Hill’s equation describes how a substance or ligand will bind to a receptor protein in the presence of other ligands. This is called cooperative binding. The Hill coefficient is a numerical expression of the fraction of a macromolecule saturated by the ligand; it estimates the degree of cooperativeness in the binding process. A coefficient of 1 indicates binding is an independent process regardless of the presence of other ligands. Coefficients greater than 1 indicate a positive propensity to bind, while those less than 1 indicate a negative propensity.

Use the following equation to determine the Hill coefficient:

θ = [L]^n / [L]^n + Kd

where θ represents the percentage of occupied binding sites, L is the concentration of free (unbound) ligands, n is the Hill coefficient that represents the degree of cooperativity and Kd is the dissociation constant. Kd is equal to the ligand concentration when half of the binding sites are filled.

## Sciencing Video Vault

Assume L to be constant.

Solve the equation for n.