The role of shear forces in primary and secondary nucleation of amyloid fibrils

Significance

Amyloid formation is linked to a large number of devastating human diseases affecting the function of the brain and other organs. Common to these diseases is the deposition of amyloid protein aggregates, calling for extensive studies of the mechanisms of deposition. The aim is to find the underlying steps in the mechanism, which steps are associated with neuronal cell death and how to prevent these steps. A second aim is the molecular and physical principles governing each step. The current study shows that the detachment of newly formed aggregates from catalytic surfaces may be the rate-limiting step in protein aggregation and that shear forces may play a role in this process.

Abstract

Shear forces affect self-assembly processes ranging from crystallization to fiber formation. Here, the effect of mild agitation on amyloid fibril formation was explored for four peptides and investigated in detail for A$\mathbf{\beta }$42, which is associated with Alzheimer’s disease. To gain mechanistic insights into the effect of mild agitation, nonseeded and seeded aggregation reactions were set up at various peptide concentrations with and without an inhibitor. First, an effect on fibril fragmentation was excluded by comparing the monomer-concentration dependence of aggregation kinetics under idle and agitated conditions. Second, using a secondary nucleation inhibitor, Brichos, the agitation effect on primary nucleation was decoupled from secondary nucleation. Third, an effect on secondary nucleation was established in the absence of inhibitor. Fourth, an effect on elongation was excluded by comparing the seeding potency of fibrils formed under idle or agitated conditions. We find that both primary and secondary nucleation steps are accelerated by gentle agitation. The increased shear forces facilitate both the detachment of newly formed aggregates from catalytic surfaces and the rate at which molecules are transported in the bulk solution to encounter nucleation sites on the fibril and other surfaces. Ultrastructural evidence obtained with cryogenic transmission electron microscopy and free-flow electrophoresis in microfluidics devices imply that agitation speeds up the detachment of nucleated species from the fibril surface. Our findings shed light on the aggregation mechanism and the role of detachment for efficient secondary nucleation. The results inform on how to modulate the relative importance of different microscopic steps in drug discovery and investigations.

The acceleration of self-assembly processes due to mechanical agitation has been reported for centuries and the effect of stirring on the rate of crystallization was described as a widely known phenomenon by Miers and Isaac in 1906 (1). The authors reported a sudden burst of precipitation at the end of the lag phase for stirred but not quiescent supersaturated samples. Similar bursts have much later been described for amyloid beta peptide (2). Vigorous stirring or shaking is commonly used to shorten the time needed for reducing a solution from supersaturated to saturated state. For example, agitation through stirring in industrial crystallizers is used to speed up the reaction and to ensure a homogeneous product (3). The shear forces due to convection and agitation speed up secondary nucleation by facilitating the detachment of newly formed aggregates from the crystal surface (4–6). Another contribution to the acceleration of aggregate formation in industrial crystallizers comes from contact nucleation, also referred to as collision breeding, whereby contacts between a growing crystal and walls of the container, the stirrer, or other crystals result in the formation of contact nuclei (7).

The self-assembly of amyloid fibrils is very sensitive to environmental factors such as the solution composition, temperature, pressure, etc. In the field of amyloid protein aggregation, vigorous shaking has historically been used as a means to compensate for the challenge of obtaining a homogeneous starting material, because massive fragmentation is less sensitive to impurities than secondary nucleation and can be used to increase the reproducibility of the obtained data (8–12). However, by carefully controlling amyloid sample purity, homogeneity, and aggregation conditions, agitation is not needed (8, 13), and molecular and environmental factors can be investigated in a systematic manner (see for example ref. 14).

Mechanistic studies carried out over the last few decades have shed light on the underlying microscopic steps of amyloid fibril formation. This process typically follows a double nucleation mechanism akin to that reported for crystallization as well as fiber formation in other systems (8, 15–18) and proposed for prion replication (19). Nucleation may occur in supersaturated solutions of monomers and refers to the formation of clusters of a critical size, whose rate of growth through monomer addition is larger than the rate of dissociation back to monomers (20).

In the case of primary nucleation, heterogeneous nucleation at a foreign surface may be more efficient than homogeneous nucleation in bulk (21–27). The reduction in surface energy can be even higher when there is a match in structure and molecular properties between the surface and the self-assembling substance (3, 28). The most efficient nucleation may occur on the surface of aggregates of the same type of monomers as the ones in the solution, known as secondary nucleation. When treating kinetics of systems with large conformational changes, such as amyloid formation, the nucleation rate constants often cover multiple steps, including the conversion to fully growth-competent aggregates. Master equation solutions to the coupled differential equations that describe the time evolution of the system can be used to globally fit data obtained at multiple starting conditions to resolve the rate constants for the isolated mechanistic steps: primary nucleation, secondary nucleation, fragmentation, and elongation (29, 30). This now enables us to investigate the effect of gentle agitation on these steps in further detail.

High-throughput kinetic studies commonly rely on the use of fibril-binding fluorescent dyes to probe the rate of amyloid formation in 96-well plates. If the assays involve moving the plate relative to a fixed light source, gentle agitation is unintentionally introduced into the system, which accelerates fibril formation (31). The current study builds on this observation. By taking control of the amount of gentle agitation applied, we investigate the generality and mechanistic origin of the effect of shear forces on amyloid formation. The mechanistic investigations are focused on A$\mathrm{\beta }$42 from Alzheimer’s disease. In vitro, this peptide forms monomorphic fibrils as seen by solid-state-NMR (32), and small angle X-ray studies reveal four monomers per fibril plane, i.e., two monomers per plane in each of two filaments wrapping around each other (33). Nonseeded aggregation reactions were set up at a range of peptide concentrations and were complemented with seeded reactions and with reactions with an inhibitor to find which microscopic steps in the self-assembly process are affected by gentle agitation. While a previous perspective asked whether shear forces would accelerate secondary nucleation by facilitating the detachment of new aggregates and thereby freeing up the catalytic surfaces (34), we find that increased shear forces accelerate secondary as well as primary nucleation. In contrast, we find no effect of gentle agitation on elongation or fragmentation of fibrils.

