*3.1. Elucidation of* Θ *and Spectroscopic Measurement*

The spectroscopic measurement used in this study exhibits the transition of dispersed peptide-coated gold colloid to aggregated gold colloid through a networking of peptides on the colloidal surface. The surface charge or surface charge potential of each colloid should ideally be neutral, in order to avoid mutual repulsions which would impede aggregation. It is speculated that an aggregation of Aβ1–40 coated gold colloid takes place at an isoelectric point, pI, of Aβ1–40 (pI = 5.2) [39]. If so, a constant pHo (~pI) is expected to be observed regardless of the sizes of gold colloid. However the observed pHo for Aβ1–40 coated gold colloid ranging from *d* = 10 nm to *d* = 100 nm scanned between pHo = 4.38 ± 0.06 for *d* = 100 nm and pHo = 6.20 ± 0.01 for *d* = 40 nm [40]. The extracted pHo implies the amount of positive charge, i.e., [H3O<sup>+</sup>], required to neutralize the colloidal surface. This work demonstrated the correlation between ΔpHo and *d*pH as a key concept in extracting the change of surface charge potential of the gold colloidal particle. Due to the fact that the bare gold colloid possesses surface plasmon (electrons) over its surface, the excess amount of [H3O<sup>+</sup>] needs to be supplied in order to neutralize the surface. Thus, the ΔpHo shows the difference of the amount of [H3O<sup>+</sup>] required between bare gold colloid and the peptide-coated gold colloid. Essentially, this means that the ΔpHo indirectly shows the amount of the negative charges quenched due to the attachment of the peptides over the surface and the changing surface charge potential of the colloidal surface.

The measured quantity *d*pH is defined in a method described in Section 4.3.1. Since λpeak(1) is the first derivative of λpeak(pH), it has the dimension of Δλ/ΔpH (Δλ indicates the wavelength change associated to the transition from a dispersed stage to an aggregated stage, and ΔpH indicates the amount of H3O<sup>+</sup> ion needed for that transition). The marking wavelengths λmax and λmin indicate that the colloid is at the aggregated stage (λmax) or at the dispersed stage (λmin). In practice, the marking wavelengths can be treated as dimensionless numbers or as an index (or with arbitrary units), with the replacement of λpeak(1) by ΔΛ/ΔpH, where ΔΛ implies the difference of an index Λ. Overall, *d*pH indicates an inverse of λpeak(1) and it is proportional to ΔpH, if ΔΛ is treated as a constant. Therefore, because ΔpH ∝ –log Ω and *d*pH ∝ log Ω, where Ω is a constant associated with charge. Thus, in principle, there should be a linear correlation between *d*pH and ΔpH.

A. Wang et. al. reported a pH dependence in protein coverage [41], and it is presumable that the surface charge condition is fully influenced by the residual pH condition. This suggests that the peptides start occupying and aggregating at the gold surface as the pH point gets closer to pHo. If this is the case, peptides may not adsorb on the gold surface with our reported Θ values at pH > pHo. However, our work is designed to determine pHo, where the coverage of amyloidogenic peptide was already completed, our approach allows us to extract Θ only at pHo, and it limits a quantitative conclusion regarding the pH dependence of Θ.

#### *3.2. Orientation of the Peptide over the Surface of Gold Colloidal Surface*

Relatively high Θ (i.e., Θ >0.5) can be accommodated by filling the surface area with a greater number of smaller unit surface area. Thus, the most supported orientation of the prolates is a spiking-out orientation, as sketched in Figure 5. While a "lie-down" orientation was highly expected to establish more interaction between peptide and the gold surface, the higher coverage was only established by creating a larger amount of smaller contacting areas. As supporting evidence, a very similar orientation was reported by Stellaci's group for bipolar polymer spiking out of gold nanoparticle sphere [42–48]. Considering that the gold colloid has a partially negative surface charge, any positively charged sequence can interact with it electrostatically. Since Aβ1–40 coated gold colloid is dissolved in an aqueous solution, hydrophobic segments of Aβ1–40 (sequences 23–40, C-terminal side) must be used for contacting the gold colloidal surface, causing hydrophilic segments of Aβ1–40 (sequences 1–22, N-terminal side) to face outside, making it soluble in water. Among the hydrophobic sequences (23–40), only 28Lysine (28Lys, 28K) can be positively charged at neutral conditions. Therefore, it is hypothesized that –N+– part of the 28Lysine is responsible for contacting on the gold colloidal surface as shown Figure 5.

