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Proc Natl Acad Sci U S A. Oct 24, 2006; 103(43): 15806–15811.
Published online Oct 12, 2006. doi:  10.1073/pnas.0604035103
PMCID: PMC1635084
Biophysics

Characterization of the nanoscale properties of individual amyloid fibrils

Abstract

We report the detailed mechanical characterization of individual amyloid fibrils by atomic force microscopy and spectroscopy. These self-assembling materials, formed here from the protein insulin, were shown to have a strength of 0.6 ± 0.4 GPa, comparable to that of steel (0.6–1.8 GPa), and a mechanical stiffness, as measured by Young's modulus, of 3.3 ± 0.4 GPa, comparable to that of silk (1–10 GPa). The values of these parameters reveal that the fibrils possess properties that make these structures highly attractive for future technological applications. In addition, analysis of the solution-state growth kinetics indicated a breakage rate constant of 1.7 ± 1.3 × 10−8 s−1, which reveals that a fibril 10 μm in length breaks spontaneously on average every 47 min, suggesting that internal fracturing is likely to be of fundamental importance in the proliferation of amyloid fibrils and therefore for understanding the progression of their associated pathogenic disorders.

Keywords: atomic force microscopy, force spectroscopy, nanotechnology, prions, protein aggregation

Amyloid fibrils are filamentous assemblies of peptides and proteins (1, 2) that were initially observed in connection with clinical disorders, including Alzheimer's disease and type II diabetes. It is increasingly apparent, however, that the amyloid state is accessible to many different amino acid sequences under appropriate conditions and can therefore be considered an inherent characteristic of polypeptide molecules. Amyloid fibrils have a number of underlying similarities and, in particular, share a common core structure, composed of a dense network of hydrogen bonds stabilizing an elongated stack of β-strands, perpendicular to the fibril axis and separated by 4.8 Å (3). The fibrils have been shown to consist of one or more protofilaments (46), the highest level of generic substructure. When multiple protofilaments are assembled together the resulting fibrils have morphologies ranging from twisted rope-like structures to flat tapes (48) with nanometer-scale diameters. The further self-assembly of fibrils can result in the formation of spherulitic structures (9) or intractable plaques in patients, and the fibrils or their precursors have been found in at least some cases to give rise to high cellular toxicity (10), a phenomenon thought to be responsible for the neurodegeneration associated with many of the amyloid disorders.

Recent investigations of amyloid fibrils, including the determination by solid-state NMR of several structures of peptide and protein molecules within a fibril (1113) and a structure by x-ray diffraction of a crystalline peptide with fibril-like characteristics (14), have resulted in increasingly sophisticated structural and biochemical descriptions of these aggregates (15). Yet many of the most fundamental properties of these fibrils in terms of their mechanical rigidity and resistance to breakage are still unknown, despite the fact that these properties are increasingly recognized to be of importance for understanding their behavior in biology (1, 16, 17). In this article, we describe the measurement of such properties of amyloid fibrils composed of insulin by using atomic force microscopy (AFM) and spectroscopy. From these measurements, we have been able to determine the material properties of the fibrils, in particular their strength and stiffness, and to show that these characteristics are likely to be related to the growth and propagation of amyloid fibrils in disease.

Results

Force Spectroscopy Studies of Insulin Fibrils.

To provide a detailed mechanical characterization of amyloid fibrils we used an approach that brings together imaging and force spectroscopy (18, 19). Fibrils from insulin were deposited onto nanoscale grooves fabricated into a silicon substrate by using a focused ion beam. The surface was then imaged by using AFM until a fibril with a specific morphology was observed to be suspended over a groove. Here, we have chosen to focus our attention on two-filament insulin fibrils, as these are the simplest examples of mature fibrils. Two-filament insulin fibrils were identified on the basis of their height in force microscopy images, and the dimensions of these structures were consistent with previous cryo-electron microscopy (6) measurements. Force-distance curves were then acquired by moving the AFM probe to different locations along the suspended fibril and applying a given load while monitoring the deflection of the cantilever that acts as the force sensor.

