Scaling Behavior in Twisted, Helical and Undulating Lysozyme Amyloid Fibrils

We combine atomic force microscopy single-molecule statistical analysis with polymer physics concepts to study the molecular conformations of lysozyme amyloid fibrils. We use different denaturation conditions to yield amyloid fibrils of different types. At 90\r{ }C and pH2, highly laminated twisted and helical ribbons are found, in which as many as 17 protofilaments pack laterally for a total width approaching 180 nm. In the case of 60\r{ }C and pH2, we find thin, wavy fibrils, in which the scaling behavior varies at multiple length scales. We use bond and pair correlation functions, end-to-end distribution and worm-like chain model to identify 3 characteristic length scales. At short length scales there is a first bending transition of the fibrils, corresponding to a bending length Lb. At slightly larger length scales ($>$2Lb), the fibrils become pseudoperiodic and start to undulate. Finally, at length scales larger than the persistence length Lp, the fibrils become flexible and are well described by a 2D self-avoiding random walk. We interpret these results in terms of the periodic fluctuations of the cross-section orientation of the fibrils (twisting) and the impact these have on the area moment of inertia and the corresponding propensity of the fibrils to bend.