Amyloid fibrils are well-ordered supramolecular polymers consisting of thousands of protein molecules connected via intermolecular hydrogen bonds. For intrinsically disordered proteins (IDP), amyloid form is thermodynamically more stable than the native form, and its formation in human body can lead to pathology. Namely, misfolding of small intrinsically disordered neuronal protein α-synuiclein is a hallmark of Parkinson's disease. The fibrillization is an autocatalytic process that can be induced by small amounts of pathological fibrils in a prion-like manner. We studied detailed kinetic mechanism of the α-synuiclein fibrillization and have shown that atypical sigmoidal reaction kinetics and exponential distribution of the length of formed fibrils are the results of a two-step autocatalytic cycle that includes fibril elongation via binding monomers to the ends and formation of new fibril ends due to fibril breaking . This allowed us to identify the fibril ends as the bottleneck of the process and thus the most prospective target for fibrillization inhibitors. We designed several proteins and peptides that selectively bind to the fibril ends and block their growth by creating a steric hindrance [2,3]. This approach permits inhibition of fibril formation at inhibitor concentrations orders of magnitude lower than the concentration of monomeric α-synuclein. In my talk, I will focus mostly on the application of mathematical models for determination of the reaction mechanism based on kinetic data and on design of experiments for refining the models and proving the mechanism.