Research Article: External release of entropy by synchronized movements of local secondary structures drives folding of a small, disulfide-bonded protein

Date Published: June 12, 2018

Publisher: Public Library of Science

Author(s): Atsushi Sato, Andre Menez, Mahesh Narayan.


A crucial mechanism to the formation of native, fully functional, 3D structures from local secondary structures is unraveled in this study. Through the introduction of various amino acid substitutions at four canonical β-turns in a three-fingered protein, Toxin α from Naja nigricollis, we found that the release of internal entropy to the external environment through the globally synchronized movements of local substructures plays a crucial role. Throughout the folding process, the folding species were saturated with internal entropy so that intermediates accumulated at the equilibrium state. Their relief from the equilibrium state was accomplished by the formation of a critical disulfide bridge, which could guide the synchronized movement of one of the peripheral secondary structure. This secondary structure collided with a core central structure, which flanked another peripheral secondary structure. This collision displaced the internal thermal fluctuations from the first peripheral structure to the second peripheral structure, where the displaced thermal fluctuations were ultimately released as entropy. Two protein folding processes that acted in succession were identified as the means to establish the flow of thermal fluctuations. The first process was the time-consuming assembly process, where stochastic combinations of colliding, native-like, secondary structures provided candidate structures for the folded protein. The second process was the activation process to establish the global mutual relationships of the native protein in the selected candidate. This activation process was initiated and propagated by a positive feedback process between efficient entropy release and well-packed local structures, which moved in synchronization. The molecular mechanism suggested by this experiment was assessed with a well-defined 3D structure of erabutoxin b because one of the turns that played a critical role in folding was shared with erabutoxin b.

Partial Text

The three-fingered protein domain (TFPD) is a small, functional module composed of 60 to 90 amino acid residues that form three successive fingers [1–5]. A cluster of three disulfide bonds form “disulfide box” that is a rigid core structure. This core structure and another nearby disulfide bond hold the fingers together (Fig 1). The structure of the TFPD was initially established in erabutoxin b [6,7], from Laticauda semifasciata, which binds to the nicotinic acetylcholine receptor (nAChR). Activins, bone morphogenetic proteins, inhibins, Urokinase/plasminogen activator receptors and others have been found to have from one to three TFPDs [1].

The results of this study suggested that protein folding proceeded in a two-step process. In a single-step model, the assembly and activation processes could proceed in parallel. The results in Table 2 denied this possibility because the native-like mutual relationships among secondary structures were not formed by the time of 4S species formation. In other words, the native-like secondary structure formation proceeded without any support from the native-like molecular-wide mutual correlations, while the formation of the native-like mutual correlations among the secondary structures had to wait for the 4S species formation. Therefore, the results in Table 2 suggested a two-step folding process, where the native-like secondary structures were prepared so that various combinations of secondary structures could be evaluated in the assembly process to determine whether to proceed to the second step of the activation process. Native, molecular-wide, mutual correlations were established in this activation process. For the foldability of the proteins, a secondary structure with the capability to drive entropy release, similar to the disulfide bond S43-S54, should be present as a member of the productive combination. For the fast folding proteins, this rate-limiting assembly process could have been overlooked. The use of YNGK at the active turns allows for the freezing and visualization of such a rapid process.

Protein folding can be described as a process to create a new hierarchy that functions to release entropy efficiently. Protein folding is motivated by a need to release the inevitably accumulated internal thermal fluctuations to the external environment. The release of the internal thermal fluctuations is equivalent to the release of internal entropy. In the rate-limiting assembly process, all the secondary structures as candidate members of the lower hierarchy were waiting for combination and behaved without any native mutual collaboration. This mutual ignorance enabled stochastic exploration for the correct combination of moving secondary structures. In the activation process, the higher hierarchy was established by the collaboration of the secondary structures in the selected combination, which had been evaluated in the assembly process. This occurs in the lower hierarchy, while the new function belongs to the new higher hierarchy. The mutual ignorance among the secondary structures in the assembly process was all of a sudden replaced by native collaborations, which are mutually supportive with molecular-wide global synchronization. The synchronized Brownian movements in the lower hierarchy provided the inertial moment. In the higher hierarchy, this inertial moment drove the displacement of thermal fluctuations in the cluster of atoms such as in finger 3. The thermal fluctuations were thus released in the form of a soliton wave. The positive feedback propagated and stabilized both the function of the higher hierarchy and the selected combination of the secondary structures in the lower hierarchy. The formation of a compact and flexible structure and the efficient entropy release were thus established.




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