Materials and Methods

Chemicals and Consumables.

Sodium dihydrogen phosphate dihydrate, disodium hydrogen phosphate, MES monohydrate, guanidine hydrochloride, sodium azide, and EDTA disodium salt were purchased from Sigma-Aldrich, and thioflavin T (ThT) from Calbiochem. 1,4-bis(3-carboxy-4-hydroxyphenylethenyl)benzene (X34) was synthesized as previously described (18, 35, 36). Axygen MaxyClear Snaplock Microtubes, Corning® 96-well Half Area Black/Clear Flat Bottom PEG-ylated Polystyrene Microplates (3881) and wwPTFE 0.2 $\mathrm{\mu }$m 50 MM disc filters were purchased from Fischer Scientific.

Expression and Purification of Peptides and Proteins.

The genes for A$\mathrm{\beta }$(M1-42) and A$\mathrm{\beta }$(M1-40), herein referred to as A$\mathrm{\beta }$42 and A$\mathrm{\beta }$40, respectively, were prepared using overlapping PCR from synthetic oligonucleotides with codons optimized for expression in Escherichia coli (E. coli), and cloned into a PetSac plasmid as reported (37). The gene for the tau fragment tau304-380C322S, which comprises the amyloid core of Alzheimer’s disease–derived fibrils (38), here referred to as tau, was synthesized with codons optimized for expression in E. coli and cloned into a Pet3a plasmid (purchased from Genscript).

The amyloid peptides were expressed in E. coli. The strain T7 Express (New England Biolabs) was used for A$\mathrm{\beta }$(M1-40) and BL21 Star DE3 pLysS (Invitrogen) for A$\mathrm{\beta }$42 and tau. A$\mathrm{\beta }$42 and A$\mathrm{\beta }$40 were purified from inclusion bodies after repeated sonication and centrifugation, followed by a series of ion exchange and size exclusion steps as described (8, 39). Tau was purified from boiled sonicate as described (18). The purified proteins were analyzed by MALDI mass spectrometry and for A$\mathrm{\beta }$(M1-42) and A$\mathrm{\beta }$(M1-40), the initial Met remains at the N terminus (37) whereas for tau304-380C322S it is removed. The resulting sequences of the purified peptides studied here are thus A$\mathrm{\beta }$(M1-42): (MDAEFRHDSGYEVHHQKLVFFAEDVGSNKGAIIGLMVGGVVIA), A$\mathrm{\beta }$(M1-40): (MDAEFRHDSGYEVHHQKLVFFAEDVGSNKGAIIGLMVGGVV), tau: (GSVQIVYKPVDLSKVTSKSGSLGNIHHKPGGGQVEVKSEKLDFKDRVQSKIGSLDNITHVPGGGNKKIETHKLTFRE).

The Brichos domain (residues 88-197 of human pro-SPC), herein referred to as Brichos, was expressed and purified as previously described (40).

Monomer Preparation.

Prior to each experiment, an aliquot of ultrapure freeze-dried peptide was reconstituted in 6M GuHCl before being injected onto a Superdex 75 gel filtration column pre-equilibrated in freshly made, degassed and filtered experimental buffer, 20 mM sodium phosphate, 0.2 mM EDTA, 0.02% NaN₃, at pH 8.0. The peak fraction was collected and the protein concentration was determined by integrating the chromatogram obtained by monitoring the absorbance at 280 nm using a molar absorption coefficient of 1,400 to 1,490 M⁻¹$·$ cm⁻¹ for A$\mathrm{\beta }$40, A$\mathrm{\beta }$42, and tau, depending on construct and experiment.

Aggregation Kinetics.

The formation of amyloid fibrils in supersaturated monomer solutions in 20 mM sodium phosphate, 0.2 mM EDTA, 0.02% NaN₃, at pH 8.0 was followed in PEG-ylated low binding 96-well plates with clear bottom (ref 3881, Corning) in a plate reader (BMG Fluostar Omega) at 37 ^°C via the increase in fluorescence of the amyloid-specific dye 4-bis(3-carboxy-4-hydroxyphenylethenyl)-benzene (X34) at 2 $\mathrm{\mu }$M for tau, or ThT at 5 and 20 $\mathrm{\mu }$M for A$\mathrm{\beta }$42 and A$\mathrm{\beta }$40, respectively. The level of agitation of the samples was controlled via the cycle time setting, with either no plate parking (continuous reading) or parking for defined time periods between readings. In kinetics experiments for samples with multiple initial monomer concentrations, to allow dense spacing of data point also for the idle condition, this was achieved using the so-called flying mode, which causes minimal mechanical insult. Flying mode was also used for idle conditions in the experiments with Brichos.

Seeded Aggregation Reactions.

Seeds of A$\mathrm{\beta }$42 were prepared by incubating 50 $\mathrm{\mu }$l freshly isolated monomers at 2.5 $\mathrm{\mu }$M in 20 mM sodium phosphate, 0.2 mM EDTA, 0.02% NaN₃, at pH 8.0 in PEG-ylated low binding 96-well plates with clear bottom (ref 3881, Corning) in a plate reader at 37 ^°C. The seeds were used immediately after reaching plateau in seeded aggregation reactions, by adding 50 $\mathrm{\mu }$l of 2.5 $\mathrm{\mu }$M freshly isolated monomers.

