β-Synuclein suppresses both the initiation and amplification steps of α-synuclein aggregation via competitive binding to surfaces

α-Synuclein is an intrinsically disordered protein that is associated with the pathogenesis of Parkinson’s disease through the processes involved in the formation of amyloid fibrils. α and β-synuclein are homologous proteins found at comparable levels in presynaptic terminals but β-synuclein has a greatly reduced propensity to aggregate and indeed has been found to inhibit α-synuclein aggregation. In this paper, we describe how sequence differences between α- and β-synuclein affect individual microscopic processes in amyloid formation. In particular, we show that β-synuclein strongly suppresses both lipid-induced aggregation and secondary nucleation of α-synuclein by competing for binding sites at the surfaces of lipid vesicles and fibrils, respectively. These results suggest that β-synuclein can act as a natural inhibitor of α-synuclein aggregation by reducing both the initiation of its self-assembly and the proliferation of its aggregates.

α-Synuclein and β-synuclein bind to DMPS vesicles with dissociation constants, K D,α and K D,β , respectively, and stoichiometries, L α and L β , respectively. Thus, for increasing β-synuclein:α-synuclein ratios, the fraction of protein binding sites on the surfaces of the vesicles occupied by α-synuclein molecules (θ α ) will decrease as β-synuclein competes for the same protein binding sites. We therefore used a competitive binding model, which makes the assumption that α-synuclein and β-synuclein bind independently to DMPS vesicles, to determine θ α for any β-synuclein:α-synuclein ratio: where [α b ] is the concentration of α-synuclein bound to the DMPS vesicles, [DM P S] is the total DMPS concentration and [DM P S] Lα is the concentration of protein binding sites at the surfaces of the vesicles. We then expressed the total concentrations of DMPS and α-and β-synuclein as a function of the binding constants K D,α and K D,β of α-and β-synuclein for the DMPS vesicles using the relationships: The explicit expression is not shown here due to its length. The influence of different concentrations of β-synuclein on the binding of α-synuclein can be simulated using this model and is shown in Supplementary Figure 6.

Microfluidics -Data analysis
The 12 images taken along the diffusion channel were processed into a set of lateral scan profiles, which were then fitted to a set of simulated basis functions. These diffusion profiles contain information both about the spatial diffusion (along the channel width) and temporal evolution (along the channel length), which allows deconvolution of the experimental profiles and measurement of the diffusion coefficients for individual components of a mixture. A maximum entropy basin hopping algorithm with a Broyden Fletcher Goldfarb Shannon (BFGS) minimisation protocol was used to find the linear combination of simulated radii that gives the lowest residuals. This analysis yields the average radius of the sample, as well as the fractions of individual species if the sample is polydisperse [1,2].

Quartz Crystal Microbalance measurements
The QCM experiments were performed with a E4 QCM-D instrument (Q-Sense, Biolin Scientific, Stockholm, Sweden), using gold-coated QSX 301 sensors. The sensors were cleaned immediately prior to use with a hot (80 • C) mixture of water/30% H 2 O 2 /conc. NH 3 solution (5/1/1) for 30 min, followed by rinsing with water, drying, and UV/O 3 treatment.
The protocols for the attachment of monomeric and fibrillar α-synuclein closely followed methods presented previously [3]. Both fibrillar and monomeric α-synuclein samples were prepared in PBS buffer at 20µM. The fibrils were sonicated for 4 min at 20% amplitude on a 500 W ultrasonic homogenizer (Cole Parmer, Hanwell, UK) with 3 s pulses and 3 s breaks. 2-Iminithiolane (Traut's reagent) was added to give a final concentration of 1 mg/ml to the protein samples, which were incubated for 5 min and then 80 µl aliquots of the chemically activated protein solution were put onto each of the freshly cleaned gold-coated sensors for 1h in a humid atmosphere, to prevent drying. Then the sensor surfaces were rinsed with PBS buffer and incubed for 30 min with a 1% (v/v) solution of mPEG-thiol (Polypure, Oslo, Norway) in PBS. Then the sensors were rinsed with water and introduced into the microbalance. The QCM flow cells were filled with phosphate buffer at pH 6.5 and the temperature was set to 37 • C. The measurements were started once a stable frequency baseline had been established. The solutions of α-synuclein and β-synuclein for the interaction studies were introduced via a peristaltic pump at a flow rate of 150 µl/min. For each sample, 300 µl aliquots were introduced and the pump stopped during the measurements.

