Critical aggregation concentration for the formation of early Amyloid-β (1–42) oligomers

The oligomers formed during the early steps of amyloid aggregation are thought to be responsible for the neurotoxic damage associated with Alzheimer’s disease. It is therefore of great interest to characterize this early aggregation process and the aggregates formed, especially for the most significant peptide in amyloid fibrils, Amyloid-β(1–42) (Aβ42). For this purpose, we directly monitored the changes in size and concentration of initially monomeric Aβ42 samples, using Fluorescence Correlation Spectroscopy. We found that Aβ42 undergoes aggregation only when the amount of amyloid monomers exceeds the critical aggregation concentration (cac) of about 90 nM. This spontaneous, cooperative process resembles surfactants self-assembly and yields stable micelle-like oligomers whose size (≈50 monomers, Rh ≈ 7–11 nm) and elongated shape are independent of incubation time and peptide concentration. These findings reveal essential features of in vitro amyloid aggregation, which may illuminate the complex in vivo process.

concentration, cac, for the oligomer formation and to characterize the aggregates formed. Moreover, we aim to establish whether the critical concentration refers to the formation of fibrils or early non-fibrillar aggregates.

Results and Discussion
Samples of Aβ42. In order to obtain homogenous samples and reproducible measurements of Aβ42 aggregation, it is crucial to start with monomeric material and to control carefully the sample preparation procedure. As described in detail in the Methods section, first we obtained the monomeric peptides, following established disaggregation protocols. Then we took great care to eliminate any residual disaggregation agents in the final samples and followed a very methodical sample preparation protocol in order to ensure that the results were as reproducible as possible. The samples used for the FCS measurements contained as fluorescent probe a fixed concentration of fluorescently labelled Aβ42 (denoted by Aβ*), and different concentrations of unlabelled Aβ42 (denoted by Aβ°) in a physiological buffer.

Diffusional properties of Aβ42 at different concentrations and incubation times.
We studied the early aggregation of Aβ42 using Fluorescence Correlation Spectroscopy (FCS), an established technique which measures the changes in the diffusional properties of fluorescent probes in a confocal volume at the single molecule level 25 . Fluorescence correlation (FCS) curves of samples containing labelled and unlabelled Aβ42 were measured as a function of incubation time (within the first 2-3 hours after preparation) and total Aβ42 concentration. The analysis of the FCS curves then yields the diffusion correlation times of monomers and aggregates and their contributions to the diffusion term of the correlation curve, which are related to the size and concentration of these species. In order to be able to extract quantitative information about the aggregation process and the size and conformation of the aggregates, we developed a model for the composition and properties of the samples based on a few reasonable assumptions and applied it in a detailed data analysis (see SI).

