Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong modularity in the dependence patterns. In these analyses, intercorrelated high-dimensional biomedical features often form communities or modules that can be interconnected with others. While the interconnected community structure has been extensively studied in biomedical research (e.g., gene co-expression networks), its potential to assist in the estimation of covariance matrices remains largely unexplored. To address this gap, we propose a procedure that leverages the commonly observed interconnected community structure in high-dimensional biomedical data to estimate large covariance and precision matrices. We derive the uniformly minimum variance unbiased estimators for covariance and precision matrices in closed forms and provide theoretical results on their asymptotic properties. Our proposed method enhances the accuracy of covariance- and precision-matrix estimation and demonstrates superior performance compared to the competing methods in both simulations and real data analyses.</p

DataSheet1_The total mass and spatial–temporal variability of aerial cryosphere over the Tibetan Plateau from 2003 to 2020.docx

Changes in snow, ice, and ecological system over the Tibetan Plateau (TP) are extremely sensitive to local precipitation and radiation budget, which are largely modulated by the atmospheric ice. However, how much ice is there in the atmosphere over the TP and how it is distributed are still unclear. The total mass, spatial distributions, and long-term trends of atmospheric ice over the TP were evaluated by using four sets of satellite retrieval data (Aqua, Terra, the Suomi National Polar-orbiting Partnership (Suomi NPP), and NOAA-20) and ERA5 reanalysis data from 2003 to 2020. Based on the estimations using multiple satellite datasets, we concluded that the total mass of atmospheric ice could be up to 0.26±0.03 Gt over the TP from 2013 to 2020. The spatial distributions of atmospheric ice derived from various datasets were highly consistent. In general, the southwest and northeast areas of the TP were the low-concentration areas (0.05 kg/m2 in average), while the southeast area was the high-concentration area (0.09 kg/m2 in average), and this spatial pattern was most evident in summer. The high values around (0.15 kg/m2) were centered over Linzhi and its surrounding areas. The plentiful water vapor transported by southwest summer monsoon and steep topography jointly led to rapid growth of atmospheric ice in Southeast Tibet, which was the dominant reason for the higher ice concentration in this area.</p

Integrated Scanning Electrochemical Probes Assisted by ECSTM for In Situ Imaging of the Pitting Corrosion Process of Carbon Steel in SCCP Solutions

Pitting corrosion of steel is a common phenomenon featuring a random and dynamic process. An understanding of the mechanism and origin of pitting initiation in the early stage remains ambiguous because it is difficult to sense the pitting activity, topographical variations, and local environment at or around pits of carbon steel in situ in a simulated carbonated concrete pore (SCCP) solution. In this work, integrated scanning electrochemical probes assisted by electrochemical scanning tunneling microscopy (ECSTM) were developed to concurrently image the local topography, local pH, and pitting activity in situ in the vicinity of the pits. Ex situ surface topographies and element contents were also determined by scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS). It was found that the pitting initiated at a high rate when carbon steel was immersed in SCCP solution, and then the pitting merged to form beam-like localized corrosion and uniform corrosion finally. The local pH became lower in the vicinity of the pits during the pitting initiation. The results demonstrated that the nuclei of pitting corrosion occurred close to the MnS inclusion or ferrite phase at the steel surface due to selective phase dissolution. Integrated scanning electrochemical probes enabled us to obtain correlated information about the pitting activity, topography, and local environment around pits, which is powerful for the in situ imaging of pitting corrosion with higher resolution and for further understanding the mechanism of localized corrosion of carbon steel in various service environments

Microinjection of <i>irx7</i>SMO (10 ng) and <i>irx7</i>MO2 (3 ng) drastically reduces Irx7 protein level.

<p>The heads of 35 embryos injected with control MO and <i>irx7</i>SMO, and 30 embryos injected with <i>irx7</i>MO2-6 bms and <i>irx7</i>MO2 were dissected at 72 hpf. Proteins were then extracted from these samples and Irx7 expression detected by Western blot using anti-Irx7-234 (A). Γ-tubulin was used as a loading control. The specificity of the Irx7 antibodies was first confirmed by Western blot using various recombinant Irx7 proteins of different lengths (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s006" target="_blank">Table S1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s005" target="_blank">File S3</a>) expressed from bacterial culture (data not shown). Using the information extracted from the Western blot, the protein level of Irx7 was found to be reduced by 69.01% and 87.58% respectively in the dissected heads of <i>irx7</i>SMO and <i>irx7</i>MO2 morphants when compared to the corresponding controls (B).</p

<i>In silico</i> approaches for the identification of novel ULK1 inhibitors: pharmacophore model, molecular docking and molecular dynamics simulations

