The amyloid β peptide M1-42 with sequence MDAEFRHDSGYEVHHQKLVFFAEDVGSNKGAIIGLMVGG VVIA (here referred to as Aβ42) was expressed in an Escherichia coli BL21 Gold (DE3) strain from a synthetic gene and purified using ion exchange and size exclusion as described elsewhere (Walsh et al., 2009).

Lyophilised Aβ42 peptide was dissolved in 1 mL 6 M GuHCl and monomeric peptide was isolated by size-exclusion chromatography in degassed buffer (20 mM sodium phosphate, 200 μM EDTA, 0.02% sodium azide, pH 8.0) on a Superdex 75 10/300 GL column (GE Healthcare). The center of the peak was collected, and the peptide concentration was determined by integrating the area under the absorbance curve using ε₂₈₀ = 1,440 L mol^–1 cm^–1. The collected Aβ42 monomers were kept on ice and used the same day. Samples of 3 μM monomeric Aβ42 in presence of varying concentrations of urea, urea and NaCl and GuHCl were prepared. Additionally, dilution series of 1.6–5 μM Aβ42 in presence of 0.25 M, 1 M, 2 M, and 3 M GuHCl and 1.6–18 μM Aβ42 in the presence of 0.25 M, 1 M, 2 M, and 3 M urea were prepared. The wider range of peptide concentrations used in the presence of urea was motivated by the slower kinetics. All samples were prepared in low-binding tubes (Axygen) and supplemented with 6 μM thioflavin T (ThT, CalBiochem) from a concentrated stock that had been filtered through a 200 nm syringe filter.

Eighty microliter of each sample was carefully pipetted into multiple wells of a 96-well half-area, low-binding, polyethylene glycol coated plate (Corning 3881), and the aggregation kinetics was studied by following the ThT fluorescence at 37°C under quiescent conditions in a plate reader (Fluostar Optima, Fluostar Omega, BMG Labtech). The ThT fluorescence was measured through the bottom of the plate using a 440 nm excitation filter and a 480 nm emission filter. Each experiment was repeated at least twice with 3–4 repeats of each sample.

Aβ42 seeds were prepared in buffer (20 mM sodium phosphate, 200 μM EDTA, 0.02% sodium azide, pH 8.0) without denaturant and with 0.25 M, 1 M, 2 M, or 3 M urea or 0.25 M, 1 M, or 2 M GuHCl at 37°C under quiescent conditions in a plate reader using ThT fluorescence as a validation of fibril formation. About 0.2–30% preformed seeds were added to 3 μM Aβ42, supplemented with 6 μM ThT, and the aggregation was followed as described above. The fraction of monomers in seeds at time zero is thus equal to (added amount of seeds)/(monomer + added amount of seeds). For technical reasons, investigations of the saturation of the elongation constant at high Aβ42 concentrations are difficult. Addition of seeds is necessary to investigate the effects on the elongation step alone, but at high Aβ42 concentrations addition of seeds results in very high aggregation rates, meaning the reaction is complete before sufficient data can be acquired.

The half time of aggregation (t_1/2) is defined as the point where the ThT value is halfway between the initial baseline and the plateau value. The scaling exponent, γ, was obtained by plotting the t_1/2 of each concentration against the initial monomer concentration (m₀) on a double logarithmic plot and fitting a straight line to the data points:

The differential equations describing the time evolution of aggregate mass concentration, M(t), and aggregate number concentration, P(t) are

for a single step nucleation process, or more generally

for a multi-step secondary nucleation process, along with

where k_n, k₂, k₊ are the rate constants for primary nucleation, secondary nucleation and elongation, respectively. K_M is the saturation constant for secondary nucleation and n₂ and n_c are the monomer scaling exponents (reaction orders) of primary and secondary nucleation, respectively. These models are used to fit the overall ThT fluorescence curves. Consequently, the rate constants are weighted averages over any conformations that are present in the fibrillar or monomeric state. An approximate solution to Equations 3, 4 is:

where the parameters are defined by

where P₀ is the aggregate number at the start of the reaction, P_∞ is the aggregate number at equilibrium as described in Meisl et al. (2014), that is, after reaction completion, M₀ is the mass concentration of fibrils at the start of the reaction and M_∞ is the mass concentration of fibrils at equilibrium. The reaction order of secondary nucleation n₂ = 2, as previously established, was consistent with all data. The reaction order for primary nucleation, n_c was fitted in the presence of denaturant and generally found to increase with denaturant concentration.

