Proposed Structure of Digital Channelizer.

<p>Proposed Structure of Digital Channelizer.</p

Longitudinal Principal Component Analysis With an Application to Marketing Data

We propose a longitudinal principal component analysis method for multivariate longitudinal data using a random-effects eigen-decomposition, where the eigen-decomposition uses longitudinal information through nonparametric splines and the multivariate random effects incorporate significant store-wise heterogeneity. Our method can effectively analyze large marketing data containing sales information for products from hundreds of stores over an 11-year time period. The proposed method leads to more accurate estimation and interpretation compared to existing approaches. We illustrate our method through simulation studies and an application to marketing data from IRI. Supplementary materials for this article are available online.</p

Magnitude Response of Designed Prototype Filter.

<p>Magnitude Response of Designed Prototype Filter.</p

Ratio of maximum-minimum eigenvalue of each sub-band data of the received signal in Fig 4(A).

<p>Ratio of maximum-minimum eigenvalue of each sub-band data of the received signal in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136349#pone.0136349.g004" target="_blank">Fig 4(A)</a>.</p

(a) Spectrum of Received Signal Containing 3 Sub-channels, (b)~(d) Channelized Signals Using Proposed Structure.

<p>(a) Spectrum of Received Signal Containing 3 Sub-channels, (b)~(d) Channelized Signals Using Proposed Structure.</p

Ribo-seq count table for all genes analyzed.

Acute cellular stress is known to induce a global reduction in mRNA translation through suppression of cap dependent translation. Selective translation in response to acute stress has been shown to play important roles in regulating the stress response. However, accurately profiling translational changes transcriptome-wide in response to acute cellular stress has been challenging. Commonly used data normalization methods operate on the assumption that any systematic shifts are experimental artifacts. Consequently, if applied to profiling acute cellular stress-induced mRNA translation changes, these methods are expected to produce biased estimates. To address this issue, we designed, produced, and evaluated a panel of 16 oligomers to serve as external standards for ribosome profiling studies. Using Sodium Arsenite treatment-induced oxidative stress in lymphoblastoid cell lines as a model system, we applied spike-in oligomers as external standards. We found our spike-in oligomers to display a strong linear correlation between the observed and the expected quantification, with small ratio compression at the lower concentration range. Using the expected fold changes constructed from spike-in controls, we found in our dataset that TMM normalization, a popular global scaling normalization approach, produced 87.5% false positives at a significant cutoff that is expected to produce only 10% false positive discoveries. In addition, TMM normalization produced a systematic shift of fold change by 3.25 fold. These results highlight the consequences of applying global scaling approaches to conditions that clearly violate their key assumptions. In contrast, we found RUVg normalization using spike-in oligomers as control genes recapitulated the expected stress induced global reduction of translation and resulted in little, if any, systematic shifts in the expected fold change. Our results clearly demonstrated the utility of our spike-in oligomers, both for constructing expected results as controls and for data normalization.</div

Impact of TMM normalization and spike-in based RUVg normalization on expression quantification.

(a) Observed log2 fold change for spike-in constructed true positives plotted against the expected; comparing between results from different normalization approaches. Data points represent mean plus/minus standard errors calculated from each group of true positives that share the same expected log2 fold change. Black data points (i.e. "Original”) are results from log2 transformed counts without further normalization. Black line indicates the ideal correlation (i.e. an intercept of 0 and a slope of 1). (b) A volcano plot showing the relationship between fold change (treatment versus control) and p value from differential expression tests for RUVg normalized data. Data points are color-coded in green for spike-in oligomers, in red for endogenous genes that are significantly differentially expressed at 5% FDR, and in blue for endogenous genes that are not differentially expressed. (c, d) Venn diagrams summarizing the number of shared and distinct differentially expressed genes found with and without normalization. Unnormalized (unnorm) in blue. Normalized (either TMM or RUVg) in pink. Numbers labeling each area indicate the number of genes belonging to each group, with the size of the area drawn in proportion to the size of the group. (e) Spike-in based RUVg normalization results are robust against the exact set of spike-in oligomers used as control genes. Boxplots comparing between the across sample biological CV to the across subsampling technical CV for endogenous genes. The technical CV here is calculated based on the normalized quantification level of endogenous genes across 10 iterations of spike-in oligomer subsampling for control gene selection.</p

Supplemental S1 to S16 Figs.

