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relatively simple to demonstrate 3 that the rate constant for aggregation will be
an inverse exponential function of the square of the net charge.
In the case of the calcium-induced precipitation of a s1 -casein, the net protein
charge - the algebraic sum of charges from lysine, arginine and histidine
(all positive) and aspartic, glutamic and phosphoserine (all negative) - is
reduced by the binding of ionic calcium. From the published calcium-binding
isotherm, 1 we know the number of calcium ions bound per protein molecule in
any calcium ion solution. The rate of precipitation can be measured by
monitoring the increase in solution turbidity with time, and a straight line plot
of the logarithm of this rate versus Q 2 testifies to the validity of this approach. 3,4
Changes in the net charge carried by the protein can be produced by chemical
modification of the amino acid residues. 5,6 Positively charged lysine residues
can be converted to neutral residues at the pH of the kinetic experiments by the
reaction with an acyl chloride (e.g., dansyl chloride), or they are made negative
by the reaction with fluorescent labelling reagent, fluorescamine. Negative
charge can also be introduced by iodinating tyrosine residues, the di-iodo
tyrosine hydroxyl group having a value of pK a ΒΌ 6.36 for the free amino acid.
We select this particular set of reagents because in each case the extent of
modification can be measured by spectrophotometry, an important consider-
ation where accuracy and reliability in determining this parameter is essential,
due to the extreme sensitivity of the precipitation reaction to the net protein
charge. Each of these modifications effectively increases the negative charge of
the protein, thereby reducing its propensity for calcium-induced precipitation
and slowing down the rate of aggregation. However, once the protein charge is
corrected for the measured extent of modification (from the number of lysine
residues changed from +1 to 0 or from +1 to 1, or the number of
di-iodotyrosines introduced), the logarithm of the rate of precipitation has
been shown to remain linear in Q 2 , the same relationship as followed by the un-
modified protein (see Figure 1). That the precipitation reaction follows this
simple DLVO-based model attests to the flexibility and mobility of the casein
polymer; these characteristics allow it to respond in this non-specific fashion,
where just the overall average charge dominates its stability behaviour.
10.3 Introduction of Calcium Sequestrants
The preceding studies of the calcium-induced precipitation of a s1 -casein were
initiated in the late 1970s as part of a programme investigating casein micelle
formation and structure. At that time, questions focused on the role of calcium
phosphate in the casein micelle. One possible mechanism recognized the
sequestrant action of phosphate and viewed the calcium phosphate as a 'sink'
for ionic calcium, controlling its level and through that the amount of casein-
bound calcium and the strength of the casein-casein interactions. A test of this
hypothesis has been provided by introducing phosphate anions into a solution
of Ca 21 + a s1 -casein and observing the effect on the rate of precipitation.
A parallel series of experiments 7 monitored the influence of addition of citrate,
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