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. The pore's effective dielectric constant relaxes 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 as the dielectric penalty relaxes — this is why a real selectivity filter is held near ~2.8 Å, not wider. Correction to the source model's own narrative: evaluating this exact formula at the 2.8 Å default gives P_reject(Na⁺) ≈ 74%, not the ≈99% the original description claimed — the live chart and readout below plot the formula's actual output rather than repeat that figure, so what you see always matches what the sliders compute.
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; drag along the rejection-vs-radius chart to see where the current setting sits.
- 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, and enters the Boltzmann factor in the rejection formula directly.
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.