Modeling the Effect of Monomer Conformational Change on the Early Stage of Protein Self-Assembly into Fibrils

Filamentous self-assembly of proteins is an important process implicated in a plethora of human diseases and of interest for nanotechnology. Using rate equations, we analyze the early stage of the process in solutions that initially contain fibrillation-passive protein monomers and in which the nascent fibrils are practically insoluble. The analysis is based on a model accounting for the conformational and/or other changes the passive monomers experience to transform themselves into fibrillation-active monomers and thus become fibril nuclei. The model allows exact, comprehensive, and simple mathematical description of the early stage of fibrillation, which reveals the usually neglected role of the nucleation nonstationarity in this stage of fibrillation. We obtain exact and user-friendly expressions for experimentally accessible quantities such as the size distribution of fibrils, their number and mass concentrations, the rate and nonstationary period of fibril nucleation, and the delay time of fibril formation. Analyzing available experimental data, we find that the theory successfully describes the fibrillation time course of pathological and nonpathological ataxin-3, a protein involved in the neurodegenerative disorder spinocerebellar ataxia type-3. The analysis provides mechanistic insight into the reason for the higher fibril nucleation and elongation rates of the pathological ataxin-3.