Allostery

allostery is coupling in which a perturbation at one region of a protein changes a functional property elsewhere. It can act through altered conformational ensemble populations and need not require a large change in the mean structure.

A molecule binding away from the principal ligand site and changing its affinity or efficacy. The direction and size of modulation can depend on the orthosteric ligand and measured response.

Coupling between equilibria such that favouring one state changes another measured equilibrium. For example, preferential ligand binding to an assembled state can shift an assembly equilibrium; the coupling follows from consistent free-energy differences around the thermodynamic cycle.

Binding at one site changes binding at another. Positive cooperativity can produce a steep occupancy response. Several independent sites alone do not establish cooperativity.

An empirical occupancy relation, with half-occupancy concentration $K_{1/2}$ and Hill coefficient $n$. A fitted $K_{1/2}$ need not be an individual site's microscopic dissociation constant.

The positive concentration giving half of the maximal response in a Hill equation. This effective threshold need not equal an individual binding site's microscopic dissociation constant.

A Hill activation function is an increasing saturating input function for phenomenological regulation of gene expression. For positive $K,n$, its value is one-half at $u=K$. The Hill coefficient controls steepness; it need not equal a literal molecular binding-site count.

The slope of $\log [\theta /(1-\theta )]$ against $\log [L]$ in a Hill equation description. A value above one supports positive cooperative binding under the model's assumptions. It does not by itself count occupied sites or identify a molecular mechanism.