Before revision:  We derive an analytic expression for the lag-time distribution, which agrees well with existing experimental results for the aggregation of bovine insulin into amyloid fibrils. Our solution provides a way to interpret small-volume experiments on fibril formation, providing insight into the mechanisms at play in early-stage aggregation  .
After revision:  We derive an analytic expression for the lag-time distribution, which agrees well with existing experimental results for the aggregation of bovine insulin . Our expression decomposes the lag time variability into contributions from primary nucleation and autocatalytic growth and reveals how each of these scales with the key kinetic parameters. Our analysis shows that significant lag-time variability can arise from both primary nucleation and from autocatalytic growth and should provide a way to interpret small-volume experiments on fibril formation, providing insight into the mechanisms at play in early-stage aggregation .