Lysosomal Membrane Permeabilization by Nanoparticles

Nanoparticle Dose

Particle count 30

Particle size (nm) 40

Surface reactivity 0.55

Intralysosomal dissolution 0.30

Membrane State

Membrane integrity100%

Pore events

Cathepsin released

Elapsed (min)

0.0

Diffusion D (µm²/s)

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How it works

Endocytosed nanoparticles are trafficked into lysosomes, where the acidic lumen (pH ≈ 4.5) can both dissolve the particle and destabilize the phospholipid membrane — the "Trojan horse" mechanism of nanotoxicity. This simulator models cumulative membrane damage D(t) (0 = intact, 1 = failed) from particle–membrane contacts plus ion release from intralysosomal dissolution, competing against a constant lipid-repair rate:

dD/dt = k0 · R · S(r) · C(t) · [1 + β·diss] − k_repair · (1 − D)
S(r) = 1/√(r / r0)   (smaller, higher-curvature particles pack tighter contact area)
C(t) = particles currently adsorbed to the membrane (within contact shell)
Pore nucleation rate  λ(D) = λ_max · exp(6·(D − 1))   (Poisson process)

Free nanoparticles undergo Brownian motion inside the lysosome; each is displaced every frame by a random step scaled to the Stokes–Einstein diffusion coefficient D = k_BT / (6πηr), so smaller particles jitter faster and reach the membrane sooner. As D(t) rises, the instantaneous pore-nucleation rate λ climbs sharply (an exponential rupture-threshold model consistent with lipid-bilayer failure statistics); each nucleated pore is drawn as a breach and releases a burst of cathepsin markers (red) that diffuse from the lysosome into the surrounding cytosol — the step known experimentally to trigger cathepsin-dependent apoptosis.

Particle count / size — dose and geometry: more particles and smaller radii raise both contact frequency and the S(r) curvature term.
Surface reactivity — stand-in for surface charge/redox activity (e.g. cationic vs. anionic coatings); directly scales the damage rate k0·R.
Intralysosomal dissolution — represents composition-dependent ion release in the acidic lumen (high for ZnO/CuO-type oxides, near zero for inert gold), adding to membrane stress.

This is a simplified, illustrative rate model — real LMP kinetics depend on lipid composition, particle coating chemistry and cell type — but the qualitative behaviour (dose- and reactivity-dependent damage accumulation, a rupture threshold, and stochastic pore nucleation) matches the mechanism reported across the nanotoxicology literature for cationic polymers, metal-oxide nanoparticles and some carbon nanomaterials.

Nanoparticle Cathepsin (post-release) Lysosomal membrane

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