R: Michaelis-Menten model

MM {drc} | R Documentation

## 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`.

### 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.

### 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.

### Note

At the moment the implementation cannot deal with infinite concentrations.

### Author(s)

Christian Ritz

### 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

[Package drc version 3.0-1 Index]