**Figure 5.** The proposed attachment structure of Aβ1–40 over the surface of a gold colloidal particle. At the left top sketch shows the proposed peptide orientation adsorbed over gold nano particle. In the middle the blow up of each peptide with a prolate shape is shown. Inside the prolate, a sketch of Aβ1–40 is shown within a prolate of *a* = 1.4 nm and *b* = 2.2 nm. On the top, a blow up and hypothesis of sequences responsible for the adsorption on the gold surface are shown and 28K was speculated to be in a direct contact with gold surface. At the further right, a structure of Lysine (K) is shown and -NH3 + group is estimated to be a central point for an adsorption.

Due to more complexities in structure, identification of binding sites for α-syn and β2m were less clear. Even so, a similar approach and rough estimation of the site is possible. For α-syn, residues 61–95, or the so-called NAC (Non-Aβ Component) region [49,50], is highly likely to be the region where the peptide is bound to the nano-gold surface. More specifically, 80K, 96K, and/or 97K are candidate residues that could be responsible for the colloidal attachment.

In a similar way, however, with a more complex situation, β2m is considered to possess hydrophobic (and aromatic-rich) region in residues 62–70 implying 63R (63Arginine), 66K, or 69H to be a plausible binding sites to the nano-surface [51]. If we assume multiple concurrent contacting spots are available, the mobility of β2m must be reduced and this can separate the binding property of β2m different from the other two peptides. In order to explain a negative correlation observed in

Θ vs. Sd plot (Section 3.4), β2m was speculated to be a prolate with negative side facing outward. It is quite likely that the sequence from 50 to 58 are the section responsible for the above-mentioned section since the negatively charged section of 52D (52Aspartic Acid), 54E (54Glutamic Acid), and 56D are located therein.

The current model used for extracting Θ was tested for chicken ovalbumin as an example of a globular protein. There was no correlation found between *d*pH and ΔpH, and we assume that the model can be applied only for amyloidogenic peptides that clearly exhibits folded and unfolded conformations which are drastically different. Also the section of adsorption site has to be clearly determined no matter which size of the gold colloid was applied, otherwise clear mapping of charge distribution due to peptide (as explained in Section 3.4) cannot be obtained. The prolate shape localizes a partial charge in a relatively smaller region, which can become an adsorption point. In contrast, a globular protein takes a spherical shape creating a broader and more homogeneous partial charge distribution. This results in a less sensitive response in aggregation as a function of pH change, which results in a poorly defined *d*pH value in Equation (1), and reducing a correlation between ΔpHo and *d*pH.

#### *3.3. Networking of the Peptide at an Interfacial Area*

While the aggregation of Aβ1–40 coated gold colloid develops highly condensed networking which results in the mutual overlapping of gold colloids in both horizontal and latitudinal directions, the aggregation of β2m-coated gold colloid was less condensed, and TEM images enabled us to observe the spacing between adjacent gold colloids (Δ = 1.9 ± 0.7 nm), particularly around the edge area of the aggregates. Since Aβ1–40 and β2m both approximate as prolate tops with similar dimensions, the information on this spacing between adjacent gold colloid can be extrapolated to these two peptide systems. This result implies that the peptide layer covered the gold colloidal surface at a thickness of 0.95 nm [52]. If we consider a monolayer of peptide with spiking-out orientation, the adjacent distance between two gold colloid should correspond to 2*b*. This assumption strongly contradicts the extracted Δ (~2 nm) since calculated 2*b* value are 4.4 nm for Aβ1–40, 14.8 nm for α-syn, and 9.2 nm for β2m based on the values shown in Table 2. In order to allow peptides to be constrained within 2 nm spacing, the most probable conformation allows the peptides to be bent or spiraled around each other at the interface. Since amyloidogenic peptides studied in this work are all regarded as disordered proteins, it is reasonable to assume that disordered regions are flexible enough to take best suited configuration including a bent form in order to fit in 2 nm inter-colloidal surfaces. The process of gold colloidal aggregation is summarized as the process of a mixture (interaction) between monomer and gold colloidal surface, followed by the adsorption of each monomer over the nano-colloidal surface, and under acidic pH, the networking of peptides forming the gold colloid aggregation (Figure 6).

