Prion Propagon Population Spectrum (2D)

Propagation Parameters

Elongation rate k₊ 1.0

Fragmentation rate k_frag 0.6

Cell-division interval 14 s

Culture State

Propagons (fibril seeds)

Free monomer pool

240

Mean fibril length

0.0

Generation

Cell is prion-free [psi-]

How it works

This is the same nucleated-conformational-conversion model as the 3D swarm version, viewed as population statistics instead of individually rendered monomers. Once a fibril ("propagon") exists, it grows by capturing free monomer onto its ends and is periodically sheared by chaperones into two shorter fibrils — every break mints a brand-new growing end:

dL/dt = k+ · [monomer] · (growing ends)
Fragmentation rate per fibril ≈ k_frag · (L − 1)
New propagons created by a break = +1 per fragmentation event

Instead of tracking 3D positions of 240 monomers, this view tracks only what is physically meaningful for propagation: the length spectrum of every fibril (top bar chart — one bar per propagon, colored by lineage) and the propagon count over time (bottom strip chart, with division events marked). Both panels are driven by the exact same stochastic rules as the 3D model.

Elongation rate k+ — how fast free monomer is captured onto fibril ends.
Fragmentation rate k_frag — how often fibrils are cut; too low and propagons cannot keep pace with dilution.
Cell-division interval — every division randomly keeps each existing propagon with 50% probability (the rest release their monomers back to the free pool) and dilutes the free pool by 15%.
Inject Misfolded Seed — adds one new length-1 fibril, mimicking exposure to an infectious/misfolded template.

The outcome is a threshold effect: if k_frag is too low relative to the division rate, stochastic loss during partitioning drives propagon count to zero — the population "cures" itself ([psi-]) even though monomer is still abundant. If k_frag is high enough, propagon number is replenished faster than dilution removes it, and the prion state is mitotically stable indefinitely.

Free monomer pool (bottom strip) Propagon / fibril length (top spectrum)