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

<div><p>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 <i>Naja nigricollis</i>, 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.</p></div

Interpretation of the elution profiles of mutants on HPLC.

<p>Labels N, C, D, and U on top of the elution profiles represent the averaged retention times of these respective species. Numbers in the parentheses in the first column are the sampling times after the initiation of folding reactions. Relative hydrophobicity was calculated as the sum of the hydrophobicity of four tetra-peptides at turns (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.t001" target="_blank">Table 1</a>). (A) Rigid YNGK at turn 2 delayed the elution of 4S species. (B) YNGK at turn 4 introduced analogous consequences as at turn 2. In contrast, YNGK at turn 3 (but much less so at turn 1) accelerated the elution of 4S species. This contribution of YNGK was suppressed in mutant 17 by YNGK at turn 4 (Fig 4E). (C) Comparison of retention times among mutants with the same sums of hydrophobicity. Mutants 5 and 7 and mutants 12 and 13 had equal sums of hydrophobicity. The contribution of YNGK at turns 3 and 4 to the retention time was greater than that of YNGK at turn 1. (D) Absence of YNGK restored the normal correlation between the retention time and the summation of the hydrophobicity of four turns. (E) Summary of the effect of YNGK on retention time. The species without YNGK (mutants 11, 15, 16 and native) form a rough border in the diagram to separate short-retention time mutants in the upper-left region and long-retention time mutants in the lower-right region. Linearity between the hydrophobicity and the retention time was assessed for three groups of mutants. red square: Mutants with YNGK at turns 2 and 4 (mutants 2, 4, 15, and 17), R² = 0.967 (linear regression); green triangle: Mutants with YNGK at turns 1 and 3 but not 2 or 4 (mutants 1, 3, 5, 12, and 13), R² = 0.011 (linear regression); blue triangle: Mutants without YNGK (mutants 11, 15, 16), R² = 0.901 (linear regression); red circle: Native (Tox62).</p

Proposed folding model.

<p>In the earlier stages of the folding, each intermediate is essentially formed as a cluster of locally consistent secondary structures. The absence of native correlations among the local structures results in an equilibrium state of the intermediates. Therefore, the intermediates are saturated with entropy and the formation of S43-S54 as an innovation provides the means to address this entropy. In the assembly process, the rate-limiting stochastic process searches for a productive combination of local structures in terms of relative orientations and synchronization. Positive feedback processes initiate the activation process, and the successful propagation optimizes and establishes the global synchronization of secondary structures for efficient entropy release. The efficiency of entropy release can be estimated as entropy release per unit of time. The number of steps per cycle can represent time per cycle, which is smaller for the compact native state, where S17-S41 further restricts alternative movements. Furthermore, a logarithm of the number of steps can be proportional to the entropy release per cycle. This assumption is based on the expectation that, in the process to load the external thermal fluctuation in local structures, such as finger 3, the number of possible structural configurations at step n could be proportional to n, provided that the surface area to accept the external thermal fluctuation is not altered. In other words, the probability to choose the current configuration is proportional to 1/n. Then, ln (n), which is the integral of 1/n, measures the accumulated difficulty to reverse the whole process back to the initial state. Therefore, ln(x1)/x1 > ln(x2)/x2, where x1, the number of steps in the cycle of native form, < x2, the number of steps in the cycle of the D form. It is noteworthy that x1 cannot be shorter than the possible cycle time of the synchronized global movements. <i>(i)-(iv)</i>, critical evidence listed in the text to support the respective states or steps in this model; blue arrow, processes for 2S (S3-S24, S55-S60) species formation; black arrow, processes where 2S and S43-S54 are involved; green arrow, processes where 2S and S17-S41 are involved; box, intermediates or folded native protein; curved white arrow, disulfide bond S43-S54 as the key architecture that drives the process to release entropy; arrow in dashed circle, locally closed, self-consistent equilibrium in the movements of atoms or the flow of the physical state in various forms; dashed circle represents stochastic and flexible feature in combination with the secondary structures and the absence of correlations within the pseudo-external environment (see text); arrow in circle, the asymmetric movement of atoms or the flow of the physical state in various forms, without a self-consistent property because of the inevitable external input or output; cyclic arrow, recursive and irreversible cycle of the state of molecules, where the movements of the local atoms are globally synchronized, forming a chain of numerous local circles.</p

Simulation of synchronized oscillation in 5ebx.pdb.

<p>The calculated locations of the α carbon atoms for Q10 (Q10CA) and C41 (C41CA), as well as for the CD2 atom of Y25 (Y25CD2) and the CD atom of P44 (P44CD), were superimposed as isolated balls on the structure of 5ebx.pdb. The red, pink, or white balls for the last three atoms are shown at the simulated locations for the oscillation range of ±10 degrees from the original positions, which are shown as black balls. The cyan and magenta rods drawn on the bonds are the axes of rotation. The apparent locational deviation of some black balls from the 5ebx.pdb structure was due to artificial data processing in the graphical tool to draw the 5ebx.pdb structure smoothly. The big red or big blue balls are at the positions where the rotations along the magenta axes are at the maximum (+10 degree), while the pink balls show the next locations to visit. Curved magenta and cyan arrows show the rotation of the atoms approaching the positions of the respective big red or big blue balls. Blue balls show the coordinates when the CD of P44 moves as shown in the figure, without limitation from CD2 of Y25 by van der Waals contacts. In contrast, we assumed that the CD of P44 hits the CD2 of Y25 to trigger the formation of a soliton wave (see text for details). It was postulated that the phase of rotation along the cyan rods, except for the one built with K15 and C3, was preceded by rotations along the magenta rods. This delay was to take into account a correlation that the approaching P44 forced the swing along the cyan rods described above. Additionally, the flexible feature of turn 4 should not have transmitted the physical movement of the latter half of finger 3 (such as peptide 50–55) to the floppy peptide chain 41–49 directly. In this simulation, the postulated delay in phase was 45 degrees.</p

Side and top views of the simulation of a synchronized oscillation in 5ebx.pdb.

