R: Reaction velocity of an enzymatic reaction

Puromycin {nls} | R Documentation

## Reaction velocity of an enzymatic reaction

### Description

The `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.

### Format

This data frame contains the following columns:

conc
  a numeric vector of substrate concentrations (ppm)
rate
  a numeric vector of instantaneous reaction rates (counts/min/min)
state
  a factor with levels `treated` `untreated`

### Details

Data on the ``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 ``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.

### Source

Bates, D.M. and Watts, D.G. (1988), Nonlinear Regression Analysis and Its Applications, Wiley, Appendix A1.3.

Treloar, M. A. (1974), Effects of Puromycin on Galactosyltransferase in Golgi Membranes, M.Sc. Thesis, U. of Toronto.

### Examples

    data(Puromycin)
    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)

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