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The presence of amyloid fibrils is a hallmark of more than 50 human disorders, including neurodegenerative diseases and systemic amyloidoses. A key unresolved challenge in understanding the involvement of amyloid in disease is to explain the relationship between individual structural polymorphs of amyloid fibrils, in potentially mixed populations, and the specific pathologies with which they are associated. Although cryo-electron microscopy (cryo-EM) and solid-state nuclear magnetic resonance (ssNMR) spectroscopy methods have been successfully employed in recent years to determine the structures of amyloid fibrils with high resolution detail, they rely on ensemble averaging of fibril structures in the entire sample or significant subpopulations. Here, we report a method for structural identification of individual fibril structures imaged by atomic force microscopy (AFM) by integration of high-resolution maps of amyloid fibrils determined by cryo-EM in comparative AFM image analysis. This approach was demonstrated using the hitherto structurally unresolved amyloid fibrils formed in vitro from a fragment of tau (297-391), termed ‘dGAE’. Our approach established unequivocally that dGAE amyloid fibrils bear no structural relationship to heparin-induced tau fibrils formed in vitro. Furthermore, our comparative analysis resulted in the prediction that dGAE fibrils are closely related structurally to the paired helical filaments (PHFs) isolated from Alzheimer’s disease (AD) brain tissue characterised by cryo-EM. These results show the utility of individual particle structural analysis using AFM, provide a workflow of how cryo-EM data can be incorporated into AFM image analysis and facilitate an integrated structural analysis of amyloid polymorphism.

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of 'pure fragmentation'. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time-dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

Atomic force microscopy, AFM, is a powerful tool that can produce detailed topographical images of individual nano-structures with a high signal-to-noise ratio without the need for ensemble averaging. However, the application of AFM in structural biology has been hampered by the tip-sample convolution effect, which distorts images of nano-structures, particularly those that are of similar dimensions to the cantilever probe tips used in AFM. Here we show that the tip-sample convolution results in a feature-dependent and non-uniform distribution of image resolution on AFM topographs. We show how this effect can be utilised in structural studies of nano-sized upward convex objects such as spherical or filamentous molecular assemblies deposited on a flat surface, because it causes ‘magnification’ of such objects in AFM topographs. Subsequently, this enhancement effect is harnessed through contact-point based deconvolution of AFM topographs. Here, the application of this approach is demonstrated through the 3D reconstruction of the surface envelope of individual helical amyloid filaments without the need of cross-particle averaging using the contact- deconvoluted AFM topographs. Resolving the structural variations of individual macromolecular assemblies within inherently heterogeneous populations is paramount for mechanistic understanding of many biological phenomena such as amyloid toxicity and prion strains. The approach presented here will also facilitate the use of AFM for high-resolution structural studies and integrative structural biology analysis of single molecular assemblies.

Understanding how molecules in self-assembled soft-matter nanostructures are organized is essential for improving the design of next-generation nanomaterials. Imaging these assemblies can be challenging and usually requires processing, e.g., staining or embedding, which can damage or obscure features. An alternative is to use bioinspired mineralization, mimicking how certain organisms use biomolecules to template mineral formation. Previously, we have reported the design and characterization of Self-Assembled peptide caGEs (SAGEs) formed from de novo peptide building blocks. In SAGEs, two complementary, 3-fold symmetric, peptide hubs combine to form a hexagonal lattice, which curves and closes to form SAGE nanoparticles. As hexagons alone cannot tile onto spheres, the network must also incorporate nonhexagonal shapes. While the hexagonal ultrastructure of the SAGEs has been imaged, these defects have not been observed. Here, we show that positively charged SAGEs biotemplate a thin, protective silica coating. Electron microscopy shows that these SiO2-SAGEs do not collapse, but maintain their 3D shape when dried. Atomic force microscopy reveals a network of hexagonal and irregular features on the SiO2-SAGE surface. The dimensions of these (7.2 nm ± 1.4 nm across, internal angles 119.8° ± 26.1°) are in accord with the designed SAGE network and with coarse-grained modeling of the SAGE assembly. The SiO2-SAGEs are permeable to small molecules (<2 nm), but not to larger biomolecules (>6 nm). Thus, bioinspired silicification offers a mild technique that preserves soft-matter nanoparticles for imaging, revealing structural details <10 nm in size, while also maintaining desirable properties, such as permeability to small molecules.