arXiv2004
Amyloid fibers are aggregates of proteins. They are built out of a peptide called $β$--amyloid (A$β$) containing between 41 and 43 residues, produced by the action of an enzyme which cleaves a much larger protein known as the Amyloid Precursor Protein (APP). X-ray diffraction experiments have shown that these fibrils are rich in $β$--structures, whereas the shape of the peptide displays an $α$--helix structure within the APP in its biologically active conformation. A realistic model of fibril formation is developed based on the seventeen residues A$β$12--28 amyloid peptide, which has been shown to form fibrils structurally similar to those of the whole A$β$ peptide. With the help of physical arguments and in keeping with experimental findings, the A$β$12--28 monomer is assumed to be in four possible states (i.e., native helix conformation, $β$--hairpin, globular low--energy state and unfolded state). Making use of these monomeric states, oligomers (dimers, tertramers and octamers) were constructed. With the help of short, detailed Molecular Dynamics (MD) calculations of the three monomers and of a variety of oligomers, energies for these structures were obtained. Making use of these results within the framework of a simple yet realistic model to describe the entropic terms associated with the variety of amyloid conformations, a phase diagram can be calculated of the whole many--body system, leading to a thermodynamical picture in overall agreement with the experimental findings. In particular, the existence of micellar metastable states seem to be a key issue to determine the thermodynamical properties of the system.