Human αS was expressed in E. coli and purified as previously described in (Grey, Linse et al., 2011). α S monomers were isolated by size exclusion chromatography in 10 mM MES [2-(N-morpholino)ethanesulphonate] buffer at pH 5.5 using a 24 ml Superdex75 column (GE healthcare). Protein samples corresponding to the central region of the peak were then collected. The peptide concentration was determined by absorbance at 280 nm using an extinction coefficient 5,800    M − 1 c m − 1 . To obtain high concentration required for scattering experiments, samples were lyophilized after size exclusion column.

E. coli cell pellet containing matchout deuterated αS was prepared in the Deuteration Laboratory of the Institut Laue-Langevin (ILL) in Grenoble, France as described by (Hellstrand et al., 2013a). A high cell density fed-batch culture using 85% deuterated Enfors minimal medium was carried out with computer-controlled temperature at 30°C and pO₂ at 30% saturation (Haertlein, Moulin et al., 2016). The degree of deuteration was 75%. Deuterated αS monomers were isolated as described above.

The lipids used in this study were the phospholipids 1,2-dioleoylysn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-phospho-l-serine (DOPS), 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine and (POPC), 1-palimtoyl-2-oleoyl-sn-glycero-3-phosho-l-serine (POPS), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dimyristoyl-sn-glycero-3-phospho-l-serine (DMPS), and the ganglioside lipids GM1 and GM3 from ovine brain. All lipids were obtained from Avanti Polar Lipids (Alabaster, AL, Unites States). In the preparation of mixed lipid vesicles, lipids were weighted and mixed with the desired proportion (PC:other 9:1). The powder was dissolved in chloroform:methanol (3:1 volume ratio) mixture. The solvent was evaporated under a stream of N 2 gas, and the lipid film was then dried in a vacuum oven over night. The lipids were finally dispersed in the desired buffer (10 mM MES buffer at pH 5.5) and vortexed for a few minutes.

Vesicles were formed either via sonication or extrusion. The sonication was performed for 15 min, 10 s on/off duty at 75% amplitude on ice. The lipid dispersions were centrifuged for 10 min at 1361 rad/s in order to pellet any contaminating particles from the sonicator tip. The supernatant was collected and used as the vesicle dispersion. Extruded vesicles were prepared using a 100 nm pore size filters with 21 passes in total.

In the present study, we analyze and discuss scattering data from fibrils formed at different conditions, in the presence of model membranes with various lipid compositions, obtained at different neutron scattering facilities. For simplicity, samples are numerically labelled and are described in the Table 1, grouped together according to the scattering facility at which the samples were measured, as the sample preparation was different for each facility. A more detailed description of the sample preparation and the SANS experimental conditions is provided in the following text. The buffer used for all samples was a 10 mM MES buffer at pH = 5.5.

Small angle neutron scattering (SANS) experiments were carried out at three different facilities. Below we describe the experimental procedures for each set of experiments.

Samples 1–4 were measured at the D22 beam line located at Institut Laue-Langevin (ILL) in Grenoble France. Three different sample-to-detector distances, 17.6, 5.6, and 1.4 m, with collimation lengths of 17.6, 5.6, and 2.8 m, respectively, were combined. The neutron wavelength was 6.0 Å with the wavelength spread of 10%. Detector patterns were reduced using Grasp software (C. Dewhurst), including thickness and background, as well as direct flux normalization to obtain scattered intensity in absolute units. Scattering curves obtained at the different sample-to-detector distances were combined giving a total q-range comprised between 0.002 and 0.6 Å⁻¹, where q is the wave vector transfer. Samples were measured in single stopper cylindrical cells 120-QS Hellma quartz cuvettes with a 1 mm path length. Measurements were taken at 37°C with the use of a rotating rack to prevent the sedimentation of the fibrils.

Samples 5–7 were measured at the LOQ beamline located at the ISIS Neutron and Muon Source, Chilton, United Kingdom. Samples were measured in single stopper cylindrical cells 120-QS Hellma quartz cuvettes with a 1 and 2 mm path length. A fixed sample-to-detector distance (4 m) combined with a white beam and time-of-flight detection provided a q range of 0.009–0.25 Å⁻¹. The raw scattering data collected at the LOQ instrument in ISIS were corrected for the efficiency and spatial linearity of the detectors, the sample transmission and the background scattering using the instrument dedicated software Mantid (https://www.mantidproject.org/) and the standard procedure indicated in the software guide. Data were then converted into scattered intensity data I(Q). These data were then placed on an absolute scale (cm⁻¹) by comparison with the scattering profile collected from a calibration standard, constituted of a solid blend of hydrogenous and perdeuterated polystyrene which has been measured with the same instrument configuration as per established procedures (Wignall and Bates 1987). Measurements were performed at 37°C with the aid of a rotating rack in order to prevent the sedimentation of the fibrils.

