Principles of Protein Structure - G. Schulz 1982

Thermodynamics and Kinetics of Polypeptide Chain Folding
Folding Pathways

Just as a ball rolls down a mountain into the deepest point of a valley, a polypeptide chain folds into the conformation with the lowest Free energy. In both cases, the ball and the polypeptide chain follow a specific path and reach the lowest kinetically permissible point (a local minimum), which does not necessarily correspond to the absolute lowest point (the global minimum). The question is whether the ball (or chain) always follows the same path after leaving the mountain peak (which can be viewed as a broad plateau corresponding to a vast number of unfolded chain Conformations)—that is, whether a channel exists that guides the ball on its downward journey.

Disulfide Bonds serve as Specific Indicators of folding. Searching for such a pathway is a formidable task, as it requires characterizing the conformations of the chain in solution. All spectroscopic Methods yield only the most general results when describing chain folding (circular dichroism, for example, allows one to estimate the proportion of a-helices averaged over all existing conformations). The most precise, albeit limited, structural information can be obtained by studying The formation of S—S bonds, since these bonds appear only when two Cys residues are properly oriented.

Currently, the most suitable subject for such experiments is bovine pancreatic Trypsin inhibitor (BPTI) [793]. BPTI is a small protein of known Structure, containing 58 Amino Acids in a single chain and three disulfide bridges. To study the formation and rearrangement of S—S bonds during folding, it is essential that the reactions involving Cys residues are carefully controlled. For this purpose, low-molecular-weight thiol-disulfide systems with a known redox potential [451] are used, such as highly purified reduced and oxidized forms of dithiothreitol. Purified Reagents, such as iodoacetate, are also employed to cap free thiols. There is no need for Denaturing Agents, since fully reduced BPTI exists in an unfolded form under physiological conditions.

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Fig. 8.1. Covalent intermediates along the folding pathway of bovine pancreatic trypsin inhibitor (BPTI) [451, 793]. Designations are explained in the text. "Correct" disulfide bonds are shown in the far-right box. In intermediate states, such as II_A and II_B, the "correct" disulfide bonds are depicted in the same font as in the N-state. The folding pathway shown in the figure pertains to rapidly folding chains, i.e., 85% of the unfolded molecules.

The addition of a disulfide (such as oxidized dithiothreitol) to a solution of reduced BPTI initiates the folding process. Three distinct intermediate stages (I, II, and III [451]) can be clearly identified in this process, as shown in Fig. 8.1. Transitions from one stage to the next are characterized by significantly different time constants, indicating differences in activation barriers. Stage I features two predominant species, I_A and I_B, containing correct and incorrect disulfide bridges, respectively. Because the formation and Cleavage of S—S bonds occur within microseconds, the relative frequencies of these single-disulfide molecules reflect their relative thermodynamic stabilities. The conformation I_B does not develop further; only conformation I_A proceeds to the next stage, where three predominant two-bridge forms are generated: II_A, II_B, and II_C. All of them retain the first correct bridge; II_A and II_B acquire an incorrect bridge, whereas II_C acquires a correct one. Interestingly, form II_C does not progress further, despite containing two correct bridges. Only forms II_A and II_B advance to stage III, which features a single species containing the initial correct bridge plus an additional correct bridge. This transformation proceeds very slowly because it requires a conformational change with a high activation energy. Conversely, the transition from stage III to the native protein is extremely rapid.

Folding requires intermediate states that are not part of the native conformation. The most surprising result is that folding is not a sequential, ever-closer approximation to the native structure, but rather requires states II_A and II_B, which are excluded from the final native structure. This aspect is even more pronounced in the case of Ribonuclease, whose refolding has also been tracked in a similar manner [458]. Like BPTI, this protein can be renatured solely through the formation of disulfide bridges. However, unlike BPTI, the Cytology/cytology/16.html">Early stages of ribonuclease folding require at least three bridges, which may be formed at random, further supporting the necessity of non-native intermediates. It follows that protein folding is initiated by nucleation at local chain segments and that, before further folding can proceed [459], the necessary free energy contribution (—ΔS_chain) must be provided by disulfide bridges. The in vitro folding process is very slow, taking about 20 minutes.

