Unfolding Kinetics. Figure 4.5 gives an example (the enzyme
alkaline phosphatase) of kinetic parameters for protein denaturation. It is
seen that the activation enthalpyDH{would be very large, in accordance
with the cooperative transition from native to unfolded state. Although the
bonds involved are weak, they are numerous, and most of them have to
break simultaneously. The value ofDH{was obtained using Eq. (4.11), by
taking the temperature dependence of the denaturation reaction (enzyme
inactivation, in this case); it is larger thanDN?UH, but of the same order of
magnitude. The largeDH{implies a very strong dependence of the reaction
rate on temperature, as illustrated in Figure 7.9. The large positiveDS{
compensates for the largeDH{, causing a fairly smallDG{and a fairly fast
reaction rate.
Many proteins follow this trend. Some results are given in Figure 7.9.
It seems logical to assume that the molarDH{andDS{values are roughly
proportional to molar mass (M). The number of bonds to be broken, and
the corresponding bond enthalpies and contact entropies, will be
about proportional to molecular size. Also the increase in
conformational entropy of the peptide chain upon unfolding will be about
proportional to the number of amino acid residuesn, and thereby toM.
(Remember thatSconf¼RlnO(per mole), where the number of degrees of
freedomOis the number per residue, presumably about 7, to the powern.
This would yield DS¼Rnln 7.) A rough correlation is indeed observed
between the activation enthalpy and entropy and molar mass, but it is far
from perfect. This may be due to denaturation occurring separately in
separate domains in the same molecule (especially for largeM), and to
variation in the number of 22 S 22 S 22 bridges or other conformational
details.
The reasoning just given implies another oversimplification. Figure 7.5
shows thatDN?UHandDN?USare not constant but depend markedly on
temperature. It may be argued that this relates to differences inHandS
between the native and the unfolded states and not to the activation
enthalpy and entropy, but it is very unlikely that the latter two behave quite
differently from the former. The ‘‘observed’’ DH{ is thus an apparent
activation enthalpy.
Does this imply that the idea of an activation free energy etc. would
not apply? Figure 7.10a gives an example of the first-order rate constant for
unfolding (a fully reversible reaction in the present case). It is seen to be
about 1 s^1 at Tden,67 8 C. By applying Eq. (4.11) we arrive at
DG{¼84 kJ?mol^1 , definitely higher than the free energy difference
between the two states, which is, by definition, zero at this temperature.
Consequently,DH{will be higher thanDN?UH. (It seems unlikely thatDS{
is greatly different fromDN?US.)
singke
(singke)
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