Principles of Protein Structure - H. Schulz 1982

Mechanisms of polypeptide chain folding and association
Aggregates of globular proteins
Free energy of association

The Free energy of association can be estimated from The Structure of the contact surface. Based on the point interactions listed in Table 5.5, a comparative estimate of the binding energy, i.e., the free energy of association, can be made and, as shown above, the most stable oligomers can be identified. However, interface surfaces can also be analyzed in greater detail to determine the absolute value of the free energy of association from the crystal structure. Using the equation , the calculated values of can then be compared with the experimental values obtained from the constant

Let us now consider the Methods for calculating

The Thermodynamics of association is similar to that of folding. As a result of association, the Contact surfaces of the subunits become buried. This can be viewed as The transfer of a surface (atoms) from Water to the interior of the protein. Concurrently, a decrease in the Entropy of the system occurs, since the associated monomers (oligomers) are characterized by a higher degree of order than the free ones. Consequently, the free energy of association takes the form:

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This equation can be compared with equations (3.2) and (3.3): and ∆S_ass correspond to ∆G_tot and ∆S_chain, while the value of ∆S_trans remains the same. Thus, we can use Figures 3.3,b and 3.3,c.

Entropy serves as the main driving force for association. For nonpolar surfaces, the value of ∆G_trans is proportional to the water-accessible surface area (Fig. 1.8). For polar surfaces, the value of ∆G_trans is smaller, yet remains of the same order of magnitude (Fig. 3.3). Thus, in all cases, the value of ∆G_trans is approximately proportional to the total buried surface area. Chothia and Janin [266] determined the areas of the buried contact surfaces for the Proteins listed in Table 5.6. As can be seen from these data, two-thirds of the buried surfaces are formed by nonpolar groups (Table 5.6). Therefore, the authors did not introduce a large error by using proportionality constants for nonpolar surfaces (Fig. 1.8). To obtain the value of ∆S_ass, theoretical data for free particles were used [267]. The values of ∆G_calc,ass calculated in this way are given in Table 5.6. They are in approximate agreement with the experimental data, which indicates the adequacy of our concepts regarding The Nature of the forces driving the association process.

Table 5.6 Free Energy of Protein Association^a

^a The surface area was determined from crystal structure data taken from reference [266]. The accessible surface area was determined in Fig. 1.9.

Of greatest interest is The change in free energy that accompanies Conformational Changes in the aggregating structure. In many oligomers, the absolute free energy of association is significantly less important than its change during conformational rearrangements caused by Ligand binding. Based on such changes in free energy, one can attempt to explain the phenomena of cooperative action and regulation. To date, the best-known example of ligand-induced changes in an aggregated structure is Hemoglobin. A comparison of the buried surfaces of its oxy and deoxy forms (Table 5.5) allows us to evaluate THE CONTRIBUTION OF free energy during the change in the aggregated structure [268]. It should be noted, however, that in this case we are dealing with a small difference between two large quantities; estimating it requires a high degree of accuracy, which is currently quite difficult to achieve.