71 Network analysis We used a weighted gene co-expression network analysis32 in the context of antibody-bound peptide presence/absence to identifymodules of peptide co-occurrence.We used all LLD samples (1,784) and the subset of selected peptides with no missing values (2,770) to build the network. The soft thresholding power was chosen by visually inspecting the model fit of powers from 1 to 20. It was decided to use a power of 7. A network was built using Pearson correlation between antibody’s presence/absence profiles, followed by hierarchical clustering. A cut-off height for merging of 0.5 was used and a minimal module size of 10 peptides was required for a module to be called. The peptide identity from the identified modules was checked and a sequence similarity analysis was run. Module eigengenes were extracted using WGCA. Eigengenes were correlated between modules. Strong module correlation was defined on the basis of achieving a PBonferroni < 0.05. Peptides belonging to a module of at least 10 peptides were used to build a visual network graph (igraph). A maximum spanning tree algorithm was used to build the network. To check if co-occurrence modules might be driven by batch effects (due to PhIP-Seq plates), we computed the prevalence of each peptide within a module. If a common batch effect was present in all peptides of a module, we would expect to see a significant batch effect adding variation to the mean prevalence within all modules (Null hypothesis, Prevalence ~ Peptide + Batch). If this batch effect was different per peptide, then the batch effect would show a significant interaction with the peptide (Alternative hypothesis, Prevalence ~ Peptide + Batch + Peptide*Batch). If the alternative hypothesis was true, the batch would have a different effect per peptide, and thus it is not the only explanation to observe high co-occurrence between antibody-bound peptides. We fitted the null and alternative hypothesis in two linear models, and computed a P-value for the peptide–batch integration by computing a likelihood ratio test between both models. All tested models showed a significant interaction effect, indicating that batch most likely has a different effect per peptide. Peptide similarity Sequence similarity between peptide groups of interest was estimated using Clustal Omega.33 Clustal Omega uses this distance matrix to build guiding trees for the progressive multiple sequence alignment algorithm. This distance is internally calculated using the k-tuple method.34 Phenotype association analysis Jaccard distances between all samples were used as the dependent variable in a PERMANOVA against, sex, age and PhIP-Seq plate in order to identify covariates of interest. To associate individual enrichment profiles to available phenotypes, we performed a logistic regression on the presence/absence of antibody-bound peptides using the phenotype of interest, PhIP-Seq plate, age and sex as covariates on 1,437 baseline participants. We controlled the FDR at 0.05 using the Benjamini-Hochberg procedure.35 Determinants of the human antibody epitope repertoire
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