Oligomer Quantification.

The mass concentration of fibrils at the half-time of aggregation can be related to the rate constants approximately by using the late-time limit of the early-time kinetic equations (Eq. 8 from SI Appendix of ref. 41):

$$\begin{array}{c}\hfill M(t)\simeq \frac{{\alpha }_1}{3{\alpha }_2}{e}^{\overline{\kappa }t}.\end{array}$$ [1]

${\alpha }_1=k_{\text{o1}}m{(0)}^{n_{\text{o1}}}$ and ${\alpha }_2=k_{\text{o2}}m{(0)}^{n_{\text{o2}}}$ are the early-time rates of oligomer formation through primary and secondary nucleation. $\overline{\kappa }={({\alpha }_2{\rho }_{\text{conv}}{\rho }_{+})}^{1/3}$ is the rate of fibril proliferation by secondary processes, where ${\rho }_{\text{conv}}=k_{\text{conv}}m{(0)}^{n_{\text{conv}}}$ and ${\rho }_{+}=k_{+}m(0)$ are the rates of oligomer conversion and fibril elongation, respectively.

At the aggregation half-times for idle and agitated reactions with the same initial monomer concentration, the fibril mass concentrations are obviously equal. This gives us the relation:

$$\begin{array}{c}\hfill \frac{{\alpha }_{1,i}}{{\alpha }_{2,i}}{e}^{{\overline{\kappa }}_i{t}_i}=\frac{{\alpha }_{1,a}}{{\alpha }_{2,a}}{e}^{{\overline{\kappa }}_a{t}_a},\end{array}$$ [2]

where we have used subscripts $i$ and $a$ to refer to idle and agitated parameters and half-times.

Eq. 6 from SI Appendix of ref. 41 gives expressions for the oligomer concentrations. Its late-time limit can thus be used to give an expression for the ratio $r_S$ of agitated to idle oligomer concentrations at these times:

$$\begin{array}{c}\hfill r_S=\frac{{\alpha }_{1,a}/{\alpha }_{1,i}}{{\overline{\kappa }}_a/{\overline{\kappa }}_i}{e}^{{\overline{\kappa }}_a{t}_a}/e^{{\overline{\kappa }}_i{t}_i}.\end{array}$$ [3]

Using the above relation this can be simplified to:

$$\begin{array}{c}\hfill r_S=\frac{{\alpha }_{1,a}/{\alpha }_{1,i}}{{\overline{\kappa }}_a/{\overline{\kappa }}_i}\frac{{\alpha }_{1,i}/{\alpha }_{1,a}}{{\alpha }_{2,i}/{\alpha }_{2,a}}=\frac{{\alpha }_{2,a}/{\alpha }_{2,i}}{{\overline{\kappa }}_a/{\overline{\kappa }}_i}.\end{array}$$ [4]

The presented equations assume dissociation is still slow relative to aggregation, as in WT A$\mathrm{\beta }$42. We know, however, that aggregation of Alexa-S8C is much slower than that of WT. Alexa-S8C oligomers may dissociate more rapidly than WT oligomers. In the limit of fast dissociation ($k_{d2}\gg \overline{\kappa }$, the oligomer concentration at all but the earliest times is given instead by the pre-equilibrium ${\alpha }_2/k_{\text{d2}}$, where $k_{\text{d2}}$ is the rate of dissociation of oligomers on fibril surfaces. This would give

$$\begin{array}{c}\hfill r_S=\frac{{\alpha }_{2,a}/{\alpha }_{2,i}}{k_{d2,a}/k_{d2,i}}.\end{array}$$ [5]

If secondary nucleation is accelerated primarily by an increase in oligomer conversion only $\overline{\kappa }$ changes in these expressions (by increasing), so we expect $r_S<1$ if pre-equilibrium does not hold, and $r_S=1$ if it does. If instead secondary nucleation is accelerated by shear forces detaching oligomers from fibrils faster and thus boosting the rate of oligomer formation, we expect $r_S>1$ if pre-equilibrium does not hold. If it does hold, it is hard to predict, as it is unclear what effect shear has on fibril-mediated oligomer dissociation, but it seems likely to increase oligomer formation more strongly than dissociation (and thus $r_S>1$) due to larger oligomers being more susceptible to shear-induced detachment than smaller monomers.

Quantifying the size of the predicted effect seems futile given this uncertainty on the magnitude of $k_{\text{d2}}$ and on how shear affects it. Moreover, the error in $r_S$ induced by errors in the choices of $t_i$ and $t_a$ cannot be computed without knowledge of ${\kappa }_i$ and ${\kappa }_a$ for Alexa-S8C, and these are unknown. So all we can really say is that although our observed $r_S=1.25$ is consistent with increased oligomer detachment, it does not prove it.

Cryogenic Transmission Electron Microscopy (cryo-TEM).

Sample preparation for cryo-TEM was done as previously described by Törnquist et al. (2). In brief, A$\mathrm{\beta }$42 monomer was isolated by gel filtration in 20 mM sodium phosphate, 0.2 mM EDTA, 0.02% NaN₃, at pH 8.0. Subsequently, the pH was adjusted to 6.8 by adding 21% phosphoric acid. Solutions of 13 $\mathrm{\mu }$M A$\mathrm{\beta }$42 were kept quiescent in a quartz cuvette at 37 ^°C for 6 h before being flash frozen on the cryo-TEM grid. In order to see the effects of vortexing, the same solution of A$\mathrm{\beta }$42 was either plunged directly after incubation or vortexed for 1 min before the plunge.

