Amyloid particles facilitate surface-catalyzed cross-seeding by acting as promiscuous nanoparticles

Significance The formation of disease-associated fibrillar amyloid structures can be accelerated by preformed amyloid seeds. This seeding process is thought to occur solely through elongation at amyloid fibril ends, resulting in the templated propagation of the protein conformation encoded in the seeds. We demonstrate that amyloid seeding does not always proceed through templated elongation and show that amyloid seeds are nanoparticles that can accelerate the formation of new heterologous amyloid without templating the protein conformation encoded in the seeds. We provide experimentally testable criteria to distinguish seeding through a templated elongation mechanism from surface catalysis and present mechanistic insights into the amyloid seeding and cross-seeding phenomenon. These findings have wide implications for our understanding of the molecular basis of amyloid cross-interactions.

1 Kent Fungal Group, School of Biosciences, University of Kent, CT2 7NJ, Canterbury, UK 2 School of Physical Sciences, University of Kent, CT2 7NJ, Canterbury, UK * To whom correspondence may be addressed, Email: W.F.Xue@kent.ac.uk

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Supplementary text Figures S1 to S6 Table S1 SI References

Background theory
A full description of the dynamic mechanism of any amyloid assembly reaction can be formally written using the chemical master equation (1): Eq. S1 In Eq. S1, C is a column vector that describes the distribution of a discrete set of species involved in the mechanism (e.g. monomers, dimers, trimers, etc.) and their molar concentrations at any time t. The matrix k represents the rate constants of all possible microscopic reaction steps (e.g. monomers to dimers, dimers back to monomers, dimers to trimers, trimers back to dimers, etc.). Thus, Eq. S1 represents a generic ordinary differential equation (ODE) system consisting of an infinite number of coupled equations, each describing a possible microscopic reaction step. Four processes has been shown to be crucial for amyloid assembly, primary nucleation, growth by elongation at fibril ends, secondary nucleation catalyzed by surfaces of existing amyloid fibrils, and fibril fragmentation. Thus, in Eq. S1, the rate constants in k can be broken up and grouped to individual terms, each describing a key process. The overall reaction progress of amyloid assembly reactions can be monitored by the amyloid specific fluorescent dye Thioflavin T (ThT), which is sensitive to the mass fraction of monomers in the amyloid state (2). Thus, for the analyses of ThT traces of amyloid assembly reactions from single type of monomers, Eq. S1 can be collapsed into three ODEs: In Eq. S2, m(t) is the free monomer concentration and M(t) is the concentration of monomers in amyloid fibrils, at any time t. The total monomer concentration is, therefore: mtot = m(t) + M(t).
During any amyloid formation reaction, the change in M concentration can be approximately taken to be proportional to the ThT fluorescence signal, and depends on the reaction velocities (n) of primary nucleation, elongation, and secondary nucleation. Primary nucleation velocity depends on the free monomer concentration (m), and can be approximated as D B · ( ) B Z where nc is the size of nuclei formed in solution and kn is the primary nucleation rate constant (3,4). Secondary nucleation velocity depends on the free monomer concentration and the fibril mass concentration which is proportional to the concentration of monomers in amyloid fibrils (M), and can be approximated as ] ] · · ( ) B^ where n2 is the size of the nuclei formed on the existing fibril surfaces and k2 is the secondary nucleation rate constant (3,4). Elongation velocity depends on the free monomer concentration (m) and the particle concentration of fibrils or fibril seeds, F. In addition, the net elongation velocity also depends on the rate of monomers dissociating from the fibril ends. Therefore, the elongation velocity can be expressed as ( a ( ) − M ) · ( ) where k+ is the elongation rate constant and kd is the monomer dissociation rate constant. Fragmentation does not contribute to changes in M because the total number of monomers in the amyloid state in an amyloid fibril breaking into two is considered to be the same. F(t) in Eq. S2 is the particle concentration of amyloid fibrils in molar unit, and therefore, this is the seed concentration at any given time t. The change in F concentration depends on the reaction velocities of primary nucleation, secondary nucleation and fragmentation. Elongation at fibril ends does not contribute to changes in F since the growth of fibrils in size through elongation does not lead to an increase in the number of fibrils. The reaction velocity for fragmentation can be assumed to be negligibly small compared to the other two contributions to changes in F under quiescent experimental conditions, and under conditions where fibril seeds are small in size (5). The contributions from primary and secondary nucleation to changes in F can be approximated in similar manner as in the case of M. Putting all of the considerations above into Eq. S2 yields the following ODE system that can be used to describe experimental ThT traces.
For the analyses of ThT traces of heterotypic amyloid assembly reactions from two types of monomers, Eq. S2 can be expanded to include additional three equations for the second monomer type, as well as additional terms compared to Eq. S2 and Eq. S3 to account for the contributions of cross-interactions, e.g. surface catalyzed heterogeneous nucleation, cross-elongation at fibril ends, and co-aggregation. However, for cross-seeded reactions, since the particle concentration and the monomer equivalent concentration of the heterologous seeds is likely to remain relatively constant due to negligible fragmentation and monomer dissociation under quiescent growth conditions, terms describing co-aggregation can be assumed to be negligible. Eq. S3 can then be modified to include cross-seeding due to elongation of heterologous seeds or surface catalyzed nucleation on heterologous seeds: a,ee ( ) · ee ( ) + ],ee · ee ( ) · ( ) B^, ff eė ( ) = − a,ee ( ) · ee ( ) ̇( ) = −̇( ) In Eq. S4, the index 'II' denotes concentrations and rate constants arising due to the heterologous seeds added. Interestingly, the monomer equivalent concentration of heterologous seeds Eq. S4 can be solved numerically with given initial concentrations of monomers and seeds, and analytical or numerical solutions can be fit globally to experimental data series (e.g. (6)) to validate model predictions and to extract information regarding kinetic rate constants. Here, the equation system Eq. S4 was solved numerically for relevant sets of initial concentrations and globally fit to ThT traces of seeded amyloid forming reactions (Supplementary Figure S4) as previously described (2). Experiments with specific initial concentrations of seeds were also designed to allow isolation of the elongation and surface nucleation terms in Eq. S3 and S4 to resolve the heterologous crossseeding mechanism as detailed below.
An amyloid assembly reaction trace reported by ThT and normalized to the upper stationary baseline is sensitive to the mass fraction of monomers in the amyloid state (2). Thus, the normalized ThT signal intensity, I, can be assumed to be proportional to the following: Eq. S5 To isolate the reaction rates that account for elongation and enable its comparison with the rates of surface catalyzed nucleation (i.e. secondary nucleation for homologous seeds and heterogeneous nucleation for heterologous seeds), the initial reaction rates can be evaluated. Using Eq. S3 and S5, the change of normalized ThT signal as function of time is: The initial slope of the normalized ThT signal, ̇n = ( = 0), is then for a self-seeded reaction: In Eq. S7, m0 , M0 and F0 are the concentration of free monomers, the concentration of monomers in the seeds added, and the particle concentration of seeds added, at the beginning of a reaction when t = 0s, respectively. If the monomer dissociation rate constant kd is negligibly small compared with the elongation rate constant k+, as commonly the case for amyloid assembly under their normal growth conditions (4), Equation S7 can be further simplified: n =̇n ≈ D B · n B Z + a n · n + ] ] · n · n BĤ JH − n = D B · n B Z + a n · n + ] ] · n · n Bn = D B · n B Z qr + a · n + ] ] · n · n B^qr Eq. S8 Analogously, for a cross-seeded reaction, using Eq. S4 and S5 and inputting that the concentration of homologous seeds, M0 and F0, is zero: n =̇n ≈ D B · n B Z + a n · n + ] ] · n · n B^+ a,ee n · ee ( ) + ],ee ],ee · n,ee · n B^, ff HJH − n = D B · n B Z + a,ee n · n,ee + ],ee ],ee · n,ee · n B^, ff n = D B · n B Z qr + a,ee · n,ee + ],ee ],ee · n,ee · n B^, ff qr Eq. S9 As seen above, apart from the difference in the identity of the seeds and the rate constants associated with their reactions, Eq. S8 and S9 are identical. Thus, the initial slope of seeded amyloid formation reactions monitored by ThT, k0, can be expressed using Eq. S8 for any single type of seeds. Eq S8 (and S9) is, therefore, particularly useful for analyzing self-seeded as well as cross-seeded amyloid assembly reactions because M0 and F0 can represent the concentrations of any type of homologous or heterologous seeds added, and the initial seed concentrations can be easily varied experimentally. The initial particle concentration F0 is linked to the monomer equivalent concentration M0 in added seeds through the length distribution of the seeds added (1):

