Hill function — hill • sdbuildR

Computes the Hill function with configurable slope, midpoint, and upper asymptote.

Usage

hill(x, slope = 1, midpoint = 0.5, upper = 1)

Arguments

x: Value at which to evaluate the function
slope: Slope of Hill function at the midpoint. Defaults to 1.
midpoint: Midpoint of Hill function where the output is upper/2. Defaults to 0.5.
upper: Upper asymptote (maximal value) of the Hill function. Defaults to 1.

Value

Numeric value given by $$f(x) = \frac{upper \cdot x^{slope}}{midpoint^{slope} + x^{slope}}$$

Details

The Hill function is a smooth S-shaped curve (when slope > 1) bounded between 0 and upper. It transitions from near 0 to near upper around the midpoint, with the steepness of this transition controlled by slope. See https://en.wikipedia.org/wiki/Hill_equation_%28biochemistry%29 for more details.

Examples

hill(0)
#> [1] 0

# Adjust parameters
hill(0, slope = 5, midpoint = 0.5, upper = 10)
#> [1] 0