Based on the fact that all experimental observation needs to involve a second layer, we deduce that the first layer is responsible for the coverage of nano-gold surface and the second layer is the result of networking to the first layer of each peptide coated gold colloid. Due to the spiking-out orientation of the first layer, this would leave accessible another site for further networking as the peptide conformation becomes unfolded. The networking between dual peptides at an interface matches with a speculation of a dimer formation concluded in our previous work [53].

**Figure 6.** A demonstrative picture of peptides being adsorbed over a surface of gold nano-particle (NP) and adsorption of peptide with spiking out orientation under pH 10 (bottom left) and forming a network with each other in order to form gold colloid aggregates at pH 4 (bottom right). The color of peptide and gold colloid are shown in the same color.

#### *3.4. Verification of the Relationship between Physical Displacement and Coverage Ratio*

Our first instinct was that Θ was dominated by the molecular interaction between gold surface and peptide's terminus responsible for an electrostatic interaction. Therefore, the surface field reflecting from the surface curvature would be proportional to molecular interaction and may influence the surface interaction and coverage. However, by assuming that simple term of curvature is proportional to an inverse of radius, we did not see any correlation between a curvature and Θ, as also implied by the complex relationship between Θ and d shown in Figure 4. This implies that at least obvious chemical interaction does not explain the intrinsic reasoning of Θ and its nano-size dependence. While no correlation between the gold colloidal size and its coverage ratio of peptide (Θ) was found in our study, we attempted to find justification of Θ for a given nano-size of gold colloid by using a mathematical approach without involving intermolecular forces. The most simplified explanation of higher or lower coverage is gained from calculating how much space is wasted by a given unit adsorbent. However, the coverage ratio cannot be simply predicted as a function of surface area. For example, if the area to be covered increases, the unit area of an adsorbent may not utilize given space without leaving an unoccupied area, and so the coverage ratio may not increase. The equatorial belt area was used as an index of the effectiveness of space usage, and the spacing between each prolate (S*d*) should be correlated with the coverage ratio (Θ). For example, a prolate of Aβ1–40 (*a* = 1.4 nm and *b* = 2.2 nm) covering a 40 nm (*d* = 40.6 nm) has Θ = 0.86), and 100 nm (*d* = 99.5 nm)has Θ of 0.20. When maximum prolate with dimension of (*a* = 1.4 nm and *b* = 2.2 nm) was distributed equatorial belt of each gold colloid, S*<sup>d</sup>* = 0.051 nm for 40 nm with n*eq* = 50 and S*<sup>d</sup>* = 0.012 nm for 100 nm with n*eq* = 175 demonstrating that the larger the S*d*, the higher the Θ. A clear correlation between Θ and S*<sup>d</sup>* was confirmed for Aβ1–40 and α-syn as shown in Figure 7a,b as a positive slope for β2m as shown in Figure 7c as a negative slope. The finalized fitting parameters and fitting procedures will be further detailed in a report by Yokoyama and Ichiki [54].

**Figure 7.** The best optimized plot of Θ vs. Sd for (**a**) Aβ1–40 in blue, (**b**) α-syn in red, and (**c**) β2m in green, where fitting values for the linear relationship Θ = Φ Sd + ε. In each plot, there was always one deviating data point from the linear trend (*d* = 80 nm for Aβ1–40 and α-syn, *d* = 60 nm for β2m), and the insets show the plot when each outlier point was removed. Supporting information of this figure is available at Supplementary Materials.