Monomeric Aβ42.
In order to check that the starting peptides were properly disaggregated and to characterize the monomeric Aβ42, we first measured samples containing only labelled Aβ42, Aβ*, at low concentration. The FCS power series of these samples (see Supplementary Figure S1) show a single fluorescent species with a mean diffusion time through the sample volume of 153.6 ± 0.2 μs (Supplementary Equation S1). From this time and the known dimensions of the sample volume, we estimated a translational diffusion coefficient of D = (1.35 ± 0.03) × 10 −10 m 2 s −1 (see Methods section). This value is in agreement with the series of diffusion coefficients obtained by Danielsson et al. for monomeric Aβ40 and several fragments of this peptide using PFG-NMR, and shows that, under our starting conditions, Aβ42 is monomeric 26 . Moreover, our value for the diffusion coefficient of monomeric Aβ42 fits well with the molar mass dependency D~M −ν with ν = 0.44 given by these authors, who interpreted this exponent as an indication that these small peptides in their native form have a random coil conformation with some structured regions. Molecular dynamics simulations combined with NMR data lead to similar conclusions for monomeric Aβ42 in aqueous solution 27 . Using the Stokes-Einstein equation, we estimate a hydrodynamic radius of 1.8 nm for Aβ42, which agrees quite well with that obtained in a recent study 28 . Aggregation of Aβ42 -Influence of incubation time. In order to study the early aggregation, we prepared samples with different total concentrations of disaggregated Aβ42, each sample with a fixed concentration of labelled Aβ42, Aβ*, but different concentrations of unlabelled Aβ42, Aβ° ( Fig. 1a and b). Then, under the same conditions as before, we recorded FCS curves of the samples at different incubation times from 10 min up to 180 min.
All correlation curves are well fitted with two diffusion correlation times (Supplementary Equation S2, Fig. 1a and b), indicating that particles of two significantly different sizes are present in the solution. The shorter of the two diffusion times, τ D1 , coincides with the one we obtained before for monomeric Aβ42. The second time, τ D2 , is about 10 times longer and we attribute it to the much bigger and thus slower diffusing Aβ42 aggregates present in the sample.
Surprisingly, this second diffusion time, corresponding to Aβ42 aggregates, is already present at the shortest incubation times, 5-10 min after the preparation of the samples, independently of the Aβ42 concentration. The value of this diffusion time fluctuates in the range from 1 ms to 3 ms but shows no systematic dependence on the incubation time (Fig. 1c). These fluctuations are due to the single molecule character of FCS, which in each  (Fig. 1e), indicating that the proportion of aggregates present in each sample is also independent of the time elapsed after sample preparation. We will confirm this observation below in a quantitative analysis, correcting the dependence of R on the brightness of the diffusing species.
So far, these experimental findings indicate that the observed aggregates are formed immediately (<10 min) after dissolving monomeric Aβ42 in the buffer, confirming a very short or inexistent lag time for the aggregation of Aβ42 in the concentration range under study, as already suggested in the literature 10,19,29 . Furthermore, they show that the early aggregation of Aβ42 leads to the formation of stable oligomers whose mean size and concentration do not change with the incubation time within the range studied.
Aggregation of Aβ42 -Influence of Aβ42 concentration. Next, we examined the influence of the Aβ42 concentration on the aggregation. As can be seen in Fig. 1b, the FCS curves shift to longer correlation times as the concentration of Aβ42 is increased, due to the growing contribution of slower aggregates. This is corroborated by the increase of the aggregates' contribution (1-R) as the Aβ42 concentration increases, as shown in Fig. 1f. In contrast, the diffusion time of the aggregates, τ D2 , does not show systematic changes as the Aβ42 concentration varies (Fig. 1d), but fluctuates randomly. These results indicate that the increase of the Aβ42 concentration leads to an increase in the number of the aggregates of Aβ42, but not to a change in their size. This behaviour is typical for cooperative, micelle-like aggregation where the aggregates are in equilibrium with the monomers. Micelle-like intermediates in Aβ fibril assembly were already reported by Yong et al. in SANS experiments for the smaller peptide Aβ40 16 .
Based on this experimental evidence, we have formulated a model for the composition and the properties of the samples under study. In the samples, monomers coexist with aggregates characterized by a mean aggregation number n (see Theory section in SI). The application of this model to the results of the FCS measurements allows us to determine the fraction of Aβ42 in solution which is aggregated (fraction of aggregated amyloid or degree of aggregation γ), as well as to estimate the parameters related to the size and conformation of the aggregates.

