Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 150

3.11.2 Isoconversional Treatment of Protein Denaturation
As an example of isoconversional treatment of the helix-coil transition, we consider
the thermal denaturation of collagen [ 185 ]. The latter is a fibrous protein present in
animal connective tissue. In its native form, collagen has a triple helical structure,
whose individual strands are held together by hydrogen bonds. On heating, collagen
undergoes thermal denaturation, during which the hydrogen bonds break, and the
helices unfold, turning into coils. The process is accompanied by significant heat
absorption that permits to monitor its kinetics by DSC.
The kinetics of the thermal denaturation of collagen and other proteins is most
commonly treated as a single irreversible step NₒD [ 186 , 187 ], whose rate de-
pends on temperature in accord with the Arrhenius equation. Such treatment of the
collagen denaturation takes its origin in the pioneering work by Weir [ 188 ], who
studied the rate of collagen shrinkage as a function of temperature. From the stand-
point of the Lumry-Eyring model, the single-step treatment can be justified only
in some special cases [ 183 , 184 ]. For example, when denaturation occurs far from
equilibrium temperature, the process can be treated as a single step describable by
a constant activation energy of the irreversible step. Under other conditions, fitting
the rate data to a single Arrhenius equation would yield effective activation energy
whose value depends on the temperature region of measurements. The closer this
region to equilibrium, the more this value would exceed the activation energy of the
irreversible step and approach the sum of the activation energy of the irreversible
step and the enthalpy of the reversible step.
The review papers [ 187 , 189 ] report about two dozen values of the activation en-
ergy for the thermal denaturation of mammalian tissues. The range of the values is
very wide (30-1300 kJ mol −1 ). The extreme values can perhaps be explained by the
strong compensation effect between the estimates of the preexponential factor and
activation energy (see Sect. 2.2.2). However, a large fraction of such variation can
be rationalized in terms of the temperature dependence of the effective activation
energy (Eq. 3.99 and Fig. 3.75 ). In accord with the Lumry-Eyring model, the inter-
val of E ef variation can be as large as Δ H 0 . Note that some of the literature values
[ 190 ] of Δ H 0 for tissue denaturation exceed 400 kJ mol −1 . That is, for denaturation
of exactly the same protein, the activation energy measured close to equilibrium
can deviate from that measured far from equilibrium by as much as 400 kJ mol −1 .
Figure 3.76 displays DSC curves for the thermal denaturation of rehydrated (sat-
urated with water) collagen. The presence of water stabilizes the denatured coiled
form of collagen, which is an aqueous solution of gelatin. The process manifests
itself in the form of well-defined nearly symmetrical DSC peaks. The endothermic
heat of the process is around 60 J g −1 [ 191 ]. As expected for any kinetic process, the
DSC peaks shift to higher temperature with increasing the heating rate.
The importance of the reversible step N ⃔ U in these regular DSC data is high-
lighted by TM DSC (Fig. 3.77 ). The latter demonstrates that a substantial fraction
(~ 25 %) of the total heat flow signal arises from reversible process. This obviously
lends support to the Lumry-Eyring mechanism (Eq. 3.93) and suggests that the
measured kinetics is determined by both reversible and irreversible steps.