Kinetic modelling was performed to highlight the most contributing mechanisms of $\alpha$-syn aggregation in SAAs. The differential equations used are displayed in the Results & Discussion sections. Equations were integrated as previously described with minor modifications [39]: the Euler solver was replaced with a more performant Runge-Kutta solver, the code used for the simulations was run on Python 2.7 instead of C++, a varying fragmentation kinetics was applied to accurately simulate the intermittent shaking of SAAs, oligomeric populations were not considered since SAAs amplification processes mostly involve fibrils and protofibrils.

Escherichia Coli BL21(DE3) Gold were transformed with pT7-7 vector cloned with the gene encoding $\alpha$-syn. The overnight preculture of transformed cells was diluted 100-fold in Luria-Bertani medium and induced at an OD${}_{600}$ value of 0.6–0.8 with 1 mM Isopropyl-$\beta$-D-thiogalactoside and, after 5 h incubation at 37 ${}^{\circ }$C, the cells were harvested at 4000 rpm (JA-10, Beckman Coulter, Fullerton, CA, USA). The extraction was carried out through osmotic shock using 100 mL of buffer TRIS 30 mM, EDTA 2 mM and sucrose 40%, at pH 7.2 according to Shevchik et al. [40] and Huang et al. [41]. The suspension was then ultracentrifuged at 20000 rpm (Type 70 Ti rotor, Beckman Coulter, Fullerton, CA, USA) for 25 min and pellet was collected and resuspended with 90 mL precooled ultrapure water additioned with 38 $\mu$L of MgCl${}_2$ 1 M and then ultracentrifuged a second time. Supernatants derived from these two centrifugation steps, were joined and dialyzed against 4 litres of buffer 20 mM TRIS/HCl at pH 8.0. The protein then was loaded in the FPLC system and an anion exchange chromatography was carried out with 0–50% linear gradient of NaCl 1 M (GE Healthcare HiPrep™ Q HP 16/10 Column). The collected fractions were lyophilized and resuspended in 10 mM TRIS/HCl, 1 mM EDTA and urea 8 M at pH 8.0 for the chemical denaturation. To eliminate all the protein formed aggregates, two size-exclusion chromatographies (HiLoadTM 16/600 SuperdexTM 75 pg Column) were performed with 20 mM phosphate and 0.5 mM EDTA at pH 8.0 as elution buffer. Purified $\alpha$-synuclein ($\alpha$-syn) was dialyzed against Milli-Q water and lyophilized in batches for long-term storage. The purity of the monomeric $\alpha$-syn was evaluated by SDS-PAGE. Roche cOmplete™ protease inhibitor cocktail was added only during the extraction step in the quantity suggested by the producer.

Lyophilized aliquots of $\alpha$-syn were resuspended in NaOH 3.5 mM (pH 11.5) right before the experiments to avoid the instantaneous formation of aggregates. At high pH, the negatively charged monomers (the isoelectric point of $\alpha$-syn is 4.67) experience an electrostatic repulsion that impedes the aggregation and favours the dissociation of small aggregates [42, 43]. The $\alpha$-syn solution was then brought to the desired pH by adding concentrated buffers (PIPES or phosphate buffers, depending on the experiment). In all the reaction buffers used, ThT was present at a concentration of 10 $\mu$M together with NaN${}_3$ (0.08%). Each sample/condition analysed was replicated in three distinct wells in clear-bottom 96-well plates (TECAN©, #30122306). We added acid-washed glass beads in each well, of different size and number depending on the experiment, to enhance the aggregation speed and increase homogeneity among replicates. The plates were always sealed with a sealing tape to minimize evaporation during the experiments. Plates were inserted in a BMG LABTECH ClarioStar fluorimeter and subjected to the incubation/shaking protocol of Shahnawaz et al. [27] (T = 37 ${}^{\circ }$C, 29 min incubation, 1 min double-orbital shaking at 500 rpm). While testing the effect of detergent we used conditions more similar to the ones of protocols making use of it [28, 29, 44] by using $\alpha$-syn 0.08 mg/mL in phosphate buffer (40 mM) pH 7.4 + 170 mM NaCl, 6 $\times$ 1 mm diameter glass beads and 15 $\mu$L of CSF for a final volume of 100 $\mu$L per well. Cycles of 1 min shaking (500 rpm double orbital) and 1 min rest at 42 ${}^{\circ }$C were used. Once every 30 minutes, the fluorescence was read from the bottom using an excitation and emission wavelength of 450 nm and 480 nm, respectively.

