Polyphosphates diminish solubility of a globular protein and thereby promote amyloid aggregation

Structural changes of globular proteins and their resultant amyloid aggregation have been associated with various human diseases, such as lysozyme amyloidosis and light-chain amyloidosis. Because many globular proteins can convert into amyloid fibrils in vitro, the mechanisms of amyloid fibril formation have been studied in various experimental systems, but several questions remain unresolved. Here, using several approaches, such as turbidimetry, fluorescence and CD spectroscopy, EM, and isothermal titration calorimetry, we examined the binding of polyphosphates to hen egg-white lysozyme under acidic conditions and observed polyphosphate-induced structural changes of the protein promoting its aggregation. Our data indicate that negatively charged polyphosphates bind to protein molecules with a net positive charge. The polyphosphate-bound, structurally destabilized protein molecules then start assembling into insoluble amorphous aggregates once they pass the solubility limit. We further show that the polyphosphates decrease the solubility limit of the protein and near this limit, the protein molecules are in a labile state and highly prone to converting into amyloid fibrils. Our results explain how polyphosphates affect amorphous aggregation of proteins, how amyloid formation is induced in the presence of polyphosphates, and how polyphosphate chain length is an important factor in amyloid formation.

Structural changes of globular proteins and their resultant amyloid aggregation have been associated with various human diseases, such as lysozyme amyloidosis and light-chain amyloidosis. Because many globular proteins can convert into amyloid fibrils in vitro, the mechanisms of amyloid fibril formation have been studied in various experimental systems, but several questions remain unresolved. Here, using several approaches, such as turbidimetry, fluorescence and CD spectroscopy, EM, and isothermal titration calorimetry, we examined the binding of polyphosphates to hen egg-white lysozyme under acidic conditions and observed polyphosphate-induced structural changes of the protein promoting its aggregation. Our data indicate that negatively charged polyphosphates bind to protein molecules with a net positive charge. The polyphosphate-bound, structurally destabilized protein molecules then start assembling into insoluble amorphous aggregates once they pass the solubility limit. We further show that the polyphosphates decrease the solubility limit of the protein and near this limit, the protein molecules are in a labile state and highly prone to converting into amyloid fibrils. Our results explain how polyphosphates affect amorphous aggregation of proteins, how amyloid formation is induced in the presence of polyphosphates, and how polyphosphate chain length is an important factor in amyloid formation.
Protein aggregation is a complex process and resultant aggregates can differ in morphology, from soluble or highly ordered oligomers to insoluble amorphous aggregates or amyloid fibrils (1,2). Amyloid fibrils, which are highly ordered filamentous assemblies, possess a core structure of extended cross-␤-sheets, in which individual ␤-strands are perpendicular to the fibril axis (3). Growing evidence has pointed to the toxic potential of oligomeric states and/or intermediates formed during fibril formation, and to their involvement in cellular dysfunction in amyloid-related diseases (4,5). In contrast to nucleation-dependent growth of amyloid fibrils, which occurs with a lag time (6), amorphous aggregation, in which various assemblies without organized intermolecular interactions are formed, is generally rapid and occurs without a detectable lag phase (7)(8)(9)(10). Amorphous aggregation is associated with the development of cataracts (11) and precipitation of recombinant proteins during their expression and purification (12). Several amyloidogenic proteins can form both types of aggregates in vitro, competing both kinetically and thermodynamically in the aggregation process (8 -10, 12-16). However, neither the role played by amorphous aggregation in amyloid fibril formation, nor the molecular mechanisms underlying amyloid fibrillation, are fully understood.
