\HeaderA{Puromycin}{Reaction velocity of an enzymatic reaction}{Puromycin}
\keyword{datasets}{Puromycin}
\begin{Description}\relax
The \code{Puromycin} data frame has 23 rows and 3 columns of the
reaction velocity versus substrate concentration in an enzymatic
reaction involving untreated cells or cells treated with Puromycin.
\end{Description}
\begin{Usage}
\begin{verbatim}Puromycin\end{verbatim}
\end{Usage}
\begin{Format}\relax
This data frame contains the following columns:
\describe{
\item[conc] a numeric vector of substrate concentrations (ppm)

\item[rate] a numeric vector of instantaneous reaction rates (counts/min/min)

\item[state] a factor with levels
\code{treated} 
\code{untreated} 

}
\end{Format}
\begin{Details}\relax
Data on the \dQuote{velocity} of an enzymatic reaction were obtained
by Treloar (1974).  The number of counts per minute of radioactive
product from the reaction was measured as a function of substrate
concentration in parts per million (ppm) and from these counts the
initial rate, or \dQuote{velocity,} of the reaction was calculated
(counts/min/min).  The experiment was conducted once with the enzyme
treated with Puromycin, and once with the enzyme untreated.
\end{Details}
\begin{Source}\relax
Bates, D.M. and Watts, D.G. (1988),
\emph{Nonlinear Regression Analysis and Its Applications},
Wiley, Appendix A1.3.

Treloar, M. A. (1974), \emph{Effects of Puromycin on
Galactosyltransferase in Golgi Membranes}, M.Sc. Thesis, U. of
Toronto.
\end{Source}
\begin{Examples}
\begin{ExampleCode}
plot(rate ~ conc, data = Puromycin, las = 1,
     xlab = "Substrate concentration (ppm)",
     ylab = "Reaction velocity (counts/min/min)",
     pch = as.integer(Puromycin$state),
     col = as.integer(Puromycin$state),
     main = "Puromycin data and fitted Michaelis-Menten curves")
## simplest form of fitting the Michaelis-Menten model to these data
fm1 <- nls(rate ~ Vm * conc/(K + conc), data = Puromycin,
           subset = state == "treated",
           start = c(Vm = 200, K = 0.05), trace = TRUE)
fm2 <- nls(rate ~ Vm * conc/(K + conc), data = Puromycin,
           subset = state == "untreated",
           start = c(Vm = 160, K = 0.05), trace = TRUE)
summary(fm1)
summary(fm2)
## using partial linearity
fm3 <- nls(rate ~ conc/(K + conc), data = Puromycin,
           subset = state == "treated", start = c(K = 0.05),
           algorithm = "plinear", trace = TRUE)
## using a self-starting model
fm4 <- nls(rate ~ SSmicmen(conc, Vm, K), data = Puromycin,
           subset = state == "treated")
summary(fm4)
## add fitted lines to the plot
conc <- seq(0, 1.2, len = 101)
lines(conc, predict(fm1, list(conc = conc)), lty = 1, col = 1)
lines(conc, predict(fm2, list(conc = conc)), lty = 2, col = 2)
legend(0.8, 120, levels(Puromycin$state),
       col = 1:2, lty = 1:2, pch = 1:2)
\end{ExampleCode}
\end{Examples}