Why amyloid fibrils have a limited width

Amyloid fibrils can grow indefinitely long by adding protein chains to the tips of the fibril through β-sheet hydrogen bonding; however, they do not grow laterally beyond ∼10-20 nm. This prevents amyloid fibrils from growing into two-dimensional or three-dimensional arrays. The forces that restrict lateral association of β-sheets in amyloid fibrils are not immediately apparent. We hypothesize that it is the helical symmetry of amyloid fibrils that imposes the limit on fibril width by incurring an increasing separation between helically related molecules as a function of radial distance from the helical axis. The unavoidable consequence is that backbone hydrogen bonds that connect symmetrically related layers of the fibril become weaker towards the edge of the fibril, ultimately becoming too weak to remain ordered. To test our hypothesis, we examined 57 available cryo-EM amyloid fibril structures for trends in interstrand distance and β-sheet hydrogen bonding as a function of radial distance from the helical axis. We find that all fibril structures display an increase in interstrand distance as a function of radius and that most fibril structures have a discernible increase in β-sheet hydrogen bond distances as a function of radius. In addition, we identify a high resolution cryo-EM structure that does not follow our predicted hydrogen bonding trends and perform real space refinement with hydrogen bond distance and angle restraints to restore predicted hydrogen bond trends. This highlights the potential to use our analysis to ensure realistic hydrogen bonding in amyloid fibrils when atomic resolution cryo-EM maps are not available. Significance Statement The number of amyloid fibril structures determined has exploded in recent years due to advances in structural biology techniques. However, we are still at the beginning stages of understanding amyloid fibril assembly. One important property that is critical to fibril formation and mechanical properties is the fibril width. Despite the diversity of fibril folds discovered, all amyloid fibrils are constrained to a width of 10-20 nm. Here, we use simple geometry and structural analysis to identify that the limited width of amyloid fibrils arises from the helical twist of β-sheets in amyloid fibrils. Our findings provide important considerations for the accurate modeling of hydrogen bonds in amyloid fibrils as well as for the possible prediction and design of amyloid-based nanomaterials.