In the conversion to amyloid fibrils, the conformational stability of globular proteins and their solubility in aqueous solution are assumed to be important factors (17,18). In most cases, amyloid fibrils and amorphous aggregates are formed in physiological solutions when the properties of the surrounding solvent, such as the solution pH, temperature, type and concentration of salts, and presence of additives, destabilize the native conformation of the proteins in solutions (8 -10, 18 -20). The solubility of globular proteins is determined by their amino acid content, the pK a values of the ionizable residues, the protein conformational states, and environmental factors such as pH, temperature, salt type, and salt concentration (21). In defining the phase diagram of a protein's aggregation, determining its solubility curve is essential (10,22). Interestingly, recent studies have shown that the concentrations of proteins in the cell are typically close to their solubility limit, suggesting that many proteins in vivo are exposed to risk of aggregation under stress or due to aging (23)(24)(25). How decreased solubility and stability of globular proteins affect their propensity to convert into fibrillar structures remains an unclarified issue that may be crucial to understanding amyloid fibril formation in vivo.
In this context, polyanions, such as ATP, DNA, heparan sulfate, and polyphosphate, are important variables affecting protein stability and solubility (26 -31). Many low-molecular weight salts, for example, NaCl, Na 3 PO 4 , and Na 2 SO 4 , affect protein aggregation in diverse ways, such as the Hofmeister effect (32)(33)(34), preferential interactions (33,35), and specific binding (36,37). Compared with salt-associated protein aggregation, the polyanions described above were found to dramatically increase the aggregation of amyloidogenic proteins and stabilize the resultant aggregates, in a manner significantly dependent on the net charge and size of the polyanions (26 -31, 38). However, the specific nature of the interactions involved in amorphous aggregation and amyloid fibril formation is not fully understood. Here, under acidic conditions, we investigated the effects of polyphosphates on the aggregation of a globular protein, hen egg-white lysozyme (HEWL), 2 focusing on the decrease in stability and solubility of the protein.
HEWL, comprising 129 amino acid residues, is a basic protein with isoelectric point (pI) of ϳ11.2 and a net charge of ϩ19 at pH Ͻ 3 that forms well-defined amyloid fibrils under acidic conditions (39,40). The protein has a structure highly homologous to human lysozyme, which forms amyloid fibrils in individuals suffering from hereditary nonneuropathic systemic amyloidosis (also known as lysozyme amyloidosis) (39).
Phosphate is essential for life. It accumulates in cells as polyphosphate, which is a linear polymer of P i linked by phosphoanhydride bonds (41,42). Interestingly, recent studies have revealed that polyphosphates promote amyloid fibril formation of several amyloidogenic proteins (30,38), whereas another study showed inhibition of protein aggregation, in which polyphosphates played a chaperon-like role (43). However, little is known about the mechanisms by which polyphosphates promote or inhibit amyloid fibril formation.
We examined the binding of polyphosphates to HEWL molecules, the resultant structural changes of the protein, and subsequent protein aggregation using turbidimetry, fluorescence, and circular dichroism (CD) spectroscopy, transmission electron microscopy (EM), and isothermal titration calorimetry (ITC). Our results offer a model in which protein aggregation is modulated by binding of polyphosphate molecules.