Plunging and cryo-TEM imaging processes were performed as previously reported (42). The specimens were collected and plunged using an automatic plunge freezer system (Leica EM GP), which is set in a controlled chamber temperature and relative humidity. Specimens were prepared as thin liquid films on glow-discharged lacey formvar carbon-coated copper grids (Ted Pella) and plunged into liquid ethane at $-$184 ^°C. In this way, the specimens were vitrified and adopted a glass-like state, avoiding the formation of ice crystals, and thereby preserving the original microstructures. The specimens were stored under liquid nitrogen until transferred into the electron microscope (JEM 2200FS) by using a Fischione Model 2550 cryotransfer tomography holder. Zero-loss images (by using an in-column energy filter) were recorded digitally with the acceleration voltage set to 200 kV and with a TVIPS F416 camera using SerialEM under low dose conditions with a 10 eV energy selecting slit in place. The contrast of all images was autoadjusted by ImageJ. The cryo-TEM images were analyzed by counting the number of protrusions per 100 nm fibril length, here defined as the protrusion index. This was done in a double-blinded process, where all images (in total 30 images) first were randomly labeled by one person, and then manually analyzed by a second person who did not know which images belonged to which sample.

Sample Preparation Prior to μFFE.

Prior to all measurements, size exclusion chromatography was used to ensure A$\mathrm{\beta }$42 samples to be monomeric. Both wild-type A$\mathrm{\beta }$(M1-42) and 100% Alexa 488–labeled S8C mutant were purified in ÄKTApure™ system with a Superdex™ 75 Increase 10/300 GL column (Cytiva), using a 20 mM sodium phosphate buffer with 0.2 mM EDTA at pH 8.0. The monomer peak elution was monitored by absorbance at both 280 nm and 488 nm, and the WT and S8C concentrations were calculated using extinction coefficients of ${ϵ}_{280}$$=$ 1 400 M⁻¹ cm⁻¹ and ${ϵ}_{488}$$=$ 73 000 M⁻¹ cm⁻¹, respectively.

The two A$\mathrm{\beta }$42 proteins were mixed at a total concentration of 2 $\mathrm{\mu }$M with a labeled to nonlabeled ratio of 1:3.5. This ratio was chosen based on previous studies, where it was seen to produce similar kinetics and fibril morphology to that of fully unlabeled protein (42). The aggregation was followed by measuring the quenching of the fluorescence of the Alexa 488 label (${\lambda }_{\mathit{ex}}$$=$ 485 nm and ${\lambda }_{\mathit{em}}$$=$ 520 nm).

The 96-well-plate was read with a cycle time equal to the minimum cycle time (201 s) for the agitated reaction, and a cycle time of 1,200 s for the idle reaction. When the aggregations reached $t_{1/2}$, samples were collected and replicates were pooled together.

Microfluidic Device Fabrication.

Device masks were designed using AutoCAD software (Autodesk) and printed on acetate transparencies (Micro Lithography Services). Negative molds of the electrophoresis device designs were fabricated via single-photon litography techniques as described elsewhere (43) with UV exposure performed with custom-built LED-based apparatus (44), with their features examined using a profilometer (Dektak, Bruker). Subsequently, Polydimethylsiloxane (Dow Corning, primer and base mixed in 1:10 ratio) was applied and degassed before baking at 65 ^°C for 1.5 h. Devices were cut from their molds and holes for tubing connection (0.75 mm) and electrode insertion (1.5 mm) were executed with biopsy punchers, cleaned through sonication in a cleaning solution by submersion in an ultrasonication bath, and bonded to glass slides using oxygen plasma. Immediately before each use, devices were rendered hydrophilic via prolonged plasma exposure (45).

$\mathrm{\mu }$FFE Device Operation.

Liquid-electrode microchip free-flow electrophoresis ($\mathrm{\mu }$FFE) devices were operated as described previously (46). Briefly, fluids were introduced to the device by PTFE tubing, 0.012"ID $\times$ 0.030"OD (Cole-Parmer) from glass syringes (Gas Tight, Hamilton) driven by syringe pumps (Cetoni neMESYS). $\mathrm{\mu }$FFE experiments were conducted at flow rates of 1,000, 200, and 10 $\mathrm{\mu }$L h⁻¹ for auxiliary buffer, electrolyte, and sample, respectively. Potentials were applied by a programmable benchtop power supply (Elektro-Automatik EA-PS 9500-06) via bent syringe tips inserted into the electrolyte outlets. All experiments were performed on a custom-built single-molecule confocal fluorescence spectroscopy setup equipped with a 488 nm wavelength laser beam (Cobolt 06-MLD 488 nm 200 mW diode laser, Cobolt). Photons were detected using a time-correlated single photon counting module (TimeHarp 260 PICO, PicoQuant) with a time resolution of 25 ps. Using a custom-written Python script, single-molecule events were recorded as discrete events using a Lee filter of three from the acquired photon stream as fluorescence bursts with 0.001 $\mathrm{\mu }$s of the interphoton time and containing 22 photons minimum. Using these parameters, the single-molecule bursts and their intensities were reported as a function of device position. Bursts corresponding to aggregates were distinctly characterized by a higher photon intensity detected per event than monomeric protein (47).

Results and Discussion

First, we explore whether gentle agitation affects amyloid fibril formation across a set of four amyloid-forming proteins (Fig. 1). Second, we study in detail the mechanistic origin of the effect in the case of the A$\mathrm{\beta }$42 peptide. We aim to identify which of the microscopic steps of amyloid fibril formation are affected by mild agitation and to what extent (Fig. 2). Our findings provide a more detailed understanding of the underlying mechanisms of aggregation.

Fig. 1.

