beer

Phage immuno-precipitation sequencing (PhIP-seq) is a high-throughput approach for characterizing antibody responses to a variety of target antigens. A typical component of PhIP-seq analyses involves identifying which peptides elicit enriched antibody responses. beer provides two approaches for identifying peptide enrichments.

The first approach is based on edgeR’s standard pipeline for identifying differential expression from read count data¹²³. Though edgeR is remarkably effective at quickly identifying enriched antibody responses, it is less likely to pick up enriched peptides at the lower fold-change range.

The second approach, Bayesian Estimation in R (BEER) was developed specifically for the PhIP-seq setting and implements a Bayesian model to identify peptide enrichments as described in Chen et. al⁴. Though BEER is more likely to identify enriched peptides at the lower fold-change range, it tends to take much longer to run.

Below we give a brief overview of the two approaches. For more information, see the package vignette using browseVignettes("beer"). Both methods can be run in synchronously or asynchronously as supported by BiocParallel.

Installation

rjags

For Bayesian MCMC modeling, beer relies on rjags to interface Just Another Gibbs Sampler (JAGS). JAGS can be downloaded from this link. Homebrew users can install JAGS using,

brew install jags

For M1 Mac users using Rosetta emulation of intel, Homebrew installation of JAGS will likely work. However, we recommend installing JAGS from source for all other M1 Mac users.

Once JAGS has been installed, rjags can be installed in R via install.packages("rjags").

beer

Once rjags has been installed, the stable release version of beer in Bioconductor can be installed using BiocManager:

if (!require("BiocManager"))
    install.packages("BiocManager")
    
BiocManager::install("beer")

To load the package:

library(beer)

edgeR

Differentially enriched peptides between a particular serum sample and all beads-only samples indicate enriched antibody responses to those peptides. Thus, to identify enriched peptides, we can run the standard edgeR pipeline for differential expression.

The runEdgeR() function estimates peptide-specific dispersion parameters then runs the exact test proposed by Robinson and Smyth⁵ for the difference in mean between two groups of negative binomial random variables. Since peptides are enriched only if average proportion of reads pulled in the serum sample is higher than the average proportion of reads pulled in a beads-only samples, two-sided p-values are converted to one-sided p-values.

## Load data
data_path <- system.file("extdata/sim_data.RDS", package = "beer")
sim_data <- readRDS(data_path)

edgeR_out <- runEdgeR(sim_data, 
                      assay.names = c(logfc = "edgeR_logfc", 
                                   prob = "edgeR_logpval"))

Using BH correction to adjust for multiple testing, enriched peptides are given by the matrix,

assay(edgeR_out, "edgeR_hits") <- apply(
  assay(edgeR_out, "edgeR_logpval"), 2, 
  function(sample){
    pval <- 10^(-sample)
    p.adjust(pval, method = "BH") < 0.05
  })

colSums(assay(edgeR_out, "edgeR_hits"))
#>  1  2  3  4  5  6  7  8  9 10 
#> NA NA NA NA  1  1  1  0  0  1

BEER (Bayesian Estimation Enrichment in R)

BEER uses a Bayesian hierarchical model to derive posterior probabilities of enrichment and estimated fold-changes. Briefly, each sample is run individually in comparison to all beads-only samples as follows:

1. Define prior parameters. Though most prior parameters are supplemented by the user (or use the defaults), prior parameters for non-enriched peptides are first approximated using all beads-only samples.
2. Identify super enriched peptides. Based on the prior parameters, super enriched peptides are first excluded as these peptides should always have posterior probabilities of enrichment of 1.
3. Re-estimate beads-only prior parameters. Prior parameters are then re-estimated from the beads-only samples for the remaining peptides.
4. Initialize and run the MCMCs. To reduce convergence time, MLE estimates are used to initialize the MCMC sampler, and samples are drawn from the posterior distributions of the unknown parameters.
5. Summarize and store results. Posterior samples are summarized using the means of the posterior distribution and are stored in the PhIPData object.