Results
To assess the ability of negatively charged phosphate groups in a linear chain linked by phosphoanhydride bonds to promote aggregation of positively charged HEWL, we first tested three different sodium phosphates in acidic solution containing 10 mM HCl (pH 2): pyrophosphate (Pyro-P), tripolyphosphate (Tri-P), and tetrapolyphosphate (Tetra-P). Turbidity assays were used to detect protein aggregation in each solution. The concentration of HEWL was 1.0 mg/ml (70 M), and concentrations of the phosphates varied from 0 to 1.0 mM, where molarity of the polyphosphate species was used as the phosphate concentration. After mixing the respective solutions (that is, HEWL, HCl, and phosphates) and incubating for 1 h at room temperature, turbidity of the solutions was recorded as the apparent absorbance at 600 nm. No significant increases in the turbidity were observed when Pyro-P and Tri-P were used at any of the concentrations tested (Fig. S1). However, as seen in Fig. 1A, the turbidity of the solutions increased greatly in the presence of Tetra-P. The same measurements were conducted for protein concentration of 0.2 mg/ml, and the turbidity similarly increased until reaching a plateau (Fig. 1B). In Fig. 1, A and B, the turbidity data are plotted against the logarithmic concentration of Tetra-P, showing the solution turbidity increasing at a certain Tetra-P concentration (ϳ0.1 mM). These data suggest that under the conditions used, two or three phosphate groups are insufficient to cause protein aggregation, and the aggregation-inducing capacity of Tetra-P arises from its longer polymeric nature.
Similar experiments were conducted to examine the effects of NaCl on protein aggregation induced by Tetra-P. Here, the electrostatic shielding effect of NaCl was expected to suppress Tetra-P-induced protein aggregation. 2.0 M NaCl was added at various ratios into several turbid HEWL-Tetra-P solutions. In these preparations, concentrations of the protein and Tetra-P were maintained at a constant level after the addition of NaCl; the final concentrations were 1.0 and 0.2 mg/ml of HEWL, and 1.0, 0.5, and 0.2 mM Tetra-P. The turbidity measurements were similarly conducted after 1 h of incubation at room temperature (see Fig. 1, C and D, for the protein solutions at 1.0 (C) and 0.2 mg/ml (D), which contained 1.0 mM Tetra-P). For all the protein-Tetra-P solutions studied, the turbidity decreased with increases in NaCl concentration, resulting in transparent solutions (i.e. zero turbidity) at concentrations of more than 0.3-0.4 M NaCl ( Fig. 1, C and D, and Fig. S2, A, C, and E). These results suggest that in Tetra-P-induced aggregation of HEWL, electrostatic interactions are predominantly involved.
We examined the amyloidogenic propensity of these solutions at various NaCl concentrations by adding an amyloidsensitive dye, thioflavin T (ThT), at 5 M into several HEWL-Tetra-P-NaCl solutions in which the concentrations of the protein and Tetra-P were maintained at constant levels. The concentrations of NaCl in these solutions are indicated by arrows (Fig. 1, C and D, and Fig. S2, A, C, and E). These 10-set sample solutions at different NaCl concentrations were subjected to repeated ultrasonic irradiation and changes in ThT fluorescence were measured during the intermittent sonication (Fig. S3). Interestingly, upon ultrasonic irradiation, the solutions containing 0.3-0.4 M NaCl exhibited a marked increase in ThT fluorescence after a lag time of ϳ4 -8 h (Fig. 1, E and F, Fig.  S2, B, D, and F, and Fig. S4, A-E for the time-dependent data of all the samples). For the solutions at concentrations lower and higher than 0.3-0.4 M NaCl, the increase in ThT fluorescence was largely suppressed. These results indicate that ultrasonication triggered amyloid aggregation of the protein molecules in the vicinity of their solubility limit. CD spectra of these solutions were recorded after the ThT fluorescence measurements were taken (Fig. 1G). The CD data clearly indicated the formation of ␤-sheet structures, characterized by a peak around 220 nm, for the solutions that showed high ThT fluorescence (Fig.  1F). EM images obtained for these samples confirmed the formation of fibrillar aggregates (Fig. 1, H and I).
We then investigated the effects of longer polyphosphates, with 10 -15 phosphate groups (S-PolyP) and with 60 -70 phosphate groups (L-PolyP), on protein aggregation. The same turbidity measurements as shown in Fig. 1, B and D, were conducted. The turbidity of the solutions containing S-PolyP or L-PolyP increased at lower concentrations of the polyphosphates as the chain lengths became longer (Fig. 2, A and B). Addition of NaCl to the turbid solutions containing S-PolyP and L-PolyP resulted in decreased turbidity as NaCl concentration increased (Fig. 2, C and D). The turbidity reached 0 at NaCl concentrations around 0.6 -0.8 M, which were larger values than those (i.e. 0.3-0.4 M) detected for Tetra-P. These results suggest that electrostatic attraction between polyphosphate and HEWL becomes stronger with increasing chain lengths.
The 10-set samples containing NaCl at different concentrations, which are indicated by arrows in Fig. 2, C and D, were subjected to ultrasonic irradiation, and changes in ThT fluorescence were recorded (Fig. 2, E and F