Gentle agitation affects the aggregation kinetics of multiple amyloid proteins. Kinetic traces are shown for four proteins formed with agitation (red) or under idle conditions (blue). All reactions are performed with freshly purified monomers, (A) 2.5 $\mathrm{\mu }$M A$\mathrm{\beta }$42, (B) 2.5 $\mathrm{\mu }$M A$\mathrm{\beta }$40, (C) 5.0 $\mathrm{\mu }$M tau and (D) 25 $\mathrm{\mu }$M IAPP. The data for IAPP are replotted from Fig. 1A in ref. 31 after normalization. For IAPP, a cycle time of 60 min was used for the idle condition. For the other three proteins, a cycle time of 15 min was used for the idle condition. The data are plotted as mean of 8 replicates, N $=$ 8 for A$\beta$42, N $=$ 4 for A$\beta$40, and N $=$ 3 for tau and IAPP. The shaded area represents SD.

Fig. 2.

A schematic representation of the microscopic steps involved in fibril formation. The rate constant of primary nucleation, elongation, fragmentation, and secondary nucleation is denoted by $k_n$, $k_{+}$, $k_{-}$, and $k_2$, respectively. We show arrows of the same size, but some steps might have lower rates compared to others.

Is the Acceleration of Amyloid Formation by Gentle Agitation a General Phenomenon?

The acceleration of amyloid formation due to gentle agitation has been reported for IAPP and A$\mathrm{\beta }$40 (31). Here, we extend those findings to a fragment of tau, which spans the amyloidogenic core of fibrils derived from Alzheimer’s disease patients (38), and for A$\mathrm{\beta }$42. The acceleration of aggregation due to mild agitation is shown for the four amyloid proteins IAPP (31), A$\mathrm{\beta }$42, A$\mathrm{\beta }$40, and tau in Fig. 1. In these examples, the aggregation was monitored in a plate reader where the fluorescence intensity of amyloid-specific dyes was recorded at a specified cycle time. In this setup, the movement of the plate over the optics for fluorescence intensity recording causes a gentle agitation of the studied samples. The higher the reading frequency, i.e., the shorter the cycle time, the more agitation is applied to the samples. In the following, we use the word agitated to denote continuous reading, and the word idle to denote experiments conducted using a reading frequency of 0.05 per min or less (15 min cycle time or more, cf. below).

How Can Quiescent Conditions Be Approached?

In order to find out whether the overall aggregation rate approaches a constant value below a certain agitation rate, the fibril formation of A$\mathrm{\beta }$42 was monitored via ThT fluorescence at different reading frequencies, here expressed as cycle times. At around 900 s between readings, the half-time (50% fibril mass, t_1/2) reached a plateau at around 150 min, Fig. 3A. This implies that the observed effects are highly reproducible and that the cycle time needs to be fixed at 15 min or longer to study aggregation kinetics that approach truly quiescent conditions.

Fig. 3.

(A) The effect of gentle agitation on the half-time of 2.5 $\mathrm{\mu }$M A$\mathrm{\beta }$42. The level of gentle agitation was controlled via the reading frequency. The data points represent the mean of N $=$ 4 and the error bars show the SD. (B and C) Examples of schematic data (30) to illustrate how the double logarithmic plots of the half-time of aggregation versus the initial monomer concentration would look in different scenarios, compared to the data for A$\mathrm{\beta }$(M1-42) under gentle agitation caused by continuous reading (D). Data for A$\mathrm{\beta }$40 (50) (B) represent the saturation of the secondary nucleation at higher concentrations and data for A$\mathrm{\beta }$42 at low ionic strength (14) (C) a competition between secondary nucleation ($k_2$) and fragmentation ($k_{-}$), where fragmentation dominates in low concentrations and secondary nucleation at high concentrations. The data in (D) are most similar to the scenario in (B).

Which Steps in the Mechanism Might Be Affected by Mild Agitation?

For agitation to accelerate the overall kinetics, it must be accelerating one or more of the microscopic steps. An overview of these steps is shown in Fig. 2. If agitation leads to a significant increase in convection, this would increase all the rates of all steps involving collisions between monomers and/or fibrils. With more movement of the solution, there could be an increased propensity for fibrils to fragment (8). Finally, if the movement increases the shear forces in the solution, the detachment of secondary nuclei from fibril surfaces may be accelerated, thus leading to an acceleration of the secondary nucleation (34). We would also expect this to increase the rate of primary nucleation, as it has been shown that most primary nucleation in amyloid systems occurs on surfaces such as plate walls and the air–water interface (24, 25, 27, 48, 49). Increased shear forces could increase the rate of detachment of primary nuclei from these interfaces.

Is the Acceleration Caused by an Increased Fragmentation Rate?

The half-time of protein aggregation reactions is known to scale as a power of the initial monomer concentration ($t_{1/2}\sim m{(0)}^{\gamma }$), with the scaling exponent $\gamma$ depending on the underlying mechanism of aggregation. This exponent can be identified from the slope of a log–log plot of half-time versus initial monomer concentration (30). For fragmentation-dominated kinetics, $\gamma =-1/2$. For secondary nucleation-dominated kinetics $\gamma =-(n_2+1)/2$, where $n_2$ is the reaction order of secondary nucleation and equals approximately 2 for A$\mathrm{\beta }$42 aggregation (8). A mixture of fragmentation and secondary nucleation can be identified by negative curvature in the log–log plot, with slope $\gamma =-1/2$ at low monomer concentrations, and $\gamma =-(n_2+1)/2<-1/2$ at high monomer concentrations (14)(reproduced schematically in Fig. 3C). This is because the secondary nucleation rate increases with monomer concentration but the fragmentation rate does not. Thus, secondary nucleation comes to dominate at high monomer concentration, with fragmentation dominating at low concentrations (30). This curvature in the log–log plot was seen (but not recognized at the time) upon 100 rpm of orbital shaking of A$\mathrm{\beta }$42 aggregation reactions in ref. 8, showing partial transition to fragmentation-dominant kinetics at this shaking speed (SI Appendix, section S1 and Fig. S1).

