Heating during agitation of β2-microglobulin reveals that supersaturation breakdown is required for amyloid fibril formation at neutral pH

Amyloidosis-associated amyloid fibrils are formed by denatured proteins when supersaturation of denatured proteins is broken. β2-Microglobulin (β2m) forms amyloid fibrils and causes dialysis-related amyloidosis in patients receiving long-term hemodialysis. Although amyloid fibrils of β2m in patients are observed at neutral pH, formation of β2m amyloids in vitro has been difficult to discern at neutral pH because of the amyloid-resistant native structure. Here, to further understand the mechanism underlying in vivo amyloid formation, we investigated the relationship between protein folding/unfolding and misfolding leading to amyloid formation. Using thioflavin T assays, CD spectroscopy, and transmission EM analyses, we found that β2m efficiently forms amyloid fibrils even at neutral pH by heating with agitation at high-salt conditions. We constructed temperature- and NaCl concentration–dependent conformational phase diagrams in the presence or absence of agitation, revealing how amyloid formation under neutral pH conditions is related to thermal unfolding and breakdown of supersaturation. Of note, after supersaturation breakdown and following the law of mass action, the β2m monomer equilibrium shifted to the unfolded state, destabilizing the native state and thereby enabling amyloid formation even under physiological conditions with a low amount of unfolded precursor. The amyloid fibrils depolymerized at both lower and higher temperatures, resembling cold- or heat-induced denaturation of globular proteins. Our results suggest an important role for heating in the onset of dialysis-related amyloidosis and related amyloidoses.

Amyloid fibrils, fibrillar aggregates of denatured proteins or peptides stabilized by intermolecular cross-␤ structures, are associated with many amyloidoses, including neurodegenerative disorders, such as Alzheimer's and Parkinson's diseases, and dialysis-related amyloidosis (DRA) 2 (1)(2)(3)(4)(5). The kinetics of amyloid formation are common to amyloidogenic proteins and are typically separated into nucleation, elongation, and equilibrium phases. The nucleation phase, the duration of which is considered a lag time, is often long because of its high freeenergy barrier. Once amyloid nuclei form, the elongation of fibrils occurs rapidly. The equilibrium phase is a thermodynamic state where the monomer concentration has reached its solubility. Seed-dependent elongation is a common property of amyloid formation, in which the nucleation phase is shortened or escaped. Another type of protein misfolding leads to amorphous aggregates (6). Amorphous aggregates with no ordered structure are seen in cataracts, in inclusion bodies, or during protein preparation (7,8). Rapid amorphous aggregation without a lag time competes with the slow nucleation-dependent amyloid formation, producing kinetic complexity of amyloid formation (9 -12).
␤ 2 -Microglobulin (␤2m), a typical amyloidogenic protein with a folded native structure, is a component of the major histocompatibility complex 1. It is filtered by the glomerulus and catabolized by proximal tubular cells in the kidneys in healthy persons. However, ␤2m remains in the blood and sometimes forms amyloid fibrils in patients receiving longterm hemodialysis. Accumulation and deposition of these amyloids in tissues cause DRA (13,14). It has been established that amyloid formation of acid-unfolded ␤2m readily occurs (15)(16)(17). The atomic structure of ␤2m fibrils under acidic conditions has been reported (5). In contrast, amyloid formation under neutral pH conditions, under which patients develop diseases, does not occur easily because of the amyloid-resistant native structure (18,19). Based on previous studies performed with N-terminal truncated or mutant ␤2m (20) or those in the presence of additives, such as collagen, heparin (21), SDS (14), or glycosaminoglycans (14), the denaturation or local enrichment of ␤2m on biological membranes or extracellular matrix molecules has been suggested to induce amyloid formation in vivo. Recently, Cremers et al. (6) reported that polyphosphates with linearly linked phosphate units are markedly effective in inducing amyloid fibrils of various proteins. We found that polyphosphates effectively induced amyloid formation of ␤2m at neutral pH (22). However, the exact mechanism of DRA, in particular the factors inducing amyloid nucleation in patients, remains unclear.
Studies on protein aggregation have been also performed from the thermodynamic perspective. Otzen and colleagues (23,24) reported the relationship between thermodynamic parameters and polymorphism of glucagon amyloid fibrils. Dzwolak and colleagues (25) reported the thermal stability and degradation of insulin fibrils. We also investigated the effects of heat on the amyloid formation of ␤2m and other proteins using calorimetry, and compared thermodynamic parameters with those of protein folding (26 -29). Recently, we examined the effects of heating on ␤2m at low pH (12). Acid-unfolded ␤2m formed amyloid fibrils and amorphous aggregates competitively in a temperature-and NaCl concentration-dependent manner. A unified phase diagram of conformational states suggested that amyloid fibrils depolymerize at both low and high temperatures, reminiscent of cold and heat denaturation of globular proteins (30,31). The phase diagram also accommodated a region of amorphous aggregates, which were formed under the strong forces of precipitation. Taken together, amyloid fibrils and amorphous aggregates may correspond to crystals and glasses of solutes, respectively, and the breakdown of supersaturation may lead to the formation of crystal-like amyloid fibrils (12,32). However, such a diagram has not been constructed at neutral pH where DRA develops, and the relationship between protein folding/unfolding and amyloid formation is not clear. Recently, Wang et al. (33) reported the thermodynamic phase diagram of ␤-amyloid peptide based on a coarsegrained molecular dynamic simulation, in which amyloid fibrils depolymerized with an increase in temperature similar to our heat-induced depolymerization of ␤2m fibrils (12).
Here, we demonstrate that amyloid formation of ␤2m occurs even under neutral pH conditions at high temperatures. Of note, although heating caused unfolding (i.e. denaturation) of ␤2m, a necessary condition of amyloid formation, it was not sufficient for amyloid formation. Amyloid formation occurred only when heat unfolding was performed under agitation, which forced the breakdown of supersaturated unfolded monomers. In other words, both unfolding and breakdown of supersaturation were required. In this report, we use "unfolding" and "denaturation" interchangeably, although the definitions of the two terms may differ. We also use "formation of amyloid fibrils" and "amyloid misfolding" interchangeably to reflect the differences between protein folding and misfolding. The temperature-and NaCl concentration-dependent conformational phase diagrams revealed that the unfolding temperature of the native state decreases once amyloids form, which was exactly reproduced by the linked function of protein folding/unfolding and amyloid misfolding.

