**5. Conclusions**

The surface properties of nano-gold colloidal surfaces due to adsorption of amyloidogenic peptides were successfully monitored and characterized by observing the response of spectroscopic features as a function of an external pH change. This surface property change was found to be linearly correlated with the coverage ratio of the peptide onto the colloid, Θ. With the simplification of the space occupied by a peptide into a prolate, the Θ could be extracted through a simplified tessellation logic applied for a sphere. The simulation suggested that a prolate needs to have a spiking-out orientation with representative prolate axial length of (*a*, *b*) = (1.4 nm, 2.2 nm) for Aβ1–40, (*a*, *b*) = (4.6 nm, 7.4 nm) for α-syn, and (*a*, *b*) = (2.5 nm, 4.6 nm) for β2m. Of note, these values were similar to the values estimated by the reported protein structural data. However, the above-mentioned prolate dimensions could not reproduce the cases when Θ is less than ~0.50. A lower Θ is required to have less unit coverage area; this increase of unit area was interpreted as a gyration motion of each peptide, which kept a fixed contact spot but changed the tilting angle. The average tilting angle of the prolate was (θτ) (Aβ1–40) = 35 ± 2◦, (θτ) (α-syn) = 18 ± 2◦, and (θτ) (β2m) = 29 ± 6◦, indicating that when the colloid coverage ratio is below 0.5 a prolate can possess high degree of freedom in mobility while still maintaining a high level of interaction with the gold nano-particle surface. At the same time, it indicated many other possibilities of conformation including multiple contacting points or an ensemble of different adsorption orientations. The resulting Θ was fully explained by a relationship between the distances of each unit monomer under a given colloidal area. However, the degree of affinity for a second layer required us to account for the distribution of partially positive charge (δ+) over a peptide. The segment possesses a δ+ that was considered to be highly used when Aβ1–40 and α-syn each interacted with a nano-gold colloidal surface. This possesses a distribution of centering around the prolate axis. On the other hand, the δ+ of β2m was used to interact with each monomer, and the charge distribution was spread around with a distortion, resulting in a high exposure for the counter acting monomer. Therefore, it guided us to predict that β2m possesses different charge distributions than Aβ1–40 and α-syn, and sequences or sections of peptide corresponding to δ+ or δ– thus postulated. In closing, we demonstrated that nano-scale geometrical simulation with a simplified protein structure (i.e., prolate) successfully represents peptide adsorption orientation, providing insights into interfacial conformation and indicating the presence of electrostatic intermolecular and interfacial interactions for these pathophysiologic peptide cases.

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/20/21/ 5354/s1.

**Author Contributions:** Conceptualization, K.Y.; methodology, K.Y. and E.D.; software, K.Y. and J.J.; validation, K.Y., and A.I.; formal analysis, K.Y., K.B., P.S., J.J., E.D., N.R., J.B., I.D., and A.I.; investigation, K.Y., K.B., J.J. and A.I.; resources, K.Y., I.D., and A.I.; data curation, K.Y.; writing—original draft preparation, K.Y.; writing—review and editing, K.Y., J.B., N.R., and A.I.; visualization, K.Y., E.D., and N.R.; supervision, K.Y.; project administration, K.Y.; funding acquisition, K.Y.

**Funding:** This research received no external funding.

**Acknowledgments:** We are grateful for the support by Geneseo Foundation at the initial stage of this project. Ishan Deshmukh and Akane Ichiki thank for the gracious support by SUNY Geneseo Chemistry Department Alumni Summer Research Scholarship. We also thank Jonathan Bourne for helpful discussion during preparation of this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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