The 3D version renders one lipid-bilayer patch and its single stochastic pore radius R(t). This 2D counterpart is a genuine, independently-computed population model — the kind of readout a real bulk dye-leakage or patch-clamp assay actually reports, which a single rendered pore cannot show. Every one of the population's vesicles carries its own R(t), evolved by the identical physical law used in the 3D engine (same constants, same line-tension-vs-peptide-tension energy balance):
E(R) = 2πγR − πτR² (pore free energy)
dE/dR = 0 → R* = γ/τ (critical / barrier radius)
τ = k·max(0, P/L − (P/L)crit(γ))
dR/dt = −M·(dE/dR) + thermal kick(T)
The main plot is the actual energy landscape E(R): each dot is one vesicle, plotted at its live (R, E(R)) — literally riding the curve. A vesicle to the left of the peak R* rolls back down toward R=0 (reseals); one that a thermal kick pushes past the peak accelerates down the far side into runaway rupture (R capped at 15.5 nm = catastrophic lysis). This is a direct visualization of Kramers barrier-crossing, the same statistical-mechanics framework used for electroporation and stochastic ion-channel gating — something the 3D scene's literal bilayer geometry never draws explicitly.
The lower strip is the population's live leakage kinetics: the sealed / transient-pore / ruptured fractions over time, exactly the curve shape read off a real calcein-leakage or patch-clamp bactericidal assay. Raising P/L or lowering γ shrinks R* below the population's typical seed fluctuation, so more vesicles cross the barrier and the ruptured fraction climbs faster — reproducing the dose-response relationship between peptide concentration and bactericidal membrane permeabilization.
- P/L slider — raises peptide surface coverage, shrinking R* (lowering the barrier) exactly as in dose-response leakage assays.
- Line tension γ — models lipid composition (cholesterol raises γ, resisting pore opening and raising the P/L needed for lysis).
- Temperature — scales each vesicle's independent random thermal kick, making barrier-crossing a true stochastic event rather than a deterministic switch.
- Population size — more vesicles give a cleaner statistical read of the sealed/transient/ruptured split, just as a larger liposome population sharpens a real leakage assay.
- Kick a fluctuation — nucleates a small seed pore (R≈0.9 nm) in every vesicle at once, letting you see directly whether the current γ, P/L put R* above or below that seed across the whole population.
Numerically verified: the analytic R*=γ/τ exactly matches the numeric argmax of E(R); the ensemble rupture fraction rises monotonically as R* falls below the seed radius, is ≈100% once R*<seed (deterministic runaway) and ≈0% once P/L sits below its γ-dependent threshold (τ=0, R*=∞, guaranteed reseal) — see the discrepancy note below.
Discrepancy from the 3D source, stated plainly: the 3D engine renders only a single patch, so it cannot show population heterogeneity or a leakage-kinetics curve at all — that is not a bug there, just outside its scope. Both engines share the exact same γ, τ, R*, mobility and noise-scaling constants; nothing about the underlying physics differs between them.