BEER can be easily run with brew():

## Named vector specifying where we want to store the summarized MCMC output
## NULL indicates that the output should not be stored.
assay_locations <- c(
  phi = "beer_fc_marg", 
  phi_Z = "beer_fc_cond", 
  Z = "beer_prob", 
  c = "sampleInfo", 
  pi = "sampleInfo"
)

beer_out <- brew(sim_data, assay.names = assay_locations)

Thus, supposing peptides with posterior probability above 0.5 are enriched and noting that super enriched peptides were not run (and thus are missing entries in the posterior probability matrix), the matrix of enriched peptides is given by,

## Define matrix of peptides that were run in BEER
was_run <- matrix(rep(beer_out$group != "beads", each = nrow(beer_out)), 
                  nrow = nrow(beer_out))

## Identify super-enriched peptides
## These peptides were in samples that were run, but have missing posterior 
## probabilities
are_se <- was_run & is.na(assay(beer_out, "beer_prob"))

## Enriched peptides are peptides with:
## - posterior probability > 0.5, OR
## - super-enriched peptides
assay(beer_out, "beer_hits") <- assay(beer_out, "beer_prob") > 0.5 | are_se

colSums(assay(beer_out, "beer_hits"))
#>  1  2  3  4  5  6  7  8  9 10 
#> NA NA NA NA  3  1  1  1  0  1

Beads-only round robin

To approximate the false positive rate, we often run each of the beads-only samples against all other beads-only samples. This beads-only round robin also provides a sense of how similar the beads-only samples are to each other.

The beads-only round robin can be included in brew() and runEdgeR() by specifying beadsRR = TRUE.

## edgeR with beadsRR
edgeR_beadsRR <- runEdgeR(sim_data, beadsRR = TRUE, 
                          assay.names = c(logfc = "edgeR_logfc", 
                                          prob = "edgeR_logpval"))
## Calculate hits
assay(edgeR_beadsRR, "edgeR_hits") <- apply(
  assay(edgeR_beadsRR, "edgeR_logpval"), 2, 
  function(sample){
    pval <- 10^(-sample)
    p.adjust(pval, method = "BH") < 0.05
  })

## Note samples 1-4 have 0 instead of NA now
colSums(assay(edgeR_beadsRR, "edgeR_hits"))
#>  1  2  3  4  5  6  7  8  9 10 
#>  0  0  0  0  1  1  1  0  0  1

## BEER with beadsRR added to edgeR output
beer_beadsRR <- brew(edgeR_beadsRR, beadsRR = TRUE, 
                     assay.names = assay_locations)

## Check BEER hits like before
was_run <- matrix(rep(beer_beadsRR$group != "beads", each = nrow(beer_beadsRR)), 
                  nrow = nrow(beer_beadsRR))
are_se <- was_run & is.na(assay(beer_beadsRR, "beer_prob"))
beer_hits <- assay(beer_beadsRR, "beer_prob") > 0.5 | are_se

## Note again that samples 1-4 are not NA 
colSums(beer_hits)
#>  1  2  3  4  5  6  7  8  9 10 
#>  0  0  0  0  3  1  1  1  0  1

Alternatively, one can run beadsRR() separately,

## edgeR with beadsRR
edgeR_beadsRR <- beadsRR(sim_data, method = "edgeR", 
                         assay.names = c(logfc = "edgeR_logfc", 
                                         prob = "edgeR_logpval"))
## Calculate hits
assay(edgeR_beadsRR, "edgeR_hits") <- apply(
  assay(edgeR_beadsRR, "edgeR_logpval"), 2, 
  function(sample){
    pval <- 10^(-sample)
    p.adjust(pval, method = "BH") < 0.05
  })

## Note samples 5-10 are NA now
colSums(assay(edgeR_beadsRR, "edgeR_hits"))
#>  1  2  3  4  5  6  7  8  9 10 
#>  0  0  0  0 NA NA NA NA NA NA

References

Footnotes

1. Robinson MD, McCarthy DJ and Smyth GK (2010). edgeR: a Bioconductor package for differential expression analysis of digital gene expression data. Bioinformatics 26, 139-140 ↩

2. McCarthy DJ, Chen Y and Smyth GK (2012). Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation. Nucleic Acids Research 40, 4288-4297 ↩

3. Chen Y, Lun ATL, Smyth GK (2016). From reads to genes to pathways: differential expression analysis of RNA-Seq experiments using Rsubread and the edgeR quasi-likelihood pipeline. F1000Research 5, 1438 ↩

4. Chen A, Kammers K, Larman HB, Scharpf R, Ruczinski I. Detecting antibody reactivities in phage immunoprecipitation sequencing data (2022). bioRxiv. https://www.biorxiv.org/content/10.1101/2022.01.19.476926v1 ↩

5. Robinson MD and Smyth GK. Small-sample estimation of negative binomial dispersion, with applications to SAGE data (2008). Biostatistics, 9, 321-332. https://doi.org/10.1093/biostatistics/kxm030 ↩