*2.6. Kinetics of Protein Denaturation*

Activation energy (*E*a) for α-Lac and β-Lg denaturation was calculated using the results obtained from HPP-treated samples. The denaturation of α-Lac and β-Lg with time after HPP treatment can be described by the general rate equation

$$-\frac{dc}{dt} = kc^n,\tag{3}$$

where <sup>−</sup>*dc dt* is the rate of denaturation, *k* is the rate constant, *c* is the concentration of α-Lac or β-Lg, and *n* is the order of reaction.

It has been reported that HPP denaturation of α-Lac follows first-order kinetics in whole milk [38]. For first-order kinetics (*n* = 1), the integration of Equation (3) gives

$$
\ln(c\_t/c\_o) = -kt.\tag{4}
$$

The semi-logarithmic plot of Equation (4) gives a straight line with high coefficients of correlation (*r*2), and the value of the ordinate intercept *b* (time, *t* = 0) appears close to zero. The slopes of the lines obtained correspond to the rate constant (*k*).

Furthermore, the reaction kinetics for β-Lg in HPP was also reported as a second-order reaction by Anema et al. [39] in skim milk and Hinrichs et al. [40] in whey proteins. For non-first order kinetics (*n* -1), the integration of Equation (3) gives

$$(c\_t/c\_o)^{1-n} = 1 + (n-1)kt.\tag{5}$$

The graphical representation of Equation (5) yields straight lines, and the ordinate intercept b (time, *t* = 0) should be 1 if the treatment follows the estimated reaction order. The rate constant (*k*) is obtained from the slope of the lines. The Arrhenius equation relates the treatment temperature and the rate constant of a denaturation process as given in Equation (6):

$$k = A e^{-E\_a/RT} \,\text{.}\tag{6}$$

where *A* is the pre-exponential factor, *Ea* is the activation energy, *R* is the universal gas constant, and *T* is the absolute temperature.

By taking the logarithms of both sides, Equation (6) gives a linearized form as

$$\text{Inrk} = (-\text{Ea}/R) \times (1/T) + \ln A. \tag{7}$$

The graphical representation of Equation (7) (lnk vs. 1/*T*) determines the effect of temperature on the rate of constant (*k*). The gradient of Equation (7) is equal to –*E*a/R, and thus the activation energy (*E*a) is calculated.