Critical aggregation concentration.
For each FCS curve, we calculated the experimental value of the degree of aggregation γ by applying the data analysis procedure described in the SI. Figure 2 shows the degree of aggregation γ determined from all the measurements performed at different incubation times (grey dots in Fig. 2), plotted against the total Aβ42 concentration in solution. The Aβ42 concentration in solution was estimated for each sample and incubation time from the FCS data as described in the SI. The fraction of aggregated amyloid γ is negligible at Aβ42 concentrations lower than 0.02 μM, but it increases sharply at concentrations around 0.1 μM and stabilizes at higher concentrations.
This critical-concentration dependence of the degree of aggregation is typical for a spontaneous cooperative aggregation process such as, for example, the self-assembly of surfactants into micelles. In these processes, at low concentrations, only monomers are present in solution. However, when the concentration exceeds a critical aggregation concentration (cac), aggregates form abruptly. Above the cac, the number of aggregates increases, but not their size, which remains within a narrow distribution. In order to extract quantitatively a value of γ we applied a fit model developed in our group for the self-assembly of surfactants 30,31 . We fitted this model to the mean γ-value of each sample (coloured horizontal bars in Fig. 2), weighted by the standard deviation of the values at different incubation times. In spite of the strong fluctuations and bias of some of the γ-values, the confidence interval of the fitted curve overlaps with all but one of the error bars. From this weighted fit, we obtain a value of cac = 91 ± 14 nM for Aβ42 in vitro under physiological conditions and a transition concentration interval of σ = r·cac = 33 nM (Fig. 2, see SI for further details on the fit). These results indicate that under our experimental conditions the transition from monomeric to aggregated Aβ42 occurs in a concentration interval between 60 nM and 120 nM.
To our knowledge, these are the first experimental data reported for the degree of the early aggregation of Aβ42. They provide direct experimental evidence for the existence of a critical concentration for the early aggregation of this amyloid. Moreover, the fact that these data follow the model for surfactant self-assembly suggests that the early aggregation of Aβ42 shows an analogous micelle-like cooperative behaviour. The model allows for a quantitative estimation of the cac of Aβ42.
The value we obtain for the cac of Aβ42 is of the same order as other values reported for this amyloid, despite disparate experimental conditions and measuring techniques. It is half the reported limit of 0.2 μM below which aggregates could not be detected using thioflavin T as a fluorescent probe 19 , a result that evidences the higher sensitivity of FCS for this kind of studies. Iljina et al. recently reported cac values of Aβ40 and Aβ42 using a sample preparation and an analysis method different to ours 20 . They estimated one value of the cac of 28 nM from the concentration of soluble Aβ42 species in equilibrium with fibrils. They also present a figure with Aβ42 oligomer concentrations as a function of initial monomer concentrations (Fig. 2b in that work) and indicate the Aβ42 concentration at which the oligomer concentration ceases to increase as a second estimation of the cac (≈85 nM, taken from that figure). These data show a similar tendency to those in our Fig. 2 and could probably also be fitted with our aggregation model with a cac between 50-70 nM. Our cac value of about 90 nm is in better agreement with their estimation taken from the oligomer concentrations than with that from the fibril supernatant. This agreement supports the interpretation that this cac corresponds to the formation of oligomers in the early aggregation steps.
Size and conformation of the aggregates. Our detailed quantitative model also allows us to characterize the aggregates regarding their size and conformation. From the relationship between the diffusion times of the aggregates and the experimental (uncorrected) mean aggregation numbers, we obtain an exponent ν = 0.75 for the molar mass dependence of the diffusion coefficient of the aggregates, D~M −ν , (step 4 of Data analysis procedure in SI and Supplementary Figure S2). This result indicates that the early aggregates of Aβ42 have an elongated structure, in very good agreement with the reported cylindrical geometry of Aβ40 micellar assemblies 16 .
Furthermore, the size distribution of the early Aβ42 aggregates can be estimated based on the corrected mean aggregation numbers (see steps 5 and 7 of the Data Analysis Procedure in the SI). Figure 3 shows the histogram of the relative number of aggregates against their corrected mean aggregation numbers. This distribution can be well described by a log-normal curve, typical of naturally occurring growth processes. From the fit of this curve to the experimental data, we obtain a mean aggregation number of 50 Aβ42 molecules per aggregate, with most (68%) of the aggregates formed by 28 to 88 monomers. This corresponds to a mean hydrodynamic radius of the aggregates between 7.3 nm and 10.7 nm. These results are in accordance with those obtained for the smaller peptide Aβ40 16 , where micelle-like assemblies of 30-50 monomers and elongated geometries of around 7 nm hydrodynamic radius were detected. For Aβ42, we obtain slightly higher values of the aggregation number and hydrodynamic radius, as expected for this longer peptide. Those authors also observed no concentration dependence of the size or the conformation of the aggregates. However, our results differ from the much smaller sizes reported by other groups for Aβ42 oligomers 20,28,32 . This disagreement can be attributed to the presence of small proportions of a highly disaggregating solvent in the samples used in those works that could be expected to have an influence on the aggregation process. It must be noted that differences in the sample preparation protocols or in the conditions used for the aggregation study (especially temperature and salt concentration) can lead to disparate types of oligomers and fibrils 33 .

Conclusions
Our results show that Aβ42 forms aggregates of 28-88 monomers when the monomer concentration exceeds a certain concentration in solution. This aggregate size does not change with time or with Aβ42 concentration within the ranges studied. These findings provide direct experimental evidence that early Aβ42 aggregation follows a micelle-like cooperative process. This process would be the primary nucleation pathway for the formation of oligomers that may behave as nuclei for a further slow aggregation into fibrils 29 . Analysis of the degree of aggregation using a model describing micelle formation allows us to determine quantitatively the critical aggregation concentration as cac = 90 nM for the early Aβ42 aggregation in vitro under physiological conditions. The transition from monomeric to aggregated Aβ42 occurs in a critical nanomolar concentration interval between 60 nM and 120 nM.
The use of FCS has allowed us to observe the behaviour and to estimate the concentration only of the dissolved amyloid peptide despite its high adsorption to the interfaces. The big difference between the real and the nominal Aβ42 concentrations in in vitro experiments may explain the higher cac-values given by those studies that refer to the nominal concentrations.
The recently proposed surface-mediated aggregation pathway 24 seems not to be effective below the critical concentration regime, but it may contribute to aggregation above the cac. Our results do not provide further information about this contribution. The role of this pathway should be evaluated in further studies.
The observed high molecular weight oligomers with an elongated geometry would correspond to the reported protofibrillar aggregates, which are mainly responsible for the neurotoxic damage 2 . Recent studies show that the degree of toxicity of amyloid oligomers depends both on their size and on their conformation, especially on the solvent-exposed hydrophobicity of the aggregates 7,13,[33][34][35] . Regarding the size, the oligomers observed in this study would not have the highest toxicity according to previous studies 13  We think that the results obtained in this study in vitro reveal essential features of the early aggregation of Amyloid-β (1-42) in aqueous solution and give estimates of the parameters involved, which could also be relevant in vivo, yielding pivotal information to understand the mechanisms regulating neurodegenerative diseases.