Samples 8–19 were measured at NG7 SANS instrument located at NIST Center for Neutron Research, Gaithersburg, MD, United States. Measurements were performed at four sample to-detector distances (1, 4, 13, and 15.3 m with lenses), and a neutron wavelength of 6.0 Å (sample-to-detector distances of 1, 4, and 13 m) and 8.1 Å (15.3 m with lenses), to obtain a q range spanning from 0.001 to 0.5  Å⁻¹. The wavelength spread is approximately 12% (Glinka, Barker et al., 1998). The data was reduced to the absolute scale using the Igor software by following the standard protocol at NCNR to correct the effect of the background, empty cell, detector efficiency, and the transmission of each sample (Kline 2006). Samples 8–11 were measured in 2 mm path length demountable Ti cells with quartz windows, and samples 12–19 were measured in 1 mm path length banjo quartz cells. Measurements were performed at room temperature. The cells were mounted on a slowly rotating stage to prevent sedimentation during the experiment.

The current work explores, with the use of SANS, the structural organization of αS fibrils at pH 5.5, which is close to their isoelectric point. In these conditions, the fibrils are not colloidally stable, but precipitate out of solution by aggregating into clusters that are prone to sediment (Pogostin, Linse et al., 2019). A total of 19 different samples, for simplicity labeled from 1 to 19, were investigated.

Figure 1 shows SANS patterns, I(q), acquired from all 19 samples probed. The data are shifted with an arbitrary scale for better representation. The data on the absolute scale are shown in Supplementary Figure S1. As can be observed from Figure 1, the scattering patterns from the different samples are strikingly similar. They show a power law scattering, I ( q ) ∼ q − d , over essentially the full q -range covered by the experiments. All 19 data sets were fitted with a simple power law at lower q-values, giving a mean value 〈 d 〉 = 2.6 with standard deviation σ = 0.3 (Supplementary Figure S2). A solid line illustrating d = 2.6 is shown for comparison in Figure 1. We note that slight deviations from a perfect straight line can be observed for some of the samples, in particular sample number 16. One reason for the deviations could be that the clusters are not homogeneous fractal objects, but there are some heterogeneities and a slight variation of the fractal dimension with the probed length scale. At higher q-values there may also be a coupling with the fibril cross section form factor. However, these deviations are minor, in particular if we focus on low q regime, and the overall picture supports that we have fractal aggregates with an average fractal dimension of 2.6.

αS fibrils have the shape of homogeneous cylinders, with a radius R = 5   nm (Pogostin, Linse et al., 2019). Long cylinders typically scatter as I ( q ) ∼ q − 1 (Pedersen 1997), at lower q -values ( q R ≪ 1 ) . The much steeper q -dependence observed here, I ( q ) ∼ q − 2.6 , is a signature of dominating attractive fibril-fibril interactions and that the fibrils aggregate further into fractal clusters, where the value d = 2.6 can be interpreted as a fractal dimension (Lazzari, Nicoud et al., 2016). The value 2.6 is similar, but slightly larger than what is typically found for rod clusters ( d = 2.0 − 2.2 ) (Mohraz, Moler et al., 2004; Solomon and Spicer 2010). However, the exact value that reflects the fibril packing in the clusters, is expected to depend on the cluster formation mechanism (Murphy, Hatch et al., 2020), for example through diffusion-limited or reaction-limited cluster aggregation (Weitz et al., 1985; Lazzari, Nicoud et al., 2016). As a comparison, we note that one particular case of rigid-rod clusters corresponds to the case where randomly oriented rods are connected end-by-end, forming a chain. This case corresponds to the freely-jointed-chain (FJC) model used to describe semi-flexible polymers (Rubinstein and Colby 2003). It is also associated with the random-walk model of translational diffusion (Evans and Wennerström 1999) and is characterized by d = 2.0 . The value d = 2.6 observed here implies a denser packing compared to the FJC model.