<p>(A) Side view, (B) Top view. Figure notations are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.g006" target="_blank">Fig 6</a>.</p

Folding rates of mutants.

<p>Folding rates of mutants.</p

The C form was more native-like than the D form.

<p>(A) HPLC elution profiles of the refolding reaction mixture of Tox62. The N, D, and C forms were eluted at 2.7 min, 4.9 min, and 5.3 min, respectively. Elution profiles at 45 and 90 min are not shown, for clarity. Each peak was assigned based on the previous results [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref012" target="_blank">12</a>], and electrospray mass spectrometry confirmed this assignment. U denotes the fully unfolded protein. (B) Binding property of IAM-C and IAM-D to nAChR. Monoiodoacetamide was added to the refolding mixture to block free sulfhydryl groups, and the acetamide labeled D form (IAM-D) and C form (IAM-C) were prepared with HPLC. The binding to nAChR was assessed as previously described [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref031" target="_blank">31</a>]. white square: N form, triangle:IAM-C, circle: IAM-D. (C) CD spectra of N, D and C forms. A positive peak at approximately 228 nm revealed a micro environment of aromatic residues in the folded structure, and a small negative peak at approximately 216 nm, as well as a large positive peak at approximately 197 nm, showed a beta structure [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref011" target="_blank">11</a>]. ─:N form, ----:C form (after correction for 22.1% of N form and 7.1% of D form), ┄┄┄: D form (after correction for 13.8% of N form and 55.3% of C form).</p

Four disulfide bridges and a β pleated sheet characterize the TFPD.

<p>The structure of erabutoxin b from <i>Laticauda semifasciata</i> (3EBX.pdb [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref002" target="_blank">2</a>]). The Turn 2 in Lk1 is unique to erabutoxin b, while the rest of the structure is essentially shared with Toxin α [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref002" target="_blank">2</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref005" target="_blank">5</a>]. Tox62 is a chimeric protein used in this study with the amino acid sequence </p><p>LECHNQQSSQPPTTKTC<u>SPGE</u>TNCYKKVWRDHRGTIIERGCGCPTVKPGIKLNCCTTDKCNN</p>, using the underlined SPGE motif that forms turn 2 in erabutoxin b and the rest of the sequence coming from Toxin α. A previous study had shown that this SPGE motif in Tox62 reduced the folding rate [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref008" target="_blank">8</a>]. Labels R and G represent R39 and G40, which were predicted to form a turn (see text). Four disulfide bridges, 3–24 (cyan), 17–41 (red), 43–54 (green), and 55–60 (yellow), are shown with sulfur atoms. The four turns targeted for mutation are shown in purple (QSSQ (7–10, turn 1), SPGE (18–21, turn 2), DHRG (31–34, turn 3), and PGIK (48–51, turn 4)) and were replaced with other sequences to prepare mutants. The fifth turn in the structure (residue 57–60) was not colored because it was not a major subject of this study. Lk1 and Lk2 are the peptide chains of C17-SPGETN-C24 and C41-G-C43, respectively. They link the N-terminal and C-terminal structural domains.<p></p

Absence of mutual correlations among local structures at the rate limiting step.

<p>Absence of mutual correlations among local structures at the rate limiting step.</p

The D form is the immediate precursor to the native form.

<p>(A) Exponential decay of unfolded species. The logarithm of 1-N, where N was the species other than the C, D, U (fully unfolded species), and U2 forms (2 disulfide-bonds species), was plotted against time. (B) The D form is the direct precursor to the native form. triangle; observed D, square; observed N and their linear interpolation, ――; calculated N from observed D and their linear interpolation. (C) The validity of the folding model of Tox62 in Fig 3D. The model was assessed using one of the ten refolding datasets for Tox62, by model fitting using Kintecus, [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198276#pone.0198276.ref032" target="_blank">32</a>] to obtain R squared values of 99.6 (N), 99.4 (C) and 99.4 (D). rhombus; observed N, triangle; observed D, square; observed C, each line was calculated by Kintecus. (D) Estimation of relative rate constants of the folding reactions. Ten independent datasets for Tox62 folding were processed independently using Kintecus. Averaged percent R squared values are 99.4 (N), 98.4 (C), and 98.2 (D) when 6 principal reactions were involved in the fitting. The application of the criteria described in the methods section identified reactions other than C to N as indispensable principal reactions because they were essential to maintaining percent R-squared values higher than 98.0, as indexed in the Kintecus fitting. The reactions D to U2 and C to D were eliminated based on the following results. By including these reactions, the rate constants of the 5 principal reactions fluctuated to increase the averaged standard deviations to 1.184 times for D to U2 and 1.384 times for C to D. Pair-wise, one-tailed Student’s t-test assessed the significance of the increase in standard deviations for the rate constants of the principal reactions. The p-values for the reactions D to U2 and C to D were 0.031 and 0.029, respectively. Reaction C to N was maintained, due to the unaltered average of the standard deviation (1.007 times), low significance (p = 0.235) in the t-test, and negligible contribution to the overall reactions.</p