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The growth of amyloid fibrils requires a disordered or partially unfolded protein to bind to the fibril and adapt the same conformation and alignment established by the fibril template. Since the H-bonds stabilizing the fibril are interchangeable, it is inevitable that H-bonds form between incorrect pairs of amino acids which are either incorporated into the fibril as defects or must be broken before the correct alignment can be found. This process is modeled by mapping the formation and breakage of H-bonds to a one-dimensional random walk. The resulting microscopic model of fibril growth is governed by two timescales: the diffusion time of the monomeric proteins, and the time required for incorrectly bound proteins to unbind from the fibril. The theory predicts that the Arrhenius behavior observed in experiments is due to off-pathway states rather than an on-pathway transition state. The predicted growth rates are in qualitative agreement with experiments on insulin fibril growth rates as a function of protein concentration, denaturant concentration, and temperature. These results suggest a templating mechanism where steric clashes due to a single mis-aligned molecule prevent the binding of additional molecules.


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