Structural and Mechanical Properties of Amyloid Beta Fibrils: A Combined Experimental and Theoretical Approach

Abstract

In this combined experimental (deep ultraviolet resonance Raman (DUVRR) spectroscopy and atomic force microscopy (AFM)) and theoretical (molecular dynamics (MD) simulations and stress–strain (SS)) study, the structural and mechanical properties of amyloid beta (Aβ40) fibrils have been investigated. The DUVRR spectroscopy and AFM experiments confirmed the formation of linear, unbranched and β-sheet rich fibrils. The fibrils (Aβ40)_n, formed using n monomers, were equilibrated using all-atom MD simulations. The structural properties such as β-sheet character, twist, interstrand distance, and periodicity of these fibrils were found to be in agreement with experimental measurements. Furthermore, Young’s modulus (Y) = 4.2 GPa computed using SS calculations was supported by measured values of 1.79 ± 0.41 and 3.2 ± 0.8 GPa provided by two separate AFM experiments. These results revealed size dependence of structural and material properties of amyloid fibrils and show the utility of such combined experimental and theoretical studies in the design of precisely engineered biomaterials.

Graphical abstract

Biomaterials encompass various facets of medicine,¹ biology,² chemistry,^3,4 and materials science.⁵ Their applications include scaffolds for cell culture^6–10 and catalytic reactions,^11–15 devices,^16–23 and bioimplants.^6,24,25 However, the majority of materials used in these applications consist of classical nonbiological polymeric molecules.²⁶ Biological materials possess lower immunogenic and inflammatory potential than nonbiological polymers²⁷ and, thus, would be better suited for fabrication of artificial body parts and tissue scaffolds in the fields of tissue engineering and regenerative medicine.²⁸ Additionally, these materials can be used as building blocks for electronic devices and nanowires.^29,30

Amyloid beta (Aβ) peptides are promising biomolecules that are capable of forming a variety of materials under diverse conditions.^3,4,31–34 Their stability, accurate self-assembly,³⁵ and easy functionalization⁶ provide an excellent set of material properties that can be exploited for the aforementioned applications.^28,36 Driven by intermolecular forces such as hydrogen bonds, electrostatic and hydrophobic interactions, and π−π stacking, they can self-assemble molecule by molecule to produce supramolecular architectures (fibrils). This process proceeds through the formation of a natively unfolded intermediate to produce energetically stable, highly ordered, and β-sheet-rich fibrils.³⁷ The fibrils possess characteristic morphologies (hollow cylinders, twisted, and flat ribbons) ~ 100 Å in diameter and have variable lengths up to several micrometers.^3,38–42

The fibrils formed by small fragments of Aβ peptides possess high mechanical strength, elasticity, thermochemical stability, and self-healing.^4,27,43–45 These properties compare very favorably to most proteinaceous and nonproteinaceous materials.⁴⁶ They are most likely related to their macromolecular nature and in particular, to the physical and chemical constraints imposed by the individual amino acid residues. However, due to their heterogeneity, high-resolution molecular structures of low molecular weight Aβ amyloid oligomers cannot be easily determined because they are noncrystalline solid materials which are not amenable to X-ray crystallography and liquid state NMR.^47–53 Additionally, due to the fast rate of aggregation, structural determination of the early aggregates by using these experimental techniques is extremely difficult. Despite the availability of a sizable amount of data, there are no systematic studies to elucidate the roles of amino acid sequence and structure pertaining to the fundamental material properties such as great strength, sturdiness, and elasticity.

Here we have combined deep ultraviolet resonance Raman (DUVRR) spectroscopy and atomic force microscopy (AFM) techniques with molecular dynamics (MD) simulations and stress–strain (SS) calculations to derive a fundamental understanding of the sequence-structure-material properties relationship of these materials. In particular, structural and mechanical properties such as secondary structure and Young’s modulus (Y) of the Aβ40 fibrils provided by the DUVRR spectroscopy and AFM experiments are compared with the corresponding properties of (Aβ40)_n fibrils, for n = 5, 6, 7, 8, 9, 10, 12, 15, 20, 25, 30, 40, 50, 60, 80, and 120, where n is the number of monomers, derived from MD simulations and SS calculations. These results will elucidate size dependence of structural and mechanical properties of the Aβ40 fibrils and help the development of design rules for the accurate modeling of biomaterials.