Methods
Preparation of monomeric Aβ42. For the disaggregation of the amyloid peptides, the protocols reported by Stine et al. were followed 36,37 . The commercial peptides (unlabelled Amyloid-β(1-42) from GenScript USA Inc. and HiLyte Fluor 488-β-amyloid(1-42) from AnaSpec Inc.) were treated with hexafluoroisopropanol (HFIP) in order to break down the potential aggregates present in solution. The amyloid was dissolved in HFIP at a concentration of about 1 mg/ml and the solution was incubated during 1 h with occasional mixing and then shaken for about 20 min. Next, the solution was split up into several vials and the HFIP was evaporated under a stream of nitrogen. The vials were transferred into a desiccator and vacuum was applied during 3 h to remove the remaining traces of HFIP. The resulting dried aliquots of monomeric Aβ42 were sealed and stored at −20 °C.

Sample preparation.
To study the early aggregation process, the samples were freshly prepared from the previously disaggregated monomeric amyloid. The peptide was first suspended in anhydrous dimethyl sulfoxide (DMSO) to a concentration of ≈1 mM and shaken for about 15 min in order to dissolve it. Then a certain volume of PBS buffer (pH 7.2, 150 mM NaCl) was added to obtain the desired final concentration of amyloid. The solution was gently stirred for 1-2 min prior to use. For samples with both labelled and unlabelled amyloid, instead of PBS buffer, solutions with labelled amyloid were used for the dilution of the unlabelled peptide. The potential effect of the DMSO on the aggregation process was not considered, as no systematic variations of the aggregated amount were observed for samples with similar amyloid concentrations and different percentages of DMSO.
For this study, samples were prepared with a fixed nominal concentration (0.3 μM) of the fluorescently labelled Amyloid-β (1-42) (Aβ* and different concentrations of unlabelled Amyloid-β (1-42) (Aβ°), nominally in the range from 0.1 μM to 45 μM. In addition, samples containing only the labelled amyloid were prepared in order to characterize the monomeric Aβ42 and to check that the starting samples were properly disaggregated.
Due to the strong adsorption of Aβ42 to the interfaces, only a fraction of the initial nominal concentration was finally available in the sample solutions. Nevertheless, the real concentration of dissolved Aβ42 could be estimated for each sample from the FCS measurements (see Theory section in SI). If not otherwise indicated, all Aβ42 concentration indicated throughout this study refer to these experimentally determined real concentrations in solution.

Measurement of FCS curves.
For each sample, Fluorescence Correlation Spectroscopy (FCS) measurements were performed as a function of the time after the dissolution of the peptide (incubation time). About 100 μl of the sample were placed into a well of a 96-well glass-bottom microplate (Whatman Ltd.) and left about 5 min to achieve a constant temperature (25 °C) and to equilibrate. Usually a significant decrease of intensity was observed during this time, which is attributed to the adsorption of the amyloid to the interfaces.
The FCS setup has been described before 38,39 and is summarized in the SI. Power series with samples containing only Aβ* and mixtures of Aβ* and Aβ° were performed in order to select a suitable excitation power for the FCS measurements that avoids distortions due to photobleaching and optical saturation. These measurements were also used for the characterization of the monomeric Aβ42 (see SI for details). Data analysis. FCS curves were fitted using Supplementary Equation S1 and S2 to obtain the diffusion correlation times of monomers and aggregates and their contributions to the diffusion term. Further data analysis was performed based on a model describing the composition and properties of the samples in order to extract quantitative information on the aggregation process and the size and conformation of the aggregates. This model is explained in detail in the Theory section of the SI, as well as the derived data analysis procedure. Parameter uncertainties indicate standard errors. Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.