Monomeric $\alpha$-syn at the concentration of 2 mg/mL was incubated in 100 mM PIPES buffer with 500 mM NaCl at 37 ${}^{\circ }$C in two wells (250 $\mu$L per well) of a 96-wells plate, under constant agitation at 500 rpm. One of the two wells contained 10 $\mu$M ThT in order to monitor the aggregation. Once the plateau of the ThT aggregation profiles was reached (usually after seven days), the sample without ThT was subjected to cycles of sonication, using an immersion sonicator, in order to obtain smaller aggregates (5 cycles of 15 seconds sonication at 12 $\mu$m oscillation amplitude and 15 seconds rest). The solution containing the preformed aggregates was then split in aliquots, diluted to the desired concentrations, and stored at –80 ${}^{\circ }$C for later use. One aliquot was analysed by Western blot (details of the procedure used in Supplementary Fig. 1, Supplementary Material) to evaluate the pattern of the obtained aggregates (Supplementary Fig. 1, Supplementary Material).

To avoid problems related to biological variance of CSF samples, CSF aliquots from a single female hydrocephalic patient of 67 years old were used in this work. This patient showed no cognitive or motor impairment. Lumbar puncture was performed according to international guidelines [45, 46]. Following a standardized procedure, 12 mL of CSF were collected in a sterile polypropylene tube and centrifuged at room temperature for 10 min (2000$\times$ g). Aliquots (0.5 mL) were frozen at –80 ${}^{\circ }$C. In the CSF sample used, the core Alzheimer’s disease biomarkers were measured using Lumipulse G600-II (Lumipulse) $\beta$-Amyloid 1–40, Lumipulse $\beta$-Amyloid 1–42, Lumipulse Total Tau and Lumipulse p-Tau 181 assays (Fujirebio Europe, Gent, Belgium), resulting in a profile not compatible with the presence of Alzheimer’s disease with all measured biomarkers falling within the normal range.

To extract the position of inflection points, ThT fluorescence profiles were fitted with Boltzmann’s sigmoidal functions by using the non-linear fitting routine of OriginPro 9.0. Linear regression analyses were performed with the linear regression tool of Microsoft Excel.

We started our analysis by making simulations to understand the simplest kinetic model that could explain the aggregation kinetics of $\alpha$-syn during incubation/shaking cycles. We wanted to reproduce the linear relations initially observed by Shahnawaz et al. [27] and by Arosio et al., [47] between the $t_{1/2}$ (time to the half of the maximum value) and the logarithm of the seed (preformed aggregates) mass concentration. A nucleated polymerization model (Fig. 1) [48, 49] with intermittent fragmentation (Fig. 1) could produce an approximate linear relation (Fig. 2). In this model, secondary nucleation was not included [50]. Indeed, the rates of the secondary nucleation processes during $\alpha$-syn aggregation have a strong pH dependence. Indeed, it has been previously shown that starting from pH 6, secondary nucleation provides a minor contribution in the aggregation kinetics of $\alpha$-syn [51].

The simulated range of seed masses shown in Fig. 2 is arbitrary and not related to experimental values. The range of seed masses, for which it is possible to obtain this linear relation depends on the kinetic constants of the processes, which themselves depend on the nature of the protein-protein interaction and on experimental variables like temperature, pH, shaking cycles, protein concentrations and ionic strength. Optimizing the experimental variables, to maximize the differentiation between seed masses, is the first step in developing SAAs for the diagnosis of synucleinopathies.

We evaluated the impact on $\alpha$-syn aggregation of different experimental factors such as the addition of glass beads, starting monomer concentration, solution pH, size and number of glass beads, addition of human CSF and use of detergents.

