How the disulfide conformation determines the disulfide/thiol redox potential

Protein disulfides can adopt a wide variety of conformations, each having different energies. Limited experimental data suggest that disulfides adopting a high energy have an enhanced likelihood for reduction, but the exact nature of this relation is not clear. Using a computational approach, we give insight on the conformational dependence of the redox behavior of the disulfide bond, which relates structure to reactivity. The relative energy of different conformations of the diethyl disulfide model system correlates with the disulfide/thiol redox potential E°. Insight in the calculated redox potentials is obtained via quantitative molecular orbital theory, and via the decomposition of E° into a vertical electron affinity and a subsequent reorganization term. We have identified the determinants of the disulfide conformational energies and characterized the barrier to rotation around the disulfide bond. Our findings on the diethyl disulfide model system can be transferred to examples from the Protein Data Base. In conclusion, strained disulfide conformations with a high conformational energy have a large tendency to be reduced. Upon reduction, unfavorable interactions are released. This explains why reorganization effects and not a higher tendency to accept electrons account for the high reduction potential of high-energy disulfides.

However, also non-pH dependent factors as intramolecular strain and conformational space due to the protein chain are suggested to influence the disulfide/thiol redox potential (Wouters, Fan, & Haworth, 2010). Protein disulfides can adopt a wide variety of conformations, each having different energies. Limited experimental data suggest that disulfides adopting strained conformations have an enhanced likelihood for reduction to dithiol , but the exact nature of this relation is not clear. For example, disulfides bridging β-sheets (cross strand disulfides) have recently been categorized as 'forbidden disulfides'. This concept was introduced to identify disulfides that disobey the 'rules' defining the constraints imposed by protein structure on disulfide formation (Wouters et al., 2010). These forbidden disulfides are suggested to adopt strained conformations necessary for their function as redox switches (Haworth, Feng, & Wouters, 2006;Wouters et al., 2010).
We will investigate if the disulfide/thiol redox potential (E°) can be related to the disulfide conformation and how the redox potential exactly depends on disulfide conformation. To this end, the conformational dependence of calculated E°values will be scrutinized via quantitative molecular orbital (MO) theory and via the decomposition of E°into a vertical electron affinity and a subsequent geometry reorganization term, in analogy with earlier work (Roos, De Proft, & Geerlings, 2013). We will identify the structural determinants of the disulfide energies and characterize the barrier to rotation around the S-S bond. As such, insight in non-pH dependent factors determining the disulfide redox potential will be given. Diethyl  disulfide  with  different  conformations  (Supplementary Table S1) are fully optimized (R) or fully optimized with fixed dihedral angles (F) at the MP2/6-31++G(d,p) level Gaussian09 (Frisch et al., 2009). All subsequent energy calculations are performed at the MP2/6-311++G(d,p) level. The MP2 level of theory has been shown to perform well for describing electron capture by disulfides in among other studies (Gamez et al., 2010a;Gamez et al., 2010b;Roos, De Proft et al., 2013). If indicated, the IEF-PCM model with UFF radii and the default cavity in Gaussian09 (Frisch et al., 2009) was used for simulating aqueous solution. Redox potentials are calculated as described in (Billiet, Geerlings, Messens, & Roos, 2012;Ho, Klamt, &, Coote, 2010;Roos, De Proft et al., 2013). Gas phase free energies DG gas are calculated at the optimum geometry at the MP2/6-31++G(d, p) level from the vibrational frequencies, assuming that reaction species behave as an ideal gas within the rigid rotator harmonic oscillator approximation. Free energies of solvation DG solv are calculated using the IEF-PCM solvent model with UAHF radii and the default cavity in Gaussian03 at the hf/6-31+G(d) level (Frisch et al., 2003).