The data obtained from these individual measurements have four readily identifiable regions, as shown in Fig. 1. At the beginning of the experiment, the AFM probe is not in contact with the sample and no cantilever bending is observed. When the separation between the tip and the sample is progressively reduced, eventually the tip comes into contact with the fibril, and then a linear elastic region is found when the fibril bends under the applied load. In this region the observed spring constant is that of the serial cantilever-fibril system, and the deflection of the fibril under the load is the horizontal distance between the coupled cantilever-fibril deflection curve and the cantilever deflection originating from the point of contact. At higher applied forces, nonlinear deformations are observed until the sample eventually breaks under the load. The tip then makes contact with the surface of the groove beneath and the magnitude of the slope of the force-distance curve is equal to the cantilever spring constant.

Fig. 1.
Mechanical manipulation of a two-filament insulin fibril with the atomic force microscope. (A) Insulin amyloid fibrils were deposited onto a patterned gold surface, and contact mode AFM topographic images were obtained in aqueous 0.01 M HCl (image size ...

To define the strength of the fibrils, we examine the nonlinear elastic behavior, in Fig. 1B, and point of fracture observed for high mechanical loads during force spectroscopy measurements. We can estimate the mean ultimate strength of the structures by computing the maximal value of the stress tensor (19, 20), σxx = Ezζ″(x), where z is the distance from the neutral axis, and ζ(x) describes the shape of the fibril under load. Maximal stress occurs at the bottom edge of the fibril z = r under the tip for x = L/2 if the load is applied in the middle of the suspended fibril. Neglecting the shear contribution to the deflection, we get σmax = zLFmax/8I, which yields a value of 0.6 ± 0.4 GPa for the strength, a number of the same order of magnitude as that of spider silk (1–1.5 GPa) (21) and steel (0.6–1.8 GPa) (22).

To define the stiffness of the fibrils, we examine the linear behavior of deflections during force spectroscopy. In the linear elastic region, the effective spring constant is observed to decrease when the tip of the AFM cantilever is moved from the edge of the grooves toward the center of the suspended fibril (Fig. 2). To interpret these data quantitatively, we envisage a fibril as a continuous material strongly adsorbed to the substrate, with a transverse load applied at a defined point on the fibril by the AFM probe (23). For such a material, with bending rigidity CB, shear modulus G, and cross-sectional area A, suspended over a gap of length L, the spring constant of the fibril under the load k at a dimensionless fraction f of the total length from the nearest edge is given by (24):

equation image

where 3/4 ≤ ξ ≤ 1 is a shape factor associated with the fibrils, as described in Materials and Methods. The spring constant can be measured as a function of the position of the applied load for each force-distance curve obtained on a suspended structure; fitting the data observed for the fibrils to this equation yields the values for the elastic and shear moduli of E = 3.3 ± 0.4 GPa and G = 0.28 ± 0.2 GPa (Table 1).

Fig. 2.
Determination of the bending rigidity of two-filament insulin fibrils from mechanical manipulation in the atomic force microscope. (A) Force-distance curves were acquired on 21 independent samples of two-filament insulin fibrils, corresponding to >2,000 ...
Table 1.
Summary of the mechanical properties of insulin amyloid fibrils from force spectroscopy and statistical analysis of shape fluctuations

Determination of the Rigidity of Insulin Fibrils.

To test the assumptions inherent in this analysis, we have used a second and fundamentally different technique to measure independently the bending rigidity of the fibrils by analyzing for an ensemble of structures the average magnitude of the thermally induced fluctuations from their rigid rod-like ground state. Fibrils were deposited onto a mica substrate, and AFM topographic data were then acquired in tapping mode (Fig. 3A). The geometry of the fibrils was mapped to piecewise polynomials by using an algorithm developed for this purpose (Fig. 3B). With the worm-like chain model developed for the statistical mechanics of semiflexible polymers (25) (see Materials and Methods), the measurement of the mean square fluctuations u2 enables an estimate to be made of the bending rigidity of the two–filament fibrils such that:

equation image

The values for the mechanical properties of insulin amyloid fibrils obtained with this approach are in excellent agreement with the corresponding data from the force spectroscopy measurements (see Table 1), for instance the determination of the persistence length of the fibrils with this method yields 42 ± 30 μm, compared with the corresponding value of 22 ± 3 μm from the force spectroscopy data.

