Enthalpy of the protein

Thus, the enthalpy Hp of the protein-macrosystem can be obtained, if the enthalpy of the protein solution, H, and the enthalpy of the pure buffer, Hb, can be determined. The enthalpy value Hp corresponds to an ensemble average of the protein-macrosystem. Due to ergodicity the value is also equivalent to the time average behaviour the single protein-microsystem [19]. Therefore we may drop the differentiation between the... 

If the enthalpy of the protein-system H > is formulated relative to the enthalpy //n of the fraction of proteins in the native state N one obtains the relation... 

The transition enthalpies of the s- and p-fractions obtained from the feed with a comonomer molar ratio of 85 15 were equal to 6 and 7 J/g, respectively, i.e. the values are very close. This, therefore, can be indicative of almost the same average length of oligoNVCl blocks. Moreover, as we have already stressed, the fractions also had virtually the same final comonomer composition. However, since the solution properties of these fractions are drastically different, one can draw the conclusion that this is apparently due to a specific distribution of hydrophobic and hydrophilic residues along the polymer chains. In turn, because of all the properties that are exhibited by the s-fraction, this fraction can be considered to be a protein-like copolymer [27]. 

Work from Sturtevant s laboratory detailed the kinetics and thermodynamics of zinc binding to apocarbonic anhydrase (carbonate dehydratase) selected data are recorded in Table II (Henkens and Sturtevant, 1968 Henkens etal., 1969). The thermodynamic entropy term A5 at pH 7.0 is 88 e.u. (1 e.u. = 1 cal/mol-K), and this is essentially matched by the binding of zinc to the hexadentate ligand cyclohexylenediamine tetraacetate where AS = 82 e.u. At pH 7.0 the enthalpy of zinc-protein association is 9.8 kcal/mol, but this unfavorable term is overwhelmed by the favorable entropic contribution to the free energy (AG = AH - T AS), where —TAS = -26.2 kcal/mol at 298 K (25°C). Hence, the kinetics and thermodynamics of protein-zinc interaction in this example are dominated by very favorable entropy effects. 

Where this factor plays a role, the hydrophobic interaction between the hydrocarbon chains of the surfactant and the non-polar parts of protein functional groups are predominant. An example of this effect is the marked endothermic character of the interactions between the anionic CITREM and sodium caseinate at pH = 7.2 (Semenova et al., 2006), and also between sodium dodecyl sulfate (SDS) and soy protein at pH values of 7.0 and 8.2 (Nakai et al., 1980). It is important here to note that, when the character of the protein-surfactant interactions is endothermic (/.< ., involving a positive contribution from the enthalpy to the change in the overall free energy of the system), the main thermodynamic driving force is considered to be an increase in the entropy of the system due to release into bulk solution of a great number of water molecules. This entropy... 

Imidazole groups in solution have enthalpies of ionization of about 30 kJ/mol (7 kcal/mol), whereas carboxylic acids have negligible enthalpies of ionization. But the changes in the enthalpy of the solvating water molecules also make important contributions to these values, and so the solution values cannot be extrapolated to partly buried groups in proteins. 

The use of differential scanning microcalorimetry for measuring the thermal denaturation of proteins is described in Chapter 17, section Ale. Typically, 0.5-1 mg of protein in 1 mL of buffer, or 0.1-0.2 mg in 0.5 mL with the most sensitive apparatus, is required for an accurate determination of the enthalpy of denaturation. The thermodynamics of dissociation of a reversibly bound ligand may be calculated from its effects on the denaturation curve of a protein.14 The binding of ligands always raises the apparent Tm (temperature at 50% denaturation) of a protein because of the law of mass action the ligand does not bind to the denatured state of the protein, and so binding displaces the denaturation equilibrium toward the native state. 

Dilute solutions are used experimentally because one is interested in studying the intramolecular interactions responsible for the stabilization of the structure rather than any interactions between different molecules. Other factors, such as aggregation and reduced solubility of the protein in the denatured state, also make this the concentration region of choice. j Other scientists sometimes refer to it as a second-law enthalpy. 

Figure 16.8 The excess heat capacity, C xcess = Cp (protein + buffer) - C/,(buffer), as a function of temperature, obtained from a differential scanning calorimeter. The shaded area is intergrated to yield the enthalpy of the transition. AtransCp is the difference in the baseline heat capacity at Tm.

On the other hand, the ratio obtained for pancreatic trypsin inhibitor calculated per mole of monomer unit is near 0.5, suggesting that the cooperative unit of this protein is a dimer. Thus, we see that it is not possible to generalize completely about the size of a cooperative unit from a knowledge of the protein structure, but that the comparison of these two enthalpy measurements provides insights into the presence of discrete units within the protein domain. 

The balance of favorable minimization of hydrophobic area and unfavorable reduction of conformational states upon folding will determine the stability of the protein. As these forces tend to be large and comparable in magnitude, the free enthalpy of formation of a protein is the sum of two large opposing forces and may thus be negative or positive. In any case, a folded and catalytically active protein is always just a few kilojoules away from instability. 

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