Data acquisition
Lipid-induced aggregation Lipid-induced aggregation experiments were performed under quiescent conditions at 30 • C, pH 6.5 in the presence of 350 µM DMPS vesicles and increasing concentrations of α-synuclein and β-synuclein (0 -200 µM), as described in the Results section. At the end of each aggregation experiment, the fibril concentration was determined by ultracentrifugation of the sample for 30 min at 90 k rpm and determining the remaining free monomer concentration in the supernatant by measuring absorbance at a wavelength of 280 nm using an extinction coefficient of 5,960 M −1 cm −1 , correcting for ThT absorbance as described previously [4]. For Alexa-568-α-synuclein, a correction for absorbance by the Alexa-568 dye was also performed, according to the manufacturer's protocol (Life Technologies, Carlsbad, California). By assuming that the ThT signal was proportional to the fibril mass, the change in mass over the time course of the experiment could then be calculated.

Determination of the degree of co-aggregation of α-and β-synuclein
In order to detect the relative quantities of α-synuclein and β-synuclein incorporated within the fibrils formed in the presence of DMPS, α-synuclein and β-synuclein were each labelled at their primary amine groups with Alexa Fluor 568 (Alexa-568) by NHS ester conjugation according to the manufacturer's protocol (Life Technologies, Carlsbad, California). Each protein was then purified by a single size exclusion chromatography (Superdex 200 Increase 10/300 GL, GE Healthcare, Buckinghamshire, UK) step in which labelled monomeric protein was eluted in 20 mM phosphate buffer, pH 6.5, 0.01% NaN 3 . The efficiency of labelling was determined using UV absorbance at 280 nm and 577 nm to be c.a. 10 %. Fibrils were formed by incubating 100 µM monomeric Alexa-568-β-synuclein in the presence of an equal concentration of unlabelled monomeric α-synuclein and either DMPS vesicles or α-synuclein seed fibrils. When the ThT signal reached the plateau phase, the reaction mixtures were ultracentrifuged (90 krpm for 30 min) and the pellets washed with the reaction buffer (20 mM phosphate buffer, pH 6.5, 0.01% NaN 3 ) in order to isolate the resulting fibrils and to wash off any monomeric α-synuclein and β-synuclein. This step was carried out twice before measuring the fluorescence spectrum of the resuspended fibrils from 580 and 680 nm. Labelling reduced the lipid binding affinities and slowed down the kinetics of lipid-induced α-synuclein aggregation, effects likely to be due to a perturbation of the α-helical region upon addition of the negatively charged dye at the Nterminus, but did not change the mass of fibrils formed (Supplementary Figure 2). We compared the fluorescence intensity at 600 nm of fibrils formed when α-synuclein seed fibrils were incubated in the presence of unlabelled monomeric αsynuclein and Alexa-568-β-synuclein (I 600nm,Alexa−568−β−syn ) to that of fibrils formed when α-synuclein seed fibrils were incubated in the presence of monomeric Alexa-568-α-synuclein and unlabelled β-synuclein (I 600nm,Alexa−568−α−syn ). The ratio of the two intensities gives the upper bound of the level of incorporation of β-synuclein within α-synuclein fibrils.
Theoretical modeling α-synuclein aggregation in the presence of lipid vesicles A full kinetic model for α-synuclein aggregation in the presence of lipid vesicles involves the simultaneous action of protein binding to vesicles, surface primary nucleation and fibril elongation. In the limit of fast binding of α-and β-synuclein onto the surface of vesicles, the resulting set of kinetic equations can be solved by analysis through the method of matched asymptotics. The resulting analytical solution evolves through two main reaction stages. In the first stage (boundary layer) a quasi-equilibrium between bound and free α-and β-synuclein is established, leading to Eqs. S5 and S6. In the second stage (slow manifold) α-synuclein molecules bound to vesicles nucleate and generate aggregates that are capable of further growth. Under these circumstances, the rates of the nucleation and growth steps depend on θ α to powers ν and , respectively. The fundamental kinetic equations describing this slow stage of the reaction are therefore given by: where [P ] is the number concentration of aggregates, k + , k n are the rate constants for elongation and primary nucleation in the presence of DMPS, respectively, n is the reaction order of the nucleation step relative to free monomeric αsynuclein, ν and are the reaction orders of the nucleation and elongation steps, respectively, and K M is the Michaelis-Menten constant describing saturating filament elongation. The early time behaviour of the solution to Eqs. S9 and S10 ([α f ](t) = [α f ](0)) yields a t 2 -behaviour for the mass concentration [M ] of aggregated protein: (S11) where n b = ν + is the reaction order of lipid induced aggregation with respect to θ α . A global fit of aggregation data at early time points was performed using this model and the web-based software AmyloFit [6]. It is noteworthy, that the analytical solution used previously to describe the lipid-induced aggregation data [4] corresponds to Eq S11 under conditions of full lipid coverage by one species (α-synuclein) corresponding to θ α = 1.
Aggregation of α-synuclein at pH 4.8 Fibril amplification processes (processes involving a change in the number of fibrils) of α-synuclein aggregation are greatly enhanced at mildly acidic pH [5]. They are most readily observed in the presence of nanomolar seed fibril concentrations and micromolar monomeric α-synuclein concentrations [5]. We begin with the linear polymerization model [7]: and take the derivative of dM (t) dt , which allows us to formulate an equation for the rate of fibril amplification, dP (t) dt : Where k + is the fibril elongation rate constant, m(t) the soluble monomer concentration, M (t) is the mass concentration of fibrils and P (t) the number concentration of fibrils. At early times in the aggregation reaction, the monomer concentration and the fibril number concentration can be assumed to be constant, hence m(t) = m(0) and P (t) = P (0). At the half-time of the reaction, d 2 M (t) dt 2 is small for sigmoidal curves; we therefore assume that d 2 M (t) , which gives: Our results show that β-synuclein does not perturb the elongation of α-synuclein fibrils under the solution conditions where secondary nucleation can be studied, i.e. the presence of β-synuclein does not appear to affect k + . In the experiments designed to probe the effect of β-synuclein on the secondary nucleation of α-synuclein (see details at the beginning of this section), the α-synuclein concentration, m(0), was kept constant, so for the purposes of this analysis the only variable in equation S16 is dm(t) dt t=t 1/2 . Therefore: Thus measurements of dm(t) dt t=t 1/2 provide information on how the apparent secondary nucleation rate of α-synuclein varies in the presence of increasing concentrations of β-synuclein. The ThT fluorescence signal was first used to define the change in fibril mass over time, as for the lipid-induced aggregation experiments at pH 6.5, then fitted to a sigmoidal curve and the first derivative at t 1/2 was computed. This latter term was normalised to the values at [β-synuclein] = 0 µM to give the relative secondary nucleation rate at each β-synuclein:α-synuclein ratio.    Figure 5: The interaction between β-synuclein monomers and α-synuclein fibrils at pH 6.5. Diffusion profiles taken at 12 positions with the microfluidic diffusional sizing device described previously (See Experimental Section for details). The diffusion profiles of 2.5 µM monomeric Alexa-568-β-synuclein (blue) and 100 µM Alexa-647-α-synuclein fibrils (purple) were used to define their respective R H values. The diffusion profiles of monomeric Alexa-568-β-synuclein in the presence of unlabelled α-synuclein fibrils at concentrations of 12.5 µM (red) and 100 µM (green) were used to estimate the proportion of monomeric β-synuclein attached to α-synuclein fibrils, which was less than 5% and about 10%, for α-synuclein fibrils:β-synuclein monomer ratios of 5 and 40, respectively.  , the values of the concentration of α-synuclein bound to 350 µM (solid lines) DMPS vesicles was calculated from the competitive binding model (see Experimental Section) using the binding constants (K D and L) determined using CD measurements individually for α-synuclein and β-synuclein and Eqs. 7 and 8 in the Experimental Section. The black circles represent conditions for which experimental aggregation data were obtained (see Figure 3 in the main text)