Monomeric Aβ42 peptide was isolated in 20 mM sodium phosphate buffer, 200 μM EDTA, 0.02% sodium azide, pH 8.0 by size-exclusion chromatography as described above. The sample was diluted with buffer and denaturant and ThT was added. The final concentrations were 1 M and 3 M of GuHCl or urea, or 1 M urea + 1 M NaCl, 9-10 μM Aβ42 and 1 μM ThT, pH 8.0. The aggregation kinetics were recorded using a Fluostar Optima plate reader (BMG Labtech) at 37°C under quiescent conditions. Samples for cryo-TEM were taken once the aggregation reaction had reached the fluorescence plateau. Five microliters were loaded on a lacey carbon filmed copped grid and flash frozen in liquid ethane at −180°C. The frozen samples were stored in liquid nitrogen and images were taken by a 120-kV electron microscope (Philips CM 120 BioTWIN Cryo). Alternatively, a Fischione Model 2550 cryo transfer tomography holder was used to transfer the specimen into the electron microscope (JEM 2200FS) equipped with an in-column energy filter (Omega filter), which allows zeroloss imaging. The acceleration voltage was 200 kV for the JEM2200FS electron microscope and zero-loss images were recorded digitally with a TVIPS F416 camera using SerialEM under low dose conditions with a 30 eV energy selecting slit in place.

The SPR experiments were performed using a Biacore3000 instrument (GE Healthcare), and CM3 sensorchips with carboxylic acid groups on short dextran chains. The four lanes of the sensorchip surface were activated with a mixture of 0.2 M 1-Ethyl-3-(3-dimethylaminopropyl)-carbodiimide and 0.05 M N-hydroxysuccinimide in water, followed by injection of short fibrils, ca 50 nm, produced by vigorous shaking of a fibrillar sample, at 0.5 μM in 10 mM NaAc, pH 4, to enable coupling of the fibrils via primary amines. The injection of fibrils led to an increase of ca. 3000 RU, after which the remaining functional groups on the sensorchip were reacted with 50 μl of 1 M ethanolamine, and the buffer flow was changed to 20 mM sodium phosphate, 200 μM EDTA, 0.005 % Tween20, pH 8.0. Monomers were added to grow the fibrils on the chip until a signal of ca. 20000 RU had been added. The sensorchip was then used to study monomer association and dissociation kinetics by injection of monomer at a series of concentrations, in flow buffer with 1, 2 or 3 M urea or 1 M GuHCl, after which the dissociation was followed during buffer flow with the same denaturant concentration as during the injection. For the data analysis, we solved the rate equations describing linear growth/dissociation of fibrils, with binding/dissociation of monomeric species to their surface. The relevant differential equations are given in (He et al., 1997), which are expanded to allow for two classes of binding sites at ends and sides of fibrils. The equations can be solved noting that during the dissociation phase m₀ = 0 and during the association phase m₀ = constant. In practice, because the amount of fibrils detected in the SPR measurement may vary between measurement cycles and between repeats, the concentration of bound monomer m_b, is given by the differential equation

where α is the number of monomer binding sites per monomer in the fibril and k_a and k_d are the rate constants of monomer association and dissociation, respectively. M₀, P₀ and m₀ denote the mass concentration of fibrils, the number concentration of fibrils and the monomer concentration. This equation takes into account the change in the length of the absorbed fibrils by addition (k₊) or dissociation (k_off) of monomer from the fibril ends. In the association part of the reaction this equation can be solved for m_b(0) = 0, to give the equation that describes the baseline corrected SPR data as

where c₁ and c₂ are constant dependent on the above constants and the conversion of bound concentrations to SPR signal. In the dissociation case we set m₀ = 0 giving

where a₁, a₂ and a₃ are constants and the conversion of bound concentrations to SPR signal. In both cases the parameters of interest are the association/dissociation rate constants in the exponential, k_a and k_d.

