Interactive patches over amyloid-$\beta$ oligomers mediate fractal self-assembly

The monomeric units of intrinsically disordered proteins self-assemble into oligomers, protofilaments, and eventually fibrils which may turn into amyloid. The aggregation of these proteins is primarily studied in bulk with no restriction on their degrees of freedom. Herein we experimentally demonstrate that amyloid-$\beta$ ($\mathrm{A}\beta$) aggregation under diffusion-limited conditions leads to its fractal self-assembly. Confocal microscopy and scanning electron microscopy with energy dispersion x-ray analysis were used to confirm that the fractal self-assemblies were formed from $\mathrm{A}\beta$ rather than the salt present in the two supporting media: deionized water and phosphate buffered saline. The results from the molecular docking experiments implicated that electrostatic and hydrophobic patches on the solvent-accessible surface area of the $\mathrm{A}\beta$ oligomers mediate the fractal self-assembly. These implications were tested with laser light scattering experiments on the oligomers formed by breaking mature fibrils of $\mathrm{A}\beta$ through sonication, which were observed to self-assemble into fractals when sonicated solutions were drop casted. The electrostatic interactions modulate the fractal morphologies with pH of the solution, which leads to a morphological phase transition observed through the variation in their fractal dimension. These transitions provide experimental evidence for the existing theoretical framework in terms of different kinetic models. The higher surface-to-volume ratio of these fractal self-assemblies may have applications in drug delivery, biosensing, and other biomedical applications.

Figure 1

The fractal morphologies were obtained from the freshly prepared solution of $\mathrm{A}\beta$ in (a)–(f) DI water and in (a*)–(f*) PBS buffer, respectively, at different pH.

Figure 2

The nonconfocal (a)–(f) and confocal mode (a*)–(f*) images of the morphologies obtained from the freshly prepared solution of $\mathrm{A}\beta$ in the DI water at different pH.

Figure 3

The SEM images of the morphologies obtained from the freshly prepared solution of $\mathrm{A}\beta$ in PBS buffer at (a)–(f) different pH. (g) The energy dispersion x-ray (EDAX) spectra show the elements present in the areas chosen in the fractal morphology obtained at pH $6.5\pm 0.1$, shown in (h) for selected area 1 (see Sec. S1, Supplemental Material [35] for selected area 2). (i) The weight and atomic contributions of the elements in the EDAX spectra shown in (g).

Figure 4

The molecular docking was performed on the (a) modeled structure of $\mathrm{A}\beta$ monomer with $\beta$-sheet structure [38] obtained from Dr. Bogdan Barz, Forschungszentrum Jülich, Germany. The electrostatic and hydrophobic patches on the (b) monomer and (c) docked tetramer. SASA of the docked structures and interactive patches formed using (d) electrostatics-based and (e) hydrophobic-based docking, respectively. The fractional SASA of the polar and ionic and hydrophobic residues on the SASA of the docked structures formed using (d*) electrostatics-based and (e*) hydrophobic-based docking, respectively.

Figure 5

The optical microscope images and the corresponding size distribution measured using DLS for matured fibrils after (a) and (a*) 0 min, and $\mathrm{A}\beta$ solution of matured fibrils after sonication time of (b) and (b*) 2 min; (c) and (c*) 5 min; (d) and (d*) 10 min; (e) and (e*) 15 min; and (f) and (f*) 30 min.

Figure 6

(a) The radius of gyration ($R_g$) of $\mathrm{A}\beta$ aggregation as a function of time measured for 5 days at similar pH for which the fractal morphologies were observed. (b) The $d_f$ as a function of pH; it depicts a morphological phase transition in the fractal self-assembly of $\mathrm{A}\beta$. The $d_f$ for fractal self-assembly obtained in PBS buffer at pH $11.5\pm 0.1$ is not shown due to inaccuracy in the $d_f$ mainly because of the contrast of the image (see Sec. S6, Supplemental Material [35]).