In the case of Lysozyme, the first two native disulfide bonds form an order of magnitude faster than the subsequent two, indicating the presence of a preferred folding pathway [460]. However, this pathway is not necessarily unique, as demonstrated by other studies on lysozyme [162]. In those experiments, researchers successfully renatured eight possible isomers (of reduced lysozyme), each containing a single permanently blocked Cys residue per protein molecule. All isomers proved to be enzymatically active structures. This fact rules out a unique role for any single disulfide bond in the folding process. It should be emphasized that none of the four native disulfide bonds are obligatory for the Formation of the other three correct S—S bonds.

Folding is cooperative. Much like helix–coil transitions (see Appendix), the folding and unfolding of a protein chain is a cooperative process. Let us examine this general principle more specifically for BPTI. All intermediate forms in this case are unstable; the conformational equilibrium shifts from the unfolded, reduced protein to the Native State containing three S—S bonds. As seen in Fig. 8.2, the molecular population is significant only for these two states, and BPTI can be well-approximated as a two-state system.

Folding can differ significantly between Proteins with and without disulfide bonds. The folding of cystine-containing proteins occurs one to two orders of magnitude slower than that of Proteins of the same size lacking disulfide bonds (Section 8.2). Since the formation of the disulfide bond itself is not the rate-determining step of the process, these proteins apparently belong to different classes in terms of their folding behavior. For this reason, investigating the folding mechanism of a disulfide-containing protein may be of limited relevance for the folding of proteins lacking such cross-links.

Fig. 8.2. Two-state model of protein folding [451].

Bovine pancreatic trypsin inhibitor (BPTI) was incubated in a solution containing 1 mM reduced and 30 mM oxidized dithiothreitol. The fully reduced form of BPTI generated under these conditions is unfolded. After equilibrium of the folding–unfolding transition was established, the protein was alkylated with iodoacetate, separated by gel Electrophoresis, and quantitatively characterized. According to the electrophoretic data, only the unfolded state R and the native states NSHSH (=III; Fig. 8.1) and NSS (=N; Fig. 8.1) are present at equilibrium. Intermediates I and II of the folding process are absent.

The slow and hindered unfolding and refolding of proteins containing S—S bonds can be explained from a physiological perspective. Such proteins are typically extracellular, where they must remain stable under various fluctuating environmental stresses. Kinetic stability allows them to maintain a quasi-native state under denaturing conditions as long as the time constants of the environmental impact remain shorter than the unfolding rate constants. The half-unfolding time of BPTI (stage III —II, Fig. 8.1) is several hours [451].

In some cases, slow folding and slow unfolding of the chain can determine the lifespan of a protein. Once folding is completed within The Cell, such a protein must be secreted into the extracellular space. As soon as it unfolds, it becomes susceptible to protease degradation, since refolding proceeds via the formation of mobile intermediates with relatively long half-lives.

Typically, in disulfide-containing proteins, a fraction of the S—S bonds is essential for thermodynamic stability. Let us reconsider the extent to which disulfide bonds are required for the Stability of the native structure. The set of cross-links, unique and characteristic of the ordered state of the chain, stabilizes this state by reducing the Entropy of the unfolded chain form that possesses the same set of cross-links. For a protein of 120 residues, THE CONTRIBUTION OF four S—S bonds to the stability of the native conformation is approximately 4x2 = 8 kcal/mol (Eq. (8.2)). Given that most extra-epithelial proteins have a $\Delta G_{\text{tot}}$ of about 10 kcal [413] and that they denature when all disulfides are reduced (Table 4.1), it follows that thermodynamic stability of these proteins requires the energetic contribution of one or more disulfide bonds; the exact number varies depending on the protein (Table 4.1).