Polyphosphates diminish protein solubility
As the solubility of HEWL was largely modulated by the additions of polyphosphates and NaCl (Figs. 1 and 2), the effects of these additives on the secondary structure of the protein were examined by CD spectroscopy. After preparing several solutions of HEWL and Tetra-P according to the compositions and concentrations shown in Fig. 1B, CD spectra of these solutions

Polyphosphates diminish protein solubility
were recorded after 1 h of incubation (Fig. 3A). The results indicated that as the protein solutions became turbid with increasing concentrations of Tetra-P, the secondary structure of the proteins was largely disrupted. Similarly, according to the solution preparation shown in Fig. 1D, NaCl was added to the turbid protein-Tetra-P solutions (Fig. 3B). As NaCl concentrations increased, the previously turbid solutions became trans-parent and CD spectra indicated a recovery of protein structure. These results indicate that Tetra-P-induced aggregation was accompanied by structural disruption of protein molecules and the original state was restored upon addition of NaCl.
Thermal stability of the protein solutions (0.2 mg/ml) containing 10 mM HCl, 1 mM Tetra-P, and NaCl at several concentrations, was examined by CD spectroscopy. Fig. 3C shows the

Polyphosphates diminish protein solubility
temperature-dependent CD intensity at 222 nm for these samples. The turbid solutions at 0 and 0.2 M NaCl showed a deposition behavior of protein during the heating process. At 0.35 M NaCl, near the protein solubility limit, the protein showed an aggregation behavior at higher temperatures. The solution at 0.6 M NaCl showed a typical thermal denaturation curve similar to that of the control sample without Tetra-P. After cooling the samples to 25°C, their spectra were again recorded (Fig. 3D), which confirmed that thermal stabilization of the proteins depends on NaCl concentration.
Similarly, the effects of L-PolyP and NaCl on protein secondary structure were examined by CD spectroscopy. As shown in Fig. 3, E and F, very similar results were obtained; the secondary structure of the protein was largely disrupted with increasing concentrations of L-PolyP, and the addition of NaCl restored the secondary structure. The temperature-dependent changes in CD intensity at 222 nm were recorded for the HEWL-L-PolyP solutions containing NaCl at 0.4 -1.0 M (Fig. 3G). The protein in solution at 0.4 -0.6 M NaCl, near its solubility limit, showed aggregation at higher temperatures. The protein solutions at 0.8 and 1.0 M NaCl showed typical thermal denaturation curves. These CD data indicate that in the labile state near the solubility limit modulated by Tetra-P and L-PolyP, the protein molecules are structurally destabilized and prone to partially unfolded states, resulting in efficient conversion into amyloid fibrils under ultrasonic irradiation.
ITC measurements were conducted to determine the thermodynamic parameters (⌬G bind , ⌬H bind , and ⌬S bind ) for the binding of Tetra-P to the protein under acidic conditions (10 mM HCl). Calorimetric titrations of Tetra-P into the protein solutions at various concentrations  M: 0.5-2.75 mg/ml) were performed at 25°C (Fig. 4, A-F, upper panels). Each peak in the binding isotherm represents a heat change associated with a single injection, resulting in exothermic

