Preformed liposomes are loaded with a concentrated (NH₄)₂SO₄ solution, then the external buffer is exchanged for one with none — a steep transmembrane ammonium gradient. Neutral NH₃ is lipid-soluble and leaks out down its gradient; the NH₄⁺ left behind re-equilibrates (NH₄⁺ ⇌ NH₃ + H⁺), releasing a proton inside every time an NH₃ escapes. The liposome interior slowly acidifies. A weakly basic drug added outside (e.g. doxorubicin, pKa ≈ 8.3) is mostly neutral at physiological pH and diffuses freely across the bilayer — but once inside the acidified core it gets protonated, can no longer cross back out, and is trapped. This is remote (active) loading: near-quantitative encapsulation into intact, pre-made vesicles, no encapsulation during formation needed.
Henderson–Hasselbalch, unionised (membrane-permeant) fraction:
f_u(pH) = 1 / (1 + 10^(pKa - pH))
Net inward drug flux (only the neutral form crosses):
J = P_mem(T) · (f_u(pH_out)·C_out − f_u(pH_in)·C_in)
Interior acidification as the NH4+ pool is titrated by
escaping NH3 (simplified single-exponential approach to
a floor set by the initial ammonium load):
pH_in(t) = pH_floor + (pH_in0 − pH_floor)·exp(−k·t)
Once inside, low pH_in ⇒ f_u(pH_in) ≈ 0, so the drug is
kinetically trapped as its charged, membrane-impermeant form.
This 2D cross-section reuses the exact chemistry from the 3D version unchanged (pKa=8.3, pH_out=7.4, the pH-floor/rate/permeability curves) — checked with a standalone Node scratch script sweeping ammonium 50→400 mM and temperature 20→65 °C: pH_floor runs 5.6→2.5 monotonically, and the loading-efficiency curve always rises and plateaus below 100% (never overshoots or goes negative), so no correction was needed. Because the underlying model has no angular dependence — permeability and pH depend only on distance from the membrane — a 2D disk cross-section is a faithful, not a flattened, representation of the same radially-symmetric mechanism.
- Internal (NH₄)₂SO₄ — a bigger starting pool means more H⁺ released as NH₃ leaks out, so the interior settles at a lower (more acidic) floor pH and can trap more drug before the gradient runs out.
- External drug dose — more neutral drug outside means a steeper concentration term in the flux equation, so molecules cross faster — but total capacity is still capped by the ammonium pool.
- Temperature — bilayer permeability to the neutral drug and to NH₃ both rise sharply near/above the lipid's phase-transition temperature, which is why remote loading is normally run hot (55–65 °C for common formulations).
- Loading efficiency plateaus, it never reaches 100% instantly — once the ammonium pool is titrated and pH_in bottoms out, remaining free drug stops being pulled in.
Drag the liposome cross-section to pan, scroll/pinch to zoom.