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File:Hill-Langmuir equation.svg

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Summary

Description
English: Graph of the Hill-Langmuir equation with different values of n
Date
Source Own work
Author D Wells
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Source code
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R code

library(ggplot2)
library(data.table)
ka_c=0.75

hill <- function(l, n=1, ka=ka_c){
  1 / (1 + (ka/l)^n)
}

ligand_conc = c(0, exp(seq(log(0.001), log(1.75), by=0.01)))

data <- rbind(data.table(ligand_conc, fraction=hill(ligand_conc, 0.2), n=0.2),
              data.table(ligand_conc, fraction=hill(ligand_conc, 0.5), n=0.5),
              data.table(ligand_conc, fraction=hill(ligand_conc, 1), n=1),
              data.table(ligand_conc, fraction=hill(ligand_conc, 2), n=2),
              data.table(ligand_conc, fraction=hill(ligand_conc, 4), n=4))

svg(height=3, width=5)
ggplot(data, aes(ligand_conc, fraction, colour=forcats::fct_reorder2(as.factor(n), ligand_conc, fraction), group=n)) + 
  geom_line(data = data.table(ligand_conc=c(0.001, ka_c, ka_c), fraction=c(0.5,0.5,0), n=NA), colour="blue", linetype="dashed") +
  annotate("text", x = ka_c*1.1, y = 0.1, label = expression(italic(K[A])), colour="blue") +
  geom_line(size=1) + 
  coord_cartesian(xlim = c(-0.01,1.75), ylim = c(-0.01, 1), expand=F) +
  scale_colour_manual(values = c("black","#BD0026","#F03B20","#FD8D3C","#FECC5C"), name="Hill\nCoefficient") +
  ylab("Fraction of receptor bound by ligand") +
  xlab("Free Ligand Concentration") +
  theme_classic()
dev.off()

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Graph of the Hill-Langmuir equation with different values of n

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27 April 2020

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Date/TimeThumbnailDimensionsUserComment
current12:42, 27 April 2020Thumbnail for version as of 12:42, 27 April 2020450 × 270 (107 KB)D WellsUploaded own work with UploadWizard

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