In the presented paper, theoretical as well as electron microscopy and X-ray diffraction experimental approaches were employed for studding the process of A beta amyloid formation. Using quantitative estimates of a number of monomers which form the nuclei of amyloid fibrils the sizes of folding nuclei of amyloid fibrils for A beta 40 and 42 have been determined for the first time. We have shown that the size of the primary nucleus of A beta 42 peptide fibrils corresponds to 3 monomers, the size of the secondary nucleus for this peptide is 2 monomers. Applying the same analysis to A beta 40 we conclude that the size of the primary nucleus is 2 monomers, and the size of the secondary nucleus is one monomer. Summation of our theoretical and experimental results has allowed us to propose a new model of the structural organization of amyloid fibrils. Our model suggests that the generation of fibrils takes place along the following simplified pathway: a monomer -> a ring oligomer -> a mature fibril consisting of ring oligomers. These data shed more light upon our understanding of what sizes of the oligomers could represent main targets for future therapies (tetramers for A beta 42 and trimers for A beta 40), and aid in the development of inhibitors of A beta 40 and 42 oligomer formation. (C) 2016 Published by Elsevier Inc.