Fig. 3.
Measurement of the bending rigidity of fibrils by analysis of thermal fluctuations. (A and B) The shape of the fibrils was automatically extracted from the AFM height data (A Left) by using a tracing algorithm (A Right) and secants (see Materials and ...

Measurement and Analysis of Insulin Fibril Growth Kinetics.

The internal fracture of amyloid fibrils is potentially a key feature of the kinetics of amyloid growth (16, 17). This kinetic effect is a consequence of the fact that, because growth occurs only at the ends of the fibrils, an increase in the number of free ends through breakage of existing fibrils can dramatically enhance the rate at which the monomer in solution can be incorporated into the aggregates. These effects have previously been predicted and studied theoretically (26), in particular in the context of prion diseases (27), and it has been shown that an alteration in the scission rate constant is by itself enough to cause dramatic changes in the rates of proliferation of amyloid fibrils and can potentially determine the development and transmission of disease conditions (17, 27). To examine experimentally how such effects would influence the kinetics of fibril growth, preformed insulin fibrils were added to a solution of insulin monomers at 60°C and the increase in average fibril length was determined by dynamic light scattering (2830). By incorporating breakage into the nucleation-dependent growth mechanism of amyloid formation (Fig. 4A) a differential equation (see Materials and Methods) for the average length of a fibril in this seeded growth experiment (i.e., not limited by nucleation) can be written as:

equation image

The initial concentration of monomer, x0, was varied in our experiments, and the initial rate of change of the average fibril length was determined (Fig. 4B). A least-squares fit of the data revealed an elongation rate constant of k+ = 1.8 ± 0.2 × 105 M−1·s−1 and a breakage rate constant of kd = 1.7 ± 1.3 × 10−8 s−1. Interestingly, the experimentally determined ratio of the rates kd/k+ ≈ 10−13 M is precisely in the region where computational studies predict (27) the predominant formation of elongated fibrils, such as those observed in this study, rather than the short aggregates predicted to result from more frequent breakage.

Fig. 4.
Breakage of amyloid fibrils. (A) A proposed mechanism of amyloid fibril formation involves nucleation (row 1), elongation (row 2), dissociation (row 3), and breakage (row 4). The breakage rate constant was determined from seeded growth experiments. ( ...

To carry out an independent test of the influence of breakage on the kinetics of fibril assembly, we monitored the average length of a growing suspension of fibrils by using AFM, as shown in Fig. 4C. The solution to the differential equations for the nucleated growth model without breakage (see Materials and Methods) results in values of the average fibril length that are dramatically in excess of those observed experimentally (dashed line in Fig. 4C). However, when the terms describing the contributions from internal breakage on the kinetics of amyloid growth are included into the differential equations, and the values determined independently from the light-scattering experiments in Fig. 4B are used for the rate parameters, we find excellent agreement with the measured lengths from the AFM growth experiment (shaded region in Fig. 4C). This result demonstrates explicitly that breakage is a fundamental process in the proliferation of fibrils and has to be taken into account for a quantitative understanding of amyloid growth. In future experiments using this approach it may be possible to monitor directly the reduction in length of fibrils undergoing breakage over long time periods and quantitatively characterize the effect of different compounds or solution conditions on this process.

Discussion

The results of this study enable a number of important issues in the amyloid field to be addressed, including the nature of the interactions that stabilize the fibrils. The present spectroscopy measurements reveal that the forces that are required to fracture amyloid fibrils mechanically range from 300 to 500 pN (Fig. 1B). Force unfolding measurements (31) have previously demonstrated that the forces required to unfold individual domains of proteins such as titin range from 150 to 300 pN, suggesting that the interactions within the amyloid core, which include hydrogen bonding in the cross-β structure and other factors such van der Waals and electrostatic forces, are of similar origin and nature to those responsible for the resistance to unfolding of native structural motifs in proteins (32).

