Quantile-normalize intensity measurements

Introduction

Previously when investigating measurement variation (GFP/RFP/FAPI), we learned that there’s significant variation between batches in the distributions of background-corrected pixel intensites. See here.

In this document, I apply quantile normalization to intensity measurements. Bad news, it did not work well. While quantile normalization helps to remove variation between batches in intensity measurements, but by doing so, we increases the variation between individuals. The cells do not form any clusters in the Green versus Red plot. In hindsight, this seems to make sense. By normalizing samples within plate, we artifically inflated differences between individuals…

Next to try linear mixed model…

Load packages and data

library(data.table)
library(dplyr)
library(ggplot2)
library(cowplot)
library(wesanderson)
library(RColorBrewer)
library(Biobase)

Name all plates.

plates <- c("18511_18855","18855_19101","18855_19160","18870_18511",
            "18870_18855","18870_19101","18870_19160","19098_18511",
            "19098_18870","19098_19160","19101_18511","19101_19098",
            "19160_18870","19101_19160","19160_18511", "18855_19098")

Combine intensity stats from different plates.

# make the negative ones be the samllest one within its own plate
ints <- do.call(rbind, lapply(1:length(plates), function(index) {
  tmp <- readRDS(paste0("/project2/gilad/fucci-seq/intensities_stats/",plates[index],".stats.rds"))
  tmp <- data.frame(plate=plates[index], 
                    well=as.character(droplevels(tmp$wellID)),
         rfp.sum.zoom.mean.log10=log10(tmp$rfp.sum.zoom.mean),
         gfp.sum.zoom.mean.log10=log10(tmp$gfp.sum.zoom.mean),
         dapi.sum.zoom.mean.log10=log10(tmp$dapi.sum.zoom.mean))

  tmp$rfp.sum.zoom.mean.log10[which(tmp$rfp.sum.zoom.mean.log10 == "NaN")] <- min(tmp$rfp.sum.zoom.mean.log10, na.rm=TRUE)
  tmp$gfp.sum.zoom.mean.log10[which(tmp$gfp.sum.zoom.mean.log10 == "NaN")] <- min(tmp$gfp.sum.zoom.mean.log10, na.rm=TRUE)
  tmp$dapi.sum.zoom.mean.log10[which(tmp$dapi.sum.zoom.mean.log10 == "NaN")] <- min(tmp$dapi.sum.zoom.mean.log10, na.rm=TRUE)
  return(tmp)  
}) )

Load the expression set info.

eset_fls <- list.files("../data/eset", full.names=TRUE)

anno <- do.call(rbind, lapply(1:length(eset_fls), function(index) {
  eset_index <- readRDS(eset_fls[[index]])
  pdata_index <- pData(eset_index)
  return(pdata_index)
}))

# make unique id in both
ints$unique <- paste0(ints$plate,"_",as.numeric(ints$well))
anno$unique <- paste0(anno$image_individual,"_",anno$image_label)

subset_index1 <- which(anno$unique %in% ints$unique)
anno_subset <- anno[subset_index1,]

subset_index2 <- match(anno_subset$unique, ints$unique)
ints_tmp <- ints[subset_index2,]
all.equal(ints_tmp$unique, anno_subset$unique)

[1] TRUE

ints_tmp$chip_id <- anno_subset$chip_id

Densit plots

First, look at the distribution of all batches combined versus each batch.

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Normalization

Code for one single sample

my_quantnorm <- function(reference, sample, span=.01) {
  # quantiles for intensities all samples across plates
  quants_reference <- quantile(reference, probs=seq(0,1,span))
  # intensities for a given plate
  # quantiles for intensities at each plate
  quants_sample <- quantile(sample, probs=seq(0,1,span))
  # empty vector for normalized values
  sample_normed <- vector("numeric", length=length(sample))
  
  for (index in 1:length(sample)) {
    # compare the sample intensity values with the refernece sample intensity values 
    # at each quantile; get the closes reference quantlie in terms of measurement values
    sample_order <- names(which.min(abs(sample[index]-quants_sample)))
    # get the reference intensity value of the closet quantile
    ref_order_value <- reference[which(names(quants_reference)==sample_order)] 
    # assign the reference intensity value to the sample
    sample_normed[index] <- ref_order_value 
  }
  return(sample_normed)
}

Choose smoothing parameter for RFP

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  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Choose smoothing parameter for GFP

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Choose smoothing parameter for DAPI

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Normalize intensity for each channel

DAPI choose .001; Green choose .01; Red choose .01

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

After normalization: Green versus Red by individual

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Before normalization: Green versus Red by individual

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Warning in structure(NULL, class = "waiver"): Calling 'structure(NULL, *)' is deprecated, as NULL cannot have attributes.
  Consider 'structure(list(), *)' instead.

Session information

R version 3.4.1 (2017-06-30)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.2 (Nitrogen)

Matrix products: default
BLAS: /home/joycehsiao/miniconda3/envs/fucci-seq/lib/R/lib/libRblas.so
LAPACK: /home/joycehsiao/miniconda3/envs/fucci-seq/lib/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
[1] Biobase_2.38.0      BiocGenerics_0.24.0 RColorBrewer_1.1-2 
[4] wesanderson_0.3.2   cowplot_0.9.1       ggplot2_2.2.0      
[7] dplyr_0.7.4         data.table_1.10.4-3

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.13     knitr_1.16       bindr_0.1        magrittr_1.5    
 [5] munsell_0.4.3    colorspace_1.3-2 R6_2.2.2         rlang_0.1.4     
 [9] plyr_1.8.4       stringr_1.2.0    tools_3.4.1      grid_3.4.1      
[13] gtable_0.2.0     git2r_0.19.0     htmltools_0.3.6  lazyeval_0.2.0  
[17] yaml_2.1.14      rprojroot_1.2    digest_0.6.12    assertthat_0.1  
[21] tibble_1.3.4     bindrcpp_0.2     glue_1.2.0       evaluate_0.10   
[25] rmarkdown_1.6    labeling_0.3     stringi_1.1.2    compiler_3.4.1  
[29] scales_0.4.1     backports_1.0.5  pkgconfig_2.0.1