Does protein A mirror image exist in solution? Outline of an experimental design aimed to detect it

There is abundant theoretical evidence indicating that a mirror image of Protein A may occur during the protein folding process. However, as to whether such mirror image exists in solution is an unsolved issue. Here we provide sound theoretical evidence indicating that the use of a mutant of protein A, namely Q10H, could be used to detect the mirror image conformation in solution. Our results indicate that the native conformation of the protein A should have a pKa, for the QH10 mutant, at ≈6.1, while the mirror-image conformation should have a pKa close to ≈7.3. Naturally, if all the population is in the native state for the Q10H mutant, the pKa should be ≈6.1, while, if all are in the mirror-image state, it would be ≈7.3, and, if it is a mixture, the pKa should be larger than 6.1, presumably in proportion to the mirror population. In addition, evidence is provided indicating the tautomeric distribution of H10 must also change between the native and mirror conformations. Although this may not be completely relevant for the purpose of determining whether the protein A mirror image exists in solution, it could provide valuable information to validate the pKa findings.


Introduction
A mirror image conformation is one that looks approximately like the specular image of the native state. We say approximately because we do not require the amino acids to be specular images, but only the overall topology of the molecule. At least for some proteins, the mirror image will be energetically very close to the native state and thus it could also exist in solution.
Among these proteins, we will focus our attention on the B-domain of staphylococcal protein A [PDB ID: 1BDD; a three-helix 1 bundle]. 1 This protein has been the subject of extensive theoretical [2][3][4][5][6] and experimental 1, 7-12 studies because of its biological importance and small size. In contrast to this, the mirror-image conformation has been subject of limited discussion. 2-4, 6, 12 The reason for this might be that the mirror image conformation of this protein has been observed only in some theoretical studies with different force fields but it has never been detected experimentally. As to whether this conformation is an artifact of the simulations or is difficult to observe the conformation experimentally, remains to be solved.
At this point, it is worth noting that the difficulties for experiments to detect the mirror-image conformation arise precisely because the secondary structures of the mirror-image and the native conformation of protein A are identical and the structural difference between these conformations are subtle. 6 Because of this, use of simple experiments such as circular dichroism, used to estimate the fraction of secondary-structure content, or more sophisticative technique, such as nuclear magnetic resonance (NMR) spectroscopy, e.g., to monitor the 13 C chemical shift changes that may occur at residue-level, 6 are useless for an accurate characterization of the mirror image conformation. A strong motivation to propose alternative methods to explore the possible coexistence in solution of the native and mirror-image conformation of protein A, comes from older evidence indicating that the mirror-image conformation could be a possible solution to the NMR-determined structure of protein A. 1 Indeed, according to Gouda et al., 1 ". . . distance-geometry calculations resulted in 41 solutions, which had correct polypeptide folds excluding 14 mirror-image substructures. . . " However, the mirror-image structures were excluded from the analysis of Gouda et al. 1 without providing any reason. It seems that the decision was adopted because the "mirror-image" satisfies the NOE constraints but contain D-amino acid residues (personal communication with Ichio Shimada).
Overall, we propose here a proof-of-concept of an experimental design aimed to solve this problem. Initially we will show, by using ROSETTA, 13 that a mutant of protein A, hereafter the Q10H protein, exhibits the ability to fold into the native conformation (see Figure 1) as well as into the mirror-image conformation (see Figure 2). Later, we estimate the fraction of the native and mirror-image populations of the protein Q10H by using a recently introduced method, that take into account the protein dynamics in water by using a constant-pH MD simulation, to accurately determine the pKa values of ionizable residues, and fractions of ionized and tautomeric forms of histidine (His), in proteins at a given fixed pH. 14 Indeed, we explore the dependence of the electrostatically-calculated pKa and fractions of the imidazole ring forms of H10 as a function of pH for both the native-like and mirror-image conformations present in solution to the extent of 100%. Figure 2 shows a superposition of the lowest-energy conformations for both the native-like (green-ribbon) and the mirror-image (yellow-ribbon) of protein Q10H obtained by using ROSETTA. 13 These two structures were used to compute 15 for each ionizable residue along the sequence the value of the pKa variations (∆ = [pK a Native − pK a Mirror ]) at pH 7.0. The result of this analysis is shown in Figure 3 (as blue dots) where one of the largest change in ∆, namely larger than ±1.0 pK units, occurs for H10. This large shift on the pKa of residue H10 appears to be a consequence of the close proximity of H10 to D38 in the mirror-image conformation of protein Q10H (see Figure 2).

Analysis of the pKa variations as a function of pH
There is another change of ∆ larger than ±1.0 pKa unit and it occurs for residue K8 (see blue dots in Figure 3), a residue that pertains to the flexible N-terminal region of the mutant protein Q10H, viz., ranging from residues T1 trough E9. The origin of the large computed shift in the pKa of residue K8 is the following. In the native structure of protein Q10H residue K8 is well exposed to the solvent. On the other hand, in the mirror image structure of this protein residue K8 is close to E16, making a favorable electrostatic interaction. However a close inspection of these two structures indicates that the favorable electrostatic-interaction between K8 and E16, observed in the mirror image conformation, could also occur on the native conformation, e.g., by a rearrangement of the backbone-torsional angles of the flexible N-terminal region of the protein Q10H.
If this were feasible, the computed pKa shift for K8 should be ≈ 0. Consequently, monitoring the pKa shift of K8 does not appear to be the right choice for the purpose of an accurate determination of the coexistence between the native and the mirror image states in solution. Unlike the origin of the pKa shift for K8, the interaction between H10 and D38 cannot take place in both the native and the mirror-image conformations (see Figure 2) and, hence, from here on we will focus our attention on H10 only.
At this point is worth noting the following. Consideration of the protein dynamics in water is very important for an accurate computation of conformational-dependent values, such as the pKa's. However, this effect was not tacked into account in the computation of the ∆ values shown, as blue-dots, in the Figure 3. Consequently, we carried out a constant-pH MD simulation of both the native-like Q10H mutant and its mirror-image conformations. 14 During the simulations, at constant-pH 7.0, it is reasonable to consider all acid (Asp, Glu) and base (Lys, Arg) residues in the ionized state, because their respective pK 0 's (3.5, 4.0, and 10.5, 12.5, respectively) are shifted by more than 2.5 pK units from the pH (7.0) at which the calculations were carried out. For the same reason, the only Tyr in the sequence was consider as neutral. However, histidine residue pKa's (6.5) can vary

