self start for Hill Function
Self starter for Hill function with parameters Ka, n and a
hill1(x, Ka) SShill1(x, Ka) hill2(x, Ka, n) SShill2(x, Ka, n) hill3(x, Ka, n, a) SShill3(x, Ka, n, a)
x |
input vector (x). Concentration of substrate in the original Hill model. |
Ka |
parameter representing the concentration at which half of maximum y is attained |
n |
parameter which controls the curvature |
a |
parameter which controls the maximum value of the response (asymptote) |
For details see https://en.wikipedia.org/wiki/Hill_equation_(biochemistry)
The form of the equations are:
hill1:
1 / (1 + (Ka/x))
.
hill2:
1 / (1 + (Ka/x)^n)
.
hill3:
a / (1 + (Ka/x)^n)
.
hill1: vector of the same length as x (time) using the Hill 1 function
hill2: vector of the same length as x (time) using the Hill 2 function
hill3: vector of the same length as x (time) using the Hill 3 function
Zero values are not allowed.
require(ggplot2) ## Example for hill1 set.seed(1234) x <- 1:20 y <- hill1(x, 10) + rnorm(20, sd = 0.03) dat1 <- data.frame(x = x, y = y) fit1 <- nls(y ~ SShill1(x, Ka), data = dat1) ## Example for hill2 y <- hill2(x, 10, 1.5) + rnorm(20, sd = 0.03) dat2 <- data.frame(x = x, y = y) fit2 <- nls(y ~ SShill2(x, Ka, n), data = dat2) ## Example for hill3 y <- hill3(x, 10, 1.5, 5) + rnorm(20, sd = 0.03) dat3 <- data.frame(x = x, y = y) fit3 <- nls(y ~ SShill3(x, Ka, n, a), data = dat3) ggplot(data = dat3, aes(x, y)) + geom_point() + geom_line(aes(y = fitted(fit3)))
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