Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 148

a constant pressure, the helix-coil transition can be initiated by either cooling or
heating. In the latter case, a protein is said to be thermally denatured. Heating of a
protein causes breaking of hydrogen bonds that hold polypeptide chains in the heli-
cal conformation. As a result, the helices unfold, forming disordered coils. Since
the polypeptide chains do not break but only change their conformation, the process
is a phase transition somewhat similar to polymer melting. It is accompanied by
significant absorption of heat that qualifies it as a first-order transition.
Unfolding of proteins is a very complex phenomenon that involves interplay of
kinetic and thermodynamic factors. A largely simplified mechanism of the process
was proposed by Lumry and Eyring [ 182 ].

Kk

NUD ⇔→ , (3.93)

where N, U, and D stand respectively for the native, unfolded, and denatured states,
K is the equilibrium constant of the reversible step, and k is the rate constant of the
irreversible step. The model is found to be most suitable for denaturation under
the conditions of high irreversibility [ 183 ]. A similar mechanism (Eq. 3.93) is used
to describe the kinetics of various processes that include so-called pre-equilibria.
Two most known examples are surface-catalyzed reactions that involve a revers-
ible adsorption step (the Eley-Rideal mechanism) and enzyme-catalyzed reaction
that involves a reversible formation of a bound state between the enzyme and its
substrate (the Michaelis-Menten mechanism) [ 18 ]. The application of the Lumry-
Eyring model to the kinetics of protein denaturation has been discussed at length in
the literature [ 183 , 184 ].
The rate equation for the Lumry-Eyring model is derived as follows. The rate of
the formation of the denatured state is:

d
d

x

D

(3.94)

= kx ,

U

t

where x D and x U are respectively the mole fractions of the denatured and unfold-
ed states. The unknown concentration of the unfolded state can be eliminated
considering that the sum of all three fractions is unity, and the fraction of the native
state x N is related to that of the unfolded state via the equilibrium constant:

x
x

(3.95)

U
N

K = .

Then

x
K

U

(3.96)

x =− − 1 x .

U D