Amyloid formation of ␤2m upon heat unfolding under agitation
We monitored the conformational change of ␤2m upon heating at neutral pH by far-UV CD measurements. ␤2m samples in 20 mM sodium phosphate buffer (pH 7.0) and 1.0 M NaCl were heated from 25 to 90°C with a heating rate of 0.5°C/min. Without stirring, the CD spectrum demonstrated reversible heat unfolding, with ␤2m refolded to the native state after cooling to 25°C (Fig. 1, A and B). In contrast, under stirring, structural conversion to the pronounced ␤-sheet conformation occurred at 60°C, and ␤2m did not refold to the native conformation ( Fig. 1, C and D).
To confirm that the conformational change under stirring led to amyloid formation, we carried out thioflavin T (ThT) assays (Fig. 1, E and F, and Fig. S1). We added 5 M ThT to the same samples as above and measured the ThT fluorescence at 485 nm at a heating rate of 1°C/min. We simultaneously measured the light scattering (LS) at 450 nm to monitor the total amount of aggregates. In the absence of stirring, neither ThT fluorescence nor LS changed up to 90°C. Under stirring, both ThT fluorescence and LS increased markedly beginning at ϳ66°C, which was near the midpoint temperature (T m ) for heat unfolding of ␤2m under these conditions (Fig. 1, E and F, and Fig. S1).

Temperature dependence of heat-induced amyloid formation
ThT assays with 0.1 mg/ml ␤2m were performed in 20 mM sodium phosphate buffer (pH 7.0), 1.0 M NaCl, and 5 M ThT at varying temperatures under stirring. Amyloid formation occurred at all temperatures between 40 and 90°C, although the reaction accelerated markedly with an increase in temperature (Fig. 2, A and B). After these assays, we measured the final ThT intensity at 25°C to remove complexity caused by thermal effects on ThT fluorescence. ThT fluorescence at 25°C did not depend on the reaction temperature, although the final LS value slightly increased with an increase in temperature. In contrast, the lag time became significantly shorter at higher temperatures (Fig. 2C). We also carried out CD measurements at the reaction temperatures. All CD spectra after heat-induced transition exhibited ␤-structures typical for amyloid fibrils (Fig.  2D). Additionally, we confirmed amyloid formation by TEM images (Fig. 2, E-J).

