conformational stability, and it is seen to be fairly small, in this case about
25 kJ?mol^1 at its maximum. Equation (7.3) then yields lnK&10, implying
that a fractione^10 & 4? 10 ^5 of the molecules would be in the unfolded
state. ForDG¼10 kJ?mol^1 , it would amount to about 2%.
According to Eq. (7.3), a van’t Hoff plot, i.e., ofRlnKversus 1/T,
would yield from its slopeDH, and from its interceptDS. There is, however,
a difficulty, sinceDHandDSgenerally depend on temperature in the case of
protein unfolding, as illustrated in Figure 7.5.DHcan also be determined by
DSC (differential scanning calorimetry: see Figure 6.25 for an explanation).
The example given in Figure 7.6a shows a sharp peak in heat uptake,
almost like a melting transition. When results from a van’t Hoff plot and
DSC can be compared, good agreement is mostly observed for single-
domain proteins (within 5%or so). From such results and the observed
denaturation temperatures, and with some interpolation, values forDHand
DScan be derived as a function of temperature, to obtain curves like those
in Figure 7.5.
Figure 7.4 shows that the transition N?U occurs over a very small
range of the variable applied. This is typical for acooperative transition,
where several bonds are broken (or formed) simultaneously. In other words,
the molecule would either be in the native or in a (nearly) fully unfolded
state. Also the narrowness of the peaks on DSC plots (Figure 7.6) points to
a cooperative transition. For the unfolding at high temperature, the
FIGURE7.6 DSC diagrams (increasing temperature) showing denaturation of
proteins; initial heat uptake (‘‘base line’’) has been shifted to zero. (a) Lysozyme (pH
2.5). (b) Transferrin.