R: Self-Starting Nls Michaelis-Menten Model

SSmicmen {stats} | R Documentation

## Self-Starting Nls 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)

José Pinheiro and Douglas Bates

### See Also

`nls`, `selfStart`

### Examples

    PurTrt <- Puromycin[ Puromycin$state == "treated", ]
    SSmicmen(PurTrt$conc, 200, 0.05)  # response only
    local({  Vm <- 200; K <- 0.05
      SSmicmen(PurTrt$conc, Vm, K)    # response _and_ gradient
    })
    print(getInitial(rate ~ SSmicmen(conc, Vm, K), data = PurTrt), digits = 3)
    ## 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) # The same indeed:
    stopifnot(all.equal(coef(summary(fm1)), coef(summary(fm2))))

    ## Visualize the SSmicmen()  Michaelis-Menton model parametrization :

      xx <- seq(0, 5, len = 101)
      yy <- 5 * xx/(1+xx)
      stopifnot(all.equal(yy, SSmicmen(xx, Vm = 5, K = 1)))
      require(graphics)
      op <- par(mar = c(0, 0, 3.5, 0))
      plot(xx, yy, type = "l", lwd = 2, ylim = c(-1/4,6), xlim = c(-1, 5),
           ann = FALSE, axes = FALSE, main = "Parameters in the SSmicmen model")
      mtext(quote(list(phi[1] == "Vm", phi[2] == "K")))
      usr <- par("usr")
      arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
      arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
      text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
      text(     -0.1, usr[4], "y", adj = c(1, 1))
      abline(h = 5, lty = 3)
      arrows(-0.8, c(2.1, 2.9),
             -0.8, c(0,   5  ),  length = 0.1, angle = 25)
      text(  -0.8,     2.5, quote(phi[1]))
      segments(1, 0, 1, 2.7, lty = 2, lwd = 0.75)
      text(1, 2.7, quote(phi[2]))
      par(op)

[Package stats version 3.5.1 Index]