Host receptors (the rings/cages, fixed in a grid) recognise guest
molecules (small drifting spheres) through shape-matched, non-covalent
interactions — H-bonds, electrostatics, van der Waals — never a
covalent bond. When a guest diffuses close enough to an empty host it
can dock (dashed lines mark the non-covalent contacts); thermal motion
can also kick it back out. The equilibrium is a tug-of-war between
binding affinity and temperature, exactly as in real host–guest
chemistry (crown ethers with cations, cyclodextrin cavities with
hydrophobic guests, self-assembling cages).
Host + Guest ⇌ Host·Guest Ka = [Host·Guest] / ([Host][Guest])
P(bind | dt) ≈ Ka · (1 − 0.7·T_norm) · dt
P(release | dt) ≈ T_norm · dt / Ka
ΔG ≈ −RT·ln(Ka) (deeper binding ⇒ more negative ΔG, shown as −kcal/mol)
- Binding affinity (Ka) — how strongly the host recognises the guest; higher Ka favours binding over release.
- Temperature — more thermal jitter both speeds diffusion and increases dissociation, lowering the bound fraction at equilibrium.
- Guest concentration — more free guests in solution raises the chance any given host finds a partner.
- Host type — swaps the receptor geometry (ring, cup, cage) without changing the underlying binding kinetics.