Results and discussion
The conformation of diethyl disulfide CH 3 CH 2 S-SCH 2 CH 3 can be characterized by the dihedral angels: χ2, χ3, and χ2' (see Scheme 1). Based on the scatter plot of experimental χ3, χ2, and χ2' angles (Haworth, Gready, George, & Wouters, 2007), we select a χ3 angle of 90°a nd generate three series of structures by internal rotation around the S 2 -C b2 bond. The dihedral angels χ2, χ3 are kept frozen, while χ2' is varied in steps (see (a) -(c)) : Note that the structure of CH 3 CH 2 S-SCH 2 CH 3 is symmetrical with equivalent χ2 and χ2'. Therefore, the conformations (χ2, χ3, χ2') and (χ2', χ3, χ2) have the same energy. Apart from these conformations, some extra structures are considered in order to represent most of the experimentally found conformations . The structures are fully optimized (R) or fully optimized with fixed dihdral angles (F) as neutral disulfides and as disulfide anions (See Material and Method section and Table S1). The (68,87,68)(R) conformation has the lowest energy and is denoted as the disulfide with the lowest energy conformation. Redox potentials E°(vs. the standard hydrogen electrode) for the disulfide/thiol reduction (reaction (1)) are calculated as described in (Ho et al., 2010;Billiet et al., 2012;Roos, De Proft et al., 2013) (see Table S2).
The standard reduction potentials (E°) can be obtained via the Nernst equation: Scheme 1. Numbering of the C and S atoms and of the χ2, χ3, and χ2' angles in diethyl disulfide (H atoms omitted).
with DG the Gibbs free energy for reaction (1) in aqueous solution, E SHE the standard hydrogen electrode potential, n the number of transferred electrons (here 2), and F the Faraday constant. For E SHE , a value of 4.47 V is used, compatible with the IEF-PCM solvent model (Ho, Coote, Cramer, & Truhlar, in press).
DG is calculated according to equation (3) as the sum of the gas phase Gibbs free reaction energy DG gas and the free energies of solvation of the oxidized and reduced form, at a standard state of 1 mol/l H + : with G ðH þ ; aqÞ = 272.2 kcal/mol, obtained from (Tissandier et al., 1998). The RT lnð RT P Þ. term makes the conversion between the gas phase standard state of 1 atm and the solution phase standard state of 1 mol/l.

Disulfide/thiol reduction potential correlates with the disulfide conformational energy
The decomposition of the global reduction process in reaction (1) into: (i) the reorganization of diethyl disulfide from the lowest energy conformation ((68,87,68) (R) with DE rel = 0) to the desired conformation (DE rel ); (ii) the electron uptake (DE EA ) and the reorganization to the anion geometry (DE reorg ); and (iii) the dissociation of the disulfide anion by which two thiol molecules are formed (Antonello et al., 2002) gives insight (Roos, De Proft et al., 2013) into the relationship between the diethyl disulfide conformation and its ability to be reduced (see Figure 1 and Scheme S1).
DE rel and the adiabatic electron capture DE adiab (which is the sum of DE EA and DE reorg ) are different for each disulfide conformation. The disulfide anion dissociation via a three-step process (see reactions (6), (7), and (8) in Scheme S1) is the common part of the stepwise two-electron reduction process (Antonello et al., 2002). DE rel and DE adiab correlate with E°with a positive and negative slope, respectively ( Figure 2). This means that disulfide structures with a high conformational energy DE rel have a high E°and thus a large tendency to be reduced. This is coupled to a high adiabatic electron affinity DE adiab .
