A toy model for predicting the rate of amyloid formation from unfolded protein.

We develop a toy model for predicting the rate of amyloid formation from an unfolded polypeptide. The model assumes irreversible amyloid growth, employs a collision encounter scheme and uses a Gaussian chain approximation to describe the polypeptide sequence. A principal feature of the model is its dependence on a number of key sequence residues whose correct placement, geometric arrangement and orientation in relation to their interacting partners define the success, or otherwise, of the amyloid formation reaction. Although not realistic at the molecular level, the model captures some essential features of the system and is therefore useful from a heuristic standpoint. For the case of amyloid formation from an unstructured state, the model suggests that the major determinants of the rate of fibril formation are the length of the sequence separating the critical amino acids promoting amyloid formation and the positional placement of the critical residues within the sequence. Our findings suggest also that the sequence distance between the key interacting amino acid residues may play a role in defining the maximum width of a fibril and that the addition of non-interacting segments of long structure-less polypeptide chain to an amyloidogenic peptide may act to inhibit fibril formation. We discuss these findings with reference to the placement of critical sequence residues within the polypeptide chain, the design of polypeptides with lower amyloid formation propensities and the development of aggregation inhibitors as potential therapeutics for protein depositional disorders.