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Lock-and-Key Model

A simplified representation of receptor-ligand interactions, where the receptor's shape precisely complements the ligand's shape, ensuring specific binding.
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The statement of the theorem

Define the binding interaction between a receptor RR and a ligand LL as an equilibrium process: R+L⇌RL R + L \rightleftharpoons RL The binding affinity is characterized by the dissociation constant KD=[R][L][RL]K_D = \frac{[R][L]}{[RL]}. The geometric complementarity constraint dictates that the potential energy of interaction, U(r)U(r), must exhibit a minimum at the equilibrium distance r0r_0, and this minimum must be highly specific, such that the binding free energy ΔGbind=−RTln(1/KD)\Delta G_{bind} = -RT \text{ln}(1/K_D) is maximized only when the spatial coordinates rR\mathbf{r}_R and rL\mathbf{r}_L satisfy a geometric matching function G(rR,rL)=0\mathcal{G}(\mathbf{r}_R, \mathbf{r}_L) = 0.
Source: Wikipedia