Scaling in the aggregation behaviour of zinc-free insulin studied by small-angle neutron scattering

The aggregation behaviour of zinc-free insulin has been studied by small-angle neutron scattering as a function of protein concentration, pH, and ionic strength of the solution. The distance distribution functions for the 12 samples have been obtained by indirect Fourier transformation. The weight-averaged molecular mass and the z-averaged radius of gyration were determined. Both quantities vary systematically with the experimental conditions. They increase with decreasing pH and with increasing ionic strength. The radius of gyration scales as a power law of the weight-average mass with the exponent 0.44. A similar scaling is found for a set of oligomers structures based on the crystal structure of zinc-free insulin. The mass distribution between the oligomers was determined by a model based on these oligomers. The results from this model and the Fourier transformations have been compared to an equilibrium model recently introduced by Kadima et al. The model takes into account the variation of the effective charge of the monomer with pH and ionic strength. The neutron scattering results agree well with the predictions of the model.