Effects of NaCl on amyloid formation
To investigate the effects of NaCl on the amyloid formation, we carried out the same ThT assays as those shown in Fig. 2 (A and B) at varying NaCl concentrations (0 -3.0 M) and temperatures (50 -90°C). With 0.5-3.0 M NaCl, amyloid formation monitored by ThT fluorescence occurred at varying temperatures and NaCl concentrations. However, with 0 -0.25 M NaCl, no reaction occurred at 90°C, although amyloid fibrils formed at lower temperatures (Fig. 3, A-C, Figs. S2-S4).
We assessed the secondary structures and morphologies after ThT assays. Samples without an increase in ThT fluorescence or LS remained unfolded when monitored by CD (Fig. S5) and exhibited no fibrous aggregates when examined by TEM (Fig. S6). In contrast, the samples with increases in ThT fluorescence and LS had amyloid fibrils even at lower NaCl concentrations (Fig. S6).
We previously reported that visualization using white and blue light-emitting diode (LED) lamps is a useful method for detecting amyloid fibrils (Fig. 3, D and E) (11,34). The heattreated ␤2m samples at pH 7.0 without agitation exhibited neither turbidity nor ThT fluorescence, consistent with the reversible heat unfolding under these conditions. Under stirring, samples with lower concentrations of NaCl at higher temperatures exhibited neither turbidity nor ThT fluorescence, confirming that they remained soluble below the solubility limit. The remaining samples at pH 7.0 under agitation exhibited slight turbidity and strong ThT fluorescence, suggesting that agitation broke supersaturation and led to amyloid formation. For comparison, we prepared amorphous aggregates of ␤2m with 1.0 M NaCl at pH 2.0 (9, 12). These amorphous aggregates exhibited strong turbidity without ThT fluorescence (Fig. 3, D and E, Amorphous).

Seeding activity of heat-induced amyloid fibrils
We investigated the seeding activity of heat-induced ␤2m amyloid fibrils prepared with 1.0 M NaCl. Although no amyloid formation occurred without stirring when monitored by ThT fluorescence or LS at a heating rate of 1°C/min, it occurred in the presence of seeds even under quiescent conditions (Fig. 4A).
After these experiments, we carried out CD measurements at 25°C. The seeded sample after heat-induced transition exhibited ␤-structure typical of amyloid fibrils, whereas the nonseeded sample demonstrated refolding to native ␤2m (Fig. 4C). Under stirring, we detected no difference between heating-dependent spontaneous amyloid formation and seed-dependent reactions (Fig. 4B). Additionally, we performed differential scanning calorimetry measurements in the presence or absence of seeds, confirming that seeds broke supersaturation when combined with unfolding of the native state (Fig. 4D). These results were confirmed by LED visualization images (Fig. 3

, D and E, blue boxes).
With 250 mM NaCl at 70°C, the seeds shortened the lag time (Fig. 4E). In contrast, with 250 mM NaCl at 90°C, no reaction occurred even in the presence of seeds (Fig. 4F). TEM images confirmed amyloid fibrils and no fibrous aggregates at 70 and 90°C, respectively (Fig. 4, E and F, insets). The LED visualization images were consistent with these temperature-dependent seeding reactions (Fig. 3, D and E, green boxes). The results suggested that because the solubility of ␤2m with 250 mM NaCl at 90°C was higher than the protein concentration (8.5 M), no fibrils formed, even with seeds.

