1.1 Set Working Directory (WD)

R is always pointed at a directory on your computer. By default,

• R loads files (Plain text files / Data files etc.) from this directory.

• R outputs files (Plain text files / Data files etc.) to this directory.

• Set Working Directory (WD)
  • On Windows
    • in R interface choose : Menu - File - Change dir...
    • Choose a local directory (folder)
      • for example I use C:/Users/Admin/Documents/Konstanz_summer_school/Day2 (actrually Day 3) as my working directory
    • 
  • On MacOs
    • in R insterface choose : menu - Misc - Change Working Directory...
      • for example I use ~/Documents/Konstanz_summer_school/Day2 as my working directory
    • 
  • Verify your WD
    • type getwd() in R console prompt: after >, then press enter key
    • R should print your current WD

1.2 Download dataset and load it to R

• The dataset is accessible via the following two links Link 1 or Link 2
• Click on one of the two Links, a new web page will open then you have two options
  • Option 1: press Windows Shortcut : Control + S or MacOS Shortcut : Command ⌘ + S
  • Option 2: right click your mouse (or touchpad) and choose save as
• save data_GSH.txt to your working directory (in my case /Documents/Konstanz_summer_school/Day2)
• once this is done, type list.files() in R console prompt: after >, then press enter key
• R should print all files in your working directory. Check if data_GSH.txt is listed
• if not click on Need help ?

tmpData = readLines("https://antoinechn.github.io/Konstanz-SummerSchool/data/data_GSH.txt")
writeLines(tmpData, "data_GSH.txt")
rm(tmpData)

list.files()

1.3 Load data

This is GSH (after 1h)

data_GSH = read.table("data_GSH.txt", sep="\t", header=TRUE)

head(data_GSH)

#>   KBrO3_mM group pct_control
#> 1    0.000     1   91.521770
#> 2    0.375     1   63.591550
#> 3    0.750     1   50.508870
#> 4    1.500     1   14.285990
#> 5    3.000     1    2.477166
#> 6    6.000     1    0.377906

data_GSH = read.table("https://trello-attachments.s3.amazonaws.com/59552633a56853b5f6d1f1f9/5a92760183331b90626ce166/678efebfc21386538df65c23120fc741/data_GSH.txt", sep="\t", header=TRUE)

head(data_GSH)

data_GSH = read.table("https://antoinechn.github.io/Konstanz-SummerSchool/data/data_GSH.txt", sep="\t", header=TRUE)

head(data_GSH)

3.1 Hill dose-response model

Let’s get serious:

• define the Hill dose-response model as a function
• let’s try it
• plot it…

# define the Hill dose-response model as a function
Hill = function (x, EC50, n) {
  return(x^n / (x^n + EC50^n))
}

# let's try it
Hill(x=10, EC50=1, n=1)

# plot it...
x = seq(0, 10, 0.1)
y = Hill(x=x, EC50=1, n=3)
plot(x, y, type="b")

# define the Hill dose-response model as a function
Hill = function (x, EC50, n) {
  return(x^n / (x^n + EC50^n))
}
# let's try it
Hill(x=10, EC50=1, n=1)

#> [1] 0.9090909

# plot it...
x = seq(0, 10, 0.1)
y = Hill(x=x, EC50=1, n=3)
plot(x, y, type="b")

Problem:

• it goes up from zero to one
• and we want it to go down from 100 to 0

3.2 Extended Hill dose-response model

So we change it a bit

• define an extended Hill dose-response model as a function
• try it…
• plot it…

# define an extended Hill dose-response model as a function
Hill = function (x, EC50, n, from, diff) {
  return(from + diff * (x^n / (x^n + EC50^n)))
}

# try it
Hill(x=10, EC50=1, n=1, from=1, diff=10)

# plot it...
x = seq(0, 10, 0.1)
y = Hill(x=x, EC50=1, n=3, from=1, diff=10)
plot(x, y, type="b")

# define an extended Hill dose-response model as a function
Hill = function (x, EC50, n, from, diff) {
  return(from + diff * (x^n / (x^n + EC50^n)))
}

# try it
Hill(x=10, EC50=1, n=1, from=1, diff=10)

#> [1] 10.09091

# plot it...
x = seq(0, 10, 0.1)
y = Hill(x=x, EC50=1, n=3, from=1, diff=10)
plot(x, y, type="b")

Question

• Can you find values of from and diff that would match the data range?
  • first: what is the data range?
  • assign the values found to variables A and B

# assign the values found to variables A and B
A =
B =

now replot the data and overlay with the model

Note : make sure to define the axes limits before doing overlays…

xlims = c(0, 6) # a vector of min and max
ylims = c(0, 120)
plot(data_GSH$KBrO3_mM, data_GSH$pct_control, xlim=xlims, ylim=ylims, col="red")
par(new=T) # will overlay the next plot
x = seq(0, 6, 0.1)
y = Hill(x=x, EC50=1, n=3, from=A, diff=B)
plot(x, y, type="l", xlim=xlims, ylim=ylims, xlab="", ylab="") # turn off labels

now play with EC50 and N to fit the data better

3.3 Inverting the Hill dose-reponse model

• Can you code a function inverting the Hill dose-response model?
• Plot the function you found.

\[y = A + B \times \frac{x^n}{x^n+ {EC_{50}}^n} \]

\[x = \;?\]

invs.hill = function(y, EC50, A, B, n){
   YOUR CODE HERE
  }

invs.hill = function(y, EC50, A, B, n){
    res = (EC50 ^n /(B/(y-A)  - 1 ) )^(1/n)
    return(res)
  }

# A = 100
# B = -100
# EC50 = 0.5
# n = 1.8

Hi = seq(0.1, 100, by = 0.1)
KBr = invs.hill(y = Hi, 
                EC50 = 0.5, 
                A = 100,
                B = -100,
                n = 1.8)

plot(x = Hi, y = KBr, type = 'l',
     main = "Invers Hill function plot")