nlraa (version 1.2)

SShill: self start for Hill Function

Description

Self starter for Hill function with parameters Ka, n and a

Usage

hill1(x, Ka)
SShill1(x, Ka)
hill2(x, Ka, n)
SShill2(x, Ka, n)
hill3(x, Ka, n, a)
SShill3(x, Ka, n, a)

Value

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

Arguments

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)

Details

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: $$a / (1 + (Ka/x)^n)$$.

Examples

# \donttest{
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)))
# }