Kinetics of aggregation of amyloid β under different shearing conditions: Experimental and modelling analyses

Amyloid β (Aβ40) is a class of amyloidogenic proteins known to aggregate into a fibrillar network. The rate of aggregation and fibril yield is sensitive to external energy input, such as shear. In this work, simple shear and shaking experiments are performed on Aβ40 solution using a Couette cell and an orbital shaker, respectively. Experiments show that, under uniform shear, both the mass of fibrils and aggregation rate increase with the shear rate. In the case of orbital shaking, the lag time decreases with the rotational speed of the shaker, but the final fibril mass is the same for all agitation speeds. To explain this contrasting behavior of aggregation kinetics, a population balance model is developed to account for the effect of shear on the aggregation of Aβ. The kinetic model includes primary nucleation, secondary nucleation, elongation, fragmentation, and depolymerization steps. The effect of steady uniform shear is encoded in the depolymerization rate constant (k_d), and it is shown that k_d decreases with shear rate initially and saturates at high shear rates. A competition between elongation and depolymerization rates yields different equilibrium masses of fibril at different shear rates. The model results agree quantitatively well with experimental data on the rate of aggregation and mass of fibrils as a function of shear rate. The modeling framework can be used to explain the shear rate-dependent aggregation of other amyloidogenic proteins.