In our computer model of secondary nucleation (Šarić et al., 2014), each protein particle is represented by a hard spherocylinder (see Figure 10A) and a protein can exist in three different conformations/states: (i) the unfolded state represents unfolded protein monomers that are able to bind to the fibril surface and aggregate into micellar-like oligomers by virtue of tip-to-tip non-specific interactions; (ii) the intermediate state which represents partially folded proteins that more readily assemble into oligomers but have a lower affinity for the fibril surface, and (iii) the β-sheet state that is able to assemble into compact elongated fibrillar structures due to strong directional interactions. The interconversion rates of these states are governed by their respective internal free energies. Nominally, we set the internal energies to f_s = 0 for the monomeric state, f_i = 1kT for the intermediate state, and f_β = f_i + 10kT for the β-sheet state. This introduces an energy penalty to forming a fibrillar aggregate from monomeric proteins, which can be overcome through a nucleation process. This nucleation process involves binding and oligomerisation of monomeric protein on the fibril surface, the conversion of surface-oligomers to more tightly bound intermediate oligomers, their detachment from the fibril surface, and finally a conversion of detached intermediate oligomers into compact, thermodynamically stable fibril nuclei.

We capture the influence of denaturant in our simulations by changing the internal energy of the monomeric state as f_s→f_s + Δf_den, where Δf_den < 0 represents the stabilising effect of the denaturant. More details can be found in our previous work (Šarić et al., 2016a).

We start our simulations with a preformed fibril at the middle of the simulation box and allow monomeric proteins to adsorb to the fibril until they reach a chemical equilibrium. After the equilibration phase we turn on the possibility of interconversions between different protein states. The rate of nucleation is recorded as the inverse of the first-passage time it takes for the fibril nucleus consisting of two mutually-interacting β-sheet proteins to be formed. Several simulations were run at different starting concentrations of the monomeric protein, allowing us to extract the reaction order and the average size of the critical nucleus at each value of Δf_den. For each set of simulation parameters, we ran 9 Monte-Carlo simulations at different random seed concentrations.

Before investigating the kinetics and mechanism of assembly, we determined the morphology of the formed fibrils and their ability to bind monomers on their surface, as a function of the denaturant concentration. To determine the fibril morphology, fibrils were formed from 9 to 10 μM Aβ42 monomers in 0.25, 1, 2, or 3 M urea or 0.25, 1, 2, or 3 M GuHCl and observed using cryo-TEM.

Fibrils formed in phosphate buffer with urea are found to be structurally similar to fibrils formed in phosphate buffer alone with filaments twisted around each other forming visible nodes in cryo-TEM images. Increasing urea concentration is observed to result in longer fibrils, suggesting a decrease of the nucleation rates relative to the growth rate (Figure 1 and Supplementary Figure 1). The fibrils formed in urea also appear more dispersed and evenly distributed over the grids than fibrils formed in phosphate buffer, which often occur as large dense aggregate clusters. Fibrils formed in phosphate buffer with GuHCl are on average shorter than fibrils formed in phosphate buffer (Figure 1). At 0.25 and 1 M GuHCl the overall appearance of the fibrils resembles the morphology of fibrils formed without denaturant present, displaying two filaments wound around each other and twisted to different degrees. The morphology of fibrils formed in 2 M GuHCl differs remarkably from fibrils formed in buffer, appearing more rigid, less twisted and sometimes containing more than two filaments. These images were used to estimate fibril length for analysis of the elongation rate constant k₊ (Supplementary Figure 2). The appearance of fibrils formed in a solution containing both 1 M urea and 1 M sodium chloride resembles fibrils formed in 1 M GuHCl (Supplementary Figure 3).

