We investigate the prevalence, and so the role in the amyloidogenesis, of biased conformations in large ensembles of monomeric forms for A eta 42 and A beta 40 that can trigger the formation and growth of fibrils described by a dock-lock mechanism. We model such biased conformations as the structural monomeric units that constitute the Protein Data Bank fibrils 2beg, 2mxu, and 2lmn. These units were employed as templates to search for similar structures in statistical conformational ensembles of A beta peptides generated by molecular dynamics with an accurate force field in explicit solvation, whose high quality is revealed by comparison with residual dipolar coupling (RDC) experiments. The conformational ensembles generated by these intrinsically disordered peptides do not contain conformations highly similar to the amyloidogenic templates. This is a consequence of the low thermodynamic stability exhibited by the template-like conformations. A further constant-pH Monte Carlo study has revealed that this stability can be increased by suitable pH conditions, which helps to trigger the fibril elongation. Moreover, our analyses on the free energy landscapes, hydrogen bond prevalences, and principal component analysis distributions emphasize the relevance of many-body long-range cooperative interactions, likely acting over the infrequent preexisting structurally biased conformations, to explain the fibrils' emergence.