Depolymerization of heat-induced amyloid fibrils
First, ␤2m amyloid fibrils were prepared in 0.5 M NaCl at pH 7.0 and 70°C. The fibrils were recovered by centrifugation and

Heating-induced amyloid formation of ␤ 2 -microglobulin
then suspended in 0 M NaCl at pH 7.0. When these fibrils were incubated at 90°C, significant decreases in both LS and ThT intensities were observed (Fig. S7A). However, the LS intensity remained relatively high, and the CD spectrum did not represent the refolded ␤2m structure (Fig. S7, B and C), suggesting that fibril depolymerization occurred partially. According to the TEM images, long amyloid fibrils were observed with 0.5 M NaCl at 70°C, whereas no significant fibrils remained after the incubation with 0 M NaCl at 90°C (Fig. S7, D and E). We also examined fibril depolymerization by LED images, which demonstrated weakened ThT fluorescence (Fig. 3, D and E, Depolymerized).

Effects of ultrasonication and other salts
We examined the effects of ultrasonic irradiation (35,36) on the amyloid formation of ␤2m at pH 7.0 and 60°C with a water bath-type ultrasonicator and microplate reader. As expected, ultrasonication caused amyloid formation with 0.1-2.0 M NaCl in a manner similar to that by stirring (Fig. S8, A and D). We also investigated the effects of Na 2 SO 4 (Fig. S8, B and E) and tetraphosphate (tetP) (Fig. S8, C and F), both of which are amyloidinducing additives. The results confirmed that, when combined with other promoting factors, heating effectively induces amyloid fibrils.

Comparison of monomer folding and amyloid misfolding
To address the mechanism underlying the temperature-dependent amyloid formation/depolymerization, we recalled the thermodynamics of monomer folding/unfolding (Figs. 5 and 6 and Movie S1) (30,31). The stability of the native state of globular proteins depends on temperature, exhibiting "heat dena-turation" and occasionally "cold denaturation." We assumed folding transition from the denatured (D) to native (N) states (D º N) with the equilibrium constant of folding (K N ) to compare with amyloid "misfolding": Gibbs free energy change of folding to the native state (⌬G N (T) ϭ ϪRT ln K N ) at temperature T in Kelvin is determined by the enthalpy (⌬H N (T)) and entropy changes (⌬S N (T)), where ⌬H N (T 0 ), ⌬S N (T 0 ), ⌬C p,N , and a[NaCl] are the enthalpy and entropy changes at a reference temperature T 0 , heat capacity change of folding, and a contribution of NaCl at [NaCl] with a coefficient a, respectively. The temperature dependences of ⌬G N (T), ⌬H N (T), and T⌬S N (T), assuming T 0 ϭ 310 K, ⌬H N (T 0 ) ϭ Ϫ174.7 kJ mol Ϫ1 , ⌬S N (T 0 ) ϭ Ϫ0.5 kJ mol Ϫ1 K Ϫ1 , ⌬C p,N ϭ Ϫ5.6 kJ mol Ϫ1 K Ϫ1 , which were taken from Kardos et al. (29), and a ϭ 2.5 kJ mol Ϫ1 M NaCl Ϫ1 , which was estimated from the T m measurements (Fig. 6B, panel i), are shown in panel i of Fig. 6A.

