SSmicmen                 package:nls                 R Documentation

Michaelis-Menten Model

Description:

     This `selfStart' model evaluates the Michaelis-Menten model and
     its gradient.  It has an `initial' attribute that will evaluate
     initial estimates of the parameters `Vm' and `K'

Usage:

     SSmicmen(input, Vm, K)

Arguments:

   input: a numeric vector of values at which to evaluate the model.

      Vm: a numeric parameter representing the maximum value of the
          response.

       K: a numeric parameter representing the `input' value at which
          half the maximum response is attained.  In the field of
          enzyme kinetics this is called the Michaelis parameter.

Value:

     a numeric vector of the same length as `input'.  It is the value
     of the expression `Vm*input/(K+input)'.  If both the arguments
     `Vm' and `K' are names of objects, the gradient matrix with
     respect to these names is attached as an attribute named
     `gradient'.

Author(s):

     Jose Pinheiro and Douglas Bates

See Also:

     `nls', `selfStart'

Examples:

     data( Puromycin )
     PurTrt <- Puromycin[ Puromycin$state == "treated", ]
     SSmicmen( PurTrt$conc, 200, 0.05 )  # response only
     Vm <- 200; K <- 0.05
     SSmicmen( PurTrt$conc, Vm, K ) # response and gradient
     getInitial(rate ~ SSmicmen(conc, Vm, K), data = PurTrt)
     ## Initial values are in fact the converged values
     fm1 <- nls(rate ~ SSmicmen(conc, Vm, K), data = PurTrt)
     summary( fm1 )
     ## Alternative call using the subset argument
     fm2 <- nls(rate ~ SSmicmen(conc, Vm, K), data = Puromycin,
                subset = state == "treated")
     summary(fm2)

