Spatial Persistence of Angular Correlations in Amyloid Fibrils

Using atomic force microscopy height maps, we resolve and quantify torsional fluctuations in one-dimensional amyloid fibril aggregates self-assembled from three different representative polypeptide systems. Furthermore, we show that angular correlation in these nanoscale structures is maintained over several microns, corresponding to many thousands of molecules along the fibril axis. We model disorder in the fibril in respect of both thermal fluctuations and structural defects, and determine quantitative values for the defect density, as well as the energy scales involved in the fundamental interactions stabilizing these generic structures.

Figure 1

(a) Topographic data were acquired in air in tapping mode for fibrils deposited on mica, shown here for a two-filament insulin fibril. Scale bar 250 nm. Because of tip-sample convolution effects, the distances in the sample plane are enlarged on the scale of the tip radius (7–10 nm), but height measurements are exact. (b) The height along the fibril backbone (small solid circles) was averaged over a window of 20 nm or twice the tip radius (blue/gray trace) and clearly displays maxima and minima (open circles) separated by a twist angle of $\pi$. From this height map, the local twist phase (c) can be extracted as described in the text.

Figure 2

(a) Cumulative twist angles measured for insulin (red solid lines), SH3 (green dashed lines), and TTR fibrils (blue dotted lines). (b) Logarithm of the average torsional correlation as a function of arc length measured at integer multiples of the period and one parameter fit to an exponential decay for insulin (red squares), SH3 (green circles), and TTR fibrils (blue triangles). Inset: Example of the damped oscillation of the absolute value of the normal-normal projection for an insulin fibril.

Figure 3

The bending rigidity of insulin amyloid protofilaments, automatically traced from AFM topographs (inset), was estimated from the statistics of their shape fluctuations. Mean square fluctuations from the secant midpoint as a function of the secant length in 1000 bins, with a one parameter fit to a cubic equation describing the expected behavior for semiflexible chains.