The surface of Aβ42 fibrils plays an important role as a catalytic site for secondary nucleation. This process is believed to involve the adsorption of smaller Aβ42 species to the surface of fibrils, where nucleation takes place. In order to determine to what extent this adsorption is affected by the presence of denaturant, we performed surface plasmon resonance (SPR) experiments in the absence and presence of denaturant at several concentrations. Taking into account the growth and dissociation of fibrils, we were able to determine the rate constants for adsorption and dissociation of surface-bound species. The ratio of the dissociation and association rate constants was used to estimate the apparent equilibrium dissociation constant, K_D. We find that K_D increases significantly in the presence of denaturant, thus reflecting a reduced affinity for the fibril surface, consistent with a stabilisation of the free over the bound state and decreased surface coverage, i.e., decreased number of surface-bound peptides per unit length of fibril (Figure 2). To also highlight the effect of the ionic strength of the solution on this affinity, which is likely to be important for low concentrations of GuHCl, we also show previously determined K_D values at high ionic strengths but in the absence of denaturant.

To investigate the effect of the two denaturants on the kinetics, the aggregation of 3 μM Aβ42 was studied in 0–3 M urea or 0–3 M GuHCl (Figure 3). Aggregation in at least two independent experiments of triplicate repeats were monitored using ThT fluorescence. To quantify the aggregation propensity, the half time of aggregation is used, which is defined as the time by which half the final aggregate concentration has formed. We find that addition of urea monotonously decreases the aggregation rate of Aβ42 while addition of GuHCl increases the aggregation rate at low GuHCl concentrations and decreases the aggregation rate at GuHCl concentrations above 1 M. The maximum aggregation rate is reached at approximately 0.25 M GuHCl. This difference is likely to originate from the fact that GuHCl is charged, whereas urea is not. As we have shown previously (Meisl et al., 2017a), electrostatic shielding by charged molecules, in this case GuHCl, speeds up the rate of Aβ42 aggregation. Indeed, we find that aggregation in the presence of an equimolar mixture of sodium chloride and urea mimics the behaviour of GuHCl (Figure 3B).

The aggregation of Aβ42 in presence of urea was followed by the ThT fluorescence intensity (Supplementary Figure 4), which was shown to be proportional to the total fibrillar mass (Supplementary Figure 5). The aggregation kinetics were studied at 0, 0.25, 1, 2, and 3 M urea over time at a range of protein concentrations (1.6–18 μM). All experiments started from supersaturated monomer solutions and were conducted at 37°C under quiescent conditions. These experiments showed decreasing ThT intensity with increasing urea concentrations, which was found not to be caused by any major increase in solubility, as confirmed by SDS-PAGE, but is instead believed to be an effect of altered ThT binding or fluorescence quantum yield (Supplementary Figure 6).

The dependence of the half time on the monomer concentration, described by the scaling exponent, provides insight into possible mechanisms of aggregation. The scaling exponent varies with urea concentrations (Figure 3C). Moreover, the scaling exponent shows some concentration dependence in the absence of denaturant, evident in the curvature of the double logarithmic plot of monomer concentration against half time. This curvature indicates that one or more of the microscopic steps involved in the aggregation process may become saturated at high concentrations of monomeric peptide (Meisl et al., 2017b). The reported scaling exponents are thus averages over the whole concentration range sampled. Upon addition of urea the scaling exponent decreases, i.e., becomes more negative with a higher absolute value. The decreased scaling exponent indicates that the monomer dependence of the Aβ42 aggregation process increases in the presence of urea.