A positive linear relationship between Θ and S*<sup>d</sup>* is explained by considering that both Aβ1–40 (Figure 8(a-1)) and α-syn (Figure 8(a-2)) are simplified as a prolate with δ+ region at the adsorption side and opposite side (i.e., exposing side to the outward) as sketched in Figure 8(b-1), respectively. As the prolate attaches onto the gold surface through the δ+ region of a prolate, it also creates the δ+ region on the gold surface as indicated in Figure 8(b-1,b-2). So that an extra peptides are more invited for adsorption as the gold surface possesses more δ– region when S*<sup>d</sup>* is longer. On the other hand, if S*<sup>d</sup>* is relatively small, not enough δ– region is available for further adsorption of peptides causing the Θ decreased resulting in the positive linear relationship between Θ and S*<sup>d</sup>* (Figure 8c). As it was speculated before, Aβ1–40 may be adsorbing on to the surface through 28K and α-syn adsorbs on to the surface through 80K or 96K97K. Since those sites are located at relatively close to the N-terminal, it is speculated that δ+ portion of C-terminal side must be exposing outward and away from the colloid surface. As for Aβ1–40, we speculate that 5R6H, 13H14H, or 16K are responsible for distributing δ+ region. The speculated region with δ+ and δ– are indicated by color coded areas in a prolate and bars in sequences as δ+ in blue and δ– in red, respectively (Figure 8(a-1)) As for α-syn, all lysines in the C-terminal region (i.e., 6K, 10K, 12K, 21K, 23K, 32K and 34K) are speculated to be exposing toward the outside and away from the colloidal surface side. While much more information is needed, crude estimation of charge distribution was shown in Figure 8(a-2). In a similar manner as shown in Figure 8(a-1), region with δ+ and δ– are indicated by color coded areas in a prolate and bars in sequences as δ+ in blue and δ– in red, respectively.

**Figure 8.** A sketch explaining a positive linear proportionality between Θ vs. Sd, (**a**) simulation of prolate and charge distribution of Aβ1–40 (**(a)-1**) and of β2m (**(a)-2**). The sequences of each peptide are shown with the colored bar indicating δ– (in red) or δ+ (in blue). (**(b)-1**). A side view of a prolate top peptide with a partially positive side (δ+) of dipole attaching to the partially negative surface (δ–) of gold colloid. An extra prolate dipole attracted for the space of δ–, if Sd has enough length to let an extra prolate in. (**(b)-2**) The birds eye view of the surface showing area appears as δ– indicated by red is the highly probable are for an extra prolate to be interacted and may lead to an attachment. (**c**). A graph explaining the expected trend between Θ as a function of Sd.

Opposed to what we observed in Aβ1–40 and α-syn, β2m exhibited a negative linear slope for Θ vs. Sd plot. (Figure 7c). This is interpreted that as each β2m (sketched in Figure 9(b-1)) adsorbs onto the gold surface with δ+ segment as exposing more δ– area to the other side of gold surface as sketched in Figure 9(b-1,b-2). Thus, as Sd decreases, it creates a greater effective attraction to the extra β2m resulting in more coverage (i.e., a negative slope for Θ vs. Sd plot) as shown in Figure 9c. Since the adsorption site of β2m can be speculated to be at relatively toward the C-terminal side (i.e., 63R, 66K, or 69H), the exposing side away from the gold surface is speculated to be N-terminal side. Thus, it is estimated that18E is responsible for providing δ– region. In Figure 9a, region of δ+ and δ– are indicated by color coded areas in a prolate and bars in sequences as δ+ in blue and δ– in red, respectively.

**Figure 9.** A sketch explaining negative linear relationship between Θ vs. Sd. (**a**) simulation of prolate and charge distribution of β2m. The sequences are shown with the colored bar indicating δ– (in red) or δ+ (in blue). (**(b)-1**). A side view of a prolate top peptide with δ+ side of dipole attaching to δ– surface of gold colloid. Because a distribution of δ– is expected to be spread from the top to the side toward outside, extra prolate is more attracted as more area of δ– is available. (**(b)-2**). A top view of a focused region in b)-1, where the area appears as δ– as the prolate locate close by shortening of Sd. (**c**). A graph explaining the expected trend between Θ as a function of Sd,.

In all three cases explained above, we claim that the spiking-out orientation of the first layer established a corresponding charge distribution seen in each peptide coated gold colloid. If the orientation was lie-down orientation, enhancement of self-adsorption would not take place. For example, a lie-down orientation of prolate dipole in the case of Aβ1–40 and α-syn would exhibit a significant amount of δ+ region and not effectively squeeze the prolate dipole with the same orientation. As for the case of β2m, the lie-down orientation exposes a greater amount of δ– region, resulting in a significant repulsion for the peptide attempts to adsorb with the same lie-down orientation.