The addition of glass beads to wells containing Thioflavin-T (ThT) and monomeric $\alpha$-syn is reported in literature to be beneficial for reducing the fibrillization time and for increasing the homogeneity among replicates [52, 53]. In the simplified model that we described in Fig. 1, at t = 0 the formation of novel fibrillar species is dependent on the nucleation and fragmentation kinetics. By increasing the latter, through sonication/vigorous shaking in the presence of beads, seeding should be favoured with respect to unspecific nucleation of aggregates. To verify this hypothesis, we performed tests on equivalent samples with and without glass beads. In Fig. 3, we reported the ThT fluorescence profiles of $\alpha$-syn samples with 20 ng of seeds, subjected to a SAA protocol, without (Fig. 3A) and with (Fig. 3B) glass beads. To quantify the variability among replicates we used the maximum coefficient of variation (MCV), calculated as the maximum value of the ratio between standard deviation and mean fluorescence value of the three replicates during the course of the experiment. The replicates in Fig. 3A produced smooth fluorescence lineshapes, with high variability among replicates (MCV = 0.68). At 160 h, none of the replicates reached the final fluorescence plateau. Conversely, the replicates in Fig. 3B produced noisier fluorescence lineshapes but with less variability among replicates (MCV = 0.36). All the replicates reached the final fluorescence plateau in about 100 h. Similar results were obtained by repeating the experiment with and without glass beads with 2 ng of seeds (Supplementary Fig. 2, Supplementary Material, MCVs of 0.36 and 0.69, respectively).

A second experiment was performed to evaluate the impact of different size and number of glass beads in three different buffers, the results are shown in Fig. 4. From this image, it is possible to appreciate that a single bead of 3 mm of diameter produced a faster aggregation with respect to 17 beads with a diameter of 0.5 mm. Moreover, for any beads size and number, the aggregation of $\alpha$-syn was faster in PBS pH 7.4 compared to PBS pH 8.2 and even faster in 100 mM PIPES pH 6.5 + NaCl 500 mM. These results are in accord with the fact that, starting from pH 4.5 (the isoelectric point of $\alpha$-syn), the C-terminus of $\alpha$-syn becomes negatively charged at increasing pH [42, 54], which results in an electrostatic repulsion between monomers and between monomers and preformed aggregates. Conversely, pH values near the isoelectric point of $\alpha$-syn neutralize charge repulsion and promote conformational changes, which results in an increased aggregation proneness [55, 56].

CSF coming from a single hydrocephalus subject not suffering from neurodegenerative diseases was subsequently added to the reaction mix. In this way, we could test the different analytical variables on different aliquots from the same subject without introducing effects linked to biological variance. The detection limit and the ability to differentiate among seed masses were tested by adding in-lab made preformed aggregates (seeds) in different quantity in each well, the protocol used to produce $\alpha$-syn seeds is reported in the Materials and Methods section. The incubation/agitation protocol (29 min incubation, 1 min shaking at 500 rpm) and the reaction buffer (100 mM PIPES buffer pH 6.5 with NaCl 500 mM) of Shahnawaz and coworkers [27] were used for all the experiments described in Figs. 5,6,7 and 8. For this protocol we also analysed wells containing seeds and CSF without recombinant $\alpha$-syn to determine whether the addition of seeds could produce a significant increase in fluorescence by itself. The results of this experiment are shown in Supplementary Fig. 4 (Supplementary Material). In summary, we did not observe any significant change produced by the addition of seeds in the absence of monomeric $\alpha$-syn.