The serine/threonine kinase unc-51-like autophagy activating kinase 1 (ULK1) has been regarded as an attractive target for tumor therapy. In this study, in silico approaches, such as the pharmacophore-based virtual screening strategy, molecular docking and molecular dynamics (MD) simulations, were applied to develop novel potential ULK1 inhibitors. The pharmacophore models based on known aminopyrimidine ULK1 inhibitors were constructed to screen the dataset of 1.68 million compounds, which were obtained via screening the 2.30 million compounds in ChEMBL database by Lipinski’s rule of five. Seven novel compounds and 1 known ULK1 inhibitor stand out for the strong virtual biological activity by molecular docking, cluster analysis, Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) calculation and Absorption Distribution Metabolism Excretion Toxicity (ADMET) prediction. Their results of MD included principal component analysis (PCA) and Free Energy Landscapes surface (FELs) indicated that the protein–ligand complex was stable in simulated trajectories of 100 ns. The binding free energy (BFE) calculations showed that a total of 6 novel compounds (CL130, CL834, CL961, CL966, CL163 and CL329) with the stable binding state and stronger BFE (−61.17 to −37.01 kcal/mol) than that of original ligand 3RF (−36.66 kcal/mol). With reference to the ULK1 inhibition of 3RF (IC50 = 160 nM), it can be inferred that these compounds could be used as a new type of potential ULK1 inhibitors and be worthy of further investigation for tumor treatments. Communicated by Ramaswamy H. Sarma</p

Visualization 1.mp4

The video shows the contours of residence time of virtual fluid particles departing from 5 different phases and superimposed with the LII signal for 4 α values. From top to bottom, the five contours are corresponding to phase 0º, 90º, 180º, 270º and 360º of one acoustic forcing period. It is noticeable that the contour of phase 180º is very close to the contour of phase 0º and 90º especially nearby the nozzle centerline. The fluid particles of phase 180º whose velocity are maximum in an acoustic cycle pursued the fluid particles ejected at earlier phases running at lower velocity, leading to the overlap of the contours

The change in the expression level and/or pattern of target genes in Irx7 knockdown experiments.

<p>The expression level and/or pattern of the candidate target genes were determined from representative <i>irx7</i>SMO morphants and controls. The resulting regulatory relationship between Irx7 and these candidate genes was also inferred by comparing these two sample groups. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone-0036145-g011" target="_blank">Figure 11</a> for the resulting network, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s002" target="_blank">Figure S2</a> for the comprehensive network that also includes additional connections of the candidate genes as extracted from literature references (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s004" target="_blank">File S2</a>).</p

Irx7 knockdown does not induce apoptosis but can delay cell cycle withdrawal.

<p>Immunostaining of embryos injected with 10 ng of control MO or <i>irx7</i>SMO were conducted with anti-active caspase3 antibody (green colour) at 28, 36, 52 and 72 hpf. The nuclei were counterstained with DAPI (blue colour). In both controls (A–D) and <i>irx7</i>SMO morphants (E–H), only a few active caspase3+ cells (white arrowheads) were detected in some retinas at all stages. All cells that showed a positive anti-active caspase3 signal had the characteristic cell shrinkage and rounded morphology, as shown by the DAPI staining. While all active caspase3- cells looked healthy. Mitotic cells were detected by anti-PH3 in the retinas of controls (I) and morphants (J) at 72 hpf. PH3+ cells in the MZ and in the ectopic apical retina are indicated by green and yellow arrowheads respectively. (K) A stripchart of the number of PH3+ cell per retinal area in uninjected embryos, controls and morphants. Retinal cells that had gone through S-phase in controls and morphants were also detected by BrdU incorporation from 36 to 52 hpf (L and M) and from 52 to 72 hpf (O and P). (N and Q) The corresponding stripcharts of BrdU+ area per retinal area in the uninjected embryos, controls and morphants. The asterisks in all stripcharts represent the median of each group. Lateral is to the left and dorsal is up for all sections. The retinal region in these samples is highlighted by a dotted yellow line. Scale bar = 20 µm.</p

Irx7 gene regulatory network for zebrafish retinal development.

<p>A gene regulatory network was constructed using the expression patterns of <i>irx7</i> downstream targets as characterized in this study. The specification circuit of the network consists of TFs that specify different retinal cell types while the differentiation circuit consists of genes that carry out cell type specific functions. For example, <i>opsins</i> in the photoreceptors are responsible for visual signal transduction. Genes that have not been fully characterized yet are represented by a generic gene (<i>cell type</i>-<i>genes</i>) in the differentiation circuit. The activation of these “<i>cell type</i>-genes” by <i>irx7</i>, as well as by other TFs, symbolizes the differentiation of the corresponding cell types driven by the specification circuit. For GCs, an additional <i>“GC genes for dendritic outgrowth”</i> is created to distinguish the specific effects of <i>irx7</i> knockdown on their dendritic outgrowth (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone-0036145-g005" target="_blank">Figure 5</a>). If the actual location of the interaction is not well defined, the domain/cell type in which the effector gene is expressed will be used. In addition, different retinal regions, including, GCL, INL and ONL can have cellular interaction (≪-≫) that can trigger signal transduction and in turn modulate gene expression. Note that the network topology is a static global view which consists of information obtained from different stages and studies, thus some genes may have both positive and negative inputs if the regulation is dynamical during development. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s004" target="_blank">File S2</a> for supporting evidence of the connections and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036145#pone.0036145.s002" target="_blank">Figure S2</a> for a comprehensive network with additional connections between these genes as extracted from other literature references.</p

Irx7 regulates the expression of TFs that specify retinal cell types in ONL and GCL at 52 and 72 hpf.

<p>Whole-mount <i>in situ</i> hybridization of <i>neurod</i> (A–D), <i>crx</i> (E–H), <i>nr2e3</i> (I–L), <i>nrl</i> (M–P) and <i>atoh7</i> (Q–T) was conducted. The most common staining pattern is shown. Embryos were imaged from the ventral side and anterior is up. See text for further discussions. Scale bar = 50 µm.</p