Polyphosphates diminish protein solubility
peaks. The heat resulting from the Tetra-P dilution (that is, titration of the Tetra-P solution into the buffer solution) was very low compared with the heat change associated with the Tetra-P-protein interaction. The integration of each peak, representing the heat-liberated per injection, was plotted against the molar ratio of Tetra-P to the protein (Fig. 4, A-F, lower  panels). The experimental data were fitted to a single set of binding site models to determine the thermodynamic parameters. The parameters, ⌬G bind of Ϫ5.6 to Ϫ6.5 kcal/mol, ⌬H bind of Ϫ0.9 to Ϫ1.6 kcal/mol, and the entropic contribution ϪT⌬S bind of Ϫ4.0 to Ϫ5.3 kcal/mol, were determined for each titration experiment (Table 1). These thermodynamic parameters were plotted against the initial concentrations of HEWL in the ITC cell before the titrations (Fig. 5A). The very low dependence of the parameters on protein concentration strongly suggests that these parameters reflect the thermodynamics of the binding reactions between HEWL and Tetra-P. That is, the heat released in the binding reactions represents the involvement of electrostatic interactions, in which negatively charged Tetra-P molecules bind to sites composed of positively charged amino acid residues. Nevertheless, it is important to note that the binding of Tetra-P to HEWL was driven primarily by entropy, with a dissociation constant K D of 17-80 M, in which approximately one molecule of Tetra-P was required to bind to one molecule of protein (stoichiometry n: 0.8 -1.4, Table 1).
The bindings of S-PolyP and L-PolyP to HEWL were similarly examined under acidic conditions by ITC. The titrations of S-PolyP or L-PolyP into the protein solutions showed saturating titration curves, with the strength of the interactions for S-PolyP and L-polyP being stronger than that for Tetra-P (Fig.  S5). The thermodynamic parameters for binding were determined and plotted against the initial concentrations of HEWL in the ITC cell (Fig. 5, B and C). The results indicate that enthalpy of binding is favorable for both S-PolyP and L-PolyP, in contrast to Tetra-P. The enthalpy-driven reaction indicates that stronger electrostatic interactions play a major role in the overall binding process, probably due to the higher charge densities of S-PolyP and L-PolyP versus Tetra-P. It is noteworthy that more significant changes in enthalpy (⌬H bind ) and entropy (ϪT⌬S bind ) were observed for the interaction between HEWL and L-PolyP, compared with Tetra-P and S-PolyP.
Additionally, the binding reactions of Tri-P and Pyro-P to HEWL were examined by ITC (Fig. S6, A-D). Exothermic binding was observed for the titration of Tri-P, and fitted to the same binding model, but the heat changes were smaller than for Tetra-P (Fig. S6, A and B). Importantly, the exothermic heat changes detected for the titration of Pyro-P were too small to fit to the model (Fig. S6, C and D). As a result, the calorimetric data indicate that the binding affinities of polyphosphates for HEWL depend on their chain lengths: L-PolyP Ͼ S-PolyP Ͼ Tetra-P Ͼ Tri-P Ͼ Pyro-P.
As shown in Figs. 1 and 2, increased protein aggregation, as determined by an increase in solution turbidity, was induced at higher concentrations of polyphosphates. To evaluate the heat associated with Tetra-P-induced protein aggregation by ITC, protein solutions at 0.35, 0.49, and 0.7 mM (10 mg/ml) were titrated into a Tetra-P solution at 1.0 mM, conditions under which the solution became turbid (see Fig. S8A). Compared with titration of the buffer solution (10 mM HCl) into the Tetra-P solution, noticeable exothermic heat associated with protein aggregation was observed (Fig. 6, A-C, upper panels). The heat released per injection was plotted as a function of the molar ratio of HEWL to Tetra-P (Fig. 6, A-C, lower panels). These data were roughly fitted to a single set of binding site models, yielding the thermodynamic parameters (⌬G agg , ⌬H agg , and ϪT⌬S agg , K D , and n agg ) associated with the protein aggregation ( Table 2). The parameters (⌬G agg , ⌬H agg , and ϪT⌬S agg ) obtained for each titration were plotted against the protein concentrations in the ITC syringe (Fig. 6D). The results showed that, in contrast to the binding reaction (Fig. 5A), Tetra-P-induced protein aggregation is enthalpy-driven, resulting in the formation of thermodynamically stable aggregates that resist sonication-induced amyloid fibrillation.
The ITC experiments were repeated to evaluate the heat associated with the S-PolyP-induced protein aggregation; the protein solutions at 0.20, 0.35, and 0.49 mM were titrated into S-PolyP solutions of 0.1 mM (Fig. S7) under conditions where protein aggregation is induced (Fig. S8B). The resultant ⌬G agg , ⌬H agg , and ϪT⌬S agg values were plotted in Fig. 6E, providing very similar results to those obtained for Tetra-P, representing enthalpy-driven aggregation.

