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The dynamic structure of proteins is essential for their functions and may include large conformational transitions which can be studied by molecular dynamics (MD) simulations. However, details of these transitions are difficult to automatically track. To facilitate their analysis, we developed two scores of correlation between sidechain dihedral angles. The CIRCULAR and OMES scores are computed from, respectively, dihedral angle values and rotamer distributions. As a case study, we applied our methods to an activation-like transition of the chemokine receptor CXCR4, observed during accelerated MD simulations. The principal component analysis of the correlation matrices was consistent with the networking structure of the top ranking pairs. Both scores identify a set of residues whose “collaborative” sidechain rotamerization immediately preceded or accompanied the conformational transition of CXCR4. Detailed analysis of the sequential order of these rotamerizations suggests that an allosteric mechanism, involving the outward motion of an asparagine residue in transmembrane helix 3, might be a prerequisite to the large scale conformational transition of CXCR4. This case study provides the proof-of-concept that the correlation methods developed here are valuable exploratory techniques to help decipher complex reactional pathways.

International audience; Multiple Correspondence Analysis (MCA) is the method of choicefor themultivariate analysis of categorical data. In MCA each qualitative variable is representedby a group of binary variables (with a coding scheme called “complete disjunctive coding”)and each binary variable has a weight inversely proportional to its frequency. The datamatrix concatenates all these binary variables, and once normalized and centered thisdata matrix is analyzed with a generalized singular value decomposition (GSVD) thatincorporates the variable weights as constraints (or “metric”). The GSVD is, of course,based on the plain SVD and so MCA can be sparsified by extending algorithms designedto sparsify the SVD. To do so requires two additional features: to include weights andto be able to sparsify entire groups of variables at once. Another important feature ofsuch a sparsification should be to preserve the orthogonality of the components, Here, weintegrate all these constraints by using an exact projection scheme onto the intersectionof subspaces (i.e., balls) where each ball represents a specific type of constraints. Weillustrate our procedure with the data from a questionnaire survey on the perception ofcheese in two French cities.

Our initial aim in this study was to show that Western listeners can sort the music of 3 Western composers consistently on the basis of their compositional style. We found that they could, and proceeded to investigate what cues they might be using to accomplish that task, as well as whether their use of those cues was related to their level of musical training. In Experiment 1, we presented 21 excerpts from the keyboard music of Bach, Mozart, and Beethoven, each excerpt linked to an icon on the computer screen. Participants were to place the icons in different groups following the rule that the icons in one group could have been written by the same composer. First, they did a free sort in which they could form as many groups as they liked, and then we told them that there were just 3 composers, and they should make 3 groups in a constrained sort. In Experiment 1, the excerpts were produced with MIDI transcriptions of the scores, such that the composer's pitch and time information of the notes was preserved, but there was no variation in tempo, dynamics (loudness), or articulation (connectedness or separateness of notes in time). In spite of this simplification, listeners succeeded in clearly differentiating the composers in the constrained sort. In Experiment 2, we used more natural stimuli, 36 excerpts taken from recordings of the 3 composers by 4 pianists who had recorded substantial amounts of each: Arrau, Barenboim, Pires, and Richter. Here, the stimuli included all the expressive cues of a live performance, and in the constrained sort listeners were even better at categorizing the composers, with not very much difference between the categorizations of trained and untrained listeners. Their judgments were also strongly influenced by the pianists. Richter's performances of the 3 composers were clustered relatively close to the Mozart region of the solution, indicating their clarity and balance; in contrast, those of Barenboim were clustered in the Beethoven region, indicating their sumptuousness and passion. We used a relatively new approach to data analysis—DiSTATIS—which provided the possibility of projecting the sorting results viewed from various perspectives—composer, pianist, participant expertise—into the same space, giving a clearer picture of the results than a piecemeal account of those perspectives.