In order to better understand the fibril cluster organization, we have constructed fibril clusters using a simple fibril model. The approach by which individual fibrils are connected, is inspired by the FJC model. From the constructed fibril clusters, we calculate the corresponding scattering function, i.e., the cluster formfactor. Below, we present the model in detail and the way for calculating the scattering. As this is a new approach for describing rod clusters, that also may be used to analyze other rigid rod assemblies, we also analyze the model itself in some detail. To assess the present approach we analyze the model scattering function by comparing it with analytical Beaucage model (Hammouda 2010) of fractal objects.

In the present cluster model, individual fibrils were modeled as infinitesimally thin rods, represented by a straight line, of total N _mon point scatterers, referred to as monomers, that are separated by a distance d _mon , as schematically illustrated in Figure 2A. Thus, the fibril length, L, is given by L = ( N mon − 1 ) d mon . Fibril clusters were constructed by adding fibrils stepwise, with fibrils labeled from #1 to #N _fib , where N _fib is the total number of fibrils in the cluster. First, fibril #1, having a randomly chosen orientation, was constructed. Then, fibril #2, again with a randomly chosen orientation, was constructed. A randomly chosen monomer of fibril #2 was given the same position [(x,y,z) coordinate] as one of the monomers of fibril #1, that was also randomly chosen. The process of adding fibrils having random orientation continued, with fibril #3 connecting to fibril #2 and fibril #4 connecting to fibril #3 etc. Finally, a cluster was completed with fibril #N _fib connecting to fibril #(N _fib − 1). As an illustration, a system with N _fib = 4 and N _mon = 100 is depicted in Figure 2B.

The spherically averaged scattering intensity, P _c (q), from the cluster, was then calculated from the spherically averaged Debye scattering equation (Farrow and Billinge 2009) P c ( q ) = ∑ i = 1 N ∑ j = 1 N sin ( q r i j ) q r i j . (1) Here, r ij = | r i → − r j → | with r i → and r j → being the positions of monomers i and j, respectively. The double sum runs over the total number, N, of monomers in the cluster, N = N mon N fib , treating all monomers as identical point scatterers. Eq. 1 represents a single cluster scattering function, i.e., the cluster form factor P _c (q). A cluster, generated by the process described above, is unique and represented by a unique function P _c (q). Thus, in order to form a proper ensemble average, a sum over a number, N _c , of clusters were performed to obtain the ensemble averaged 〈 P c ( q ) 〉 .

Figure 3 displays the scattering pattern 〈 P c ( q ) 〉 obtained by averaging data from N _c = 20 simulated clusters, each with N _fib = 400, N _mon = 100 and d _mon = 1 nm. N _fib and N _mon were chosen to have reasonable computing times (≈1.5 h per cluster) on a normal PC. To confirm that N _c = 20 was sufficient to obtain a reasonable ensemble average, we compare with different averages taken with lower values of N _c in Supplementary Figure S3. We conclude that averaging over 10 clusters already results in reproducible scattering profiles.

The model cluster involve two characteristic length scales, the overall cluster radius of gyration, R g , and the mesh size, ξ , within the fibril network. Thus, the scattering pattern in Figure 3 can be divided up into three regimes (Solomon and Spicer 2010). At lower q -values, q < 1 / R g , there is the Guinier regime, where the scattered intensity is given by I ( q ) = I ( 0 ) exp ( − q 2 R g 2 3 ) . In the intermediate q-range, 1 / R g < q < 1 / ξ , the scattered intensity takes a power law I ( q ) ∼ q − d , where d corresponds to the cluster fractal dimension. Finally, for q > 1 / ξ we have I ( q ) ∼ q − 1 , which is the high q form factor of the (infinitely thin) model fibrils. The full single fibril form factor, for N _mon = 100 and d _mon = 1 nm, is shown in the Supplementary Figure S4.

