The Oosawa-Kasai model describes nucleated polymerization in two phases: (1) slow nucleation — n* monomers must assemble into a thermodynamically unfavorable nucleus; (2) rapid elongation — fibrils grow by monomer addition at rate k_e. The lag phase duration t_lag ~ k_nuc^(−1/n*). This underlies amyloid formation in Alzheimer's (Aβ), Parkinson's (α-synuclein), and prion diseases. Adding seeds bypasses the lag phase entirely.