The high level of stability of amyloid aggregates is an essential factor underlying their involvement in a range of clinical disorders (33). In light of the results from the present study, we can rationalize the origin of this stability; the very high strength, combined with the mechanical stiffness will make it exceedingly difficult for the mechanisms in place in living systems to degrade amyloid fibrils, leading to an accumulation of protein aggregates (33). Apart from their fundamental biological significance, we note that the material properties of insulin amyloid fibrils place them among the most robust natural polymers such as spider silk (21) and are even comparable to some of the strongest of all materials known, such as steel (22). Interestingly, spider silk (21) shares some degree of structural similarity with amyloid fibrils, both being β-sheet-rich protein fibrils, an aspect that can help to rationalize our findings that their mechanical properties also are of similar orders of magnitude. But, in contrast to spider silk, which requires the concerted action of a complex biological machinery (21) to polymerize into the finished form, amyloid fibrils can readily self-assemble in solution without the need for other factors. The mechanical properties measured in this study are also of very great significance for understanding the increasing evidence for the exploitation, albeit under careful regulation, of amyloid structures in living systems for functional purposes (3436), for example, in functional coatings of microorganisms (35), and show that the high level of mechanical rigidity and strength measured here are extremely favorable for novel applications as a biomaterial.

The remarkable properties identified in this study that make amyloid fibrils attractive for material and structural purposes are also those that prove to be so damaging in amyloid diseases. The intrinsic strength of amyloid fibrils undoubtedly underlies their persistence in a biological system once they are formed, but the fact that the widths of the fibrils are a few nanometers generates characteristics that differ from bulk materials. In particular, once the fibrils reach lengths of the order of microns, their inherent tendency to break under thermal fluctuations is such that it will contribute significantly to the kinetics of fibril growth by increasing the density of ends at which growth occurs. Measurements of the resistance to breakage of fibrils could therefore be of great value in understanding key properties that underlie fibril proliferation in diseases (16), including, for example, the rate of progression of systemic amyloid disorders and the transmission of specific strains of the prion diseases (17). We envisage therefore that the ability to measure the mechanical properties of specific amyloid structures, as described in this work, will be of increasing value in the detailed understanding of their varied roles in normal and aberrant biology.

Materials and Methods

Fibril Formation.

Insulin fibrils were formed in a solution of 1 mM (5.8 mg/ml) bovine insulin (Sigma, Dorset, U.K.) in 0.017 M HClaq (for a final pH value of 2.0). The solution was heated at 60°C for 24 h and then stored at room temperature for 1 week.

Mechanical Bending and Breaking of Amyloid Fibrils.

Insulin fibril suspensions were deposited on a gold-coated silicon patterned surface prepared in a focused ion beam microscope. Contact mode images using an East Coast Scientific (Cambridge, U.K.) AFM were obtained in 0.01 M HCl using rectangular silicon cantilevers (MikroMasch, Tallinn, Estonia), with springs constants calibrated with the Sader method (37). A suspended fibril was identified, the probe was moved to a point along the suspended length, the probe position was recorded, and a force-distance curve was acquired. In the mechanical bending experiments (Fig. 2) the motion of the z piezo was limited to ensure that only forces consistent with linear elastic bending were applied. The serial spring constant was determined by a linear least-squares fit of the deflection in the elastic region, and the fibril spring constant was calculated as described. The data from 21 independent measurements were binned by the dimensionless fraction across the suspended length f, and a nonlinear least-squares fit was performed for the spring constant. For the mechanical breakage experiments (Fig. 1) measurements were made on four independent samples, and the average force required to break the fibril was calculated.

Analysis of Bending Caused by Thermal Fluctuations.

