The protein alpha-synuclein (aS) self-assembles into small oligomeric species and subsequently into amyloid fibrils that accumulate and proliferate during the development of Parkinson's disease. However, the quantitative characterization of the aggregation and spreading of aS remains challenging to achieve. Previously, we identified a conformational conversion step leading from the initially formed oligomers to more compact oligomers preceding fibril formation. Here, by a combination of single-molecule fluorescence measurements and kinetic analysis, we find that the reaction in solution involves two unimolecular structural conversion steps, from the disordered to more compact oligomers and then to fibrils, which can elongate by further monomer addition. We have obtained individual rate constants for these key microscopic steps by applying a global kinetic analysis to both the decrease in the concentration of monomeric protein molecules and the increase in oligomer concentrations over a 0.5-140-mu M range of aS. The resulting explicit kinetic model of aS aggregation has been used to quantitatively explore seeding the reaction by either the compact oligomers or fibrils. Our predictions reveal that, although fibrils are more effective at seeding than oligomers, very high numbers of seeds of either type, of the order of 104, are required to achieve efficient seeding and bypass the slow generation of aggregates through primary nucleation. Complementary cellular experiments demonstrated that two orders of magnitude lower numbers of oligomers were sufficient to generate high levels of reactive oxygen species, suggesting that effective templated seeding is likely to require both the presence of template aggregates and conditions of cellular stress.