more or less complicated statistical analysis should not be considered as a rescue operation to save ailing experiments. The important message contained in several chapters in this book, and especially in Chapter 1, is that the process of designing and analyzing microarray experiments should be included in a continuous process of improvement of quality, similar to the Deming Wheel, which has been so useful for quality improvement in industrial corporations. The process will be completely successful when most of the bias has been removed, so that … no normalization is necessary.

BACKGROUND: Most microarray studies are made using labelling with one or two dyes which allows the hybridization of one or two samples on the same slide. In such experiments, the most frequently used dyes are Cy3 and Cy5. Recent improvements in the technology (dye-labelling, scanner and, image analysis) allow hybridization up to four samples simultaneously. The two additional dyes are Alexa488 and Alexa494. The triple-target or four-target technology is very promising, since it allows more flexibility in the design of experiments, an increase in the statistical power when comparing gene expressions induced by different conditions and a scaled down number of slides. However, there have been few methods proposed for statistical analysis of such data. Moreover the lowess correction of the global dye effect is available for only two-color experiments, and even if its application can be derived, it does not allow simultaneous correction of the raw data. RESULTS: We propose a two-step normalization procedure for triple-target experiments. First the dye bleeding is evaluated and corrected if necessary. Then the signal in each channel is normalized using a generalized lowess procedure to correct a global dye bias. The normalization procedure is validated using triple-self experiments and by comparing the results of triple-target and two-color experiments. Although the focus is on triple-target microarrays, the proposed method can be used to normalize p differently labelled targets co-hybridized on a same array, for any value of p greater than 2. CONCLUSION: The proposed normalization procedure is effective: the technical biases are reduced, the number of false positives is under control in the analysis of differentially expressed genes, and the triple-target experiments are more powerful than the corresponding two-color experiments. There is room for improving the microarray experiments by simultaneously hybridizing more than two samples.

BACKGROUND: In individually dye-balanced microarray designs, each biological sample is hybridized on two different slides, once with Cy3 and once with Cy5. While this strategy ensures an automatic correction of the gene-specific labelling bias, it also induces dependencies between log-ratio measurements that must be taken into account in the statistical analysis. RESULTS: We present two original statistical procedures for the statistical analysis of individually balanced designs. These procedures are compared with the usual ML and REML mixed model procedures proposed in most statistical toolboxes, on both simulated and real data. CONCLUSION: The UP procedure we propose as an alternative to usual mixed model procedures is more efficient and significantly faster to compute. This result provides some useful guidelines for the analysis of complex designs.

MOTIVATION: Identifying differentially regulated genes in experiments comparing two experimental conditions is often a key step in the microarray data analysis process. Many different approaches and methodological developments have been put forward, yet the question remains open. RESULTS: Varmixt is a powerful and efficient novel methodology for this task. It is based on a flexible and realistic variance modelling strategy. It compares favourably with other popular techniques (standard t-test, SAM and Cyber-T). The relevance of the approach is demonstrated with real-world and simulated datasets. The analysis strategy was successfully applied to both a 'two-colour' cDNA microarray and an Affymetrix Genechip. Strong control of false positive and false negative rates is proven in large simulation studies. AVAILABILITY: The R package is freely available at http://www.inapg.inra.fr/ens_rech/mathinfo/recherche/mathematique/outil.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: http://www.inapg.inra.fr/ens_rech/mathinfo/recherche/mathematique/outil.html.

MOTIVATION: In cDNA microarray experiments all samples are labeled with either Cy3 or Cy5. Systematic and gene-specific dye bias effects have been observed in dual-color experiments. In contrast to systematic effects which can be corrected by a normalization method, the gene-specific dye bias is not completely suppressed and may alter the conclusions about the differentially expressed genes. METHODS: The gene-specific dye bias is taken into account using an analysis of variance model. We propose an index, named label bias index, to measure the gene-specific dye bias. It requires at least two self-self hybridization cDNA microarrays. RESULTS: After lowess normalization we have found that the gene-specific dye bias is the major source of experimental variability between replicates. The ratio (R/G) may exceed 2. As a consequence false positive genes may be found in direct comparison without dye-swap. The stability of this artifact and its consequences on gene variance and on direct or indirect comparisons are addressed. AVAILABILITY: http://www.inapg.inra.fr/ens_rech/mathinfo/recherche/mathematique

