Protein Amyloid Aggregation
Knowles model: primary nucleation + elongation + secondary nucleation kinetics
Kinetic Parameters
Primary nuc. k_n:
1e-4
Elongation k_+:
1.00
Secondary nuc. k₂:
0.10
Initial monomer m₀:
1.00
Fragmentation k_f:
0.01
▶ Simulate
↺ Rerun
t₅₀ (half-max):
—
Final fibrils M(∞):
—
Peak nucleation:
—
Knowles model (2009):
dm/dt = −2k₊Pm − 2knmⁿᶜ − k₂Mmⁿ₂
dP/dt = k_n mⁿᶜ + k₂Mmⁿ₂ − k_f P
dM/dt = 2k₊Pm
m=monomers, P=fibril #, M=fibril mass
Secondary nucleation (k₂) creates
characteristic sigmoidal growth curve.