Discussion
In this study, we investigated the amorphous aggregation and fibrillation of HEWL in the presence of polyphosphates under acidic conditions to understand the relationship between the stability and solubility of the protein and its propensity to form amyloid fibrils. The results indicated that the negative charges present in Tetra-P, S-PolyP, and L-PolyP promoted amorphous aggregation of positively charged HEWL, and as the chain lengths of the polyphosphates increased, the concentration required to induce protein aggregation decreased. For these polyphosphates, the data obtained by ITC demonstrated chain length-dependent binding affinity for the protein, consistent with the turbidity data characterizing polyphosphate-induced protein aggregation.

Polyphosphates diminish protein solubility
Interestingly, the calorimetric data indicated that Tetra-P binds to the protein molecules in an entropy-driven process, which is then followed by enthalpy-driven amorphous protein aggregation. As described in the Introduction, regarding the effect of different low-molecular weight salts on protein aggregation, different conclusions have been drawn whether these salts affect protein aggregation primarily through direct protein-salt interactions or indirectly via changes in the structure of water (32)(33)(34)(35)(36)(37). In this context, we attribute the entropic contribution upon binding of Tetra-P to protein to the release of hydrated water molecules around the protein surface (44). As shown in studies of the Hofmeister effect (32)(33)(34), the phosphate ion is known as a kosmotropic salt, thought to be a "water structure maker." Thus, our results suggest that when four phosphate ions linked by phosphoanhydride bonds bind to HEWL, they prevent water molecules from forming a hydration