We would like to thank K. Dobbin, J. Shih and R. Simon for their comments about Martin-Magniette et al. (2005). Their remarks relate to the design of microarray experiments and notably about the use of dye-swaps. We, however, want to make it clear that our manuscript primarily focuses on the detection, quantification and correction of the gene-specific dye-bias introduced in dual-color microarray experiments. The most important point in Martin-Magniette et al. (2005) is the following: by dint of studying technical errors, we will be able to identify and then to remove most of them. For the first time, in Martin-Magniette et al. (2005), we were able to quantify the gene-specific dye bias by calculating the Labelling Bias Index, (LBI). The LBI measured on different array types shows that this artifact seems to be very low in some cases and could be thus neglected. However, it is high in other cases and it cannot thus be neglected for data issued from these array types. This measure is of crucial importance as it allows users to evaluate the impact of this bias on their data. Moreover, we think that each platform should at least know in what class it belongs for each array types. Although this artifact is not lowered nor understood, it is simply dangerous to underestimate it. The gene-specific dye bias is not an inevitability and can be well controlled, as we point out in our paper. Recently, in another paper, Dobbin et al. (2005) studied the gene-specific dye bias. Although they reached the same conclusions, some of their remarks are explained in Martin-Magniette et al. (2005): e.g. Dobbin et al. (2005) have found that ‘(the gene-specific) dye bias appears to have masked the true differential expression’. This is explained in Martin-Magniette et al. (2005): the variance associated to a gene is overestimated by the dye bias effect in model (2) of Martin-Magniette et al. Dye-swaps constitute a simple and effective design to remove gene-specific dye bias when it is high. Nevertheless, we agree with Dobbin et al. (2005), that a balanced block design may be better than dye-swaps in some situations. As the former designs allow the use of more biological samples, the estimation of the biological variability will be more precise. Even if balanced block designs are statistically more efficient, the following considerations should be taken into account before choosing the experimental design:The experimental design must be adapted not only to the research question but also to the amount of biological material available. Finally, class prediction or differential expression, e.g. the question of interest, do not necessarily imply the same experimentaldesign. Even with rigorous experimental procedures some sources of variability remain (quality and yield of target purification, labelling efficiency, …). Performing dye-swaps will allow to differentiate biological from technical variability. It is often difficult to balance the dye for every treatment in complex designs, when samples are hardly available. For instance, such situations are encountered in sex-balanced medicalstudies. Moreover, some redundant experimental procedures (quality control of mRNA, preparation of targets for indirect dye-labelling) used in dye-swap experiments, decrease the financial cost to <2-fold the cost of a single slide hybridization, thus rendering this design much more attractive.

Following publication of this work [1], the authors became aware that Local FDR has been originally defined by Efron & al. (2001) in a mixture model framework [2].

BACKGROUND: Microarray-CGH experiments are used to detect and map chromosomal imbalances, by hybridizing targets of genomic DNA from a test and a reference sample to sequences immobilized on a slide. These probes are genomic DNA sequences (BACs) that are mapped on the genome. The signal has a spatial coherence that can be handled by specific statistical tools. Segmentation methods seem to be a natural framework for this purpose. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose BACs share the same relative copy number on average. We model a CGH profile by a random Gaussian process whose distribution parameters are affected by abrupt changes at unknown coordinates. Two major problems arise: to determine which parameters are affected by the abrupt changes (the mean and the variance, or the mean only), and the selection of the number of segments in the profile. RESULTS: We demonstrate that existing methods for estimating the number of segments are not well adapted in the case of array CGH data, and we propose an adaptive criterion that detects previously mapped chromosomal aberrations. The performances of this method are discussed based on simulations and publicly available data sets. Then we discuss the choice of modeling for array CGH data and show that the model with a homogeneous variance is adapted to this context. CONCLUSIONS: Array CGH data analysis is an emerging field that needs appropriate statistical tools. Process segmentation and model selection provide a theoretical framework that allows precise biological interpretations. Adaptive methods for model selection give promising results concerning the estimation of the number of altered regions on the genome.

BACKGROUND: Thousands of genes in a genomewide data set are tested against some null hypothesis, for detecting differentially expressed genes in microarray experiments. The expected proportion of false positive genes in a set of genes, called the False Discovery Rate (FDR), has been proposed to measure the statistical significance of this set. Various procedures exist for controlling the FDR. However the threshold (generally 5%) is arbitrary and a specific measure associated with each gene would be worthwhile. RESULTS: Using process intensity estimation methods, we define and give estimates of the local FDR, which may be considered as the probability for a gene to be a false positive. After a global assessment rule controlling the false positive error, the local FDR is a valuable guideline for deciding wether a gene is differentially expressed. The interest of the method is illustrated on three well known data sets. A R routine for computing local FDR estimates from p-values is available at http://www.inapg.fr/ens_rech/mathinfo/recherche/mathematique/outil.html. CONCLUSIONS: The local FDR associated with each gene measures the probability that it is a false positive. It gives the opportunity to compute the FDR of any given group of clones (of the same gene) or genes pertaining to the same regulation network or the same chromosomic region.

BACKGROUND: Microarray data must be normalized because they suffer from multiple biases. We have identified a source of spatial experimental variability that significantly affects data obtained with Cy3/Cy5 spotted glass arrays. It yields a periodic pattern altering both signal (Cy3/Cy5 ratio) and intensity across the array. RESULTS: Using the variogram, a geostatistical tool, we characterized the observed variability, called here the spotting effect because it most probably arises during steps in the array printing procedure. CONCLUSIONS: The spotting effect is not appropriately corrected by current normalization methods, even by those addressing spatial variability. Importantly, the spotting effect may alter differential and clustering analysis.