Unexpected links reflect the noise in networks

Abstract

Background: Gene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small number of biological replicates available for analysis. Results: We propose a new statistical method for estimating the number of erroneous edges in reconstructed networks that strongly enhances commonly used inference approaches. This method is based on a special relationship between sign of correlation (positive/negative) and directionality (up/down) of gene regulation, and allows for the identification and removal of approximately half of all erroneous edges. Using the mathematical model of Bayesian networks and positive correlation inequalities we establish a mathematical foundation for our method. Analyzing existing biological datasets, we find a strong correlation between the results of our method and false discovery rate (FDR). Furthermore, simulation analysis demonstrates that our method provides a more accurate estimate of network error than FDR.

Akkermansia muciniphila mediates negative effects of IFNγ on glucose metabolism

“…This analysis was performed in IFNγKO mice so that direct effects of IFNγ could not bias the correlation. With this approach23, microbial candidates that mediate the effect of IFNγ on glucose metabolism should present a positive correlation with glucose levels and AUC-GTT if they are enriched in the presence of IFNγ, and negative correlation if they are depleted by IFNγ (see experimental outline in Supplementary Fig. 3).…”

“…Briefly, criteria for inclusion of gene–gene pairs are the following: Individual P value of correlation within each group is <0.3; combined fisher P value of all groups <0.01; the sign of correlation coefficients in four mouse strain groups should be consistent (all positive correlation or all negative correlation) and should be consistent with fold change relationship between the two genes (see ‘Methods' section in ref. 23). …”

Transkingdom interactions between Lactobacilli and hepatic mitochondria attenuate western diet-induced diabetes

“…), individual p value of correlation within each experiment is <30%, combined Fisher's p value of all experiments <5% and FDR cutoff of 10% for within edges (i and ii). Finally, the TK network was generated 20,61,[87][88][89] by adding microbe-phenotype edges where the microbe showed significant change in (WD vs ND) abundance in ileum at 8 weeks, edges showed consistent sign of per group Spearman correlation coefficient between the two experiments of three WD-fed groups (WD-stool 4 weeks, WD-stool 8 weeks, and WD-ileum 8 weeks), and satisfied principles of causality 90 (i.e., had concordance between fold change in WD vs. ND comparison and correlation sign between the two partners) in all three WD-fed groups. The network was visualized in Cytoscape.…”

Transkingdom Networks: A Systems Biology Approach to Identify Causal Members of Host–Microbiota Interactions

“…• At this point you have a network for a single group where nodes are genes and edges indicate significant correlation. Next, we identify the proportion of unexpected correlations (PUC) [50] (GD: line 83). If two elements have a regulatory relationship we expect them to behave in certain ways.…”