Differential ER-status gene co-expression network and gene expression for ER differential genes.

<p>Panel a: differential ER gene co-expression network, where node size corresponds to betweenness centrality, which quantifies the number of shortest paths between all pairs of nodes in the network in which the gene is included. Panel b: gene expression levels for 432 genes in the ER-status differential co-expression network.</p

Comparison of BicMix with related methods.

<p>Top row: Simulation with low noise. Bottom row: Simulation with high noise. Left column: Sim1 with only sparse components. Right column: Sim2 with sparse and dense components. Panel a: Recovery score on the x-axis, relevance score on the y-axis for all methods in the legend. Panel b: Stability statistic (y-axis) for the sparse components recovered by BicMix and Fabia.</p

Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering

<div><p>Identifying latent structure in high-dimensional genomic data is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for <i>biclustering</i> to infer subsets of co-regulated genes that covary in all of the samples or in only a subset of the samples. Our biclustering method, <i>BicMix</i>, allows overcomplete representations of the data, computational tractability, and joint modeling of unknown confounders and biological signals. Compared with related biclustering methods, BicMix recovers latent structure with higher precision across diverse simulation scenarios as compared to state-of-the-art biclustering methods. Further, we develop a principled method to recover context specific gene co-expression networks from the estimated sparse biclustering matrices. We apply BicMix to breast cancer gene expression data and to gene expression data from a cardiovascular study cohort, and we recover gene co-expression networks that are differential across ER+ and ER- samples and across male and female samples. We apply BicMix to the Genotype-Tissue Expression (GTEx) pilot data, and we find tissue specific gene networks. We validate these findings by using our tissue specific networks to identify trans-eQTLs specific to one of four primary tissues.</p></div

Tissue specific gene co-expression networks in the GTEx pilot data.

<p>Adipose: gene co-expression network for adipose. Artery: gene co-expression network for artery. Lung: gene co-expression network for lung. Skin: gene co-expression network for skin. Node size and color correspond to betweenness centrality.</p

Sex specific gene co-expression networks in the CAP gene expression data.

<p>Panel a: Gene co-expression network specific to males. Panel b: Gene co-expression network specific to females. Node size and color correspond to betweenness centrality.</p

Distribution of the number of genes, the number of samples, and PVE in the breast cancer data.

<p>Panel a: Distribution of the number of genes with non-zero values in each of the 53,814 loadings. Panel b: Distribution of the number of samples with non-zero values in each of the 53,814 factors. Panel c: average PVE for the components sorted by PVE within each run. The middle lines show the median PVE, the ribbons show the range of the minimum and maximum PVE across 900 runs. For panels a and b, the peaks on the far right correspond to the number of the genes and samples for the dense loadings and dense factors.</p

Schematic representation of the BicMix biclustering model.

<p>Ordered from left to right are, respectively, the <i>p</i> × <i>n</i> gene expression matrix <b>Y</b>, the <i>p</i> × <i>K</i> loading matrix Λ including both sparse and dense columns, the <i>K</i> × <i>n</i> factor matrix <b>X</b> including both sparse and dense rows, and the <i>p</i> × <i>n</i> residual matrix <i>ϵ</i>. Blue, red, and white entries in each matrix correspond to negative, positive, and zero values, respectively.</p

Sex differential gene co-expression network and gene expression levels for sex differential genes.

<p>Panel a: differential sex gene co-expression network, where node size corresponds to betweenness centrality. Panel b: gene expression levels for 61 genes in the sex differential gene co-expression network.</p

A Braided Hetero[2](3)rotaxane

A novel braided hetero[2](3)­rotaxane is demonstrated by integrating the braided structure and mechanically interlocked rotaxane, in which a heterotritopic linear tris­(dialkylammonium) guest penetrates a heterotritopic tris­(crown ether) host, resulting in the formation of braided pseudohetero[2](3)­rotaxane with different crossing and threading points. Then a braided hetero[2](3)­rotaxane is constructed through the “CuAAC” click reaction

Influence of Oxygen Vacancy-Induced Coordination Change on Pd/CeO₂ for NO Reduction

The byproduct formation in environmental catalysis is strongly influenced by the chemical state and coordination of catalysts. Herein, two Pd/CeO2 catalysts (PdCe-350 and PdCe-800) with varying oxygen vacancies (Ov) and coordination numbers (CN) of Pd were prepared to investigate the mechanism of N2O and NH3 formation during NO reduction by CO. PdCe-350 exhibits a higher density of Ov and Pd sites with higher CN, leading to an enhanced metal–support interaction by electron transformation from the support to Pd. Consequently, PdCe-350 displayed increased levels of byproduct formation. In situ spectroscopies under dry and wet conditions revealed that at low temperatures, the N2O formation strongly correlated with the Ov density through the decomposition of chelating nitro species on PdCe-350. Conversely, at high temperatures, it was linked to the reactivity of Pd species, primarily facilitated by monodentate nitrates on PdCe-800. In terms of NH3 formation, its occurrence was closely associated with the activation of H2O and C3H6, since a water–gas shift or hydrocarbon reforming could provide hydrogen. Both bridging and monodentate nitrates showed activity in NH3 formation, while hyponitrites were identified as key intermediates for both catalysts. The insights provide a fundamental understanding of the intricate relationship among the local coordination of Pd, surface Ov, and byproduct distribution