International audience; We propose a new sparsification method for the singular value decomposition—called the constrained singular value decomposition (CSVD)—that can incorporate multiple constraints such as sparsification and orthogonality for the left and right singular vectors. The CSVD can combine different constraints because it implements each constraint as a projection onto a convex set, and because it integrates these constraints as projections onto the intersection of multiple convex sets. We show that, with appropriate sparsification constants, the algorithm is guaranteed to converge to a stable point. We also propose and analyze the convergence of an efficient algorithm for the specific case of the projection onto the balls defined by the norms L1 and L2. We illustrate the CSVD and compare it to the standard singular value decomposition and to a non-orthogonal related sparsification method with: 1) a simulated example, 2) a small set of face images (corresponding to a configuration with a number of variables much larger than the number of observations), and 3) a psychometric application with a large number of observations and a small number of variables. The companion R-package, csvd, that implements the algorithms described in this paper, along with reproducible examples, are available for download from https://github.com/vguillemot/csvd.

In a multiple sequence alignment, sequence co-variations result from structural, functional, and/or phylogenetic constraints. Numerous methods have been developed to calculate co-variation scores, but few studies have compared these methods to identify which methods are best suited for the analysis of protein family divergence. Here, we give an overview of widely used methods and identify simple rules for selection of appropriate methods. Specifically, we found that methods such as OMES and ELSC-which favor pairs with intermediate entropy and covariation networks with hub structure-are well suited to reveal evolutionary information on family divergence. When applied to G protein-coupled receptors, these methods support an epistasis model of protein evolution in which, after a key mutation, co-evolution of several residues was necessary to restore and/or shift protein function.

International audience; We present a generalization of the partial least square regression (PLSR) approach—called Partial Least Squares Regression Correspondence Analysis (PLSRCA)—tailored to the analysis of categorical (and heterogeneous categorical and “bipolar”) data. Just like standard PLSR, PLSRCA first computes a pair of latent variables—which are linear combinations of the original variables—that have maximal covariance. The coefficients of these latent variables are obtained from the (generalized) singular value decomposition (equivalent to correspondence analysis of the matrix Y’X) of the matrix obtained by the product of the (properly centered and normalized) data matrices (this matrix has been called a “Band of Burt” by Lebart et al., 2006). The latent variables are obtained by projecting the original data matrices and as supplementary rows and columns in the analysis of the “Band of Burt” data table. This part—called PLS-CA, generalizes Tucker inter-battery analysis to categorical and mixed data—instantiates the correspondence analysis component of PLSRCA. The latent variable from the first matrix X is then used (after an adequate normalization) to predict the second matrix Y. The effect of the first latent variable is then partialled out (i.e., “deflated”) from both matrices. This part instantiates the partial least squares regression component of PLSRCA. The process of 1) extracting latent variables, 2) predicting both matrices from the latent variable, and 3) deflation, is carried out until a specific number of latent variables has been extracted or when the first matrix is completely decomposed. We illustrate PLSRCA with genetic data and show how single nucleotide polymorphisms (SNPs) can be used to predict a set of variables measuring cognitive impairment in Alzheimer’s Disease.