Polyphosphates diminish protein solubility
structure at the protein surface due to their synergistic kosmotropic effect. At high ratios of Tetra-P to HEWL, the dehydration and resultant structural destabilization of the protein molecules induced by Tetra-P could decrease protein solubility and accelerate protein unfolding, eventually leading to protein aggregation.
As shown in Fig. 5, B and C, the binding reactions of S-PolyP and L-PolyP to HEWL were enthalpy-favored, indicating a change in binding mode from entropy to enthalpy favored with an increase in polyphosphate chain length. It is noteworthy that large ⌬H bind values were observed for the binding of L-PolyP to the protein, indicating that the effect of stronger electrostatic attractions between polyphosphate and HEWL becomes more significant for overall binding as the chain length increase. Thus, it is presumed that the enthalpy effect arising from the stronger electrostatic attraction becomes predominant over the dehydration effect described above with the increase in polyphosphate chain length.
As polyphosphate chain length increases, its interactions with HEWL seem to become more complex. For example, we observed that enthalpy-driven protein aggregation is induced when a small amount of protein solution was titrated into the solutions of Tetra-P and S-PolyP (Fig. 6, D and E). However, it was difficult to observe the binding-like aggregation with ITC when the protein solution was titrated into the longer L-PolyP solution, probably due to the generation of larger ⌬H values of binding and aggregation (data not shown). Furthermore, as shown in Fig. 2, C and D, the initial increases in turbidity were observed when NaCl was added to the protein solutions containing S-PolyP and L-PolyP. Although a detailed mechanism for this increase in turbidity is not clear, local structural changes of HEWL upon binding of these polyphosphates may affect solution turbidity.
Additionally, as shown in Fig. 1, C and D, the turbid solutions containing Tetra-P (1 mM) became transparent upon addition of NaCl at 0.3-0.4 M. We conducted the experiments using HEWL at three different concentrations: 0.1, 0.2, and 1.0 mg/ml (data not shown for the protein at 0.1 mg/ml), and all the turbid solutions became transparent when the concentration of NaCl reached 0.3-0.4 M. These results suggest that electrostatic attraction between Tetra-P (1.0 mM) and HEWL (0.1-1.0 mg/ml), which affects protein aggregation, may be saturated under these conditions.
In Fig. 7A, we present a plausible model for the aggregationpromoting effect of Tetra-P. In this model, Tetra-P-induced aggregation of HEWL occurs in two successive steps: 1) binding of Tetra-P to HEWL induces dehydration and subsequent structural destabilization of the protein molecules, and 2) as the molar ratio of Tetra-P to HEWL increases, the dehydrated and partially unfolded proteins are stabilized by forming intermo-lecular associations (i.e. aggregation). As indicated by the calorimetric data in Table 2, the stoichiometry (n agg ) associated with the Tetra-P-induced protein aggregation was 0.030 -0.035, values roughly independent of the HEWL-Tetra-P ratios studied. This result suggests that the electrostatic binding of Tetra-P to the protein and/or aggregates significantly modulates Tetra-P-induced aggregation, in accordance with the structural recovery upon addition of NaCl, as shown in Fig. 3B. We suggest that this model is practically applicable to polyphosphates with longer chains, based on the data in Fig. 2 in which S-PolyP and L-PolyP induced very similar aggregation behaviors to those induced by Tetra-P, although the binding mode changes depending on the chain length of polyphosphate (Fig. 5).
Recent in vitro studies have shown that additives such as ligands and antibodies, which bind selectively to globular proteins, substantially decrease the propensity for aggregation by inhibiting the global or local unfolding of the protein (45)(46)(47). Camelid heavy chain antibody fragments, for instance, have been shown to inhibit the aggregation of amyloidogenic variants of human lysozyme (47). The calorimetric data for Tetra-P-induced aggregation of HEWL presented here suggest that dehydration of the protein upon binding of Tetra-P is a crucial factor for aggregation, in which enthalpy-driven aggregation compensates for entropy-driven binding between the protein and Tetra-P. The relatively high ionic strength in vivo where sodium, potassium, and chloride ions as well as charged biomolecules are found has been shown to significantly influence the aggregation of proteins (32)(33)(34)(35)(36)(37). In the present study, we showed a combination effect of a simple salt (i.e. NaCl) and polyphosphates on HEWL aggregation. The coexistence of two types of salts did not show additive aggregation effects under the conditions used; NaCl played a role in shielding of the electrostatic attraction between HEWL and polyphosphates, indicating an intricate ionic strength dependence on protein aggregation. This finding provides insight into the molecular mechanism of protein aggregation in solutions containing different salts, including polyanions.
To illustrate the effects of Tetra-P and NaCl on amyloid fibrillation of HEWL, a simple phase diagram was constructed (Fig. 7B), based on data obtained in this study (Fig. 1, C and E,  and Fig. S2, A-D). The phase diagram represents conformational states of the protein, which depend on the concentrations of Tetra-P and NaCl. In the absence of NaCl, a strong electrostatic attraction between the positively charged protein and negatively charged Tetra-P induces amorphous aggregation. The addition of NaCl attenuates and ultimately suppresses the interactions causing the protein to aggregate, indicating that they are essentially electrostatic in nature. Near the protein solubility limit in the presence of 0.3-0.4 M NaCl, where the

Polyphosphates diminish protein solubility
protein molecules are in labile states and prone to partial unfolding, fibrillation can be triggered by agitation (Fig. 7B). The ranges of the labile state in which the protein molecules are in the soluble states with Tetra-P, S-PolyP, and L-polyP were estimated and shown as a function of the concentrations of polyphosphate (Fig. 7C). This result suggests that as the chain length of polyphosphates increased, the labile state of the protein extended over a wider concentration of NaCl. The results Tetra-P, and NaCl. Soluble, labile, and amorphous aggregation states of HEWL are shown depending on the concentrations of Tetra-P and NaCl. The circles represent the critical concentrations of Tetra-P at which protein solutions start to become turbid ( Fig. 1C and Fig. S2, A and C). The squares and triangles demarcate the high and low boundaries of NaCl concentrations, respectively, at which ThT fluorescence was significantly increased by sonication (Fig. 1E and Fig. S2, B and D). C, estimated ranges of the labile state. The ranges of labile state of the protein in polyphosphate solutions were estimated from the concentration range of NaCl over which ThT fluorescence was significantly increased by sonication and plotted against the logarithmic concentration of polyphosphate. The data for Tetra-P (1) and (2) were taken from Fig. 1F and Fig. S2F, respectively. Those for S-PolyP and L-PolyP were taken from Fig. 2, E and F, respectively.