DE EA nor DE reorg correlate with E°( Figure 2). A low correlation is found between the relative anion energy DE reorg2 and E°(see Figure S1). Figure 1. Disulfide/thiol reduction via different steps, according to Supplementary scheme S1. Reorganization of diethyl disulfide (RSSR) from the lowest energy conformation RSSR (ox/ox)L to the considered conformation RSSR (ox/ox) , leading to DE rel in path A. In path B, no such reorganization takes place and thus the path of the reference disulfide having the lowest energy conformation is followed. 2 Electron uptake (RSSR -(red/ox )) and reorganization step to the anion geometry RSSR -(red/red)L , giving DE adiab . ΔE EA is the vertical electron affinity: In path A: ΔE EA = Eopt (neutral) -Eopt (anion with same conformation as neutral), calculated for disulfides with a conformation different from the lowest energy conformation (68,87,68) (R). In path B: ΔE EA = Eopt (neutral) -Eopt (anion with same conformation as neutral), calculated for the disulfide adopting the lowest energy conformation (68,87,68)(R). Dissociation of the disulfide anion to dithiol 2RSH.
Step 3 is the common part of the reduction process for each disulfide conformation and is not considered for analysis since this step does not explain trends in E°. DE rel and DE adiab correlate with E°. Subscript (left/right) refers to oxidation state/geometry; for example, red/ox = reduced form of the species having the geometry of the oxidized form. L: lowest energy conformation.

Reorganization effects determine the disulfide/thiol reduction potential
Further insight in E°can be obtained from the analysis of DE adiab , which is the sum of DE reorg and DE EA . DE reorg ranges from -34 to -44 kcal/mol and contributes most toDE adiab . DE EA accounts only for -12 --18 kcal/mol (see Table S3). Compared to the reference structure with the lowest energy conformation, DE reorg is up to 10 kcal/ mol more negative (purple bar towards negative side in Figure 3), while DE EA is up to 6 kcal/mol less negative (green bar towards positive side in Figure 3), for disulfides with high-energy conformations. This means that the large tendency of high-energy disulfides to be reduced originates from favorable reorganization effects upon reduction and not from an increased ability to take up an electron.
In these structures, similar intramolecular interaction distances as in the reference structure with the lowest energy conformation are found (see Table S4). Accordingly, upon reduction, no unfavorable interactions need to be broken and DE reorg is comparable to this of the reference structure (green circle in Figure 3).

Non-covalent interactions determine DE rel
Thus, we find that reorganization effects determine E°. Insight in why reorganization effects determine E°and therefore in DE rel can be obtained from the analysis of the disulfide bond formation from two CH 3 CH 2 S . fragments (see Eqs. (4)-(6)):  Table S4)correspondence with Figure 4. Figure 2. ΔE rel and ΔE adiab correlate with E°, but ΔE reorg and ΔE EA do not.
The interaction energy DE int between two CH 3 CH 2 S . fragments contributes with~-60 kcal/mol to the total disulfide bond formation energy DE bind . The reorganization of the fragments from the equilibrium geometry of CH 3 CH 2 S . to the geometry they adopt in the disulfide DE prep contributes only with~1 kcal/mol to DE bind (see Table S5). Compared to the reference structure with the lowest energy conformation, DE prep differs less than 1 kcal/mol (Figure 4, brown bars), while DE int is up to 5 kcal/mol less negative (blue bar towards positive side in Figure 4), for disulfides with high-energy conformations.
Therefore, DE bind is determined by the disulfide bond formation energy DE int associated to reaction (6).
The disulfide conformations with χ2 (or χ2')~180°( orange circles, Figure 3b and 4) have a relatively high DE prep term. In the CH 3 CH 2 S . fragments of these structures, a CCS angle of 109°is found, while in the equilibrium structure of CH 3 CH 2 S . this angle is 115°( see Table S6). Accordingly, the large negative DE reorg term found upon reduction, even for low-energy structures having χ2 (or χ2')~180°(see Figure 3), can thus be assigned to the high DE prep term originating from the unfavorable CCS angle of 109°in the CH 3 CH 2 S . fragments. In the further analysis, the disulfides with χ2 (or χ2')~180°will be considered as a separate group in which the same effects apply as will be discussed for disulfides with χ2 and χ2' ≠ 180°.
