How to determine the size of folding nuclei of protofibrils from the concentration dependence of the rate and lag-time of aggregation. II. Experimental application for insulin and LysPro insulin: aggregation morphology, kinetics, and sizes of nuclei.

Insulin is a commonly used protein for studies of amyloidogenesis. There are a few insulin analogues with different pharmacokinetic characteristics, in particular the onset and duration of action. One of them is LysPro insulin. The behavior of LysPro insulin in the process of amyloid formation has not been studied in detail yet. To quantitatively investigate the differences between insulin and LysPro insulin in the aggregation reaction, we used thioflavin T fluorescence assay, electron microscopy, X-ray diffraction methods, and theoretical modeling. Kinetic experimental data for both insulin samples demonstrated the increase of the lag-time for LysPro insulin at low concentrations of monomers, particularly at 2 and 4 mg/mL, which corresponds to the pharmaceutical concentration. However, the morphology of insulin and LysPro insulin fibrils and their X-ray diffraction patterns is identical. Mature fibrils reach 10-12 μm in length and about 3-4 nm in diameter. The obtained analytical solution allow us to determine the sizes of the primary and secondary nuclei from the experimentally obtained concentration dependences of the time of growth and the ratio of the lag-time duration to the time of growth of amyloid protofibrils. In the case of insulin and LysPro insulin, we have exponential growth of amyloid protofibrils following the "bifurcation + lateral growth" scenario. In accord with the developed theory and the experimental data, we obtained that the size of the primary nucleus is equal to one monomer and the size of the secondary nucleus is zero in both insulin and LysPro insulin.