Handbook of Food Science and Technology 3

Figure 1.7.
 Change in micelle structure during acidification
Figure 1.8
.
 Change in micelle structure during rennet
coagulation (CMP = caseinomacropeptide) 
Hydrolysis of the Phe
105
–Met
106
bond in 
κ
-casein is accompanied by the 
release of the hydrophilic and negatively-charged C-terminal segment 
(caseinomacropeptide CMP) in whey, whereas the hydrophobic and basic
N-terminal remains associated with the micelle. The release of CMP 
destabilizes the colloidal complex by reducing the surface potential of casein 
micelles. The rate of hydrolysis is considered to be Michaelis–Menten type 
I –
Enzymatic hydrolysis 
(rennet action)
CMP
+ 
Casein micelle
paracasein
Rennet gel
(n, particle number)
II –
Aggregation
III -
Reorganisation
κ
+
κ
=
κ
−
θ
K
.
E
.
k
dt
d
m
t
2
a
n
.
k
dt
dn
=
−
G)
-
(G
.
k
dt
dG
g
∞
=
Reorganization 

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24 Handbook of Food Science and Technology 3 
kinetics (see Volume 2, Chapter 7) in which the Michaelis constant (K
m
) is 
much greater than the concentration of 
κ
casein (
κ
): 
t
m
k E
d
dt
K
θ
κ
κ
κ
−
=
+
[1.1] 
with
d
dt
κ
−
being the rate of hydrolysis of 
κ
casein, k
θ
(s
-1
) the rate constant of 
the enzymatic reaction and E
t
the total enzyme concentration. 
When the repulsive forces (electrostatic and steric) responsible for colloidal 
stability are neutralized, which is achieved at 80% hydrolyzed 
κ
-casein, close 
or adjacent casein micelles aggregate (second-order kinetics): 
2
a
d
–k
dt
n
n
=
[1.2] 
where 
n
denotes the number of casein micelles at time t, and k
a
the aggregation 
constant.
The aggregation of destabilized casein micelles is driven by electrostatic 
interactions between oppositely-charged residues, hydrophobic bonds and 
presumably calcium bridges. The rate of aggregation quickly increases with 
the increasing rate of hydrolysis of 
κ
-casein between 80 and 100% through the 
rapid increase in the aggregation constant (k
a
): 
(1 – )
–
k T
a
a0
k
k e
ψ
χ
=
[1.3] 
where k
a0
is the aggregation rate constant of uncharged particles (mol
–1
s
-1
), 
ψ
is the repulsion potential energy between casein micelles (J), 
χ
is the rate of 
hydrolysis (%), k is the Boltzman constant (J K
–1
) and T is temperature (K).
During aggregation, the equilibration of soluble calcium with colloidal 
calcium phosphate leads to a major reorganization of casein micelles and
the formation of a gel. The rate of change of the rheological properties of the 
gel is highly dependent on the concentration and the availability of calcium.

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From Milk to Dairy Products 25