Structure of Self-Assembled Globular Proteins - Food Colloids: Self-Assembly and Material Science - page 47

value of R a is close to the correlation length of the concentration fluctuations
and M a is proportional to the osmotic compressibility. 25 The quantity R a
characterizes the length-scale above which the system is homogeneous. A
simplified picture of the system is to consider it as an ensemble of close-packed
'blobs' with z-average radius of gyration R a and weight-average molar mass
M a . This picture is helpful, but it should not be taken too literally. The centre of
a blob can be chosen randomly in the system - so there is no distinction
between bonds inside a blob and those between blobs. In addition, this
representation fails completely to describe the ordered systems.
The quantities R a and M a are related in the same way as R gz and M w , 50 which
implies that the blobs have the same structure as the aggregates. The concen-
tration dependence of R a for b-LG at 100 mM NaCl is compared with that of
R gz for diluted aggregates in Figure 10. As mentioned above, for C o C g ,
aggregates are formed that increase in size with increasing concentration, which
explains why R a increases with increasing C. The aggregates are progressively
more strongly interpenetrated with increasing C, so that R a is smaller than R gz .
At some concentration close to C g , the value of R a reaches a maximum and
subsequently decreases with increasing C, showing that denser gels are more
homogeneous. Similar observations were made for OA 29 and BSA, 43 except
that for very high concentrations R a was found to increase again, especially for
OA. Since for the latter system no densification was observed in the high
q-range covered by SAXS, it was speculated that a very small fraction of the
proteins formed large dense domains. Very recent results obtained for b-LG at
lower pH also show a strong increase in R a at high concentrations. 33

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Figure 10 Concentration dependence of apparent radius R a for extensively heated b -LG
solutions (O). 28 For comparison, the values of the radius of gyration (R gz )of
the aggregates ( & ) are shown for C o C g . The solid line has slope of 1, as
predicted for monodisperse blobs with d f ¼ 2 (see text). The dashed vertical
line indicates the critical protein concentration C g