In Fig. 3D, we show a log–log plot or A$\mathrm{\beta }$42 aggregation reactions performed with agitation. The characteristic negative curvature is not seen, and the scaling exponent is far more negative than $-$1/2 at low monomer concentrations, indicating that no appreciable fragmentation is present with mild agitation. Instead, positive curvature is seen, as the slope (scaling exponent) decreases with increasing monomer concentration. This is characteristic of enzyme-like saturation effects (reproduced schematically in Fig. 3B), whereby the secondary nucleation sites on the fibril surfaces become fully occupied with monomeric protein at high enough monomer concentration, leading to a loss of dependence of the secondary nucleation rate on the monomer concentration (30, 50). This behavior is expected for A$\mathrm{\beta }$42, having previously been observed at different values of the pH and salt concentration (14, 51). “No appreciable fragmentation” here means that at all monomer concentrations examined, the rate of fragmentation must be significantly less than that of secondary nucleation in agitated A$\mathrm{\beta }$42 aggregation, and thus a decrease in its rate will have no effect on the half-times. This means that the observed higher overall rates of aggregation compared to idle aggregation reactions cannot be explained by an increase in fragmentation rate.

Is the Effect Caused by an Increase in Primary Nucleation or Elongation?

After having shown that fragmentation does not play a role, there are still three reaction steps that might control the kinetics of A$\mathrm{\beta }$42 aggregation with and without mild agitation. To decouple the effects of agitation on these steps, we first investigate reactions under heavily reduced secondary nucleation, which is achieved by the addition of pro-SPC Brichos, a known secondary nucleation inhibitor (52). Using a sufficiently high concentration of Brichos (SI Appendix, section S2 and Fig. S2) renders the secondary nucleation negligible and allows us to study the effects of agitation on primary nucleation and elongation. We find that under these conditions the agitation effect is still present (Fig. 4). We quantify this effect by fitting a nucleation-elongation model to the kinetic curves, revealing $k_{+}{k}_n$ to be 12-fold higher in the agitated aggregation reaction compared to the idle one. Note that $k_{+}$ and $k_n$ always enter kinetic models of unseeded protein aggregation as a product ($k_{+}$$k_n$); thus, from this experiment alone, we cannot distinguish how each step contributes to this overall 12-fold increase. The results imply that part of the observed effect of agitation is caused by an acceleration of primary nucleation or elongation. Further experiments are needed to distinguish between these two options (cf. below).

Fig. 4.

Aggregation kinetics experiments in the absence and presence of a secondary nucleation inhibitor Brichos. The fibril formation of 2.5 $\mathrm{\mu }$M A$\mathrm{\beta }$42 with (plus signs) or without (circles) 2.5 $\mathrm{\mu }$M Brichos was studied with gentle agitation (red) or under idle conditions (blue). The ThT fluorescence intensity was monitored as a function of time and normalized. To the kinetic traces with Brichos, the nucleation-elongation model from Amylofit (30) was fitted (black lines), giving the agitated sample a 12-fold higher $k_{+}{k}_n$ product compared to the idle sample.

Is the Acceleration Caused by an Increase in Secondary Nucleation or Elongation?

Next, we performed an aggregation reaction under the same conditions but without Brichos. We fitted the kinetic model corresponding to the known mechanism of A$\mathrm{\beta }$42 aggregation (8) while requiring that $k_{+}{k}_n$ be 12-fold higher in the agitated case (Fig. 5A). This revealed that the proliferation rate $\kappa$ (which is proportional to ${(k_{+}{k}_2)}^{1/2}$) is twofold higher with agitation under these conditions. To determine whether this was due to an increase in elongation or secondary nucleation, we collected the fibrils produced at the end of this reaction, and used them to seed two separate reactions under the same agitation conditions. We found that the reaction seeded with fibrils produced under agitation displayed faster kinetics (Fig. 5B) than reactions seeded with fibrils produced under idle conditions. Assuming no difference in idle and agitated fibril elongation rate constant, as found before (53), this finding can only be reconciled if the fibril seeds produced under agitation are shorter on average compared to idle conditions. This would lead to more fibril ends where elongation can occur. Kinetic model fitting implies the fibril seeds produced under agitation are in fact around twice as short.

Fig. 5.

Exploring the effect of gentle agitation on elongation. (A) A$\mathrm{\beta }$42 fibrils were formed from 2.5 $\mathrm{\mu }$M A$\mathrm{\beta }$42 monomers under agitated (red), and idle (blue) conditions. Using the ratio of $k_{+}{k}_n$, 12, between agitated and idle conditions as established from the Brichos experiment (Fig. 4) and fitting both curves with kinetic models featuring multistep secondary nucleation, we found $\kappa$ to be twice as high for the agitated compared to the idle condition. To test whether elongation rate is accelerated by agitation, the resulting fibrils formed in reaction (A) were used to seed new reactions, (B) after reaching the plateau. The seeded reactions were carried out at a 1:1 mass ratio of seed:monomer with a total A$\mathrm{\beta }$42 concentration of 2.5 $\mathrm{\mu }$M. Both seeded reactions were carried out using a continuous reading frequency, in red with seeds made under agitation and in blue with seeds formed under idle conditions. The data points represent individual replicates with N $=$ 4.

