Casein Interactions: Does the Chemistry Really Matter? - Food Colloids: Self-Assembly and Material Science - page 165

distribution function, perhaps making it appear close to the fewer broad
features characterizing the radial distribution function of the amorphous bulk
solid. Cross et al. 18 have recently reported a relatively featureless radial distri-
bution function for a phosphopeptide-stabilized calcium phosphate dispersion.
This contrasts with the results of Holt et al. 19 who found that the spectrum of
brushite obtained by X-ray fine-structure absorption was close to their spec-
trum from milk calcium phosphate. This proposal of a brushite-like structure
for micellar calcium phosphate was criticized by McGann et al. 20 on the basis
of its neglect of citrate involvement in the casein micelle. They concluded 20 that
micellar calcium phosphate was amorphous based on a comparison with bone
hydroxyapatite, although it should be noted that their milk sample eventually
subjected to X-ray diffraction had been freeze-dried and ground prior to
examination. Accommodating the serine phosphates of the cluster motif may
also produce strains in the lattice structure which could cause it to deviate
slightly from the crystalline. Whether this would be enough to indicate a more
amorphous nature may be in the eyes of the interpreter.
It is likely that the rigid entity that is the nanocluster will not be spherical,
but rather it will have the shape of a multi-faceted solid. The tetrahedron is the
solid geometrical object with the least number of faces, namely 4. As shown in
Figure 6(c), the bi-pyramid, composed of two identical touching tetrahedra, has
6 faces. If each of these were to be occupied by a phosphoserine cluster motif, as
illustrated in Figure 6(b), the bi-pyramid would contain 72 calcium ions and 72
phosphates made up of 48 inorganic and 24 ester phosphates from the 6 cluster
motifs. The dicalcium phosphate unit cell (brushite if hydrated, monetite if
anhydrous) has Z ¼ 4, meaning the volume of the bi-pyramid would be that of
18 unit cells or equivalent to 9 per tetrahedron. A tetrahedron drawn internal to
a cube has one-third the volume of that cube, meaning that our cube would
have a total volume of 27 unit cells, or a side length of 3 unit cells. This gives the
edge length of our tetrahedron as 3 O 2 times the unit cell length, or approxi-
mately 2.5 nm, which is of the order of the size estimated by McGann et al. 20
The cessation of growth of the calcium phosphate phase depends on the
serendipitous arrival of a closure motif. Thus some nanoclusters could be
closed off as tetrahedral, as shown in Figure 6(d). While this would distort the
stoichiometry, it would be compensated if larger nanoclusters formed from
chains of tetrahedra were also created, as illustrated in Figure 6(e) for 3
tetrahedra in the chain. Such entities would scatter X-rays or neutrons as short
cylinders or needles, their distribution of sizes being such as to give the average
observed stoichiometry.
10.5 Concluding Remark
What has emerged from our observation of an active role for phosphate in the
precipitation of a S1 -casein + Ca 21 + phosphate mixtures is a speculative, but
nonetheless plausible, estimate of the size of casein micelle nanoclusters and the
number of casein phosphoserine cluster motifs involved with each nanocluster.