Chapter 6 Exponential regulator

For this work we used a simple exponential function to apply regulatory modifiers to tag-match scores (see details in paper).

6.1 Analysis Dependencies

Load all required R libraries.

library(ggplot2)
library(tidyverse)
library(cowplot)
library(viridis)
library(RColorBrewer)

These analyses were conducted in the following computing environment:

print(version)

##                _                           
## platform       x86_64-pc-linux-gnu         
## arch           x86_64                      
## os             linux-gnu                   
## system         x86_64, linux-gnu           
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

Configuration:

theme_set(theme_cowplot())
output_directory <- "media/"

6.2 Regulator modifier equation

Below is the function we use to apply regulation to module match scores.

exp_base <- 1.1
# Exponential regulator
exp_regulator <- function(raw_match, modifier, base=1.1) {
  return(raw_match * (base**modifier));
}

6.3 Regulator behavior

Generate data to graph. We want to visualize regulated match scores as a function of raw tag match scores and module regulatory modifiers.

# generate data to visualize
data <- expand_grid(
  raw_match=seq(0, 1.0, 0.01),
  reg_modifier=seq(-10, 10, 0.1)
)

data <- as.data.frame(data)
data$regulated_match <- mapply(
  exp_regulator,
  data$raw_match,
  data$reg_modifier,
  exp_base
)
data$above_perfect <- data$regulated_match > 1.0

We expect that 90% of random pairs of tags fall between the two vertical dashed lines.

lower_5 <- 0.0579369
upper_5 <- 0.942063
ggplot(data, aes(y=reg_modifier, x=raw_match, fill=regulated_match)) +
  geom_raster() +
  geom_hline(yintercept=0, size=1, color="black") +
  geom_vline(xintercept=lower_5, size=1, color="black", linetype="dashed") +
  geom_vline(xintercept=upper_5, size=1, color="black", linetype="dashed") +
  scale_x_continuous(name="Raw tag-match score") +
  scale_y_continuous(name="Module regulation modifier") +
  scale_fill_distiller(
    name="Regulated match:  ",
    palette = "Spectral"
  ) +
  theme(
    legend.position = "top",
    legend.key.width=unit(1.5, 'cm')
  ) +
  ggsave(
    paste0(output_directory, "exp-reg-match.png"),
    width=6,
    height=6
  )

Does a given raw match + regulatory modifier beat a perfect match (with no regulation)?

ggplot(data, aes(y=reg_modifier, x=raw_match, fill=above_perfect)) +
  geom_tile() +
  ggsave(
    paste0(output_directory, "exp-reg-match-above-perfect.png"),
    width=10,
    height=10
  )