Heating-induced amyloid formation of ␤ 2 -microglobulin
The fraction of the N state (F N ) was defined by the following.
The temperature dependences of F N and F D (ϭ 1 Ϫ F N ) at 1.0 M NaCl are shown in panel iii of Fig. 6A. We constructed the temperature-and NaCl concentration-dependent folding phase diagram drawn using the following, where [NaCl] N,0.5 (T) is the midpoint NaCl concentration of folding (⌬G N (T) ϭ 0, F N ϭ 0.5) at T (Fig. 6B, panel i).
The ⌬H N (T) value, which is "negative" above 20°C, decreases with an increase in temperature because of a negative heat capacity change of folding (⌬C p,N ). The ⌬C p,N value, and thus temperature dependence of ⌬H N (T), largely result from hydrophobic interactions that stabilize the native state. On the other hand, ϪT⌬S N (T) term, which includes the decrease in conformational entropy upon folding, increases in magnitude with an increase in temperature more than that of the enthalpy term. The combined effects of destabilizing entropy and stabilizing enthalpy terms are the "negative" ⌬G N (T) (folding) around room temperature and "positive" ⌬G N (T) (unfolding) at high temperatures, leading to heat denaturation. Regarding cold denaturation, which was not evident for ␤2m, the decrease in ⌬H N (T) in magnitude directly explains the conversion of negative ⌬G N (T) (folding) to positive ⌬G N (T) (unfolding) upon cooling (30,31).
The elongation of fibrils is defined by the equilibrium association constant (K Pol ) as follows.
The equilibrium is independent of the molar concentration ofamyloidfibrils,[P].Hence,weobtainedtheequilibriummonomer concentration [M] C as follows.
[M] C ϭ 1 K Pol (Eq. 8) [M] C is referred to as the "critical concentration" (28, 29, 38, 39) because amyloid fibrils form when the concentration of monomers exceeds [M] C . By determining [M] C , we can calculate the apparent free energy change of amyloid formation (⌬G Pol (T)) by the following.
We assumed that Gibbs free energy equations (i.e. ⌬H Pol (T) and⌬S Pol (T)) also hold true for polymeric amyloid fibrils (28,29) (Fig. 6A, panel ii), where b[NaCl] represents the contribution of NaCl at [NaCl] with a coefficient b. We previously reported that the ⌬H Pol (T) value for ␤2m at pH 2 was linearly dependent on temperature, giving a ⌬C p,Pol value of Ϫ5.0 kJ mol Ϫ1 K Ϫ1 (28), a slightly smaller value than that of the native state: Ϫ5.6 kJ mol Ϫ1 K Ϫ1 (29). We assumed the same ⌬C p,Pol value for the amyloid fibrils at pH 7.
If the total protein concentration, [Prot] T , is higher than [M] C , the fraction of the polymeric P state is defined by the following.

Heating-induced amyloid formation of ␤ 2 -microglobulin
Temperature dependences of fractions of D and P states for amyloid formation are shown in panel iv of Fig. 6A Based on these considerations, we constructed the temperature-and NaCl concentration-dependent phase diagram of amyloid formation at [Prot] T ϭ 0.1 mg/ml drawn by the following, where [NaCl] Pol,0.5 (T) is the midpoint NaCl concentration of amyloid formation (F Pol ϭ 0.5), assuming b ϭ 25.0 kJ mol Ϫ1 M NaCl Ϫ1 (Fig. 6B, panel ii). The previous results (28,38,39) and current considerations argue that the solubility of monomers ([M] C ) and thus the stability of amyloid fibrils are determined by a mechanism similar to that of protein folding. This is not surprising considering that intramolecular protein folding and intermolecular amyloid misfolding are driven by similar forces, including hydrophobic interactions, hydrogen bonds, and van der Waals interactions. It is well-known that the solubility in water of hydrophobic substances against temperature exhibits a U-shaped dependence, representing the large positive ⌬C p value for "dissolution" (40). Thus, the simplified mechanism of amyloid dissolu-tion resembles the dissolution equilibrium of a hydrophobic solute in which the equilibrium solute concentration (i.e. solubility) represents the free energy change of dissolution.
Assuming the similarity of protein folding and amyloid misfolding, heat-induced depolymerization of amyloid fibrils is expected because of the increased conformational entropy. On the other hand, the low temperature-induced depolymerization (41) or decreased amyloid formation at low temperatures is expected to occur because of the decreased hydrophobic interactions. Although the rigid tight packing of side chains producing steric zippers and more extensive cross-␤ network (1) may provide distinct properties, including supersaturation-limited amyloid formation, the overall calorimetric properties of amyloid formation resemble those of protein folding.