Agitation would only produce shorter fibrils if it increases secondary nucleation more than elongation, since the average fibril length is proportional to ${(k_{+}/k_2)}^{1/2}$. This was verified by fitting a seeded aggregation model to the kinetics of the two seeded reactions. The best fit was obtained for a model in which the entire increase in $\kappa$ originates from an approximately fourfold increase in $k_2$, with no increase in $k_{+}$. To validate that the effect originates from a length difference rather than a variation in fibril morphology (53), we compared the effect of seeds formed under idle or agitated conditions after heavy sonication to equalize their length (SI Appendix, section S3 and Fig. S3). After sonication, the seeds are found to elongate at the same rate (SI Appendix, Fig. S4), confirming that the difference in seeding efficiency of nonsonicated seeds is due to a difference in the number of ends. We thus conclude that mild agitation accelerates secondary nucleation but has no detectable effect on the elongation rate.

Is Primary or Secondary Nucleation Most Affected by Agitation?

Finally, after having established that agitation does not significantly affect elongation, we can determine the increase in $k_n$, which in the absence of an effect on $k_{+}$ must be solely responsible for the 12-fold increase in $k_n{k}_{+}$. As a consistency check, we conducted a final unseeded A$\mathrm{\beta }$42 aggregation experiment for a series of concentrations ranging from 1.25 to 20 µM under idle or agitation conditions. In Fig. 6A, we verify that the 12-fold increase in primary nucleation alone cannot adequately explain the effect. In Fig. 6B, we impose the 12-fold increase in primary nucleation but also freely fit separate values $k_2$ for agitated and idle conditions. The resultant fits describe the data well, and the ratio of $k_2$ is found to be similar to that estimated in Fig. 5. We can thus conclude that mild agitation originating from, e.g., continuous plate reading accelerates primary nucleation by a factor of 12 and secondary nucleation by a factor of approximately 4.

Fig. 6.

Concentration-dependent A$\mathrm{\beta }$42 kinetics under agitated (A and B) and idle (C and D) conditions. A multistep secondary nucleation model was fitted to the data using Amylofit with either the primary nucleation rate constant fitted groupwise to agitated and idle (A and C) or with the ratio of primary nucleation rate constants between agitated and idle fixed at 12, and the rate constant for secondary nucleation fitted to each condition (B and D). Invoking fragmentation leads to another example of misfit (SI Appendix, section S6 and Fig. S7).

Does Gentle Agitation Facilitate Detachment during Primary or Secondary Nucleation?

If a significant fraction of the primary nucleation occurs at the air–water interface (AWI), agitation could serve to increase the rate of primary nucleation by facilitating the detachment of oligomers or nucleated species from the AWI. In such case, one would expect agitation to minimize the dependence of the aggregation rate on the AWI area. This is indeed found using samples of different volumes; the influence of the air–water interface on primary nucleation is most significant under quiescent conditions and therefore the effect of agitation is most visible at larger volume (SI Appendix, section S4 and Fig. S5).

Does Agitation Increase the Oligomer Population?

Having found that primary and secondary nucleation together are responsible for the acceleration of aggregation upon gentle agitation, we would expect that more oligomers are produced during agitated aggregation since such oligomers are formed by both primary and secondary nucleation, but not by fragmentation or elongation. To test this, we used a $\mathrm{\mu }$FFE technique on samples collected at the t_1/2 of aggregation under idle and agitated conditions (SI Appendix, section S5 and Fig. S6). In $\mathrm{\mu }$FFE, the sample is injected in a laminar flow, while an electric field applied perpendicularly to the flow direction makes the species deflect based on their electrophoretic mobility (Fig. 7A). The electrophoretic mobility is proportional to oligomer charge and inversely proportional to its radius. Given that the addition of a monomer to an oligomer increases its charge more than its radius, the electrophoretic mobility is expected to increase with oligomer size, as represented by the green spheres in Fig. 7A. Further explanation for this relationship can be found in ref. 54. Fibrils, however, are seen to not follow the same behavior as oligomers, showing an overall low deflection, most likely due to their size and morphology.

Fig. 7.

The effect of agitation imposed by reading frequency on the A$\mathrm{\beta }$42 oligomer population at t_1/2. A mixture of Alexa-labeled and nonlabeled A$\mathrm{\beta }$42 was aggregated to t_1/2 (SI Appendix, Fig. S6), and the oligomer population was measured using µFFE. (A) Schematic of µFFE. Samples moving in a laminar flow are deflected based on their electrophoretic mobility in the electric field applied perpendicular to the flow, with the two electrodes indicated by $-$ (gray rectangle) and $+$ (red rectangle). The fluorescence intensities of species (green spheres) passing by the analysis region (blue rectangle) are measured using a confocal fluorescence microscope. (B) Average photon count versus chamber position of species measured for idle (blue) and agitated (red) conditions. (C) Relative oligomer count at t_1/2 for idle (blue) and agitated (red) samples.

In Fig. 7B, the average photon count can be seen versus channel position for idle and agitated reactions. Higher average photon count corresponds to a larger average size, i.e., more labeled monomers per species, and a higher recorded channel position (higher deflection) suggests a larger size. That phenomenon, however, does not stand true for the fibrils, for which the degree of deflection is lower than expected for their charge, possibly as a consequence of being oriented perpendicular to the electric field. The results show that agitated conditions lead to a high population of species following the behavior we expect from oligomers with higher deflection for the bigger species. However, the idle experiment shows a very high peak at low channel position, the behavior expected for bigger fibrillar species.

By defining oligomers as a species with higher fluorescence than a monomer and less than a fibril, we can count the number of oligomeric species in each reaction (Fig. 7C). We find that gentle agitation leads to roughly 25% more oligomers at t_1/2 compared to idle conditions. This increase is consistent with agitation increasing the rate of oligomer formation via secondary nucleation (Materials and Methods). Conversely, an increase in oligomer concentration at $t_{1/2}$ is not compatible with an increase in elongation, which we have anyway ruled out. It is also not compatible with the acceleration in secondary nucleation being driven by accelerated conformational conversion of nonfibrillar to fibrillar oligomers (Materials and Methods). However, the rate constants of Alexa-labeled A$\mathrm{\beta }$42 aggregation are unknown. This prevents estimation of how errors in $t_{1/2}$ affect this analysis. So although these data cannot be construed as proof, they are consistent with our hypothesized mechanism.