#### *3.5. Justification of Lower Coverage Ratio and Associated Prolate Shape*

While the overall characteristic of the coverage of amyloidogenic peptides was relatively higher value (i.e., Θ ≥ 0.6), there were only five cases when Θ was < 0.5; Aβ1–40 coated *d* = 100 nm gold, α-syn coated *d* = 100 nm gold, β2m-coated *d* = 10, 20, and 60 nm gold. For all cases, the fit was not optimized with a prolate with spiking-out orientation but with lie-down orientation. Under the estimation that the spiking-out orientation is the best orientation to satisfy coverage stability (i.e., effective packing of the surface) and consistent with most of the coverage orientations observed in this experiment. Thus, it is hypothesized that each prolate takes a spiking-out orientation but tilts over the nano-gold surface as shown in Figure 10a and can rotate around the contact point on the nano-gold surface (Figure 10b) resulting in an occupied area with oblate shape as if it takes a lie-down orientation. In order to explain an oval shape occupying over the surface, a gyration type of motion is considered. So that the contact point of the prolate changes due to a change of tilting angle as it rotates over the surface, is plausible (Figure 10c).

**Figure 10.** A sketch of the side view of a rotating prolate. (**a**) The tilting of a prolate over the nano-gold surface and approximation for radius (*AC*) of the circular plane over the nano surface. Here, θα is a tangential angle between prolate axis and the surface line, and the tilting angle of a prolate against surface plane is given by an angle θτ. (**b**) A rotational motion of a prolate with a fixed contacting point, resulting in a circular occupied space over the surface. (**c**) A gyration motion of a prolate with a movable contacting point and tilting angle θτ, resulting in an oval (in green) occupied space with axial length of *a*g (blue circle) and *b*g (red circle).

From the geometry shown in Figure 10a, *AC* = 2*bcos*θαθβ, where θ<sup>α</sup> and θ<sup>β</sup> are the inner angles as shown in Figure 10a and the length *AC* was approximated as *AB* ≈ 2*bcos*θβ because θ<sup>β</sup> << 1. A tilting angle of a prolate, θ<sup>τ</sup> = 90◦ – θα. The extracted θ<sup>α</sup> and θ<sup>β</sup> are listed in Table 3.


**Table 3.** The list of extracted tilting angles (θ<sup>τ</sup> and θβ) for the lower coverage for (**a**) Aβ1–40, (**b**) α-syn, and (**c**) β2m. The average tilting angle for each peptide is shown at the bottom for each peptide in (θτ).

An example of extracted gyration motion was demonstrated and sketched in Figure 11 for the case of β2m adsorbed over *d* = 10 nm gold colloid (*d* = 9.80 nm). Focusing on one unit of prolate as shown in Figure 11a, the tilting angle, θτ, changes between 26◦ and 17◦ as it rotates, which modulates the surface area. The gyration of the prolate should be taking place simultaneously with the other prolates on the same surface as shown in Figure 11b. We cannot, however, deny that a stationary peptide in an unfolded conformation could occupy the space of the same size calculated by gyration motion. There is a possibility of that the adsorption is more randomized and is an ensemble of multiple orientations. For example, J. A. Yang and et. al., reported that α-syn adsorbs on the poly (allylamide hydrochloride) coated gold nanoparticles with random orientation with an increase in β-sheet and decrease in α-helix structure [55].

**Figure 11.** (**a**) The sketch showing the gyration motion of a prolate (*a* = 2.7 nm and *b* = 4.0 nm) representing β2m over a gold nano-particle with a diameter of *d* = 10 nm, where the prolate major axis tilts between 26◦ and 17◦ as it rotates over the surface. It results in an oval occupied space with *ag* = 2.7 nm and *bg* = 4.0 nm. (See Table 3) (**b**) The sketch of a gyrating prolate over the nano-gold particle surface.

