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("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.

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 defined by the three-parameter model function $$f(x, (c, d, e)) = c + \frac{d-c}{1+(e/x)}$$ 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.

Examples

Run this code

## 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
SI(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