This 2D companion strips the 3D sinusoid-and-hepatocyte scene down to the exact two-stage funnel real LNP formulators screen against: a flat side view of a liver sinusoid feeding into a hepatocyte, computed with the identical probability model as the 3D simulator.
1) Fenestral sieving (liver sinusoidal endothelium):
P_uptake(d) = 1 / (1 + exp((d - 120nm) / 15))
— particles below the ~100-150nm fenestrae cutoff
reach the space of Disse and hepatocyte surface freely.
2) Ionizable lipid protonation (Henderson-Hasselbalch):
f_protonated(pH) = 1 / (1 + 10^(pH - pKa))
— neutral at blood pH 7.4 (low immunogenicity/toxicity),
cationic once the endosome acidifies to pH ~5.5-6.0.
3) Endosomal escape (cone-shaped lipid → hexagonal HII phase):
P_escape = exp(-(pKa - 6.5)^2 / (2·0.5^2)) · NP_factor(N/P)
NP_factor = 1 / (1 + exp(-(N/P - 3) / 0.8))
— protonation must land inside the endosome's transit pH
window AND the particle needs enough excess cationic
charge (N/P) to destabilize the anionic endosomal
membrane before it fuses with a lysosome.
- pKa slider — shifts where protonation happens; too low never protonates before lysosomal fusion, too high causes premature/serum protonation and toxicity. Peak escape sits near pKa ≈ 6.5, matching clinically used ionizable lipids (e.g. the ones in approved siRNA and mRNA-LNP products).
- N/P ratio slider — the molar ratio of ionizable-lipid nitrogens to nucleic-acid phosphates; too low under-encapsulates and under-charges the particle, so escape stays weak even at an ideal pKa.
- Particle diameter slider — sets how much of the circulating dose ever reaches a hepatocyte through the sinusoidal fenestrae, independent of the chemistry.
- Dose density slider — how many particles are in circulation at once; it changes throughput, not per-particle odds.
Cytosolic yield = uptake × escape — the fraction of the injected dose that actually reaches the cytosol where Cas9/mRNA machinery can act. Drag the view to pan and scroll to zoom in on individual particles crossing the fenestrae or sitting in the endosome.