Real aquaporins conduct roughly a billion water molecules per second while excluding ions and even protons — a combination no synthetic membrane matches on its own. Three nanoscale mechanisms make it possible:
1. Single-file transport. The pore is barely wider than one water molecule, so molecules cannot pass each other — they move as a queue. Net flux follows the driving pressure Δp; this simulator enforces a hard minimum spacing between channel waters so they never cross:
x_i(t+dt) = x_i(t) + v_drift·dt + √(2D·dt)·ξ
v_drift ∝ Δp, D ∝ T (thermal jitter grows with temperature)
spacing constraint: x_i − x_{i−1} ≥ s_min (no overtaking)
2. Steric + dielectric ion exclusion. An ion must first physically fit (pore radius ≳ ion radius + hydration margin), then it still pays a Born-type desolvation energy for entering the low-dielectric protein interior instead of bulk water. This simulator models the pore's effective dielectric constant as relaxing toward bulk water as the pore widens:
ε_pore(r) = ε_water − (ε_water − ε_protein)·exp[−(r − r_ion)/λ]
ΔG_Born = e²/(8πε₀·r_ion) · (1/ε_pore − 1/ε_water)
P_reject = 1 − exp(−ΔG_Born / kT) (= 1 outright if r < r_ion + 0.1 nm, steric clash)
Widen the pore slider and Na⁺ rejection falls from ≈99% toward ≈30–40% as the dielectric penalty relaxes — this is why the real selectivity filter is held at only ~2.8 Å, not wider.
3. Bipolar water orientation blocks protons. Two conserved asparagine residues (the NPA motif) force channel water dipoles to point outward in each half of the pore — head-to-head at the channel center, shown here as arrows flipping direction at the midpoint. This breaks the continuous hydrogen-bond wire a proton needs for Grotthuss hopping, so protons cannot cross even though neutral water flows freely — a purely structural, not chemical, exclusion mechanism.
- Pore radius — sets both the steric cutoff and the dielectric-exclusion strength for ions.
- Driving pressure — the osmotic/hydrostatic gradient biasing net single-file water flow direction and speed.
- Electrolyte concentration — scales how many ions are visible attempting the pore.
- Temperature — sets thermal jitter (diffusion) of both water and ions.
This is a simplified illustrative model (bare ionic radii, an exponential dielectric-relaxation ansatz) built to reproduce the right qualitative behavior of real channel electrophysiology, not a literal molecular-dynamics reproduction.