Structural Properties of Aβ40 Fibrils

The AFM imaging of Aβ40 fibrils revealed linear, unbranched structures, which are typical for fibrillary aggregates (Figure 1a). The fibril lengths varied from a few hundred nanometers to a few microns, with thickness ranging between 3–5 nm (Figure 1b). The DUVRR spectrum of the Aβ40 fibrils (Figure 1c) was also characteristic of predominant β-sheet peptide conformation.^54,55

Figure 1.

AFM image of Aβ40 fibrils (a) and a representative height profile of a fibril (b) corresponding to blue marker. Scale bar: 500 nm. The DUVRR spectrum of Aβ40 fibrils (c) recorded with 199.7 nm excitation.

Specifically, a narrow and intense Amide I peak centered at 1675 cm⁻¹ is indicative of a well-organized cross-β core structure of amyloid fibrils.⁵⁶ The Amide I vibration consisting mainly of C=O stretching and a small contribution from out-of-phase C–N stretching is known to be sensitive to the peptide’s secondary structure.⁵⁷ The details of AFM and DUVRR experiments are provided in the Supporting Information (SI).

The structures of a wide range of (Aβ40)_n fibrils, for n = 5, 6, 7, 8, 9, 10, 12, 15, 20, 25, 30, 40, 50, 60, 80, and 120 where n is the number of monomers, were equilibrated using all-atom 50–100 ns MD simulations. They were performed using the GROMACS 4.5.6 software^58,59 utilizing the GROMOS96 53A6 force field⁵⁹ in explicit aqueous solution. The details of simulations are provided in the SI. Amyloid fibrils were essentially grown in-silico, starting with a Aβ40 fibril structure that was generously provided by Robert Tycko using a solid-state nuclear magnetic resonance (NMR) method (PDB ID: 2LMN).³⁷ The root-mean-square-deviations (rmsd) confirmed that the structures were equilibrated during the simulations. The accuracy of the simulated structures was further validated by comparing them with experimental DUVVR and NMR data such as secondary structure analysis, periodicity, and interstrand twist and angle.⁶⁰ In Aβ40 fibrils, side-chains emanating from the two separate monomer sheets were found to be tightly interdigitated like the teeth of a zipper by intermolecular forces such as hydrogen bonding, π−π interactions, and CH–π interactions.⁶¹ Additionally, there was an absence of water between the β-sheets, therefore this motif has been termed the “dry steric zipper.”⁶¹ Steric zippers were formed from self-complementary amino acid sequences, in which their side-chains could mutually interdigitate.⁶¹ The fibrils were found to be mostly β-sheet (88.0%) in character with small unordered sections (12.0%) at the beginning of each monomer sequence (Table 1). The formation of the β-sheet rich structures was supported by the measured DUVRR data. The larger fibril (n > 30) structures began to twist in order to gain structural stability and minimize repulsion (Figure 2).

Table 1.

Secondary Structure Analysis of Aβ40 Fibrils Where n = 20 to 120^a

Monomers	β-sheet (%)	Unordered (%)	Fibril Twist (°)	d (nm)	θ (nm)	Periodicity v (nm)
20	87.8	12.2	3.57 ± 1.94
30	89.2	10.8	4.17 ± 2.34
40	89.5	10.5	10.49 ± 5.11	0.477	1.50	114.5
50	90.6	9.4	8.91 ± 3.63	0.479	1.47	117.3
60	90.4	9.6	9.19 ± 3.69	0.479	1.29	133.7
80	90.7	9.3	17.36 ± 4.38	0.481	1.34	129.2
120	90.4	9.6	25.02 ± 6.05	0.481	1.32	131.2

^aFibril twist calculated from MD simulations.

This value represents the twist angle from one end of the fibril to the other. d, θ denote the inter-strand distance and twist angles between adjacent monomers, respectively. Length of the fibril, L = n × d, where n is the number of monomer units in an amyloid fibril.

Figure 2.

MD equilibrated structures of (Aβ40)_n fibrils with n = 30, 60, 80, and 120.

Smaller fibrils (<20 monomers) produced overall twists less than 1° (Table 1), and therefore have been left out. The larger fibrils possess twists greater than 8°, which further helps to stabilize their secondary structure and allows for reordering to occur before the fibril ruptures beyond repair.