Does Gentle Agitation Facilitate Detachment during Secondary Nucleation?

The ultrastructure of A$\mathrm{\beta }$42 fibrils was investigated using cryo-TEM. Using the same conditions as in an earlier study (2), we observe heavily decorated A$\mathrm{\beta }$42 fibrils after 6 h of idle incubation (Fig. 8A). These fibrils were formed during A$\mathrm{\beta }$42 aggregation (Fig. 8C) and the protrusions are interpreted as intermediates of secondary nucleation because they have disappeared at the end of the reaction (2). In a second set of cryo-TEM images, the solution containing the decorated fibrils was agitated using a vortex before freezing and imaging. In this case, the fibrils we observe are less decorated (Fig. 8B). All cryo-TEM images taken for idle and agitated samples were analyzed by counting the number of protrusions per 100 nm fibril length, here defined as the protrusion index. We plotted the distribution of the measured protrusion index as a histogram. As shown in Fig. 8D, fibrils after agitation had a protrusion index distribution shifted to lower values compared to the nonvortexed fibrils. These results are consistent with that some of the intermediate-sized species formed during the secondary nucleation step are removed from the fibril surface. The less decorated fibrils present after agitation may provide more surface for secondary nucleation and therefore accelerate secondary nucleation more efficiently compared to fibrils formed under idle conditions. This is in line with the conclusion that agitation speeds up secondary nucleation by facilitating the detachment of secondary nuclei, and also implies that detachment is the rate-limiting step of secondary nucleation under the current idle conditions.

Fig. 8.

Detachment of the products of secondary nucleation from fibrils by mechanical agitation shown by cryo-TEM. (A) cryo-TEM images of fibrils formed in a solution of 13 $\mathrm{\mu }$M A$\mathrm{\beta }$42 at pH 6.8, 37 ^°C incubated for around 6 h. Fibrils formed in this idle condition are densely covered by protrusions. (B) The solution was agitated for 1 min (using a vortex) and imaged again. The protrusion density at the fibril surface was significantly reduced by mechanical agitation. (C) Light scattering of the sample during incubation. The gap of intensity around 6 h was due to sample extraction for cryo-TEM. Signals have been normalized to the plateau value at 15 h. (D) Distribution of protrusion index (number of branches per 100 nm fibrils) for fibrils shown in cryo-TEM images. The distribution shifts toward a low protrusion index after agitation. The distribution for each sample is normalized to sum up to 100%.

Does the Role of Agitation Have Any Biological Significance?

Agitation of solutions is widely used in industrial setups to control crystallization reactions in terms of speed of formation and homogeneity of the product. Here, we show that also in amyloid formation gentle agitation can be used to control the relative importance of nucleation and growth processes as well as the relative importance of primary and secondary nucleation. This is of high relevance for the development of therapeutics against amyloid diseases. Using retardation of the overall aggregation process as a readout may accidentally lead to compounds inhibiting elongation and amplifying rather than reducing toxicity (52, 55–57). However, by taking control over the reaction and comparing idle conditions with gentle agitation, it is possible to modulate the relative importance of different steps, and to direct the therapeutic development toward inhibitors of specified steps. Such control will also be critical when investigating the underlying mechanism of amyloid formation and other self-assembly processes. While vigorous shaking leads to dominance of fragmentation in the production of new aggregates (8, 58), we show in this study that gentle agitation has no such effect and instead amplifies nucleation relative to elongation.

Finally, we may ask whether conditions of mild agitation and shear could represent any in vivo situation, or whether such situations are better represented by idle conditions. Amyloid deposition in the brain has been argued to be shear-induced (59, 60) and amyloid deposits in kidneys and blood vessels appear in locations of constant fluid shear, which seems to trigger their emergence (61, 62). These examples highlight the relevance of studying shear forces in amyloid formation, which in a typical laboratory setup may be of the same order of magnitude as in the human body (63).

Conclusion

The acceleration of amyloid formation due to gentle agitation has been established for four different peptides. One of those, A$\mathrm{\beta }$42, was chosen as a model system to elucidate the underlying mechanisms responsible for this effect. With a combination of nonseeded and seeded kinetic experiments, we exclude fragmentation and elongation as major contributors and identify the acceleration of nucleation as responsible for the observed effect. Significant effects on both primary and secondary nucleation are needed to explain the acceleration of amyloid formation caused by gentle agitation (Fig. 9). Specifically, we show that detachment of newly formed aggregates from catalytic surfaces is sped up by agitation and thus represents a rate-limiting step under idle conditions. This finding is further strengthened by an observed increase in oligomer population during agitated relative to idle aggregation, as assessed by µFFE, and by the disappearance of fibril decorations in cryo-TEM images after agitation. These insights may aid in the development of kinetic assays tailored to target specific microscopic steps. Such assays can facilitate the rational design of inhibitors of amyloidogenesis, which is a promising therapeutic strategy for the treatment of amyloid diseases.

Fig. 9.

Schematic representation of microscopic steps with those affected by mild agitation indicated by the red arrows, and those not affected dimmed to light gray.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Kinetics data and counts from microfluidics data have been deposited in Github [(1) data type. All kinetics data and counts from microfluidics data (2) repository name: Github (3) any relevant DOIs, accession numbers, or URLs needed to access the data: https://github.com/linselab/Axell_etal_2024_PNAS] (64).