In Figure 3, the simulated scattering curve is also compared with the analytical Beaucage model (Hammouda 2010). Beaucage model describes fractal objects, and it has been used to describe amyloid fractals formed by amyloid-β, a protein involved in Alzheimer’s disease (Festa et al., 2019a; Festa et al., 2019b). The model describes a low q Guinier regime, followed by a Porod regime with a power law q -dependence of the intensity, q ^-d , for q > 1 / R g , R g again being the radius of gyration. Thus, this model has three independent parameters, R g , the fractal dimension, d, and a scale factor for the intensity. The model scattered intensity is given by I B ( q ) = G exp { − q 2 R g 2 3 } + C q d ( erf { q R g 6 } ) 3 d , (2) Here, erf(x) is the error function and the so called Porod scale factor, C , is related to the Guinier scale factor G by C = G d R g d ( 6 d 2 ( 2 + d ) ( 2 + 2 d ) ) d / 2 Γ ( d 2 ) , (3) where Γ ( x ) is the gamma function. In the calculated curve shown in Figure 3, we have used G = 1.6   10 9 [here, G = ( N fib N mon ) 2 ], R g = 300   nm and d   =   2.3 . From the crossover to q − 1 in Figure 3, we estimate ξ ≈ 10   nm .

Experimentally we observe d = 2.6 indicating slightly more dense clusters than what is produced by the simple model above. In the present model, the cluster is essentially a chain of fibrils, where each fibril is connected to two other fibrils. This construction is related the freely jointed chain (FJC) model of polymers (Rubinstein and Colby 2003), which in turn is associated with the random walk model of translational diffusion. For our conceptual understanding of what influences the fractal dimension, it is interesting to compare quantitatively with the FCJ model. In our cluster model the fibrils connect at randomly chosen monomer positions. In the FJC model, on the other hand, N rigid-rod segments, of length l (the Kuhn length), are connected end-to-end. The radius of gyration of such a chain is given by (Rubinstein and Colby 2003) R g = ( 1 6 N l 2 ) 1 / 2 , (4) and the fractal dimension d   =   2 (Rubinstein and Colby 2003). Equation 4 holds only strictly for the FJC model. However, we can still use it to estimate R _g for our model cluster. In our model, we need to consider an average (random walk) step length, <l>, that here can be identified with the average separation between the two monomer positions within a fibril that are shared with other fibrils. Thus, l is limited to 1 ≤ l/d _mon ≤ (N _mon − 1). The probability of a given l-value deceases monotonically with increasing l. Defining l/d _mon = n, the number of monomers between two connections, we have 〈 l 〉 / d mon = ∑ n = 1 N mon − 1 n ( N mon − 1 − n ) ∑ n = 1 N mon − 1 ( N mon − 1 − n ) , (5) With N _mon = 100 and d _mon = 1 nm, we obtain <l> = 33 nm. With this value of <l> and N = N _fib = 400 in Eq. 4 we obtain R g = 270   nm which is only slightly smaller than the value 300 nm obtained for the model clusters described above (Figure 3).

Within this simple cluster model, reducing the effective step length l, by connecting the fibril segments randomly reduces R g   and increases d, compared to the limiting FJC case. In an attempt to decrease l further, and thereby possibly increase d, we also simulated clusters where we let fibril #(i+1) connect at the middle monomer (#50) of fibril #i, while the other parameters of the connections were randomly chosen. This decreases the maximum possible value of l from N _mon (100) to N _mon /2 (50). The calculated scattering pattern from such clusters is shown in Figure 4. By again fitting the calculated scattering curve with the Beaucage model we obtain R g = 220   nm and d = 2.5, using G = 1.6 10⁹

In Figure 4 we are also comparing with the FJC model, where fibrils are connected end-to-end. For ideal chains, like FJC chains, the form factor was derived by Debye (Debye 1947) and is consistent with d = 2 P FJC ( q ) = 2 ( e − x + x − 1 ) / x 2 , (6) where x = qR _g . Shown in Figure 4 as a solid blue line is a calculated model form factor P_FJC(q) (Eq. 6) using Rg = 800 nm. This is in good agreement with Rg = 808 nm, calculated from Eq. 4.

As seen in Figure 4, Rg decreases and d increases as the distance between connection points in a fibril with neighboring fibrils is decreasing. Shown as an inset in Figure 4 are Guinier plots, ln ( I ( q ) ) vs q² using data at low-q, from which we can do a model free evaluation of Rg from ln ( I ( q ) ) = − q 2 R g 2 / 3 . The Rg values obtained this way are 690 nm for the case of FJC model, 300 nm for only random connection points and 240 nm for the case with one of the connection points being in the middle of the fibril. The values are in good agreement with the values obtained with the Debye and Beaucage model, respectively.

