Modulation of electrostatic interactions to reveal a reaction network unifying the aggregation behaviour of the Aβ42 peptide and its variants

Abstract

The aggregation of the amyloid β peptide (Aβ42), which is linked to Alzheimer's disease, can be altered significantly by modulations of the peptide's intermolecular electrostatic interactions. Variations in sequence and solution conditions have been found to lead to highly variable aggregation behaviour. Here we modulate systematically the electrostatic interactions governing the aggregation kinetics by varying the ionic strength of the solution. We find that changes in the solution ionic strength induce a switch in the reaction pathway, altering the dominant mechanisms of aggregate multiplication. This strategy thereby allows us to continuously sample a large space of different reaction mechanisms and develop a minimal reaction network that unifies the experimental kinetics under a wide range of different conditions. More generally, this universal reaction network connects previously separate systems, such as charge mutants of the Aβ42 peptide, on a continuous mechanistic landscape, providing a unified picture of the aggregation mechanism of Aβ42.

Fig. 1. Amino acid sequence and aggregation data for Aβ42. (a) Hydrophobic residues are shown in yellow, groups that are positively charged, negatively charged or having pK value close to neutral pH are shown in blue (+), red (–) and green (n), respectively. (b) The kinetic data for the aggregation of 3 μM Aβ42 in the presence of varying concentrations of salt, measured by ThT fluorescence; three replicates at each salt concentration are shown. (c) Cryo TEM images at a low (29 mM), intermediate (57 mM) and high (329 mM) ionic strength. The fibrils were obtained by aggregation of solutions with a monomer concentration of 10 μM (note: the large circular objects are particles of ice).

Fig. 2. Half time dependence on monomer and salt concentration. The top left panel (a) shows a typical kinetic trace, in this case at a free monomer concentration of 3 μM and an ionic strength of 14.5 mM. The half time of aggregation can easily be extracted from such traces and plots of its variation with varying salt or monomer concentration are shown in the top right (b) and bottom left panels (c) respectively. The average slope of the double logarithmic plot of half time against monomer concentration gives the scaling exponent, γ, whose variation with ionic strength is plotted in the bottom right panel (d). Note the curvature in (c), indicative of a scaling exponent that depends on the monomer concentration.

Fig. 3. A schematic depiction of the reaction network for the aggregation of Aβ42. The general network (top), the special case when both fragmentation and unsaturated secondary nucleation are important (centre), resulting in a parallel network, and the special case where saturation of secondary nucleation is important (bottom) but fragmentation is negligible. The ranges of approximate scaling exponents for each of these cases as the monomer concentration increases are given below each scheme. The rate constants given denote primary nucleation (k _n), elongation (k ₊), depolymerisation (k _off), fragmentation (k _–), single-step secondary nucleation (k ₂), and the rates associated with multi-step secondary nucleation: the monomer attachment (k _a) and detachment rate constants (k _d), and the nucleus conversion/detachment rate constant (k ₂).

Fig. 4. Global fits of the aggregation curves. (a) The top panel shows a global fit of the parallel limit, eqn (1), with three free parameters, to the all kinetic traces at 14.5 mM ionic strength. Shown below is a fit of just the half time behaviour for the same dataset. (b) The same data set as in (a) is fitted by the saturation limit, eqn (3). The fit of the network in the parallel limit (a) is significantly better than that of the saturation limit (b), the mean squared error in the parallel limit being half of that in the saturation limit. Note in particular how in the saturation limit we fail to reproduce the correct half times, as this limit cannot produce a decrease in scaling exponent with increasing monomer concentration. The saturation mechanism hence cannot explain the data at low ionic strengths. (c) By contrast to (b), a fit of the network in the saturation limit, eqn (3) with three free fitting parameters, to the data at 162 mM ionic strength shows good agreement with the experimental data. For clarity not all sampled concentrations are displayed in the plots of the full time-courses; the fits were, however, performed on the entire dataset (see the ESI, Sections 1.1 and 1.2, for plots of the full dataset and an explanation of the deviation of the parallel limit fits at high monomer concentrations).

Fig. 5. Dependence of the mechanism on ionic strength. Double logarithmic plots of half time versus initial monomer concentration for representative salt concentrations, one from each of the four regimes detailed in the main text. Above each plot a schematic of the secondary process dominating the aggregation network is displayed. The differing slopes and curvature can be explained by considering which secondary mechanism dominates the generation of new fibrils. From left to right: at an ionic strength of 14.5 mM, a combination of fragmentation and secondary nucleation, with fragmentation dominating at low monomer concentrations and secondary nucleation at high monomer concentrations results in negative curvature. At an ionic strength of 32 mM, non-saturated secondary nucleation alone, i.e. a single rate determining step (RDS), describes the data over the entire monomer range. At an ionic strength of 92 mM, secondary nucleation saturates as the monomer concentration increases, giving positive curvature. At an ionic strength of 312 mM, secondary nucleation is fully saturated over the entire monomer concentration range, again requiring only a single RDS.

Fig. 6. Effect of electrostatic screening on the microscopic rates. (a) The elongation rate constant as measured in strongly seeded experiments (blue dots, experimental details in ESI Section 3.2†). (b) The product of the elongation rate constant and the primary nucleation rate constant at different ionic strengths, obtained from global fits of the specific equation valid at each ionic strength: green dots correspond to the parallel limit (three lowest ionic strengths), blue dots to the saturation limit (three highest ionic strengths); the green-blue dots are an average of the fits of the two limits in the region of intermediate ionic strength where both limits are equally valid (three intermediate ionic strengths). The blue lines are straight line fits up to 100 mM ionic strength. (c) The Michaelis constant, K _M (blue dots), as obtained from global fits in the saturation limit at high ionic strengths (the region where the saturation limit is no longer valid is marked in red). As gives the monomer concentration at which saturation effects become important, the region of monomer concentrations used in this study is marked in blue. Values of K _M outside the sampled region are likely to be less accurate, as the variation of K _M in this region will have very little effect on the aggregation kinetics. The corresponding points are shown as empty circles. The binding constant of monomers to fibrils was measured independently by SPR, and computed from the rates of adsorption and desorption (purple squares). (d) Ratio of the rates of production of new free ends from secondary nucleation and fragmentation at ionic strengths of 14.5 mM, 32 mM and 162 mM, at monomer concentrations of 2 μM (light blue) and 5 μM (dark blue). The ratio of fragmentation to secondary nucleation decreases both with increasing monomer concentration and increasing ionic strength. At ionic strengths of 162 mM and above, fragmentation is too slow to be measured. Error bars in all cases are obtained from fitting subsets of the data (see ESI Section 4.3†).