Hill equation

The Hill Equation calculator compute the fraction of ligand binding sites on a receptor protein based on the free and half occupation ligand concentrations and the hill coefficient.

INSTRUCTIONS: Choose units and enter the following:

• (L) Unbound (free) ligand concentration
• (K_A) Ligand concentration producing half occupation
• (n) Hill coefficient

Fraction of Ligand Binding Sites (`theta`): The fraction is returned as a real number. 

The Math / Science

The Hill equation describes the binding of a ligand to a macromolecule is often enhanced  if there are already other ligands present on the same macromolecule. The hill coefficient provides a way to quantify this effect. A coefficient of 1 indicates completely independent binding, regardless of how many additional ligands are already bound. Numbers greater than one indicate positive cooperativity, while numbers less than one indicate negative cooperativity.
The Hill Equation formula is:
       `theta=1/((K_A/(|L|))^n+1)`,
where:

• `theta` = fraction of the ligand binding sites on the receptor protein which are occupied by the ligand
• `L` = free (unbound) ligand concentration
• `K_A` = ligand concentration producing half occupation
• `n` = hill coefficient

References

Wikipedia (https://en.wikipedia.org/wiki/Hill_equation_(biochemistry))