In order to obtain quantitative mechanistic insights into the influence of urea on the Aβ42 aggregation process, we fitted the kinetic traces for Aβ42 in 0, 1, 2, and 3 M urea using the Amylofit platform (Meisl et al., 2016b). The kinetics are well fitted by the following model: Monomeric proteins nucleate in solution to form fibrils in the process of primary nucleation. These fibrils can then grow by the addition of monomeric proteins onto the end of existing fibrils in the process of elongation. Finally, existing fibrils can self-replicate by catalysing the formation of new nuclei on their surface via secondary nucleation. This secondary nucleation process consists of several steps in series with an initial attachment step to the fibril surface, followed by a rearrangement/detachment step (Figure 4A). Depending on the conditions, the relative balance between these steps can be shifted. When the catalytic fibril surface is fully covered, the overall behaviour is dominated by the rearrangement/detachment step, which we refer to as the saturated regime. When the surface is not fully covered, the overall rate also depends on the attachment step, which we refer to as the unsaturated regime. The aggregation of Aβ42 over a small range of monomer concentrations, in the absence of denaturant, can be explained by a model that operates exclusively in the unsaturated regime (Cohen et al., 2013). However, to explain the data obtained over a large range of Aβ42 concentrations and in the presence of denaturant the possibility of saturated secondary nucleation needs to be included. All kinetic curves at all peptide concentrations ranging from 1.6 or 2 μM to 18 μM (except for at 3 M urea where the fitted concentration range was 3.6–18 μM) were fitted by this model including primary nucleation, elongation and surface-catalyzed secondary nucleation (Figure 4 and Supplementary Figure 7). The parameters of the model are the rate constants of the three processes, elongation (k₊), primary nucleation (k_n) and secondary nucleation (k₂), the concentration at which secondary nucleation is half saturated (K_M^1/n2), and the reaction orders of primary nucleation, n_c, and secondary nucleation, n₂. The data at all conditions is consistent with a multi-step secondary nucleation model with n₂ = 2, in line with previous findings for Aβ42 aggregation in phosphate buffer (Cohen et al., 2013; Meisl et al., 2016a,2017a; Yang et al., 2018). The reaction order of primary nucleation has been previously determined to be n_c = 2 in the absence of denaturant and we here found it to increase above this value with increasing urea concentration.

We note that in aqueous solution, urea decomposes into ammonium and cyanate, which leads to carbamoylation of proteins by cyanate. The effect at early time points is likely to be minor, and we therefore focus our analysis on data up to maximum 38 h. At 2 and 3 M urea, the kinetic traces show a prolonged drift in the region where the ThT signal would normally plateau; therefore, normalisation and fitting of the data in the standard way was not possible. We instead focus on the initial part of these kinetic curves, before the half time is reached as data up to the half time generally give sufficient constraints to determine a mechanism and its rates, and this treatment avoids problems resulting from the drift behaviour. Because the possible molecular reasons for such a drift include sedimentation, clumping, gelation, etc. which are not part of our models, the traces past the initial sigmoidal part cannot be described by these models. The full data are shown in (Supplementary Figure 4).

Measurement of the total aggregate amount, as we obtain here from ThT measurements, only provides information on the combined rate constants of primary nucleation and elongation, k₊k_n, and of secondary nucleation and elongation, k₊k₂. The individual rate constants can be estimated using seeding experiments, although uncertainties on the values of these parameters are generally much larger than for the combined rate constants as the determination of the individual rate constants requires estimation of the average length of seed fibrils used, which is complicated by clumping of fibrils. Seeding experiments were performed for 3 μM Aβ42 monomers with preformed fibrils at 0, 0.2, 1, 5, and 30% in monomer equivalents (Figure 5 and Supplementary Figure 8). The seeds were prepared in solutions with the same concentration of urea as in the kinetic measurements that they were subsequently used in. We find that the half time is shortened by addition of preformed seeds at all urea concentrations studied. Even at low concentrations of preformed seeds, the seeding effect is strong, confirming that the dominant process generating new aggregates is indeed still secondary nucleation. The seeding propensity of a given amount of seeds increases with increasing urea concentrations, which is likely due to the lower abundance of densely packed fibril clusters within the seed aliquot, making more seed fibrils accessible for secondary nucleation the higher the denaturant concentration. The fits to the seeded data are generally of a similar quality to those of the unseeded data. As summarised in Supplementary information, the model used to fit all data is consistent both with the unseeded and seeded aggregation data and both types of data yield comparable rate constants.

