Disease-related amyloidogenic propensity has been unexpectedly found in proteins driven to adopt a monomeric uncomplexed state at high concentrations under near-physiological conditions. This situation occasionally arises in new health treatments, such as kidney dialysis. Assuming that under such conditions a partial retention of native structure takes place, this work identifies a structural characteristic indicating amyloidogenic propensity: a high density of backbone hydrogen bonds exposed to water attack in monomeric structure. On this basis, we propose a diagnostic tool based on the identification of hydrogen bonds with a paucity of intramolecular dehydration or "wrapping." We use this predictor to identify potentially pathogenic mutations that foster amyloidogenic propensity in human prions. Such mutations either enhance the intramolecular dehydration of beta-sheet hydrogen bonds, thus stabilizing the nucleus for rearrangement into the scrapie fold, or contribute to the destabilization of the cellular form by introducing additional underwrapped hydrogen bonds. Our predictions are consistent with known disease-related mutations and lead to a cogent explanation of the pathogenic nature of specific mutations affecting the cellular prion protein structural wrapping. On the other hand, a different wrapping of a very similar fold, mouse doppel, induces a dramatically different level of amyloidogenic propensity, suggesting that the packing within the fold, and not the fold itself, contains the signal for aggregation.