Linkage between reversible unfolding and supersaturationlimited misfolding
Three conformational states are linked after the breakdown of supersaturation (N º D º P) and are under thermodynamic equilibrium (mechanism 3 and Movie S1): Although equations for the processes of N º D and D º P did not change, the fractions of N (F N ), D (F D ), and P (F Pol ) were newly defined as follows,  The temperature dependences of the three conformational states with 1.0 M NaCl shown in Fig. 6 (A, panel v, and B, panel  iii) were distinct from those under supersaturation. Most notably, the unfolding transition started at significantly lower temperatures than that under supersaturation, indicating a significant decrease in T m for thermal denaturation. This can be simply explained by the law of mass action: the N º D equilib-rium shifts to D because the newly participating amyloid fibrils (P) drive the overall equilibrium to P. Indeed, with 1.0 M NaCl, amyloid fibrils formed at 40°C, even though the lag time was as long as 30 h (Fig. 2C), consistent with the consideration addressed here. Although the law of mass action has not been addressed previously in the formation of amyloid fibrils starting from the native state, it may have an important role in explaining the propagation of amyloid fibrils even under conditions where the precursor amyloidogenic states are negligibly small.
[NaCl] N,0.5 ͑T͒ The calculated and experimental phase diagrams are shown in Fig. 6B (panel iii). It is noted that at NaCl concentrations below 0.1 M, where the three states coexisted, we calculated the boundaries by estimating the points where the concentrations of two species are equal. This type of linkage between protein unfolding and aggregation will occur for any type of aggregate, and the consideration presented here provides a quantitative explanation as to how the linkage affects the stability of the native state.

Implications for amyloid formation under physiological conditions
Although we demonstrated amyloid formation of ␤2m at pH 7.0 and temperatures higher than 40°C, similar amyloid formation likely effectively occurs even at physiological temperatures once helped by additional amyloid-promoting factors. These include various biological factors (heparins, lysophosphatidic acids, and polyphosphates) and mechanical agitation, which will cause the onset of DRA (6,14,21,42,43). Localized unfolding and/or enhanced aggregation at air-liquid interface are likely to be additional important factors breaking supersaturation. Recently, the effects of polyphosphate on amyloid formation have been focused on (6,22). We found that tetP markedly acceleratedamyloidformationat60°C,althoughtheexactdependence on the tetP concentration was complicated. We further argue that because of the linkage of protein unfolding with amyloid misfolding, local high temperatures, even if moderate (e.g. 40°C), are an important risk factor.
Another important parameter determining the phase diagram is the protein concentration. As protein aggregates form above the solubility of their monomers, high protein concentrations enhance protein aggregation (32,44). We carried out heat-induced amyloid formation at 25.5 M (0.3 mg/ml) ␤2m under neutral pH conditions (Fig. S9). ␤2m at 25.5 M formed amyloid fibrils under several conditions, whereas ␤2m at 8.5 M did not form fibrils with lower NaCl concentrations at higher temperatures. Of note, 25.5 M ␤2m with 1.0 M Na 2 SO 4 formed a mixture of amyloid fibrils and amorphous aggregates, although 8.5 M ␤2m formed only amyloid fibrils under the same conditions (Fig. S10).

Conclusions
We demonstrated that heat unfolding under agitation effectively caused amyloid formation of intact ␤2m even at neutral pH and temperatures slightly higher than physiological. Importantly, heat-induced amyloid formation of ␤2m occurred only under agitation or seeding, which suggested that the breakdown of supersaturation is necessary for amyloid formation, in addition to protein unfolding. We formulated a relationship between the reversible protein unfolding and supersaturationlimited amyloid misfolding. Upon the breakdown of supersaturation, the law of mass action shifts the monomer equilibrium to the direction of the unfolded state, destabilizing the native state and thereby enabling amyloid formation even under physiological conditions with a negligible amount of the unfolded precursor (Movie S1). It is possible that the linked function under seeding conditions plays a role in the pathology of various amyloidoses, including the marked infectious behavior observed for prion seeds.
Finally, we compared heat-dependent protein unfolding and amyloid formation to obtain a unified mechanism of protein folding and misfolding. In the past decades, studies on protein folding/unfolding often employed heat denaturation at nonphysiological high temperatures (30,31). The thermodynamic parameters elucidated under those extreme conditions have been valuable for clarifying the mechanism of protein folding under physiological conditions, because they can be extrapolated back to the physiological conditions. The same was true for amyloid misfolding. The properties elucidated under nonphysiological high temperatures could be extrapolated to the physiological conditions. Most importantly, we elucidated that the linkage of protein unfolding and misfolding promotes amyloid formation even at physiological temperatures. Taken together, the heating and agitation used in this paper, although they were nonphysiological, will be powerful for further addressing the mechanism of amyloid formation under physiological conditions.

