We use large-scale MP2 calculations to analyze the interactions appearing in amyloid fibers, which are difficult to determine experimentally. To this end, dimers and trimers of the hexapeptide NNQQNY from the yeast prion-like protein Sup35 were considered as model systems. We studied the energy interactions present in the three levels of organization in which the formation of amyloid fibrils is structured. The structural changes in the hydrogen bonds were studied too. It was found that the most energetic process is the formation of the β-sheet, which is equally due to both hydrogen bonds and van der Waals interactions. The aromatic rings help stabilize these aggregates through stacking of the aromatic rings of tyrosine, the stability produced by the aromatics residues increasing with their aromaticity. The formation of the basic unit of the assembled proto-fiber, the steric zipper, is less energetic and is associated to both dispersion forces and hydrogen bonds. The interactions between pair of β-sheets across the peptide-to-peptide contact through the tyrosine rings are cooperative and due to dispersion effects. Moreover, the strength of this interaction can rationalize the variation of mobility of the aromatic ring in the tyrosine units found in solid NMR experiments.