#### **4. Materials and Methods**

#### *4.1. Materials*

Lyophilized powder of Aβ1–40 peptide (MW; 4.2 kDa, 98% HPLC purity) and α-syn (MW: 14.4 kDa, purity >95% by SDS-PAGE) were purchased from r-Peptide (Bogart, GA, USA). Aqueous 220 μM stock solution of Aβ1–40 and 64.2 μM stock solution of α-syn were stored at –80 ◦C. The β2m (MW: 12 kDa/mol, purity >40% by SDS-PAGE) was purchased from AbD Serotec (Raleigh, NC, USA), and aqueous 77.0 μM stock solution was stored at –20 ◦C. Gold nanoparticles were purchased from Ted Pella, Inc. (Redding, CA, USA) and have the following estimated diameters (d), reported diameter (*d*), and particles per mL in O.D. (Optical Density, <sup>ϑ</sup>) where <sup>ϑ</sup> = 0.2 at 528 nm: d = 10 nm (*<sup>d</sup>* <sup>=</sup> 9.8 <sup>±</sup> 1.0 nm, <sup>ϑ</sup> <sup>=</sup> 1.4 <sup>×</sup> 1012 particles mL<sup>−</sup>1), d = 15 nm (*d* = 15.2 <sup>±</sup> 1.5 nm, <sup>ϑ</sup> <sup>=</sup> 2.8 <sup>×</sup> <sup>10</sup><sup>11</sup> particles mL<sup>−</sup>1), <sup>d</sup> <sup>=</sup> 20 nm (*d* = 19.7 <sup>±</sup> 1.1 nm, <sup>ϑ</sup> <sup>=</sup> 1.4 <sup>×</sup> 1011 particles mL<sup>−</sup>1), <sup>d</sup> <sup>=</sup> 30 nm (*<sup>d</sup>* <sup>=</sup> 30.7 <sup>±</sup> 1.3 nm, <sup>ϑ</sup> <sup>=</sup> 4.0 <sup>×</sup> 1010 particles mL<sup>−</sup>1), d = 40 nm (*d* = 40.6 <sup>±</sup> 1.1 nm, <sup>ϑ</sup> <sup>=</sup> 1.8 <sup>×</sup> 1010 particles mL<sup>−</sup>1), d = 50 nm (*<sup>d</sup>* <sup>=</sup> 51.5 <sup>±</sup> 4 nm, <sup>ϑ</sup> <sup>=</sup> 8.2 <sup>×</sup> <sup>10</sup><sup>9</sup> particles mL−1), d = 60 nm (*<sup>d</sup>* <sup>=</sup> <sup>60</sup> <sup>±</sup> 1.0 nm, <sup>ϑ</sup> <sup>=</sup> 4.3 <sup>×</sup> <sup>10</sup><sup>9</sup> particles mL<sup>−</sup>1), d = 80 nm (*<sup>d</sup>* <sup>=</sup> <sup>80</sup> <sup>±</sup> 1.0 nm, <sup>ϑ</sup> = 2.2 <sup>×</sup> 109 particles mL<sup>−</sup>1), and d = 100 nm (*d* = 99.5 <sup>±</sup> 1.3 nm, <sup>ϑ</sup> <sup>=</sup> 1.6 <sup>×</sup> <sup>10</sup><sup>9</sup> particles mL<sup>−</sup>1). The residual components in each colloidal particle can be regarded as identical. In order to maintain stability of the nano-gold colloids against salts, deionized and distilled water were used to prepare all aqueous solutions. All sizes of gold colloids were formed by Frens derived citrate reduction method possessing traces of citrate <10<sup>−</sup>5%, tannic acid <10<sup>−</sup>7% and

potassium carbonate <10<sup>−</sup>8%. Thus, the observed size dependence in this study was not determined by the stabilizer of the gold colloids.<sup>12</sup> The optimized ratio between all peptides and gold nanoparticles was set as 1000:1 so that the concentration of gold nanoparticles was roughly 300 pM [39]. Attachment of peptides to the gold colloidal surface was known to be achieved almost instantaneously and considered to reach equilibrium within a minute. The pH range of the solutions (between pH 2 and pH 12) was achieved by adding either HCl or NaOH to the solution. The UV–Vis absorption spectra were monitored between 200 and 800 nm as the pH value varied by an increment of 0.05 pH to acidic conditions.