Height measurements were acquired by using tapping mode AFM [Molecular Imaging (Tempe, AZ) Pico Plus] of insulin fibrils deposited on mica and dried in air. The fibrils were identified in the image as two filament structures based on height measurements (6, 38, 39) and were then automatically traced by using an algorithm developed for this purpose (Fig. 3B), and the midpoint fluctuations were measured for secants connecting two points belonging to the traced backbone of the fibril (Fig. 3C). The fluctuations are related to the mechanical properties of the fibrils through the statistical mechanics of the worm-like chain model for semiflexible polymers (25). For fibrils that reach equilibrium in two dimensions on the surface before being adsorbed (Fig. 3A), the mean square midpoint fluctuations from a secant joining two points of the polymer are given by (40):

equation image

in the limit of arc lengths much shorter than the persistence length, where β = (kBT)−1 is the inverse temperature. On the other hand, if there are strong interactions with the substrate, the polymer will not equilibrate from the 3D state, but adsorption occurs when certain points of the polymer come into contact with the substrate and become attached. When the rest of the polymer adsorbs onto the surface, the resulting fluctuations are between the norm of the initial 3D fluctuations L3/24CBβ and their projection into the plane L3/48CBβ. Thus, for both cases, the measurement of the average fluctuations enables the estimation of the bending rigidity of the fibrils:

equation image

If we assume that there is additionally an experimental relative error ΔCB,upperbound/CB,upperbound = ΔCB,lowerbound/CB,lowerbound = α in the determination of the bounds, we can report the midpoint of the interval as: CB = CB,lowerbound(3 + α)/2 ± CB,lowerbound (1 + 3α)/2. Based on comparisons between independent measurements of left angle bracketu2right angle bracket, we estimate α < 48% for a sample of n = 100 fibrils.

Dynamic Light-Scattering Measurements of Fibril Growth.

Ten different values of initial insulin monomer concentration, ranging from 2 to 16 μM, at pH 2.0 in HClaq were added to the preformed insulin fibril seed (100 nM), the mixture was heated at 60°C, and the hydrodynamic radius was recorded as a function of time and transformed into average fibril length as described (28). Solutions of insulin were passed through a Whatman (Middlesex, U.K.) filter with 20-nm pore size before dynamic light-scattering experiments.

Measurement of the Growth Kinetics by AFM.

Preformed insulin fibrils were placed in a bath sonicator for 24 h and then added to a solution of insulin at pH 2 (50 nM concentration of fibrils and 1 μM concentration of insulin). The mixture was heated at 60°C, and aliquots were drawn at regular time points and deposited onto freshly cleaved mica. Images were acquired in tapping mode, and two-filament insulin fibrils were detected and traced by the algorithm described in Fig. 3A. The average fibril length as a function of time was calculated from these data and is shown in Fig. 4C.

Nucleated Growth Model with Breakage.

For a fixed initial concentration of monomer, x0, and where the monomer, fibril, and polymer concentrations are called x, y, and z, respectively and with the rate constants as shown in Fig. 4A with kd = k, one can write differential equations as follows:

equation image

equation image

Cross-Sections for Two-Filament Fibrils.

For a double helix composed of two strongly interacting filaments, the moment of inertia, I = ∫ y2dA, is the average over all of the possible orientations in one pitch. This expression reduces to the average of the moments of inertia for two circles aligned with the vertical, I = 5πr14/2, and horizontal, I[perpendicular] = πr14/2, axes, I2 = (I[perpendicular] + I)/2 = 6I1, where r1 is the radius of a one-filament fibril. The polar second moment of the area, J = ∫r2dA, used to calculate the torsional rigidity cT = GJ, is given by J = 3πr12.

The shear deflection of a double helix is to a first approximation the average of the deflection of horizontally and vertically aligned circles. For the former case the same functional form for the shear deflection of a circle holds. For the latter case, the shear deflection is that of a single circle with a radius between 2r1 and 2r1. The shear deflection δs is then given by 10FLξ/9GA f(1 − f), where A is the cross-sectional area of the double helix and it follows that ξ is between 0.75 and 1.

Acknowledgments

We thank Eugene Terentjev, Aidan Craig, and Michele Vendruscolo for helpful discussions. This work was supported by the Interdisciplinary Research Collaboration in Nanotechnology. J.F.S. is a National Institutes of Health–Cambridge Health Science Scholar. C.E.M. is a Royal Society University Research Fellow. The work of C.M.D. is supported, in part, by grants from the Wellcome Trust and the Leverhulme Trust.

Abbreviation

AFM
atomic force microscopy.

Footnotes

The authors declare no conflict of interest.

This article is a PNAS direct submission.

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