DE bind is determined by DE int and thus, since DE bind equals DE rel , also DE rel is determined by DE int . DE int is the interaction energy between two CH 3 CH 2 S . fragments and can be estimated as the sum of the disulfide binding energy DE SS;bind (Eq. (8)) and the non-covalent intramolecular interaction energy DE nonÀcov (Eq. (7)), e.g. between the CH 3 groups in each of the two CH 3 CH 2 S . fragments, calculated as follows (see Table S7, Figure 4b): with E S;trip and E S;sin the energy of the biradical sulfur atom S in, respectively, triplet and singlet state and E SS the energy of S 2 in triplet state, adopting the same S-S length as in diethyl disulfide. Figure 4b shows relative DE nonÀcov values as high as 4 kcal/mol (green bars), while the relative DE SS;bind values are lower than 1 kcal/mol (red bars). As such, the trend in DE int (Figure 4a) originates from differences in non-covalent intramolecular interactions among different disulfide conformations and not from differences in disulfide binding energy. This corresponds with the similar S-S bond length of 2.06-2.07 Å found in all structures (with the (60,-140,60) (F) structure being an exception, see further, purple circle in Figure 3, 4). All d (S 1 -S 2 ), d(Ca 1 -Ca 2 ), d(Cb 1 -Cb 2 ), d(Ca 1 -Cb 2 ), d(Cb 1 -Ca 2 ), d(S 1 -Ca 2 ) and d(S 2 -Ca 1 ) distances can be found in Table S4 (see Scheme 1 for the numbering of the C and S atoms).
Pauli repulsion, electrostatic, and orbital interactions are at the basis of DE rel .
To further understand DE rel , an energy decomposition analysis (EDA) for the rotation around the S-S bond in CH 3 S-SCH 3 is performed, in analogy with Ref. (Bickelhaupt & Baerends, 2003;discussion Weinhold, F. Angew. Chem. Int. Ed. 42, 4188-4194, 2003;Poater, Sola, & Bickelhaupt, 2006). EDA is a widely used and straightforward electronic-structure analysis method, using well-defined, physically relevant terms (Bickelhaupt & Baerends, 2000; Krapp, Bickelhaupt, & Frenking, 2006). The total bond energy between two CH 3 S . fragments A and B,DE int is given by: with DE Pauli the Pauli repulsive orbital interaction arising from anti-symmetrisation and renormalization of the DE Pauli comprises the destabilizing interactions between occupied orbitals. DV elstat is the classical electrostatic interaction and DE oi is the attractive orbital interaction arising from the energy relaxation fromE½W A W B to E½W AB of the total wave function W AB . DE oi accounts for charge transfer and polarization. The plot of DE Pauli , DV elstat and DE oi in function of the dihedral CSSC angle of CH 3 S-SCH 3 (this corresponds to χ3 in CH 3 CH 2 S-SCH 2 CH 3 ), calculated at the geometry of the lowest energy conformation of CH 3 S-SCH 3 (χ3 = 83°), shows a region of favorable χ3 angles between 70°and 120°( Figure 5). Pauli repulsion dominates when χ3 < 70°, while, compared to the reference disulfide with the lowest energy conformation, less favorable electrostatic and orbital interactions are present when χ3 > 120°.
The high DE rel of 5.40 kcal/mol of the (60,-140,60) (F) structure (purple circle in Figures 3b and 4) can now be assigned to less favorable electrostatic and orbital interactions found in the (60,-140,60) (F) structure compared to the lowest energy structure, with the effect of the orbital interaction being the largest ( Figure 5). This corresponds to a less negative DE SS;bind (Figure 4b) and shows up in the large S-S bond length of 2.09 Å. The (60,-140,60) (F) structure relaxes to the (71,-111,71) (R) structure during full geometry optimization, having a lower DE rel of 2.05 kcal/mol, in accordance with a χ3 angle in the favorable -70°< χ3 < -120°r egion (for symmetry reasons the -120°< χ3 < -70°and 70°< χ3 < 120°of CH 3 S-SCH 3 are identical).