= ·
Eq. S10 In Eq S10, N is the number of monomers per unit length of fibrils and L is the average length of the fibrils, both parameters can be estimated by imaging (1,5). In the case where the same stock of seeds are added to seeded reactions, the length distribution of the seeds added will be the same and the initial slope k0 is linearly proportional to M0, with contributions from both elongation and surface catalyzed nucleation to the proportionality constant. For self-seeded reactions, the elongation rate dominate over secondary nucleation, but for cross-seeded reaction, the relative contributions between elongation and surface-catalyzed nucleation (second and third term in Eq. S8, respectively) may vary depending on the precise protein pair. In the case where the same seeds sonicated to different extents are added to seeded reactions, the monomer equivalent concentration M0 will stay constant but the initial particle concentration F0 will vary since the average length of the seeds L will change. In that case, as seen in Eq. S8, the initial slope k0 will only be linearly proportional to F0 (with a non-zero proportionality constant) due to elongation. Thus, if a constant k0 that does not vary with changes in F0 is observed then that will mean elongation rate is negligibly small compared to the surface nucleation based contributions such as surface catalyzed nucleation, leading to prediction II (Figure 1c).     Figure 3. Under the experimental conditions used, the self-seeded elongation rate constants (Eq. S4) obtained from the globally fitted models are 4.0·10 5 M -1 s -1 and 3.5·10 4 M -1 s -1 for self-seeded Sup35NMm and Aβ42m fibril formation reactions, respectively. These rate constants for elongation are in comparable range to those reported for other amyloid forming systems (e.g. (1, 4)). The cross-seeded surface nucleation rate constants (Eq. S4) are 7.2 M -2 s -1 and 6.7·10 1 M -2 s -1 for Sup35NMm -Aβ42s and Aβ42m -Sup35NMs pairs, respectively. These values are two to three orders of magnitude smaller than the secondary nucleation rate constant for Aβ42 amyloid formation (4). All kinetic rate constants used to reproduce these globally fitted traces of seeded amyloid formation are shown in Supplementary  Table S1.   Table   Table S1. Kinetic parameters obtained from global analysis of ThT fluorescence kinetics data. Kinetic parameters used to reproduce the fitted traces of seeded amyloid formation shown in Supplementary Figure S4 (based on Eq. S4) are shown together with their respective standard error (SE). The parameters nc, n2 and n2,II are approximated to be 2 based on the same assumption used in (4). The dissociation rate constant kd is assumed to be negligible compared to k+ (Eq. S8 and Eq. S9).