Principles of Protein Structure - G. Schulz 1982

Thermodynamics and Kinetics of Polypeptide Chain Folding
Structural Elements in Unfolded Chains

Up to now, the term "thermodynamic state" has been used with respect to the unfolded chain. However, unlike the native Structure, the unfolded state corresponds to an ensemble of chain Conformations. Nevertheless, one can assume that a certain degree of order still exists even in an unfolded chain. Identifying structured elements within it, and thereby narrowing down the conformational space, is useful for analyzing the folding process; in this case, one can single out nascent forms—nucleations—with which the remaining Regions of the chain interact.

Refolding experiments reveal both rapidly and slowly folding chains. The division of unfolded chains into these two classes—fast- and slow-folding—was established in studies of Ribonuclease [440, 447, 448]. In refolding experiments on ribonuclease denatured without disrupting its disulfide bond system, it was found that 20% of the chains refold within 0.1 s (rapidly folding chains). The percentage of such chains is independent of the Denaturation method (guanidine hydrochloride [449], heating [450], etc.). The remaining 80% of the chains (slowly folding chains) convert within 10 to 100 s into fast-folding chains, which then instantly collapse. A similar, albeit less quantitative, observation has been reported for bovine pancreatic Trypsin inhibitor (BPTI), in which 15% of the chains folded significantly slower than the rest [451]. This phenomenon remains unexplained. According to one hypothesis [449, 452], in rapidly folding chains all peptide bonds are in the correct cis-trans isomers, whereas slowly folding chains contain incorrect isomers, and time is consumed on The conversion of these incorrect isomers. Cis-trans isomerization occurs most readily on the N-terminal side of a Pro residue, since in this case the activation energy barrier is only about 13 kcal/mol compared to 20 kcal/mol for other peptide bonds (Sec. 2.5). Both BPTI and ribonuclease contain four Pro residues, and in native ribonuclease two of them exist in the cis-conformation.

Antibodies can be used to identify folding nuclei. Another approach to searching for structural traces in unfolded polypeptide chains involves cleaving native polypeptide chains and testing, using specific antibodies, which of the fragments adopts its native conformation. Most of these experiments have been performed on staphylococcal nuclease [418; 453]; they showed that fragments ranging from 17 to 120 residues in length fold into the native conformation with an Equilibrium Constant K = [N]/[R] ≈ 10^-3. According to equation (3.2), this corresponds to an unfavorable Free energy change of approximately 4 kcal/mol. In principle, this method can be used to search for folding nuclei; for this purpose, it is necessary to isolate or synthesize the required polypeptide chain fragments [454]. Stable fragments corresponding to high values of K are the most likely candidates for folding nucleations.

Such nucleations must be characterized by a high degree of correlation with adjacent residues along the chain (Section 5.3), because it is precisely the interactions with these residues that enhance the Stability of the intermediate. This is evident from Flory's formula for estimating THE CONTRIBUTION OF disulfide bridges to chain Entropy [455]:

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where v is the number of cross-linked chains (twice the number of bridges), and n' is the number of statistical segments between the bridges, which, as a first approximation [456], can be taken as the number of residues between the bridges.

The shorter the chains between the bridges, the smaller the entropy decrease upon their formation. This entropy decrease is caused not by chemical properties, but solely by the reduction in the number of accessible conformations upon The formation of Disulfide Bonds. Consequently, Flory's formula can be used to estimate the entropy penalty required to bring two chain elements into proximity.

Flory's formula quantitatively demonstrates that strong correlation with adjacent chain residues is advantageous. As follows from equation (8.2), the required entropy change is smaller the shorter the chain between the interacting elements, i.e., the stronger the correlation with adjacent residues in the corresponding chain segment. Conversely, the activation entropy ΔS^≠_chain for the transition from the unfolded chain to the Native State with strong neighbor correlation is much smaller than ΔS^≠_chain for the transition to a native state with weak correlation. In accordance with equation (3.2), a lower value of ΔS^≠_chain corresponds to a lower free energy barrier and, consequently, a more stable intermediate structure. Thus, folding a chain into a structure with strong neighbor correlation requires a much smaller contribution from binding energy and solvent entropy than transitioning to a structure with weak correlation. Strong neighbor correlation facilitates the folding process and thereby significantly increases its rate.

Secondary structures, such as α-helices and β-sheets, serve as potential folding nuclei because they possess a large binding energy and strong correlation with adjacent chain residues. In this regard, it should be noted that during the refolding of BPTI, the first stable disulfide bond [451, 457] links Cys-30 of the β-sheet to Cys-51 of the α-Helix. This region exhibits the strongest neighbor correlation (the shortest segment between the bridging residues) in the native structure (Fig. 8.1).