# SSmicmen

0th

Percentile

##### Self-Starting Nls Michaelis-Menten Model

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

Keywords
models
##### 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.

##### encoding

UTF-8

nls, selfStart
library(stats) 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 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) require(graphics) xx <- seq(0, 5, len = 101) yy <- 5 * xx/(1+xx) par(mar = c(0, 0, 3.5, 0)) plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5), xlab = "", ylab = "", lwd = 2, main = "Parameters in the SSmicmen model") 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 = 2, lwd = 0) arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25) arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25) text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5)) segments(1, 0, 1, 2.7, lty = 2, lwd = 0.75) text(1, 2.7, expression(phi[2]), adj = c(0.5, 0))