With the calculations presented above we demonstrate that within the simple model used, it is possible to construct fibril clusters having different fractal dimensions, including the values that we observe experimentally. Our experimentally observed value 2.6 is similar, but slightly larger than what is typically found for rod clusters ( d = 2.0 − 2.2 ) (Mohraz, Moler et al., 2004; Solomon and Spicer 2010). However, the exact value, that reflects the fibril packing in the clusters, is expected to depend on how the clusters are formed for example through diffusion limited or reaction limited aggregation (Weitz et al., 1985; Lazzari, Nicoud et al., 2016).

In the experimental scattering patterns (Figure 1) we essentially observe only a single power law dependence of the scattered intensity I ( q ) ∼ q − d within studied q-range. Thus, we only observe one (the middle one) out of the three different q-regimes of the scattering pattern, discussed in connection with Figure 3. That we do not observe a Guinier regime with a leveling off of the scattered intensity at lower q -values implies that the formed clusters are much larger than q min − 1 ≈ 100   nm , where q _min is the minimum q -values accessible in the experiment. Neither at higher q-values do we observe any crossover to q − 1 , related to a length scale where the one-dimensional nature of the individual fibril morphology would be detected. This implies a very dense packing of the fibrils in the clusters, with the mesh size being not much larger than the fibril diameter (10 nm).

The model that we have used in Figures 3, 4 assumes infinitely thin fibrils. The mesh size of such clusters is approximately equal to 10 nm. To further illustrate the effect of a finite size cylinder, we have extended calculation, and we are showing them in the Supplementary Figure S5.

αS fibrils are a major component of Lewy bodies, a pathological feature of Parkinson’s disease (Shults 2006; Araki, Yagi et al., 2019; Lashuel 2020). They are micrometre sized intracellular inclusions in the substantia nigra, that also contain lipids, membranous organelles, as well as other proteins (Lashuel 2020; Mahul-Mellier, Burtscher et al., 2020). Agglomerates and clusters of this kind are typically consequences of dominating attractive interactions, and recent work has indicated that the accumulations of various species through an effective liquid-liquid phase separation may be effective in various biological functions (Hyman, Weber et al., 2014). Colloidal interactions in the living cell, e.g., protein-protein interactions and protein membrane interactions are typically weakly repulsive, because essentially all colloidal aggregates and macromolecules carry a net negative charge. This ensures the colloidal stability of the living cell (Wennerström, Vallina Estrada et al., 2020). An interesting question concerns the origin of, and the reason for, the effective attractive interaction resulting in the accumulation of αS fibrils, and other components, that lead to the formation of Lewy bodies. Here, in combination with a previous work (Pogostin, Linse et al., 2019), we have shown that a pH drop from neutral to mildly acidic conditions (pH = 5.5) is sufficient to switch fibril-fibril interactions from being predominantly repulsive to become predominantly attractive resulting in a dense clustering of αS fibrils. At the same time, the rate of αS fibril formation is significantly increased at mildly acidic pH (pH = 5.5) due to strongly enhanced secondary nucleation (Cohen, Linse et al., 2013).

Mildly acidic pH is indeed found in some cellular compartments such as lysosomes and also in endosomes (Demaurex 2002; Hu, Dammer et al., 2015). Attractive fibril-fibril interactions may also result from cleavage of the acidic C-terminus, which up-shifts the isoelectric point, or from increased salt screening of long-range electrostatic repulsion. The use of mildly acidic pH to induce fibril clustering likely mimics these three cases and may provide a route towards the study of fibril organization in Lewy bodies.

Dispersions of αS fibrils formed at pH 5.5 behave significantly different compared to those formed at slightly higher pH where a stable fibril hydrogel network can be formed. (Pogostin et al., 2019). At pH 5.5 the formed αS fibrils are colloidally unstable and aggregate further into clusters. Inspired by the fact that Lewy bodies appear to contain accumulations of αS fibrils, indicating effectively attractive fibril-fibril interactions, we have here investigated αS fibrils clusters at pH = 5.5 in more detail. SANS experiments performed on 19 different samples show strikingly similar result. The SANS intensities show an extended power law dependence on the scattering vector, q, that is consistent with that the clusters can be described as mass fractals, with a fractal dimension d ≈ 2.6. To further conform this conclusion, we have developed a simple model of rigid rod clusters, that was found to be able to reproduce the experimentally observed fractal dimension. The simple cluster model is closely related to the classical FJC model of polymers, that may also serve as a reference case with d = 2.