The Formation of Fibrils by Intertwining of Filaments: Model and Application to Amyloid Aβ Protein

We outline a model that describes the interaction of rods that form intertwined bundles. In this simple model, we compare the elastic energy penalty that arises due to the deformation of the rods to the gain in binding energy upon intertwining. We find that, for proper values of the bending Young’s modulus and the binding energy, a helical pitch may be found for which the energy of intertwining is most favorable. We apply our description to the problem of Alzheimer’s Aβ protein fibrillization. If we forbid configurations that exhibit steric overlap between the protofilaments that make up a protein fibril, our model predicts that fibrils consisting of three protofilaments shall form. This agrees well with experimental results. Our model can also provide an estimate for the helical pitch of suitable fibrils.