The elongation rate constants were estimated from heavily seeded aggregation experiments and TEM measurements (Meisl et al., 2014) as outlined in (Supplementary Figures 1, 2). The elongation rate was found to vary by less than an order of magnitude for all urea concentrations investigated (Figure 6). Thus, the reduced aggregation rate caused by addition of urea originates primarily from decreased rates of primary and secondary nucleation.

As the secondary nucleation rate saturates at different concentrations depending on the urea concentration, the actual rate of formation of secondary nuclei, rather than the rate constant, is the most meaningful quantity to compare. Thus, the predicted rates of secondary nucleus formation at 10% conversion of an initially monomeric sample, at a total monomer concentration of 5 μM, are computed from the fitted rate constants and shown in Figure 6E. Increasing urea concentration results in decreased rate of secondary nuclei generation. Because the reaction orders change with urea concentration, we also show the rate, rather than rate constant, of primary nucleus formation at 5 μM monomer concentration in Figure 6C. Also in this case, the rate decreases with increasing urea concentration, by approximately two orders of magnitude between 0 and 3 M urea.

Aβ42 aggregation kinetics of 1.6–5 μM Aβ42 in the presence of 0, 0.25, 1, 2, and 3 M GuHCl was studied by monitoring the ThT fluorescence intensity (Supplementary Figure 9), which was established to be proportional to the fibrillar mass at GuHCl concentrations <3 M (Supplementary Figure 5). At low GuHCl concentrations (0.25 and 1 M) the overall aggregation rate of Aβ42 is accelerated whereas at high GuHCl concentrations (2 and 3 M) the overall aggregation rate is decreased. 3 M GuHCl is experimentally difficult to work with, markedly reduces the ThT signal intensity, and the altered morphology of the fibrils results in difficulties in measuring the fibril length which is needed for any additional analysis. Thus, the aggregation experiments in 3 M GuHCl were not used in the following more quantitative analysis.

The non-monotonic aggregation behaviour in GuHCl contrasts with the effect of urea, and, as discussed later, is likely due to the charged nature of GuHCl. While at high GuHCl concentrations the scaling exponent is the same as in the absence of GuHCl, at intermediate GuHCl concentrations, the scaling exponent increases, i.e., it becomes less negative (Figure 3D). This indicates that the aggregation rate is less monomer dependent.

Global analysis using Amylofit (Meisl et al., 2016b) allows us to describe all kinetic data at all concentrations for Aβ42 aggregation in GuHCl using a multistep secondary nucleation model with n₂ = 2 (Figure 7 and Supplementary Figure 10). Although, as previously demonstrated, Aβ42 aggregation in the absence of denaturant is well fitted by a model describing secondary nucleation as a one-step event for Aβ42 concentrations between 1 and 5 μM, for consistency we use here the same, more general model as for urea. This model is able to describe the data at all denaturant concentrations. The different morphology of fibrils prepared in GuHCl makes it difficult to measure the length of individual fibrils and consequently, the elongation rate constant and thus also the other individual rate constants could not be determined accurately. Still, the combined rate constants; k₊k_n and k₊k_n, can be determined and show increased rates at low concentrations and decreased rates at 2 M GuHCl (Figure 8).

The parameter that governs when the initial step in secondary nucleation, i.e., where monomers or preformed oligomers attach to the fibril, becomes half saturated, K_M^1/n2, can only be determined accurately when it lies inside the studied concentration range. Otherwise only an upper or lower bound on its value can be given. We observe no or little signs of saturation of the secondary nucleation for Aβ42 aggregation in buffer without GuHCl in the investigated concentration range (1.6–5 μM). Thus, we can only obtain a lower bound and conclude that K_M^1/n2 ≥ 5 μM, which correlates well with the K_M obtained from the wider concentration range investigated in the urea datasets above. The secondary nucleation of Aβ42 aggregation in 0.25 M GuHCl is fully saturated in the investigated concentration range. Thus, we can conclude that K_M lies below the investigated concentration range, i.e., K_M^1/n2 < 1.6 μM. The obtained value from the fit was K_M ≈ 0.45 μM² (√K_M = 0.67 μM) and was used to calculate the secondary nucleation rate. The secondary nucleation of Aβ42 aggregation in 1 and 2 M GuHCl saturates within the studied peptide concentration range, thus K_M can be determined accurately. (Figure 8D).