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considerably at pH 7.0 at which the calculations are carried out and, hence, consideration of histidine ionization states for each of the imidazole ring of His forms must be considered explicitly. Consequently during the calculations the nine ionizations states of the two interacting His, namely between H10 and H19, were explicitly consider. 16 The average ∆ change for H10, computed from the native-like and mirror-image conformations after 10ns MD simulations, is shown as an orange dot in Figure   3. Similarly, the computed average change for the imidazole ring forms of H10 as a function of pH for both the native like and the mirror image conformations are display in hold: f ε2 f δ 1 (see Figure 4) otherwise there would be coexistence of the native-like structure with other topology in solution.

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As a second, but less restrictive, validation test we can use a recently proposed NMR-based methodology aimed to determine the tautomeric forms as a function of the ionization state of the imidazole ring of histidine. 18 In this approach, the average tautomeric fraction of the N ε2 − H form of His ( f ε2 ) can be determined by using the following equation: f ε2 = ∆ obs (1 − f H+ )/∆ ε where f H+ is the experimentally determined fraction for the ionized form of H10, at a given fix pH; ∆ obs =| 13 C δ 2 − 13 C γ |, where 13 C δ 2 and 13 C γ are the NMR-observed chemical shifts for the imidazole ring of H10 at that pH; and ∆ ε is the first-order absolute shielding difference, | 13 C δ 2 − 13 C γ | ε , between the 13 C δ 2 and 13 C γ nuclei for the N ε2 − H tautomer, i.e., present to the extent of 100%. ∆ ε is a parameter which must be estimated. 18 As a first approximation, a ∆ ε = 27.0ppm, obtained from the analysis of a His-rich protein, 16 namely Loligo vulgaris (pdb id 1E1A), a 314-residue all-β protein, 19 should be used. Naturally, the f δ 1 fraction, viz., for the N δ 1 − H tautomer, is obtained straightforwardly as: Although this second approach to compute the tautomers of H10 it is more general than the previous one, i.e., by using the 1 J Cδ 2H SSCC, the determination of the 13  limiting values are used. 24 Because these results raise concerns about the magnitude of the uncertainty associated with the predictions we did not consider this method as an alternative to the above-proposed tests to validate the pKa predictions.
All in all, the estimated tautomeric forms of the imidazole ring of His are certainly not enough to accurately determine whether the coexistence of native-like and mirror-image structures occurs in solution but it could be of valuable assistance to validate the determination made by the pKa analysis.

Discussion
We provided a proof-of-concept of an experimental design that could be used to detect the coexistence of native and mirror-image

Methods
In this section we will give a brief reference to existent theoretical methods aimed to predict (i) the 3D structure of proteins accurately; 25 or determine (ii) the pKa values of ionizable residues and fractions of ionized and tautomeric forms of histidine (His) and acid residues in proteins, at a given fixed pH. 14, 15

Determination of the native and image-mirror conformations of protein Q10H
To generate the native and mirror-image conformations of protein A Q10H we used the fast-relax protocol from Rosetta, 13,26 this is an all-atom refinement protocol that basically consists of several rounds of repacking and energy minimization. The repulsive part of the Van der Waals energy function is annealed from 2% to 100%. Essentially the algorithm explores the local conformational space around the starting structure with a radius of 2 to 3Å of rmsd (for the C α ). We performed several rounds of fast-relax using a genetic-like algorithm.  3 an a mirror image folded by hand. We discarded all the conformations obtained from this last starting point as their energies were much more higher than for the other two starting points.

Computation of the pKa and the tautomeric fractions of the imidazole ring of H10
The native-like and mirror-image conformations of protein Q10H, generated as describe in the previous section, were used as input files for the calculations of the pKa of all ionizable residues in the sequence as well as the fractions of the ionized H + and the tautomeric N ε2 − H and N δ 1 − H forms of the imidazole ring of H10. In particular, as it is well known, the tautomeric determination of the imidazole ring of His is both a very important problem in structural biology 27, 28 and a challenging task. 29 For this reason, a recently introduced electrostatic-based method to determine the pKa values of ionizable residues and fractions of ionized and tautomeric forms of histidine (His) and acid residues in proteins, 14 is applied here to the analysis of protein A mutant Q10H. Protein dynamics in water, at a given pH=7.0, was taken into account by constant-pH MD simulation 16 of both the native and mirror-image conformations of the Q10H mutant.
The ionization constants pKa and the fractions of ionized and two neutral tautomers of histidine at constant pH 7.0 are modeled by MD simulations at constant pH. As mentioned in the main text, all acid (Asp, Glu) and base (Lys, Arg) residues were kept in the ionized state because their respective pKo's (3.5, 4.0, and 10.5, 12.5, respectively) are shifted by more than 2.5 pK units from the pH (7.0) at which the calculations were carried out. On the other hand, the two existent histidine residues, namely H10 and H19, were considered to be electrostatically couple residues having nine ionization states, namely, 00, 01, 02, 10,11,12,20,21,22, where 0,1,2 represents the ionized and two neutral tautomer states, respectively. 14