  The amyloid $\beta$ peptide (A$\beta$42), whose aggregation is associated
with Alzheimer's disease, is an amphiphatic peptide with a high propensity to
self-assemble. A$\beta$42 has a net negative charge at physiological pH and
modulations of intermolecular electrostatic interactions can significantly
alter its aggregation behaviour. Variations in sequence and solution conditions
lead to varied macroscopic behaviour, often resulting in a number of different
mechanistic explanations for the aggregation of these closely related systems.
Here we alter the electrostatic interactions governing the fibril aggregation
kinetics by varying the ionic strength over an order of magnitude, which allows
us to sample the space of different reaction mechanisms, and develop a minimal
reaction network that explains the experimental kinetics under all the
different conditions. We find that an increase in the ionic strength leads to
an increased rate of surface catalysed nucleation over fragmentation and
eventually to a saturation of this nucleation process. More generally, this
reaction network connects previously separate systems, such as mutants of
A$\beta$42 and the wild type, on a continuous mechanistic landscape, thereby
providing a unified picture of the aggregation mechanism of A$\beta$42 and the
means of directly comparing the effects of intrinsic modifications of the
peptide to those of simple electrostatic shielding.
