TABLE I.

Criteria for Michaelis-Menten type kinetics are only fully satisfied by the elongation reaction. Secondary nucleation does not satisfy assumption 7 and is therefore described by the closely related Hill type kinetics instead. Primary nucleation only satisfies assumptions 4 and 5 when heterogeneous and not homogeneous. Assumption 6 is generally satisfied when the concentration of the catalyst-bound substrate is low. This may not be the case for heterogeneous primary nucleation in general, but it is for Aβ40; if the monomer-bound catalyst was present at a significant concentration relative to monomers, an extended slow increase in the fibril mass concentration toward the end of the reaction would be visible, as remaining monomers detach from the interface and attach to the ends of growing fibrils. This effect is not seen in the aggregation kinetics of Aβ40 suggesting that the concentration of surface-bound monomers is low. Assumption 6 is also satisfied for elongation due to the comparatively low concentration of growing filament ends, and for secondary nucleation because at the early times at which secondary nucleation plays a significant role, the fibril mass concentration is still much lower than the monomer concentration.

Criterion for Michalis-Menten kinetics	1° nucleation	Elongation	2° nucleation
1: Reversible initial step	✓	✓	✓
2: Irreversible final step	✓	✓	✓
3: Unimolecular final step	✓	✓	✓
4: Substrate-catalyst binding in initial step	(✓)	✓	✓
5: Final step regenerates catalyst	(✓)	✓	✓
6: Quasi steady-state bound catalyst	(✓)	✓	✓
7: Substrate-catalyst binding is bimolecular		✓