A model on an absolute scale for the small-angle X-ray scattering from bovine casein micelles

Casein micelles extracted from milk are 100-400 nm-sized particles, made up of proteins and calcium phosphates, with the latter as colloidal calcium phosphate particles (CCPs) in a size range of 2-4 nm embedded in a protein network. The hierarchical structures give rise to a variation of scattering intensity over many orders of magnitude, which can be measured by small-angle X-ray scattering and static light scattering. Expressions for the scattering intensity of a general simple model for composite particles with polydispersities of overall size and subparticles are derived, and some approximations are checked by generating scattering data for systems generated by Monte Carlo simulations. Based on the simpler models, a new model has been developed for casein micelles, where the scattering is expressed on an absolute scale and where the concentrations of, respectively, protein and CCPs are used as constraints, providing a consistent model. The CCPs are modelled as oblate ellipsoids and the protein as star structures. Correlations between the substructures of CCPs and protein structures are taken into account in terms of partial structure factors. The overall structure as well as some heterogeneities at intermediate length scale are modelled as polydisperse spheres. The model fits the data very well on all length scales and demonstrates that both the scattering from CCPs and protein is important. Thus, the model provides a detailed description of the casein structure, which is consistent with the information available in the literature.