What is Allostery, cooperativity?

A protein is allosteric when the binding of a ligand at one site changes the protein’s conformation and thereby its affinity at another site. When the sites are alike and the change raises the affinity of the others, binding is cooperative: the saturation curve is sigmoid rather than hyperbolic, and the protein switches from nearly empty to nearly full over a narrow range of ligand concentration. The Hill equation describes it:

where $Y$ is the fraction of sites occupied, $P$ the ligand concentration (or partial pressure), $P_{50}$ the value at half saturation, and $n$ the Hill coefficient — 1 for independent sites, up to the number of sites for perfect cooperativity.