Self-assembly of Fibonacci number spirals in amyloid-like nanofibril films

Fibonacci number spiral patterns can be found in nature, particularly in plants, such as the sunflowers and phyllotaxis. Here, we demonstrated this pattern can be reproduced spontaneously within self-assembling peptide nanofibril films. By high-temperature water vapor annealing of an amorphous film containing both peptide and cationic diamines, well-defined amyloid-like nanofibrils can be assembled spontaneously, during which the nanofibrils will hierarchically stack with each other following the Fibonacci number patterns. The formation of the patterns is a self-templated process, which involves stepwise chiral amplification from the molecular scale to the nano- and micro-scales. Moreover, by controlling the diameter, length, and handedness of the nanofibrils, various complex hierarchical structures could be formed, including vertically aligned nanoarray, mesoscale helical bundles, Fibonacci number spirals, and then helical toroids. The results provide new insights into the chiral self-assembly of simple biological molecules, which can advance their applications in optics and templated synthesis.