#### *4.2. TEM Imaging*

The TEM (Transmission Electron Microscopy) experiment was conducted for β2m as well as for ovalbumin, Aβ1–40, and α-syn. The β2m samples were prepared with 2.8 μL of β2m stock aqueous solution mixed with 280 μL of gold colloids ranging between 10 nm, 30 nm, 60 nm, and 80 nm in diameter, with pH ranging from 6.5 to 7.5. Before plating on the grid, the sample pH was adjusted to either pH 10 or pH 4 under room temperature. 1 μL of the mixture was then plated onto Formvar Copper Film 400 Grids Mesh. The samples were incubated on the grid for two minutes, after which excess solution was removed from the grid with filter paper. All TEM images were collected on a Morgagni model 268 TEM (FEI Co., Hillsboro, OR, USA) operated at 80 kV and were taken under both 28,000× and 71,000× magnification using a model XR-40 four-megapixel CCD Digital camera. TEM image analysis was performed by converting the image to data consisting of pixel coordinates and corresponding color index using Image J. The threshold in color index was set to recognize the group of pixels corresponding to the gold particles and the average size of the gold particles, the distance between adjacent gold particles, ratio of the area occupied by the gold particles (occupancy, %), and the total numbers of gold particles were calculated. The β2m-coated gold colloid formed relatively small aggregates as opposed to ovalbumin or Aβ1–40. The number of gold colloidal particles was extracted by individually counting each particle rather than using the "occupancy" method. Because each gold colloid was easily identified for the β2m-coated gold colloid, in many cases, the space between each gold colloids in each aggregate were observed. In this study, the space between gold particles was focused and its distance was extensively analyzed whenever space between colloids was identified. Using the length of a pixel for calibration, the number of pixels between the colloids was transformed into nanometers. The distribution of the observed length in nm was fit with a Gaussian profile and the average distance was extracted.

#### *4.3. Methods*

#### 4.3.1. pH-Dependent UV–Vis Absorption Band

Our group has been investigating the reversible self-assembly process of amyloidogenic peptide-coated colloidal gold nanoparticles extensively. These peptides are relatively small, amphiphilic peptides whose temperature/pH conditions for folded/unfolded conformations are well studied. Therefore, it has been viewed as a useful prototype system to learn how nanoscale surface potentials interact with a peptide, and if a specific oligomeric structure can be selectively constructed [11–13]. Although these peptides eventually form irreversible insoluble amyloids, the initial stage is still a reversible process. In temperature-dependent reversible processes [53], we found that a reversible process between folded and unfolded conformation took place under Aβ1–40 coated 20 nm gold colloid as pH externally changed well above or well below a critical pH point (pHo). The value of pHo for Aβ1–40 coated 20 nm gold was found to be pHo = 5.45 ± 0.05 at 20 ◦C, and a reversible process was observed between pH = 4 and pH 10. at 18 ± 0. 2 ◦C and above. Between 18 ± 0.2 ◦C and 6 ± 0.2 ◦C, only Aβ1–40 coated 30 nm gold colloid exhibited a reversible process. Under 6 ± 0.2 ◦C, only Aβ1–40 coated 40 nm gold colloid supported a reversible process between folded and unfolded conformations. The results from molecular dynamics (MD) calculations on Aβ10–35 suggested the temperature ranges

are stable for dimer or trimer formation [56]. For example, the stable dimer formation temperature range matched with the temperature range of reversible process observed for Aβ1–40 coated 20 nm gold colloid (≥~18 ◦C). The trimers were predicted to be stable at the relatively lower temperature range, which reasonably matches temperature ranges for the reversible process over 30 or 40 nm gold colloid's surface (i.e., <18 ◦C). Also, the stable temperature for trimer formation was in good agreement with the temperature range of the reversible process observed for Aβ1–40 coated 30 nm or 40 nm gold colloids. Since unfolded conformation leading to oligomerization is formed at only lower pH value than pHo, we concluded that this is evidence that oligomeric dimer units over 20 nm gold colloid particles or trimer units over 30 or 40 nm gold colloid particles were produced over a nano-gold colloidal surface at pH 4 [53]. The key intermediate oligomeric form in the reversible process has not been well studied due to its instability. We hypothesize that the activation energy required to form an intermediate oligomer can be gained from the nano-metal surface potential. While metastable folding intermediates (i.e., the oligomer form) for a folding pathway has been suggested and detected in solution [57–71], a direct identification of an exact oligomer has not been shown. Oligomer observed in negatively charged micelles and Teflon particles, β-sheet formation of Aβ on hydrophobic graphite surfaces [14], or at air–water interfaces [15] indicate an involvement of interfacial surface potential utilized for the conforming intermediate [16–20]. Our group has established a way to reproduce and control the reversible self-assembly of Aβ on spherical gold nanoparticles. The average absorption peak shift (λpeak) at room temperature (Figure 12a) is plotted as a function of the continuous operation of an external pH change (Figure 12b). The value of λpeak corresponds to the color of the solution, which in turn corresponds to the morphology of the gold colloid aggregates. When the colloids assemble in an aggregated form at pH 4, the mixture is a blue color with λpeak ~650 nm or above. On the other hand, the gold colloids are widely dispersed at pH 10, and exhibit a reddish color with λpeak ~525 nm. Therefore, a repetitive pH change enables Aβ1–40 coated 20 nm gold colloid to exhibit an oscillating feature of λpeak between 525 nm and 625 nm as they reversibly form dispersed and aggregate forms, respectively.