Seeded aggregation experiments were performed at 3 μM Aβ42 monomers with addition of preformed fibrils at 0, 0.2, 1, 5, and 30% in monomer equivalents (Figure 9). The seeds were prepared under the same conditions, i.e., the same GuHCl concentration, that they were subsequently used in. Seeding experiments confirmed that the main source of new nuclei is again secondary nucleation since the addition of small amounts of seeds shortened the lag phase at all denaturant concentrations.

We previously investigated the processes of primary and secondary nucleation using Monte Carlo simulations of a minimal computer model system of amyloid formation (Šarić et al., 2014, 2016a). In line with what we observe here for the effects of denaturants on primary nucleation, and consistent with classical nucleation theory (CNT), we previously found using simulations that a relative decrease in the free energy gain upon formation of the condensed phase resulted in increased nucleus sizes (Šarić et al., 2016b). For secondary nucleation, dissection of the effects that lead to an increased monomer dependence at higher denaturant concentrations is less straightforward as the degree of saturation of the fibril surface, in addition to the size of the converting/detaching species, affects the monomer dependence of the reaction. Here, our global fitting procedure was able to describe all experimental data assuming the reaction order remains unchanged and only the coverage varies (Figures 4–8), which was motivated by the finding by SPR of reduced affinity of monomers for the fibril surface in the presence of denaturant. However, it is still possible that there is a contribution from an increase in reaction order in the presence of denaturant.

We therefore utilised our minimal computer model system to investigate the effect of a stabilisation of the monomeric state at constant coverage for a range of monomer concentrations (Figure 10). Indeed, we find an increase in the reaction order the larger the energy difference between the monomeric and the aggregated state due to the presence of denaturant. Moreover, these simulations allow us to directly extract the nucleus size, which is found to increase along with the reaction order, confirming that both a decreased coverage and increased nucleus size are expected effects of the presence of denaturant.

Apart from variations in fibril length and clumping, the fibrils formed in urea appear to have the same morphology as those formed in buffer. Based on the kinetic data we may infer that the addition of urea causes a change in the underlying mechanism by shifting the relative importance of the microscopic steps involved in the aggregation process. This is reflected by the scaling exponent that decreases (i.e., becomes more negative) in the presence of urea, indicating that the monomer dependence of the nucleation processes increases. The scaling exponent of secondary nucleation is approximately given by γ = −(1+n₂)/2 when the process is unsaturated and approaches γ = -1/2 as it saturates. Thus, the observed decrease of the scaling exponent upon addition of a denaturant could reflect either a change in the degree of saturation or a increase in the reaction order n₂, where the latter may be the result of a change in nucleus size. Indeed, both scenarios are consistent with the denaturant lowering the free energy of the monomeric state, more than other states; however, the orthogonal measurements of affinity for the fibril surface obtained by SPR show that the affinity of monomers for the fibrils surface becomes lower (i.e., K_D becomes higher) in the presence of denaturant implying that a decrease in surface coverage at all monomer concentrations below saturation is a significant contribution to the change in monomer dependence of the aggregation reaction. In line with this finding, the kinetic data at all denaturant concentrations are well described by varying degree of saturation of secondary nucleation and a reaction order n₂ = 2 that is independent of the urea concentration. While a variation of fibril coverage, as confirmed by SPR, is sufficient to explain all data, we cannot exclude that a small increase in reaction order also occurs in the presence of urea. Therefore, we confirmed that a decrease in the free energy of the monomeric state at constant coverage indeed increases the nucleus size by minimal computer simulations of secondary nucleation, as discussed below.

