Principles of Protein Structure - G. Schulz 1982

Thermodynamics and Kinetics of Polypeptide Chain Folding
Thermodynamic Aspects
Transition Between Two Thermodynamic States of the Chain

The previous sections examined isolated, complete protein structures. We will now discuss the spontaneous formation of these structures during or after the synthesis of polypeptide chains. Although some aspects of the folding process can be described using equilibrium Thermodynamics, this approach does not cover all facets of this complex problem. To establish correlations between the Amino Acid Sequence and the three-dimensional Structure, an understanding of folding kinetics is also required. This chapter discusses experimental and theoretical data concerning both the thermodynamic and kinetic aspects of Cell/13.html">Protein Structure formation.

The folding process can be described using standard concepts of physical chemistry. During synthesis on the ribosome, or upon its completion, the polypeptide chain folds into its native globular structure. As a rule, the folding process occurs spontaneously, meaning it does not require the action of additional factors such as Enzymes or the presence of Ribosomes. The most compelling evidence for this mode of folding was obtained following the total Chemical synthesis of the enzyme Ribonuclease [410, 411].

THE PRINCIPLE OF spontaneity was originally formulated based on refolding (renaturation) experiments, which demonstrated that following the Denaturation of a native protein and subsequent removal of the denaturing agent, the chain spontaneously refolds into its initial conformation [94, 412]. However, the validity of this Conclusion was initially questioned because the Protein Denaturation might have been incomplete.

The behavior of synthetic ribonuclease and denatured Proteins indicates that not only nascent chains, but also fully synthesized chains, fold spontaneously. Consequently, the folding process can be viewed as the transition of the chain-plus-solvent system from a higher free-energy state (R, random conformation) to a lower free-energy state (N, native conformation). Standard concepts of physical chemistry are sufficient to describe this process.

During The formation of the native structure in a vacuum, The change in binding energy exceeds the Entropy change. The transition from state R to state N is described by equation (3.2) given in Section 3.5. Let us first consider the relationship between chain entropy and chain binding energy, ΔS_цепь and ΔH_цепь (equation (3.2)). Consider a polypeptide chain of 100 residues forming an α-Helix. The chain entropy is S_цепь = R ∙ ln W, where W is the probability of occurrence of a given conformation, and R is the gas constant. Consequently, the difference in entropy between states N and R is related to the probabilities of the Conformations realized in these systems:

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To compare the random and α-helical states, it is necessary to evaluate the ratio WN/WR. In the R-state, the dihedral angles at a given C_a-atom can take any values within the allowed Regions of the (φ, ψ) map (Fig. 2.3, b), whereas in the N-state, only (φ, ψ) values within a narrow region (–60°, –60°) are possible. Side-chain conformations are not taken into account; i.e., it is assumed that they have similar entropy values in both states. If the α-helical region is estimated to be 10% of the total allowed region (Fig. 2.3, b), the probability of realizing α-helical angles for a given residue will be 10%. For the entire chain consisting of 100 residues, the probability will be approximately (0.1)¹⁰⁰, which yields

If we neglect the term ΔG_{растворитель}, i.e., consider the polypeptide chain in a vacuum, we obtain

Therefore, helix formation is induced (the ΔG_цeпь value becomes negative) when the binding energy per residue exceeds 1.43 kcal/mol, which is the energy easily provided by Hydrogen bond formation. In this example, a 1°C Temperature change corresponds to a 2.1-fold change in the Equilibrium Constant K between the native and random conformations, as follows from equation (3.1). Thus, even small temperature changes exert a strong effect on the equilibrium position, in the sense that at high temperatures, the binding energy is more readily compensated by chain entropy, favoring the random conformation. This situation is characteristic of a system with large, but well-balanced, contributions from entropy and binding energy.

Highly mobile chains cannot form defined structures. The preceding remarks allow us to discuss The Role of β-Amino Acids in the formation of protein structures (Section 1.2). In β-amino acids, free rotation is possible around the C_a—C_β bond (Fig. 1.4). Therefore, for a single residue, the probability of adopting a strictly defined backbone conformation is not 0.1, but only about 0.003 (if a rotation of approximately every 10° around the C_a—C_β bond is considered a distinct structure), and the ΔS_цепь value for 100 residues becomes equal to about –1.2 kcal ∙ deg^-1 ∙ mol^-1, which is 2.5 times larger than for α-amino acids in equation (8.1). It is almost impossible to compensate for such a large chain entropy either solely by the non-covalent binding energy in a vacuum or in combination with the solvent entropy.

Thus, a chain of β-amino acids appears incapable of spontaneously adopting a defined structure. These same considerations apply to all Other types of chain molecules; high mobility prevents the formation of a definite structure.