In Fig. 5A are reported the kinetic traces, averaged on three replicates for each seed quantity, relative to a SAA performed with 17 glass beads (diameter of 0.5 mm) per well. Interestingly, the addition of human CSF produced a delay in the aggregation of $\alpha$-syn (Fig. 5A). This phenomenon was previously observed [27, 57, 58] and, although not being fully understood, it could be produced by the interaction between $\alpha$-syn and CSF protein constituents [42, 59]. From Fig. 5A and from Fig. 3, it can be appreciated the fact that most of the fluorescence profiles have two inflection points: a first inflection point, situated between 0 h and 25 h and a second one, situated between 60 h and 70 h. The presence of two inflection points in most of the observed ThT profiles indicates a two-step process occurring during the SAA. The presence of the second inflection point may be explained by the transition from the initially amplified oligomeric/proto-fibrillar aggregates into well-structured fibrils. This type of transition produced similar trends in aggregation assays involving $\alpha$-syn [60, 61] and amyloid-$\beta$[39]. According to this hypothesis, the seeded samples in Fig. 5 (which exhibit a higher fluorescence intensity at the first plateau), may have had a higher percentage of prefibrillar aggregates with respect to unseeded ones. Indeed, apart from fibrillary aggregates the added seeds contained also oligomeric/proto-fibrillar species (Supplementary Fig. 1, Supplementary Material) which may have been initially amplified in the first hours of the experiment. The drop in fluorescence after reaching the maximum value (e.g., in Fig. 5A) often occurs in protein aggregation assays and is thought to be produced by the formation of insoluble macroscopic aggregates, capable of trapping ThT molecules [62].

To accurately measure the position of the first inflection point (t${}_{\mathrm{0}}$), the first parts of the aggregation profiles were fitted with a Boltzmann’s sigmoidal function (Eqn. 1), using. In the non-linear curve fitting procedure used, the parameters A${}_{\mathrm{1}}$, A${}_{\mathrm{2}}$, t${}_{\mathrm{0}}$ and dt of Eqn. 1 were let free. With reference to Fig. 2, t${}_{\mathrm{0}}$ coincides with t${}_{1/2}$when A${}_2$ = 0, i.e., when the initial fluorescence intensity is negligible.

(1)$$y(t)=A_2+\frac{A_1-A_2}{1+\exp \left(\frac{t-t_0}{dt}\right)}$$

The results of the fitting are shown in Fig. 5B. The measured t${}_{\mathrm{0}}$ parameters were then plotted against the natural logarithm of the mass (per ng) of the added seed. From the linear regression shown in Fig. 5C, it can be appreciated that there is a good linearity between the t${}_{\mathrm{0}}$ parameters (R2 ~ 1) and the natural logarithm of the seed mass, as was expected from simulations and previous investigations [27, 47]. The linear response was maintained up to 0.02 pg (0.1 pg/mL) of seeds, which coincides with the detection limit of this protocol.

The assay optimization promoted the “seeded” aggregation and limited the spontaneous aggregation of the free monomer to obtain the maximum possible differentiation of the masses of the added seeds. From the linear regression of Fig. 5C, it is possible to notice that, although the R2 coefficient is almost equal to 1, the slope of the line was low, which represented the fact that the first inflection point of the aggregation profiles laid in a short range of time (5 h–20 h) for all the curves. In a second trial, we lowered the monomer concentration from 0.125 mg/mL to 0.08 mg/mL. This choice was made to discourage the primary nucleation kinetics, which, according to the model described in Fig. 1, depends on the square of the monomer concentration while the polymerization kinetics of the fibrils depends linearly on that. Also, the number of beads was slightly reduced from 17 to 15 to ameliorate the signal to noise ratio of each curve to allow a better fitting of the first plateau. As before, we analysed the first part of the aggregation curves extracting the t${}_{\mathrm{0}}$ parameters with the sigmoidal fitting (Fig. 6A) but we tried also to estimate the so-called lag-time to quantify the time at which the fluorescence starts to deviate significantly from its initial value. We defined it, in a similar way to the one used by Groveman et al. [28], as the time at which the fluorescence ()$F$ of each well becomes higher than the average fluorescence of the first 10 h () of the sample without seeds plus 5 standard deviations (5$\sigma$) for 5 consecutive measurements:

(2)

Where i$\mathrm{\Delta }t$s the time between two consecutive measurements (30 min in our case). The inverse of the lag-time, the lag-rate, is usually used in the SAA protocols to visualize the data, since it provides a faster and easier way to examine together the outcome of multiple experiments with respect of plotting the fluorescence profiles for all the samples in the same graph (an example of this representation is provided in Fig. 6C. Moreover, as it is defined in Eqn. 2, the estimation of lag-times does not necessarily need to reach a fluorescence plateau, making lag-times measurable also for incomplete kinetic traces. The averages of the lag-times (estimated with the threshold method of Eqn. 2) on three replicates were plotted against the natural logarithm of the seed masses per ng, the result of the linear regression procedure is shown in Fig. 6D.