Protein and chemicals
Recombinant human ␤2m protein with an additional methionine residue at the N terminus was expressed in Escherichia coli and purified as previously reported (45,46). ThT was obtained from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). All other reagents were purchased from Nacalai Tesque, Inc. (Kyoto, Japan).

ThT assays with heating
Lyophilized ␤2m was dissolved in deionized water. ␤2m concentrations were measured spectrophotometrically using a molar extinction coefficient of 19,300 M Ϫ1 cm Ϫ1 at 280 nm based on its amino acid composition. The sample solution of 2.5 ml in a cuvette with a 1-cm light path contained 8.5 M ␤2m, 5 M ThT, 20 mM phosphate buffer (pH 7.0), and variable NaCl concentrations. Amyloid formation was detected by ThT fluorescence with an excitation wavelength of 445 nm and an emission wavelength of 485 nm using an F4500 fluorescence spectrophotometer (Hitachi High-Technologies Corporation, Tokyo, Japan). Light scattering at 450 nm was also measured to detect whole protein aggregation. All fluorescence measurements were performed under stirring using a magnetic stirring bar at a stirring speed of 600 rpm, except for the experiments Heating-induced amyloid formation of ␤ 2 -microglobulin under quiescence. The sample temperature was controlled using a Peltier element (Nippon Tecmo Co., Ltd., Fukuoka, Japan) and measured by a thermocouple Compact Thermologger AM-8000K (Anritsu Meter Co., Ltd., Tokyo, Japan).

CD and TEM measurements
The sample solutions were the same as above, except for the volume. Far-UV CD spectra (212-250 nm) were obtained with a J-720 spectropolarimeter (Jasco Co., Ltd., Tokyo, Japan) using a quartz cell with a 1-mm or 1-cm path length. CD data were expressed as mean residue ellipticity.
The sample solution (5 l) was spotted onto a collodioncoated copper grid (Nisshin EM Co., Ltd., Tokyo, Japan). After 1 min, the solution on the grid was removed with filter paper. Then 5 l of 0.5% (w/v) hafnium chloride was spotted onto the grid. After 1 min, the solution was removed in the same manner. TEM images were obtained using a H-7650 transmission microscope (Hitachi High-Technologies Corporation, Tokyo, Japan) at 20°C with a voltage of 80 kV.

Seeding reactions
Seeds were obtained from the preformed fibrils of heat-induced spontaneous amyloid formation under stirring and sonicated moderately before seeding experiments. The conditions for the sample preparation and measurements were the same as for standard ThT assays, except for the addition of 5% (v/v) seeds.

Fibril depolymerization
Heat-induced amyloid fibrils of ␤2m were formed under the same conditions used for the ThT assays with 500 mM NaCl at 70°C. These fibrils were centrifuged at 15,000 rpm and 25°C for 20 min and then suspended at 5 M ThT in 20 mM phosphate buffer (pH 7.0). The CD measurement and ThT assay were carried out at 25°C, and the solution was then incubated at 90°C under stirring at 600 rpm. Intermittent ThT assays were performed every 10 min during the incubation. After the incubation, the CD measurement and ThT assay were performed at 25°C.

Microplate ThT assays
Lyophilized ␤2m was dissolved in deionized water. The sample solution contained 8.5 M ␤2m, 5 M ThT, 20 mM phosphate buffer (pH 7.0), and variable concentrations of NaCl, Na 2 SO 4 , or sodium tetP. The sample solutions of 0.2 ml were distributed into the wells of a 96-well microplate (catalog no. 675076; Greiner Bio-one Co., Ltd., Frickenhausen, Germany). The microplate was set on a Elestein SP070-PG-M water bathtype ultrasonicator (Elekon Science Co., Ltd., Chiba, Japan) on which the plate received maximal ultrasonication. Ultrasonic pulses were applied to the microplate from three directions in 1-min cycles, followed by a quiescent period of 9 min at 60°C. The frequency and power of the ultrasonic pulses were set to ϳ19 kHz and 700 W, respectively. Amyloid formation was detected using ThT fluorescence with a MTP-810 microplate reader (Corona Electric Co., Ltd., Tokyo, Japan) at 37°C with excitation and emission wavelengths of 450 and 490 nm, respectively. A multiple data collection mode with nine data points was employed.