International audience

International audience; We explore the relationships between the cortex functional organization and genetic expression (as provided by the Allen Human Brain Atlas). Previous work suggests that functional cortical networks (resting state and task based) are organized as two large networks (differentiated by their preferred information processing mode) shaped like two rings. The first ring–Visual-Sensorimotor-Auditory (VSA)–comprises visual, auditory, somatosensory, and motor cortices that process real time world interactions. The second ring–Parieto-Temporo-Frontal (PTF)–comprises parietal, temporal, and frontal regions with networks dedicated to cognitive functions, emotions, biological needs, and internally driven rhythms. We found–with correspondence analysis–that the patterns of expression of the 938 genes most differentially expressed across the cortex organized the cortex into two sets of regions that match the two rings. We confirmed this result using discriminant correspondence analysis by showing that the genetic profiles of cortical regions can reliably predict to what ring these regions belong. We found that several of the proteins–coded by genes that most differentiate the rings–were involved in neuronal information processing such as ionic channels and neurotransmitter release. The systematic study of families of genes revealed specific proteins within families preferentially expressed in each ring. The results showed strong congruence between the preferential expression of subsets of genes, temporal properties of the proteins they code, and the preferred processing modes of the rings. Ionic channels and release-related proteins more expressed in the VSA ring favor temporal precision of fast evoked neural transmission (Sodium channels SCNA1, SCNB1 potassium channel KCNA1, calcium channel CACNA2D2, Synaptotagmin SYT2, Complexin CPLX1, Synaptobrevin VAMP1). Conversely, genes expressed in the PTF ring favor slower, sustained, or rhythmic activation (Sodium channels SCNA3, SCNB3, SCN9A potassium channels KCNF1, KCNG1) and facilitate spontaneous transmitter release (calcium channel CACNA1H, Synaptotagmins SYT5, Complexin CPLX3, and synaptobrevin VAMP2).

STATIS is an extension of principal component analysis PCA tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual-STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observations. Each of the data tables also provides a map of the observations that is in the same space as the optimum compromise map. In this article, we present STATIS, explain the criteria that it optimizes, review the recent inferential extensions to STATIS and illustrate it with a detailed example.

author cannot archive publisher's version/PDF; International audience; In industries, the sensory characteristics of products are key points to control. The method commonly used to characterize and describe products is the conventional profile. This very efficient method requires a lot of time to train assessors and to teach them how to quantify the sensory characteristics of interest. Over the last few years, other faster and less restricting methods have been developed, such as free choice profile, flash profile, projective mapping or sorting tasks. Among these methods, the sorting task has recently become quite popular in sensory evaluation because of its simplicity: it only requires assessors to make groups of products perceived as similar. Previous studies have shown that this method produces sensory spaces similar to those obtained with conventional profiles but that the descriptions of the products are coarser than the descriptions yielded by sensory profiles. The aim of the present paper is to further evaluate the efficiency of the sorting task as a sensory tool. We present a series of studies highlighting the advantages and delineating the limits of the sorting task and illustrate advantages and limits using beer as the common type of stimuli. These studies underline the main issues encountered when designing sorting tasks. More precisely, we examine the potential of the sorting task to describe beer sensory characteristics, we determine the type of assessors able to perform a sorting task and we evaluate the stability of the results as well as some important methodological points (e.g. number of beers to be sorted, instructions given to the judges) that might impact the efficiency of the task.

International audience; Class A G-protein-coupled receptors (GPCRs) constitute the largest family of transmembrane receptors in the human genome. Understanding the mechanisms which drove the evolution of such a large family would help understand the specificity of each GPCR sub-family with applications to drug design. To gain evolutionary information on class A GPCRs, we explored their sequence space by metric multidimensional scaling analysis (MDS). Three-dimensional mapping of human sequences shows a non-uniform distribution of GPCRs, organized in clusters that lay along four privileged directions. To interpret these directions, we projected supplementary sequences from different species onto the human space used as a reference. With this technique, we can easily monitor the evolutionary drift of several GPCR sub-families from cnidarians to humans. Results support a model of radiative evolution of class A GPCRs from a central node formed by peptide receptors. The privileged directions obtained from the MDS analysis are interpretable in terms of three main evolutionary pathways related to specific sequence determinants. The first pathway was initiated by a deletion in transmembrane helix 2 (TM2) and led to three sub-families by divergent evolution. The second pathway corresponds to the differentiation of the amine receptors. The third pathway corresponds to parallel evolution of several sub-families in relation with a covarion process involving proline residues in TM2 and TM5. As exemplified with GPCRs, the MDS projection technique is an important tool to compare orthologous sequence sets and to help decipher the mutational events that drove the evolution of protein families.

chapitre dans des actes de colloques; absent