MM: Michaelis-Menten model

Description

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

Usage

MM.2(fixed = c(NA, NA), names = c("Vm", "K"))
  
  MM.3(fixed = c(NA, NA, NA), names = c("y0", "Vm", "K"))

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 ":"). The order of the parameters is: y0, Vm, K (see under 'Details').

Value

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.

Details

The model is given by the expression $$f(x) = y0 + \frac{Vm x}{K + x}$$ It is a three-parameter model. A commonly used derived two-parameter model (MM.2) is obtained by setting y0=0.

Examples

Run this code

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)

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

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

## Simplified models
met.mm.m2<-drm(gain~dose, product, data=methionine, fct=MM.3(), pmodels = list(~1, ~factor(product), ~1))
anova(met.mm.m2, met.mm.m1)  # model reduction not possible

met.mm.m3<-drm(gain~dose, product, data=methionine, fct=MM.3(), pmodels = list(~1, ~1, ~factor(product)))
anova(met.mm.m3, met.mm.m1)  # model reduction not possible