Electrostatics controls the formation of amyloid superstructures in protein aggregation.

The possibility for proteins to aggregate in different superstructures, i.e. large-scale polymorphism, has been widely observed, but an understanding of the physicochemical mechanisms behind it is still out of reach. Here we present a theoretical model for the description of a generic aggregate formed from an ensemble of charged proteins. The model predicts the formation of multifractal structures with the geometry of the growth determined by the electrostatic interactions between single proteins. The model predictions are successfully verified in comparison with experimental curves for aggregate growth allowing us to reveal the mechanism of formation of such complex structures. The model is general and is able to predict aggregate morphologies occurring both in vivo and in vitro. Our findings provide a framework where the physical interactions between single proteins, the aggregate morphology, and the growth kinetics are connected into a single model in agreement with the experimental data.