How the S-S bond length determines DE rel
In disulfide proteins, S-S bond lengths can be substantially different from the equilibrium S-S bond distance (~2.05 Å), see for example Cys426-Cys473 (1crw) and Cys3-Cys31 (1dfn) having a S-S bond length of~1.96 Å ( Table 1).
The plot of DE Pauli , DV elstat and DE oi in function of the S-S bond length (Figure 7), calculated at the geometry of the lowest energy conformation of CH 3 SSCH 3 , shows that the decrease in S-S bond length from 2.05 Å to 1.9 Å causes an increase in Pauli repulsion of~65 kcal/mol, while the stabilization due to electrostatic attraction and orbital interaction increases only by~31 kcal/mol each. This results in a weakening of the interaction energy of~3 kcal/mol (Figure 7). Therefore, the high relative energy of disulfides having a short S-S bond length originates from the high Pauli repulsion between the binding sulfur atoms.

Examples from the PDB
Our findings nicely agree with and explain a vast body of experimental evidence provided by the Protein Data Figure 5. ΔE Pauli , ΔV elstat ΔE oi (values relative to these of the lowest energy conformation) between two CH 3 S . fragments in function of the dihedral CSSC angle χ3 calculated at the geometry of the lowest energy conformation (χ3 = 83°) of CH 3 S-SCH 3 .
Base (PDB). The latter contains various examples that point to a link between disulfide conformation and redox potential. Thioredoxin (Trx) is a reductase with a low disulfide redox potential (e. g. -270 mV for Escherichia coli Trx (Aslund, Berndt, & Holmgren, 1997)). Trx crystallizes preferentially in its oxidized form, in which the disulfide adopts a low-energy conformation (Table 1). Disulfide binding protein A (DsbA) is a strong oxidant having a high redox potential (e. g. -80 mV for DsbA1 of Neisseria meningitides (Lafaye et al., 2009)). DsbA crystallizes preferentially in its reduced form. The disulfide conformation in the oxidized structure of the Thr176Val mutant of DsbA1 of Neisseria meningitides lies~2 kcal/mol higher in energy than the Trx disulfide (Table 1), consistent with its higher redox potential of -115 mV (Lafaye et al., 2009). For Trx, DsbA, DsbD, and glutaredoxin 1 (Grx1), a linear correlation is found between the disulfide conformational energy and the redox potential (Figure 8). This shows the predictive potential of the relation between conformation and redox potential. Other examples than the ones reported here are difficult to find, as either no redox potentials are measured or no structural information is available.
By performing our study in the assumption that all disulfides reduce to the same reaction product, namely, dithiol (see reaction 1), only the conformational dependence of the redox potential was considered. However, the NMR structure 2lqq of Mycobacterium smegmatis mycoredoxin 1 (Mrx1) (Van Laer et al., 2012) illustrates that disulfide conformation is not the only factor determining the disulfide redox potential. The M. smegmatis Mrx1 Cys14-Cys17 disulfide is present in nine different conformations. Some of them are clearly much higher in energy than expected from the redox potential of -218 mV (Van Laer et al., 2012) (Table 1). Therefore, also other factors, as for example, the well-documented pK a dependence (Huber-Wunderlich & Glockshuber, 1998;Mossner et al., 2000;Roos et al., 2007;Roos, Foloppe et al. 2013) of disulfide redox potentials, might play a role. In the scope of this manuscript and thus to demonstrate and to give insight in the conformational dependence of the disulfide/thiol redox potential, the simplified molecular model is very insightful, as all intramolecular interactions (i. e. the interactions on which the relative disulfide energy depends) are present. How the interplay between conformation and other factors from the protein environment determines the protein disulfide E°will be the subject for further research.
