Similarities in Self-Assembly of Proteins and Surfactants: An Attempt to Bridge the Gap - Food Colloids: Self-Assembly and Material Science - page 65

zero. The initial reversibility of the fibril forming process becomes irreversible
after some time, i.e., the fibrils become stable towards dilution. 11 It is not
obvious from our own measurements that there exists a critical concentration
below which no fibrils are formed. If such a concentration would at all exist, it
has to be substantially lower than 0.5 wt%, indicating a rather high bond
energy between the proteins. From electric birefringence measurements, it has
been concluded 16 that the proteins are ordered 'head-to-tail' within the fibril in
a helical configuration.
The fact that a minimal temperature is needed in order to induce fibril
formation is directly related to the fact that, at a certain elevated temperature,
the protein will partially unfold. Since we have also observed the formation of
fibrils at 41C, after having applied this (partial) denaturation step, it seems that
the elevated temperature is not essential during assembly. However, at the
lower temperature, the assembly was found to be much slower, indicating that
temperature affects the kinetics of the assembly process. The relation between
the fibrillar type of assembly and the partially unfolded state also has been
found for other proteins (ovalbumin, hen egg-white lysozyme, bovine serum
albumin). 17 In the latter case it was found that, upon partial unfolding, some
hydrophobic regions become exposed to the solvent. A requirement for
obtaining long fibrils with few branches is maintenance of a low pH and a
low ionic strength. A moderate ionic strength yields more flexible fibrils, while
an even higher ionic strength and higher pH yields more condense spherical
aggregates with a fractal dimension of around 2. 12-14
The length distribution for b-lactoglobulin fibrils is not a sharply peaked
Poisson distribution, in which case one would expect a 'full-width half-height'
of around 100 nm. In the case of reversible aggregation, the equilibrium length
distribution was predicted 1 using Equation (10), yielding a smooth and single-
peaked distribution given by

C L ¼ L exp ( aL) (21)

with the constant a being proportional to the chemical potential of the protein
in the fibrils, and depending on concentration and temperature. The peak of the
distribution is located at 1/a. So, despite the more complex nature of proteins
compared to simple surfactants, we do find a distribution with a shape that is at
least similar to the theoretical prediction from Equation (21).
It is necessary to take into account two kinetic mechanisms that play a role in
reaching the equilibrium distribution of fibrils. Firstly, there is a nucleation
event, followed by subsequent growth of the fibril and possible redistribution of
proteins between the fibrils. It is a reasonable assumption, when no shear is
applied, that every fibril is extended at the same rate independent of its length.
With this in mind, the resulting length distribution could never develop if there
is an instantaneous nucleation of all the nuclei and if protein redistribution
between the fibrils would be absent. Secondly, we also have to consider the
influence of the (apparent) long-term irreversibility of the assembly. The fact
that the attachment of proteins to the fibril becomes irreversible after some time