MM function

Michaelis-Menten model

The functions can be used to fit (shifted) Michaelis-Menten models that are used for modeling enzyme kinetics, weed densities etc.

MM.2(fixed = c(NA, NA), names = c("d", "e"), ...)
  
  MM.3(fixed = c(NA, NA, NA), names = c("c", "d", "e"), ...)

Arguments

• fixed: numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
• names: a vector of character strings giving the names of the parameters (should not contain ":").
• ...: additional arguments from convenience functions to llogistic.

Details

The model is defined by the three-parameter model function

It is an increasing as a function of the dose $x$, attaining the lower limit $c$ at dose 0 ($x=0$) and the upper limit $d$ for infinitely large doses. The parameter $e$ corresponds to the dose yielding a response halfway between $c$ and $d$.

The common two-parameter Michaelis-Menten model (MM.2) is obtained by setting $c$ equal to 0.

Returns

A list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values.

Author(s)

Christian Ritz

Note

At the moment the implementation cannot deal with infinite concentrations.

See Also

Related models are the asymptotic regression models AR.2 and AR.3.

Examples

## Fitting Michaelis-Menten model
met.mm.m1 <- drm(gain~dose, product, data=methionine, fct=MM.3(), 
pmodels = list(~1, ~factor(product), ~factor(product)))
plot(met.mm.m1, log = "", ylim=c(1450, 1800))
summary(met.mm.m1)
ED(met.mm.m1, c(10, 50))

## Calculating bioefficacy: approach 1
coef(met.mm.m1)[4] / coef(met.mm.m1)[5] * 100

## Calculating bioefficacy: approach 2
EDcomp(met.mm.m1, c(50,50))

## Simplified models
met.mm.m2a <- drm(gain~dose, product, data=methionine, fct=MM.3(), 
pmodels = list(~1, ~factor(product), ~1))
anova(met.mm.m2a, met.mm.m1)  # model reduction not possible

met.mm.m2b <- drm(gain~dose, product, data=methionine, fct=MM.3(), 
pmodels = list(~1, ~1, ~factor(product)))
anova(met.mm.m2b, met.mm.m1)  # model reduction not possible