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.

Usage

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.

See Also

SSmicmen for other models fitted to this dataset.

Examples

require(stats); require(graphics)

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))
fm2 <- nls(rate ~ Vm * conc/(K + conc), data = Puromycin,
           subset = state == "untreated",
           start = c(Vm = 160, K = 0.05))
summary(fm1)
summary(fm2)
## add fitted lines to the plot
conc <- seq(0, 1.2, length.out = 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)

## using partial linearity
fm3 <- nls(rate ~ conc/(K + conc), data = Puromycin,
           subset = state == "treated", start = c(K = 0.05),
           algorithm = "plinear")

Results

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> library(datasets)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/datasets/Puromycin.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Puromycin
> ### Title: Reaction Velocity of an Enzymatic Reaction
> ### Aliases: Puromycin
> ### Keywords: datasets
> 
> ### ** Examples
> 
> require(stats); require(graphics)
> ## Don't show: 
> options(show.nls.convergence=FALSE)
> ## End(Don't show)
> 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))
> fm2 <- nls(rate ~ Vm * conc/(K + conc), data = Puromycin,
+            subset = state == "untreated",
+            start = c(Vm = 160, K = 0.05))
> summary(fm1)

Formula: rate ~ Vm * conc/(K + conc)

Parameters:
    Estimate Std. Error t value Pr(>|t|)    
Vm 2.127e+02  6.947e+00  30.615 3.24e-11 ***
K  6.412e-02  8.281e-03   7.743 1.57e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 10.93 on 10 degrees of freedom

> summary(fm2)

Formula: rate ~ Vm * conc/(K + conc)

Parameters:
    Estimate Std. Error t value Pr(>|t|)    
Vm 1.603e+02  6.480e+00  24.734 1.38e-09 ***
K  4.771e-02  7.782e-03   6.131 0.000173 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.773 on 9 degrees of freedom

> ## add fitted lines to the plot
> conc <- seq(0, 1.2, length.out = 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)
> 
> ## using partial linearity
> fm3 <- nls(rate ~ conc/(K + conc), data = Puromycin,
+            subset = state == "treated", start = c(K = 0.05),
+            algorithm = "plinear")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>