Hill equation (biochemistry)

In biochemistry and pharmacology, the binding of a ligand to a macromolecule is often enhanced if there are already other ligands present on the same macromolecule (this is known as cooperative binding). The Hill equation, which was originally formulated by Archibald Hill in 1910 to describe the sigmoidal O₂ binding curve of haemoglobin, is used to describe the fraction of a macromolecule saturated by ligand as a function of the ligand concentration. The equation is useful for determining the degree of cooperativity of the ligand(s) binding to the enzyme or receptor. The Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites.

The Hill equation is formally equivalent to the Langmuir isotherm, and as a result, it is sometimes referred to as the Hill-Langmuir equation.

The Hill equation is commonly expressed in the following ways:

The equation's terms are defined as follows:

When appropriate, the value of the Hill coefficient describes the cooperativity of ligand binding in the following way:

Taking the reciprocal of both sides of the Hill equation, rearranging, and inverting again yields: ${\displaystyle {\theta \over 1-\theta }={[{\ce {L}}]^{n} \over K_{d}}={[{\ce {L}}]^{n} \over (K_{A})^{n}}}$.

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