The interstrand distance (d) is defined as the average distance between two adjacent monomer units within the whole fibril. The d value was calculated as a function of length (L = n × d) and all larger fibrils (40–120) produced an average value of 0.480 ± 0.0015 nm. This value is in excellent agreement with previous experimental studies on Aβ40 fibrils (0.47 nm beta-sheet spacing).³⁷ In addition, the interstrand angle (θ) between two adjacent monomer units within the fibril can provide the periodicity of these aggregates through the equation (v = 360 × d/θ). In this equation, periodicity (v) is defined as the minimum length of a fibril to make a complete turn, i.e., the length needed to cover a twist angle of 360°. This minimal length is driven by a balance between mechanical forces dominated by the elasticity (elastic energy penalty) and the electrostatic forces due to the distribution of hydrophobic regions and charges along the backbone.^41,62–64 However, amyloid fibril periodicity is tunable as shown by Adamcik et al. by adjusting the salinity or ionic environment such that at high and low salinity, fibrils form relaxed tapes and twist structures, respectively.⁶³ The average computed value of v was 125.2 ± 7.8 nm. This value is also in line with an experimental determined periodicity for amyloidgenic protofibrils such as 3-fold Aβ40 fibrils of 120 ± 20 nm and α-synuclein fibrils of 100–150 nm.^41,65 All these results suggested that equilibrated structures of large aggregates (n ~ 100) are realistic models for Aβ40 fibrils that are hundreds of nanometers to micrometers long.⁶⁶

Mechanical Properties of Aβ₄₀ Fibrils

The AFM imaging of the Aβ40 fibrils in air showed the aggregation of fibrils on mica (Figure 3a–c). However, the single fibrils were still evident. The height and width of the single strands were ~4 nm and ~30 nm, respectively (Figure 3d).

Figure 3.

AFM imaging of ensemble of Aβ40 fibrils (a) height image and (b) amplitude image. (c) High-resolution image of a single fibril, and (d) inset showing the map of elasticity distribution of a section of a single fibril. The white space in panel (d) represents the stiffer underlying mica surface.

It may be noted that the widths were typically higher than actual width owing to the radius of curvature of the AFM tip. The values of compressive Young’s modulus (Y) were obtained by nanoindentation of the fibrils in both air (dry) and hydrated (buffer) conditions. The indent curves were fitted to the Hertz model that assumes that the strain is elastic and the contact surfaces are frictionless.

The value of Y was 1.79 ± 0.41 GPa, measured for 20 fibrils. This value agrees well with the Y (2–4 GPa) determined for fibrils formed from other peptides such as α-synuclein, lysozyme, and insulin measured using different AFM methods (nanoindentation, peak force quantitative nanomechanical property mapping, and HarmoniX).^{67,4,46,68,69} AFM imaging of fibrils in PBS buffer showed a similar morphology to the Aβ40 fibril in air. The height of a single fibril in PBS was ~4 nm. This height value is close to the reported 4.6 nm height of the Aβ42 fibril in PBS.⁷⁰ The value of Y of single fibrils in PBS is 19.68 ± 8.56 MPa (sample size = 20 fibrils). Expectedly, fibrils in a hydrated state are much softer than the fibrils measured in air.⁷¹

Single strain, SS, force calculations (Figure 4a) allow us to compare the experimental values for Young’s modulus with that from the simulations. We determined the size dependence of Y for all fibrils (Aβ40)_n where n = 5, 6, 7, 8, 9, 10, 12, 15, 20, 25, 30, 40, 50, 60, 80, and 120, by using SS calculations on the structures of fibrils equilibrated through all-atom MD simulations. These calculations were performed using the COMPASSII force field and a protocol implemented in the Materials Studio 7.0 program.⁷² The details of the SS calculations are provided in SI.

Figure 4.

