Physical Chemistry of Foods

where I stands for ‘‘inactive’’ or ‘‘irreversibly changed’’ form. If, moreover,
all reactions were first order, the rate of change observed would be given by

v¼

d½IŠ

dt

¼ki½UŠ½UŠ¼fð½NŠt¼ 0 ;ku;kf;tÞð 7 : 5 Þ

If the rate constant for refoldingkfis zero, the second step is not needed,
and the unfolding step is rate determining; in this case Eq. (7.5) takes the
formv&ku½NŠ, as described above.
More realistically, all U will refold on cooling (see, e.g., Figure 7.10a),
and what is effectively observed is the loss of N and U. The rate equation
thus is

v¼


dð½NŠþ½UŠÞ

dt

¼kobs 6 ð½NŠþ½UŠÞð 7 : 6 Þ

Combination with (7.5) and invoking the equilibrium constantK¼½UŠ=½NŠ,
as in Eq. (7.3), yields for the observed rate constant

kobs¼

ki

1 þ 1 =K

ð 7 : 7 Þ

FIGURE7.10 Refolding of denatured proteins. (a) Rate constants (k) for unfolding
(U) and refolding (F) of lysozyme at various temperatures. (b) Rate constants for
inactivation (I) at 76 8 C and for reactivation (R) at 35 8 C of peroxidase at various pH.