A 145

Gene co-expression networks [12 (link), 13 (link)] are generally based on a pairwise distance or dissimilarity matrix which is often a function of correlation and thus not appropriate for relative data. Proportionality is appropriate, but ϕ does not satisfy the properties of a distance—most obviously, it is not symmetric unless β = 1:
$\begin{array}{ccc}\hfill \varphi (logx,logy)& =\hfill & 1+{\beta }^2-2\beta \left|r\right|\hfill \\ \hfill \varphi (logy,logx)& =\hfill & 1+\frac{1}{{\beta }^2}-2\frac{1}{\beta }\left|r\right|.\hfill \end{array}$
We are most interested in pairs of variables where β and r are near 1 and want to preserve the link between ϕ(log x, log y), β and r. Hence, our approach to forming a dissimilarity matrix is simply to work with ϕ(log x_i, log x_j) where i < j, in effect, the lower triangle of the matrix of ϕ values between all pairs of components. This symmetrised form of ϕ was then used to lay out a network of the 145 mRNAs that were involved in 424 pairwise relationships with ϕ < 0.05. We used the symmetrised form of ϕ as the basis of the cluster analysis and heatmap expression pattern display (e.g., S10 Fig.) described by Eisen et al. [14 ].

We tested experimentally the top 500 predictions of L3 against the top 500 predictions of CRA^{29 (link)} on the human network, HI-tested. HI-tested is a subset of the human interaction dataset HI-II-14^{5 (link)}, restricted to a single ORF for each gene, present in HI-III²⁶ , and leaving out keratins (KRT*). To test the overall efficiency of the experiment, we included 94 literature curated interactions with multiple evidence (Lit-BM-13^{5 (link)}), as well as a set of 88 positive reference interactions from the literature (PRS). In principle, the proteins of our top predictions might have special characteristics, which locally modify the recovery rate of their interactions. To have a more specific assessment, our selected positive set (“Known” PPIs) contains 100 randomly selected known links in HI-tested, connected to at least one of the nodes in the top 500 L3 predictions. To control the false positive rate, we selected a set of 144 random node pairs in the random reference set (RRS) and a more specific set of 100 random pairs involving the proteins in the top 500 L3 predictions (RND). Altogether, we pairwise tested 1,485 non-redundant pairs, in two orientations, classifying each pair as either positive, negative or undetermined. Details of the experimental protocol are summarized in Supplementary Note 1.

All participants were divided into four groups according to mGFR: group A (mGFR<30 mL/min/1.73 m (Chen et al., 2019a (link))), group B (30 mL/min/1.73 m (Chen et al., 2019a (link))≤mGFR<60 mL/min/1.73 m (Chen et al., 2019a (link))), group C (60 mL/min/1.73 m (Chen et al., 2019a (link))≤mGFR <90 mL/min/1.73 m (Chen et al., 2019a (link))), and group D (mGFR ≥90 mL/min/1.73 m (Chen et al., 2019a (link))). Statistical analysis of patient data was carried out using SPSS 26.0. Statistical significance was determined using a threshold of p = 0.05. Metabolomic data analyses were carried out using MetaboAnalyst 5.0 (https://www.metaboanalyst.ca). The mass spectrometry data which were acquired by untargeted metabolomics analysis were uploaded as comma separated values (.csv). The uploaded data file contains a data matrix of 145 (samples) × 1,094 (compounds). Before data analysis, a data integrity check was performed to ensure that all the necessary information had been collected. To minimize bias associated with the omission of censored data, all missing and zero values were replaced by half of the minimum positive values across samples in the original data. Normalization was done via log transformation and Pareto scaling.
One-way analysis of variance (ANOVA), principal component analysis (PCA), and partial least squares-discriminant analysis (PLS-DA) were used to screen out the differential metabolites. MetaboAnalyst 5.0 provided one-way ANOVA test results to determine whether the overall comparison among each group was significant. Univariate analyses provided a preliminary overview of features that are potentially significant in discriminating the conditions under investigation. Statistical significance was determined using a threshold of p = 0.05.
PCA and PLS-DA were also performed using MetaboAnalyst 5.0. PCA is an unsupervised method aiming to find the directions that best explain the variance in a data set X) without referring to class labels Y). The data are summarized into much fewer variables called scores, which are weighted averages of the original variables. PLS is a supervised method that uses multivariate regression techniques to extract, via a linear combination of the original variables X), information that can predict class membership Y). To assess the significance of class discrimination, a permutation test was performed. In each permutation, a PLS-DA model was built between the data X) and the permuted class labels Y) using the optimal number of components determined by cross-validation for the model based on the original class assignment. MetaboAnalyst supports two types of test statistics for measuring class discrimination. The first one is based on prediction accuracy during training. The second is the separation distance based on the ratio of the between-group sum of the squares and the within-group sum of squares (B/Wratio). If the observed test statistic is part of the distribution based on the permuted class assignments, the class discrimination cannot be considered statistically significant. Variable Importance in Projection (VIP), which is an important variable in PLS-DA, is a weighted sum of squares of the PLS loadings taking into account the amount of explained Y-variation in each dimension. VIP scores are calculated for each component. When more components are used to calculate the feature importance, the average of the VIP scores is used. A VIP threshold >1.0 was considered statistically significant.