The microscopic steps expected to be most affected by the addition of urea are those for which the reactants and transition state/products are most differentially affected by the denaturant. In the case of Aβ42, these are likely processes involving a transition from a denaturant accessible, disordered state, to a more compact one, in particular processes in which several species undergo such a transition. Indeed, both the primary nucleation rate and the secondary nucleation rate decrease by more than two orders of magnitude over the investigated urea concentration range. Those nucleation steps both involve more than one peptide changing from disordered to more compact, whereas the effect on the elongation rate, which is believed to only involve a single monomeric species interacting with an already ordered fibril end, is minor. Since the saturation of secondary nucleation varies with increasing urea concentrations, we compare the rate of formation (i.e. the sum of conversion and detachment) of a new secondary nucleus at a specific stage of the nucleation process, i.e., at 10% conversion to fibrils for reactions starting from 5 μM Aβ42 monomer (as described in the result section). In this calculation we assume that 90% of the monomers, i.e., 4.5 μM, are free and available to form new nuclei. The rate of this process is found to decrease by about 3 orders of magnitude between 0 and 3 M urea.

Guanidinium hydrochloride is a salt as well as a denaturant, which results in two opposing effects on the aggregation rate, with an acceleration at low GuHCl concentrations and a deceleration at high GuHCl concentrations. On the one hand, addition of GuHCl increases the ionic strength which results in reduced electrostatic repulsion between charged molecules, on the other hand we expect similar denaturing effects as for urea. As monomeric Aβ42 has a net charge between -3 and -4 at pH 8.0, addition of ionic molecules, such as GuHCl, to the solution causes increased electrostatic screening between the monomers and between the monomers and fibrils. We have previously investigated the effects of modulation of the electrostatic interactions in detail, revealing an overall increase in the aggregation rate with increasing ionic strength and that the secondary nucleation rate is fully saturated (making the monomer-independent conversion/detachment step the rate determining step) at ionic strengths above 0.2 M (Meisl et al., 2017a). Indeed, in the current data, the rates of both secondary and primary nucleation increase in the presence of 0.25 M GuHCl. However, at GuHCl concentrations above 0.25 M GuHCl, when electrostatic interactions are fully screened, the rates again decrease, in a similar manner to that observed for urea. At 2 M GuHCl the fibril morphology appears to be altered, meaning that detailed mechanistic conclusions may not be drawn from the aggregation data at the highest concentrations of GuHCl. Still, a strong retarding effect of 2M GuHCl can be deduced from the reduced values of the combined rate constants; k₊k_n and k₊k_n (Figure 8).

The competing effects of the ionic denaturant GuHCl, resulting in acceleration at low concentrations followed by deceleration of the aggregation rate as the GuHCl concentration increases, can be mimicked by an equimolar mixture of sodium chloride and urea to the solution, see Figure 3. Urea is a weaker denaturant than GuHCl, which is reflected in the higher maximum aggregation in the presence of urea/NaCl, but the qualitative behaviour caused by GuHCl is recovered. The fact that the effects of guanidine hydrochloride are not fully recapitulated by a mixture of urea and NaCl might be due to guanidine hydrochloride being a stronger denaturant than urea, or the Hofmeister effect of ions on peptide hydration.

Secondary nucleation dominates the production of new nuclei for the majority of the reaction time-course and therefore the parameters associated with this process can be determined more accurately than those associated with primary nucleation. Nonetheless, we find that a significant increase in the reaction order of primary nucleation is required to fit the experimental data well. The reaction order in the absence of denaturant is approximately n_c = 2 and at 3 M urea this has increased to n_c = 5. While the reaction order of this coarse-grained nucleation step is usually not directly equivalent to a nucleus size, its increase is likely to reflect an increase in the nucleus size. Indeed, simple classical nucleation theory (CNT) predicts an increase in the nucleus size as the nucleation barrier between the monomeric and aggregated states of the protein increases due to a stabilisation of the monomeric state by denaturant. The simulations using a minimal computer model (Figure 10) also recover such changes in nucleus size.