Amyloid fibrils are highly ordered protein aggregates associated with more than 40 human diseases. The exact conditions under which the fibrils are grown determine many types of reported fibril polymorphism, including different twist patterns. Twist-based polymorphs display unique mechanical properties in vitro, and the relevance of twist polymorphism in amyloid diseases has been suggested. We present transmission electron microscopy images of A beta 42-derived (amyloid beta) fibrils, which are associated with Alzheimer's disease, demonstrating the presence of twist variability even within a single long fibril. To better understand the molecular underpinnings of twist polymorphism, we present a structural and thermodynamics analysis of molecular dynamics simulations of the twisting of beta-sheet protofilaments of a well-characterized cross-beta model: the GNNQQNY peptide from the yeast prion Sup35. The results show that a protofilament model of GNNQQNY is able to adopt twist angles from -11 degrees on the left-hand side to +8 degrees on the right-hand side in response to various external conditions, keeping an unchanged peptide structure. The potential of mean force (PMF) of this cross-beta structure upon twisting revealed that only similar to 2k(B)T per peptide are needed to stabilize a straight conformation with respect to the left-handed free-energy minimum. The PMF also shows that the canonical structural core of beta-sheets, i.e., the hydrogen-bonded backbone beta-strands, favors the straight conformation. However, the concerted effects of the side chains contribute to twisting, which provides a rationale to correlate polypeptide sequence, environmental growth conditions and number of protofilaments in a fibril with twist polymorphisms.