Estimation of the lag time in a subsequent monomer addition model for fibril elongation

Fibrillogenesis, the production or development of protein fibers, has been linked to protein folding diseases. The progress curve of fibrils or aggregates typically takes on a sigmoidal shape with a lag phase, a rapid growth phase, and a final plateau regime. The study of the lag phase and the estimation of its critical timescale provide insight into the factors regulating the fibrillation process. However, methods to estimate a quantitative expression for the lag time rely on empirical expressions, which cannot connect the lag time to kinetic parameters associated with the reaction mechanisms of protein fibrillation. Here we introduce an approach for the estimation of the lag time using the governing rate equations of the elementary reactions of a subsequent monomer addition model for protein fibrillation as a case study. We show that the lag time is given by the sum of the critical timescales for each fibril intermediate in the subsequent monomer addition mechanism and therefore reveals causal connectivity between intermediate species. Furthermore, we find that single-molecule assays of protein fibrillation can exhibit a lag phase without a nucleation process, while dyes and extrinsic fluorescent probe bulk assays of protein fibrillation do not exhibit an observable lag phase during template-dependent elongation. Our approach could be valuable for investigating the effects of intrinsic and extrinsic factors to the protein fibrillation reaction mechanism and provides physicochemical insights into parameters regulating the lag phase.