Thermodynamic Analysis of Protein Structure Stability

When applying reversible thermodynamics, the reversibility of the N D transition should be checked. This transition generally is reversible, unless the denaturing conditions are pushed too far or when the systan is kept in the denatured state for too long a period of time. Under such circumstances new (intermolecular) bonds may be formed, preventing the protein to return to its native state. For varions proteins, especially the smaller ones, denaturation follows a two-state transition that is, it implies that only two states (or, more precisely, two populations of states), N and D, exist. Any intermediate state between N and D is not thermodynamically stable. This is illustrated in Figme 13.11. 

Comparing the differential enthalpy with the integral enthalpy (as determined by calorimetry) provides a test for the two-state assumption for a two-state transition these enthalpies are eqnal. 

FIGURE 13.10 Patterns for cooperative unfolding of proteins induced by changing environmental conditions, that is, (a) pH, (b) temperature, and (c) concentration of guanidinium chloride. 

FIGURE 13.12 Gibbs energy of the unfolding of 3-phosphoglycerate kinase in guanidinium chloride solutions. (Adapted from Tanford, C., Adv. Protein Chem., 24,1, 1970.) 

When studying protein stability by adding a denaturant, the data must be extrapolated to zero concentration of denaturant. This introduces an uncertainty, the more so because usually does not depend linearly on the denaturant concentra- 

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The most detailed thermodynamic analysis of protein structure stability is based on differential scanning calorimetry (DSC). In a DSC experiment, the heat capacity Cp of a sample is monitored while heating (or cooling) the sample. Figure 13.13 shows a typical DSC thermogram for heat-induced denaturation of a protein in solution. The thermodynamic observables are the temperature of denaturation (the temperature at half-peak area), the enthalpy change An, d (T involved in the denaturation process (the area under the peak), and the change in the heat capacity A,, dC of the solution (the shift of the baseline). 

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