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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.

Chemokines and their receptors (members of the GPCR super-family) are involved in a wide variety of physiological processes and diseases; thus, understanding the specificity of the chemokine receptor family could help develop new receptor specific drugs. Here, we explore the evolutionary mechanisms that led to the emergence of the chemokine receptors. Based on GPCR hierarchical classification, we analyzed nested GPCR sets with an eigen decomposition approach of the sequence covariation matrix and determined three key residues whose mutation was crucial for the emergence of the chemokine receptors and their subsequent divergence into homeostatic and inflammatory receptors. These residues are part of the allosteric sodium binding site. Their structural and functional roles were investigated by molecular dynamics simulations of CXCR4 and CCR5 as prototypes of homeostatic and inflammatory chemokine receptors, respectively. This study indicates that the three mutations crucial for the evolution of the chemokine receptors dramatically altered the sodium binding mode. In CXCR4, the sodium ion is tightly bound by four protein atoms and one water molecule. In CCR5, the sodium ion is mobile within the binding pocket and moves between different sites involving from one to three protein atoms and two to five water molecules. Analysis of chemokine receptor evolution reveals that a highly constrained sodium binding site characterized most ancient receptors, and that the constraints were subsequently loosened during the divergence of this receptor family. We discuss the implications of these findings for the evolution of the chemokine receptor functions and mechanisms of action.

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).

As we age, our differences in cognitive skills become more visible, an effect especially true for memory and problem solving skills (i.e., fluid intelligence). However, by contrast with fluid intelligence, few studies have examined variability in measures that rely on one's world knowledge (i.e., crystallized intelligence). The current study investigated whether age increased the variability in text based global inference generation--a measure of crystallized intelligence. Global inference generation requires the integration of textual information and world knowledge and can be expressed as a gist or lesson. Variability in generating two global inferences for a single text was examined in young-old (62 to 69 years), middle-old (70 to 76 years) and old-old (77 to 94 years) adults. The older two groups showed greater variability, with the middle elderly group being most variable. These findings suggest that variability may be a characteristic of both fluid and crystallized intelligence in aging.

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.