The link between the disulfide/thiol conformation and its reduction potential constitutes a structure-reactivity relationship. This combined with the well-known pK a dependence of the disulfide redox potential might result in quantitative structure activity relationships (QSAR) by which oxidation potentials can be predicted from structural data and vice versa the disulfide conformations found in proteins might be explained. This can be important, for example, in the case of DsbA. The latter preferentially crystallizes in its reduced form and thus structures of its oxidized form are not well represented in the PDB. Therefore, our study significantly contributes to a deeper understanding of the disulfide redox biochemistry.
In proteins, the S-S bond length is significantly affected by the steric constraints associated with the 3D structure of the polypeptide backbone. In these systems, the S-S bond length is the primary determinant of the disulfide conformational energy DE rel . This is illustrated in the PDB by the Cys426-Cys473 (1crw) disulfide of human Cdc25B and the Cys3-Cys31 (1dfn) disulfide of human defensin HNP-3 having a high conformational energy in accordance with their low S-S bond length of  The analyzed disulfide conformations are more than 2 times present in the ensemble of 20 NMR conformers. Three conformations, each present 1 time, and three conformations, each present 2 times, are not analyzed here.
~1.9 Å ( Table 1). The χ3, χ2, and χ2' angles, which determine the intramolecular distances are the secondary factors determining DE rel . Together with the S-S bond length, they determine the Pauli repulsion and electrostatic and orbital interactions between two CH 3 CH 2 S . fragments and as such DE rel of the different disulfide conformations. Mainly Pauli repulsion is at the basis of the unfavorable interactions in strained conformations having, e.g. a short S-S bond length or short d(Ca 1 -Ca 2 ) and d(S 1 -Ca 2 ) distances (Figure 7, Supplementary Figure S2). Upon reduction, the S-S bond is broken and the structure can relax such that the destabilizing Pauli repulsion can be relieved. This is reflected by the favorable DE reorg term causing the high E°of high-energy disulfides (red, blue, and purple circles in Figure 3). The disulfide conformations in which χ2 (or χ2') adopts a value of~120°or -120°constitute an exception. These conformations are transition states for rotation around the S-S bond (green circles in Figure 3). Their high E°does not originate from reorganization effects because similar intramolecular interaction distances are present as in the reference structure with the lowest energy conformation. In proteins, these conformations are stabilized by the protein scaffold, for example in the PDB structures 1de4, 3hz8 and in some conformers of 2lqq (Table 1).
Based on the energy decomposition analysis of the barrier to rotation around the S-S bond in CH 3 SSCH 3 , a region of favorable χ3 angles between 70°and 120°c ould be identified ( Figure 5). Previously, it has been shown that electronic factors favor a dihedral angle χ3 of 90°and that steric repulsion is in general responsible for larger angles χ3 (Bickelhaupt, Sola, & Schleyer, 1995;El-Hamdi, Poater, Bickelhaupt, & Sola, 2013). The existence of such a low-energy region makes it possible that, in practice, χ3 can adopt values between~87°(in the lowest energy conformation) and~100°in which case the d(Ca 1 -Ca 2 ) distance increases to more than 3.6 Å which relieves Pauli repulsion between the terminal -CH 3 groups. This is observed in the diethyl disulfide model system and in the disulfides of the 1k12, 1jpe and 1epw protein structures (Table 1).
It might also explain the very low number of experimental protein disulfides with χ3 angles below 70°and above 120° .   Table 1).

Conclusion
The pK a dependence of the disulfide/thiol redox potential is well documented but, hitherto, its conformational dependence is not. Our computational studies clearly show that the disulfide redox potential is linked to the disulfide conformation, both in model systems and in examples from the PDB. Strained disulfide conformations with a high conformational energy DE rel have a strong tendency to be reduced. We show that this is not caused by a higher electron affinity of the strained disulfide conformation. Instead, the motor behind its facile reduction is the release of intramolecular strain as the thiol is formed.

Supplementary material
The supplementary material for this paper is available online at http://dx.doi.10.1080/07391102.2013.851034.