Acute cellular stress is known to induce a global reduction in mRNA translation through suppression of cap dependent translation. Selective translation in response to acute stress has been shown to play important roles in regulating the stress response. However, accurately profiling translational changes transcriptome-wide in response to acute cellular stress has been challenging. Commonly used data normalization methods operate on the assumption that any systematic shifts are experimental artifacts. Consequently, if applied to profiling acute cellular stress-induced mRNA translation changes, these methods are expected to produce biased estimates. To address this issue, we designed, produced, and evaluated a panel of 16 oligomers to serve as external standards for ribosome profiling studies. Using Sodium Arsenite treatment-induced oxidative stress in lymphoblastoid cell lines as a model system, we applied spike-in oligomers as external standards. We found our spike-in oligomers to display a strong linear correlation between the observed and the expected quantification, with small ratio compression at the lower concentration range. Using the expected fold changes constructed from spike-in controls, we found in our dataset that TMM normalization, a popular global scaling normalization approach, produced 87.5% false positives at a significant cutoff that is expected to produce only 10% false positive discoveries. In addition, TMM normalization produced a systematic shift of fold change by 3.25 fold. These results highlight the consequences of applying global scaling approaches to conditions that clearly violate their key assumptions. In contrast, we found RUVg normalization using spike-in oligomers as control genes recapitulated the expected stress induced global reduction of translation and resulted in little, if any, systematic shifts in the expected fold change. Our results clearly demonstrated the utility of our spike-in oligomers, both for constructing expected results as controls and for data normalization.</div

The design and application of spike-in oligomers for stress response ribo-seq studies.

(a) Spike-in oligomer pooling design: A stacked barplot showing proportion of spike-in mixes used in each spike-in pool. Each mix is composed of 4 spike-in oligomers (e.g. D1, D2, D3, D4) mixed in the same 8 fold increment from oligomer 1 to oligomer 4 (proportion in percentages presented in the table to the left for mix D). Below the stacked barplot, samples receiving each spike-in pool are labeled with color code distinguishing different effects of interests to highlight the study design. Sodium Arsenite treatment (Control vs. Experiment). Donor (18505 vs. 19204 vs. 19193). Library preparation batch (T vs. U). For true negative and true positive control comparisons we compared quantification of the same oligomer between treated (Experiment) and untreated (Control) cell lines that either received the same oligomer pool (true negative; black brackets) or the cell lines were derived from the same individual but received different oligomer pools (true positive; the red bracket marked one such example), respectively. (b) Western blots for GM18505 indicate that our treatment conditions induced integrated stress response. Primary antibodies used were labeled to the left of the blots. Treatment types and durations were labeled below the blots. Treatment type "None” indicated baseline conditions, while treatment type "H2O” indicated the control condition used in the ribo-seq study. Note the band of phosphorylated eIF2α, a stress marker, only visible in Sodium Arsenite treated samples in contrast to the loading controls. (c, d, e) Boxplots summarizing impact of different normalization strategies on overall distribution of ribosome occupancy level (log2 counts) across all genes analyzed. Boxes are color coded to distinguish control samples (blue) from Sodium Arsenite treated samples (orange). The maximum and minimum values for the boxplot (i.e. the whiskers) are defined by the genes with quantification levels closest to (but without exceeding) 1.5 times of the interquartile range extending from the box.</p

(a) Spectrum of Received Signal Containing 4 Sub-channels, (b)-(e) Channelized Signals Using Proposed Structure.

<p>(a) Spectrum of Received Signal Containing 4 Sub-channels, (b)-(e) Channelized Signals Using Proposed Structure.</p