# Hill plot fitting (S-v plot)
# For a single data
# Written by S. Fushinobu (2019.10.22)
# Thanks to Carly Huitema & Geoff P Horsman
# Edit the parameters below
Hill.df <- read.csv("/Users/fushi/Documents/R/Hill.csv")
Mtitle <- "Hill plot"  # main title of the plot
Substname <- "Substrate"
Substunit <- " (mM)"
Vunit <- " (units/mg)"
Kminit <- 5               # initial values for fitting
Vmaxinit <- 10
nHinit <- 4

plot(Hill.df$conc,Hill.df$rate,main=Mtitle,xlim=c(0,max(Hill.df$conc)),ylim=c(0,max(Hill.df$rate)),xlab=paste(Substname,Substunit),ylab=paste("v",Vunit))

Hill.nls <- nls(rate ~ (Vmax * (conc ^ nH) / ((conc ^ nH) + (Km ^ nH))), data=Hill.df, start=list(Km=Kminit, Vmax=Vmaxinit,nH=nHinit))
Km <- unname(coef(Hill.nls)["Km"])
Vmax <- unname(coef(Hill.nls)["Vmax"])
nH <- unname(coef(Hill.nls)["nH"])
curve(Vmax*(x ^ nH)/((x ^ nH)+(Km ^ nH)),0,max(Hill.df$conc),add=TRUE, lty=2)

text(0,max(Hill.df$rate),paste("Km = ",signif(Km,digits=3),"±",signif(summary(Hill.nls)$parameters[1,2],digits=3),Substunit,"; Vmax = ",signif(Vmax,digits=3),"±",signif(summary(Hill.nls)$parameters[2,2],digits=3),Vunit,"\nnH = ",signif(nH,digits=3),"±",signif(summary(Hill.nls)$parameters[3,2],digits=3),Substunit),adj=0)

text(max(Hill.df$conc),max(Hill.df$rate)/20,expression(italic(v) == over(italic(V)[max] * "([S])"^italic(nH), "([S])"^italic(nH) + (italic(K)[m])^italic(nH))),adj=1)