The presence of amyloid deposits consisting primarily of Amyloid-beta (Abeta) fibril in the brain is a hallmark of Alzheimers disease (AD). The morphologies of these fibrils are exquisitely sensitive to environmental conditions. Using molecular dynamics simulations combined with data from previously published solid-state NMR experiments, we propose the first atomically detailed structures of two asymmetric polymorphs of the Abeta(9-40) peptide fibril. The first corresponds to synthetic fibrils grown under quiescent conditions and the second to fibrils derived from AD patients brain-extracts. Our core structure in both fibril structures consists of a layered structure in which three cross-beta subunits are arranged in six tightly stacked beta-sheet layers with an antiparallel hydrophobic-hydrophobic and an antiparallel polar-polar interface. The synthetic and brain-derived structures differ primarily in the side-chain orientation of one beta-strand. The presence of a large and continually exposed hydrophobic surface (buried in the symmetric agitated Abeta fibrils) may account for the higher toxicity of the asymmetric fibrils. Our model explains the effects of external perturbations on the fibril lateral architecture as well as the fibrillogenesis inhibiting action of amphiphilic molecules.