Each absorption spectrum was fit by the "Peak Fit" program in Origin (Version 9.5) and peak positions of i-th band (λi) and peak area of each band of i-th component were extracted (A*i*). The observed band average peak position is correlated with the surface plasmon resonance (SPR) of gold colloids, and the peak position of the absorption band depends on the conformation of peptide attached on the gold colloidal surface. The folded or unfolded conformation can be prepared by setting the solution to be basic or acidic, respectively. When the solution is acidic, the absorption band commonly has two or more components. Thus, the average peak position, λpeak(pH), of the SPR band at given pH is extracted by the weighted average of two components as λ*peak*(*pH*) = - *<sup>i</sup> ai*(*pH*)λ*i*(*pH*), where λ*i*(pH) and *a*i(pH) are the peak position and fraction of the *i-*th component band, and the fraction *a*<sup>i</sup> was determined by the fraction of the area (A*i*) of the band to the total area of the entire bands as: *ai* = *Ai*/ - *<sup>j</sup> Aj*.

**Figure 12.** *Cont.*

**Figure 12.** A schematic diagram explaining the spectral analysis and construction of sigmoidal plots. (**a**) The average peak position of SPR, λpeak, was monitored as a function of the pH condition for both bare gold nano-particles and peptide-coated nano gold colloids. The λpeak was extracted by utilizing the method described in Section 4.3.1. Two representative spectrum marked by -1 and -2 represent that under pH 7 and pH 2, respectively. (**b**) The constructed sigmoidal plot was fit with the Boltzmann formula shown in Equation (1). Both *d*pH and ΔpHo were obtained. Here, the sigmoidal plot i indicates that of bare gold colloid, and the sigmoidal plot ii is a typical plot observed for amyloidogenic peptide coated gold nano-particles. The upper colored bar shows the corresponding solution color for regions -1 and -2 .

Then, the average peak position was surveyed as a function of pH, and the position of the peaks were plotted as a function of pH, as shown in Figure 12b. The constructed sigmoidal plot was then analyzed and fit with a Boltzmann formula (Equation (1)) as shown in Figure 12b.

$$
\lambda\_{\text{peak}}(\text{pH}) = [\lambda\_{\text{min}} - \lambda\_{\text{max}}] / \left[1 + \exp[(\text{pH} - \text{pH}\_0) / \text{dpH}]\right] + \lambda\_{\text{max}} \tag{1}
$$

The λmin and λmax stand for the minimum and maximum of the band peak positions, respectively. Here, pHo shows the pH where color change takes place, and λpeak (pHo) = (λ min + λ max)/2. Also, *d*pH = (λmax – λmin)/4λpeak(1), where λpeak(1) is the first derivative of the λpeak(pH).

Absorption of a collective excitation of the electrons at the interface between a conductor and an insulator is hypothesized to account for the color of suspensions of these particles [72–74]. If the net anionic sites of the metal surface are neutralized by acid, aggregation should be enhanced, resulting in a color change from red to blue. As coverage increases, a shielding effect shifts pHo to the higher value. This ultimately means that greater coverage of peptide requires a less acidic condition to neutralize the surface. Bare gold colloids change their colors at lower pHs (pH < 4.5) while a peptide-coated colloidal surface shows a color change at pH = 4.5~6 depending on the degree of coverage. This pHo value change between bare gold and protein coated gold solution is direct evidence of protein adsorption on the metal colloid.