Polyphosphates diminish protein solubility
in Fig. 7, B and C, highlight the propensity of proteins near the solubility limit, modulated by polyphosphates, to convert into amyloid fibrils. Considering that in the highly crowded cytoplasm, many proteins are barely soluble (23,24), the decreased ability to regulate ion homeostasis with increasing age could be a factor responsible for the late onset of diseases associated with protein aggregation.

Materials
HEWL, HCl (1 M), NaCl, Tetra-P, Tri-P, and Pyro-P were purchased from Nacalai Tesque (Kyoto, Japan). S-PolyP and L-PolyP were purchased from Bioenex Inc. (Hiroshima, Japan). The average molecular weights of S-PolyP and L-PolyP were ϳ1006 and 5153 g/mol. Sodium ion accompanies all the polyphosphates as a counterion. In this study, the molarity of polyphosphate species was used as the phosphate concentration. ThT was obtained from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). HEWL, NaCl, and each polyphosphate were separately dissolved in Milli-Q water. HCl (1 M) was diluted to 100 mM with Milli-Q water. The concentration of HEWL was determined spectrophotometrically at 280 nm with an extinction coefficient of 2.63 ml/mg/cm. Respective solutions were mixed at the desired concentrations. All of the solutions contained 10 mM HCl (pH 2.0).

Turbidity measurements
Turbidity measurements were conducted to detect aggregation of HEWL in the solutions at room temperature. After mixing the solutions for 5 s using a benchtop vortex, the samples were placed into a quartz cuvette (path length of 10 mm). Turbidity values were recorded as the apparent absorption at 600 nm using a Hitachi U3000 spectrophotometer (Hitachi High-Technologies Corporation, Tokyo, Japan).

Detection of amyloid aggregation by sonication
Sonication-induced aggregation of the protein solutions was monitored by measuring the changes in ThT fluorescence using a microplate reader (see Fig. S3).

CD measurements
CD data were obtained with a Jasco 820 spectropolarimeter (Jasco Co., Ltd., Tokyo, Japan) using a quartz cell with a light path of 1 mm. The temperature of the solutions was controlled with a thermoelectrically controlled cell holder attached to the polarimeter. The results were expressed as the mean residue ellipticity after subtracting the buffer baseline. Wavelength-dependent spectra were recorded at 25°C.

Electron microscopy
A sample solution (5 l) was placed on a collodion-coated copper grid (Nisshin EM Co., Tokyo, Japan). After incubating for 3 min, the remaining solution was removed with filter paper. The grid was then stained with 0.5% (w/v) hafnium chloride (5 l) for 1 min. After removing the remaining solution with filter paper, EM images were obtained with a Hitachi H-7650 (Tokyo, Japan) at a voltage of 80 kV.

ITC measurements
Calorimetric experiments were conducted with a PEAQ-ITC instrument (Malvern Instruments, UK) at 25°C. In the binding experiments, protein solutions in the ITC cell were titrated with polyphosphate solutions in the injection syringe. In the protein aggregation experiments, the polyphosphate solutions in the cell were titrated with the protein solutions in the syringe. Throughout the calorimetric experiments, 18 successive injections (injection volume, 2.0 l) were performed with intervals of 180 s, and the cell was continuously stirred at 750 rpm. The thermodynamic parameters were determined from the integrated heat using the single set of binding site model supplied by Malvern Instruments. All the sample solutions were prepared in 10 mM HCl.