A mathematical model of the kinetics of β-amyloid fibril growth from the denatured state

Spontaneous conversion of beta-amyloid peptide (A beta) from soluble monomer to insoluble fibril may underlie the neurodegeneration associated with Alzheimer's disease. A complete description of A beta self-association kinetics requires identification of the oligomeric species present and the pathway of association, as well as quantitation of rate constants and reaction order. A beta was rendered monomeric and denatured by dissolution in 8 M urea, pH 10. Refolding and fibrillization were initiated by rapid dilution into phosphate-buffered saline, pH 7.4. The kinetics of growth were followed at three different concentrations, using size exclusion chromatography, dynamic light scattering, and static light scattering. A multi-step pathway for fibril formation and growth was postulated. This pathway included 1) rapid commitment to either stable monomer/dimer or unstable intermediate, 2) cooperative association of intermediate into a multimeric nucleus, 3) elongation of the nucleus into filaments via addition of intermediate, 4) lateral aggregation of filaments into fibrils, and 5) fibril elongation via end-to-end association. Differential and algebraic equations describing this kinetic pathway were derived, and model parameters were determined by fitting the data. The utility of the model for identifying toxic AP oligomeric specie(s) is demonstrated. The model should prove useful for designing compounds that inhibit AP aggregation and/or toxicity.