The R2 values and the slopes of the linear regressions for the t${}_{\mathrm{0}}$ values and the lag-times were similar, as expected, with the slope being more than twice the one calculated in Fig. 5C. The tested protocol was still able to differentiate seed masses with a detection limit of 0.02 pg. In Fig. 7, it is reported a summary of the measured t${}_{\mathrm{0}}$ values for different bead sizes and two initial monomer concentrations. The t${}_{\mathrm{0}}$ parameters were calculated both on the first and on the second inflection points in the same conditions in Fig. 7A and in Fig. 7B.

All the tested conditions produced satisfactory differentiations between seed masses with a good linear correlation between the measured t${}_{\mathrm{0}}$ parameters and the logarithm of the added seed masses. By looking at Fig. 7B and Fig. 7C, it is possible to notice that, as expected from the considerations on the nucleation and polymerization kinetics, the samples with a starting monomer concentration of 0.08 mg/mL produced an increased slope compared to the ones with 0.16 mg/mL, even though the overall experiment duration was also longer. The second inflection point showed also to be discriminative for the 0.16 mg/mL monomer concentration, as can be seen from Fig. 7A, while for the 0.08 mg/mL monomer concentration it was still not reached after 250 h. The increased number of beads, with respect to Fig. 5 and Fig. 6, produced slightly noisier lineshapes but neither a significative increase in the aggregation speed nor in seed mass discrimination. However, by substituting the 21 beads with a diameter of 0.5 mm with a single bead with a diameter of 3 mm (the total bead mass is ~ 10 times greater) we observed the almost disappearance of the first inflection point (Fig. 8A), probably due to the more rapid transition from oligomeric/protofibrillary species into fibrils. The t${}_{\mathrm{0}}$ values and the lag-times measured for this kinetics produced good results in terms of R2 and slope of the linear regression, as can be seen from Fig. 7D and from Fig. 8B.

Another variable that emerged in some protocols present in literature [28, 44, 58, 63] is the presence of detergents, such as Sodium Dodecyl Sulphate (SDS), which is commonly used in the RT-QuIC/PMCA protocols for the detection of PrPSc.

For these experiments, 2 $\mu$L of a stock solution (PBS containing 3 different SDS concentrations) were added to the reaction mix. The lag times were evaluated for each well using the formula in Eqn. 2 by considering the average fluorescence of the first 5 h instead of 10 h due to the high aggregation propensity of samples containing seeds and a final SDS concentration of 0.01%. We tested the addition of SDS in conditions more similar to the ones of protocols making use of it [28, 29, 44] by using $\alpha$-syn 0.08 mg/mL in phosphate buffer (40 mM) pH 7.4 + 170 mM NaCl, 6 $\times$ 1 mm diameter glass beads and 15 $\mu$L of CSF for a final volume of 100 $\mu$L per well. Cycles of 1 min shaking (500 rpm double orbital) and 1 min rest at 42 ${}^{\circ }$C were used. A slightly lower pH and higher shaking rpm with respect to the one of published protocols were needed to promote aggregation probably due to the different shaking efficiency of our fluorimeter compared to BMG Omega. As can be evinced from Table 1, the addition of SDS dramatically accelerated the aggregation kinetics of $\alpha$-syn both in seeded and unseeded experiments. The SDS-induced fibrillization of $\alpha$-syn was previously documented by Otzen and coworkers [58] and it is currently used to increase the speed and reproducibility of screening assays to measure the effects of antiaggregatory compounds on $\alpha$-syn fibrillization [59]. The SDS-induced $\alpha$-syn fibrils are known for containing a mixture of $\alpha$-helix and $\beta$-sheet and their morphology differs from that of only agitation-induced $\alpha$-syn fibrils. Anyway, the two morphologies can interconvert and, thanks to temperature and strong agitation, converge into ThT responsive structures rich in $\beta$-sheet motifs [63].