(a) Stress–Strain (SS) graphs of (Aβ40)₄₀–(Aβ40)₁₂₀

Single domain structures (one-fold geometry) were chosen for these calculations due to differences in interaction energy contributions to the overall strength of the material and were validated by comparison to experimentally determined geometric parameters. The largest energy contributions come from the hydrogen bonding between monomer units, while the smallest comes from the hydrophobic interactions connecting the two different domains. Furthermore, as Y values are a function of total molecular area, doubling the interaction energy by having two domains, is canceled by doubling the area (Force/Area). Therefore, a one-fold structure will produce the same Y as a 2-fold structure. The small (Aβ40)₅–(Aβ40)₂₀ fibrils provided an average modulus value of 45.0 ± 7.5 GPa which is slightly higher, but comparable to the value (13–42 GPa) of small fragments of Aβ peptides reported previously.⁴ The similarity in computed Y was due to common features of the equilibrated structures of these fibrils. The Aβ fibrils modeled computationally (Aβ40₅–Aβ40₁₂₀) were all shorter than the periodicity of their helical pitch and featured significant differences in the pure tensile properties computed.^43,73 The (Aβ40)₅–(Aβ40)₃₀ structures contained no appreciable fibril twist, which could account for the increase in tensile stiffness observed as no rearrangement or relaxation of structure was possible during SS. Typically for such fibrils, local instabilities can emerge at the ends of the fibrils (on the order of tens of nanometers) that reduce their stability and contribute to their rigidity and disassociation under extreme chemical conditions.^43,73 Additionally, for fibrils shorter than their periodicity, bending modes can occur against the cross section with the lowest moment of inertia allowing for increased flexibility as shown by our larger aggregates.^62,68 The mechanical properties of the wt-Aβ40 fibrils in implicit solvent using theoretical methods had been computed previously and were found to vary with the length of the fibril and that the long fibrils (20, 40, and 60 monomers in length) were more stable.^43,74 The value of Y calculated for (Aβ40)₃₀ (15 nm in length) was half the value of (Aβ40)₂₀ and heralds the next trend seen within the larger fibril structures. It is noteworthy that the computed values for (Aβ40)₅–(Aβ40)₃₀ values are significantly higher than the AFM measured value of ~1.8 GPa.

For the larger structures (Aβ40)₄₀–(Aβ40)₁₂₀, a monoexponential decay between Y and n was observed (Figure 4b) producing a high correlation value of 0.99.

This indicates that a scaling law might exist that could accurately calculate the lowest modulus value for much higher order aggregates. The monoexponential decay fit produced an appreciable plateau value associated with the lowest moduli that can be found for this decay. The value obtained for the plateau was 4.2 GPa (Figure 4b), which pertains to any structure greater than 200 units long. The computed value (4.5 GPa) of Y for the largest fibril (Aβ40)₁₂₀ should be considered in an excellent agreement with the experimentally measured values of 1.79 ± 0.41 and 3.2 ± 0.8 GPa using two distinct AFM methods (Table 2). It is noteworthy that the experimentally determined Y is compressive or transversal, whereas the calculated Y is purely longitudinal. This could also contribute to the difference in computed and measured values of Y (see SI).⁷⁵ These results also suggest that the models of fibrils (>100 monomers) approach a more realistic value when compared with traditional AFM stress experiments.

Table 2.

Computed Values of Young’s Modulus (Y) as a Function of Aβ40 Monomers

monomer units	Young’s modulus (GPa)
5	38.0
6	36.2
7	37.3
8	54.1
9	44.5
10	51.2
20	54.3
30	26.0
40	33.9
50	19.8
60	11.4
80	6.1
120	4.5

In this study, we have combined complementary experimental (DUVRR and AFM) and theoretical (MD simulations and SS calculations) techniques to investigate the structural and mechanical properties of Aβ40 fibrils. The AFM experiments showed the formation of linear and unbranched Aβ₄₀ fibrils with varying length (a few hundred nanometers to a few microns) and thickness (3–5 nm). The DUVRR spectrum provided a high relative intensity of the Amide I peak at 1675 cm⁻¹ that was characteristic of β-sheet rich fibrils. The MD equilibrated fibrils formed using 5, 6, 7, 8, 9, 10, 12, 15, 20, 25, 30, 40, 50, 60, 80, and 120 monomers were also dominated by β-sheets (88.0%) and formed through a zipper created by self-complementary amino acid residues. The other structural properties (twist, interstrand distance and periodicity) of these fibrils were also in agreement with experimental measurements. The AFM experiments provided the values of compressive Y of 1.79 ± 0.41 GPa (sample size = 20 fibrils) in air (dry) condition. The SS calculations on the small equilibrated (Aβ40)₅–(Aβ40)₂₀ fibrils provided an average Y value of 45.0 ± 7.5 GPa that was significantly higher than the measured value. However, the larger structures (Aβ40)₄₀–(Aβ40)₁₂₀, exhibited a monoexponential decay and produced a high correlation value of 0.99, which suggested the existence of a scaling law. The monoexponential decay using this law provided Y = 4.206 GPa that can be associated with any structure greater than 200 units long. This value is in excellent agreement with AFM nanoindention experimental value of 1.8 ± 0.41 GPa. The results reported in this study will advance our efforts to understand sequence-structure-material properties relationship of biomaterials and to develop “design rules” for their computational modeling.