Local frustration determines loop opening in protein-protein association

Local frustration, the existence of mutually competing interactions, may explain why some proteins are dynamic when others are rigid. More specifically, frustration is thought to play a key role in biomolecular recognition while it can also underpin the flexibility of binding sites. Here we show how a seemingly small chemical modification, the oxidation of two thiols to form a disulfide bond, during the biological function of the N-terminal domain of the bacterial oxidoreductase DsbD (nDsbD), introduces frustration. In oxidised nDsbD, local frustration disrupts the packing of the protective cap loop region against the active site of the protein allowing loop opening and exposure of the active-site cysteines even in the absence of any interaction partners. By contrast, in reduced nDsbD, lacking a disulfide bond, the cap loop is rigid, always shielding the active-site cysteines and protecting them from the otherwise oxidising environment of the bacterial periplasm. Our results point towards an intricate coupling between the dynamics of the active-site cysteines and those of the cap loop, which shapes the protein-protein association reactions of nDsbD resulting in optimised protein function.


Introduction
Molecular recognition, the specific non-covalent interaction between two or more molecules, underpins all biological processes. During protein-protein association, molecular recognition often depends on conformational changes in one or both of the protein partners. Important insight into the mechansims of molecular recognition has come from NMR experiments probing dynamics at the µs-ms timescale, which often underpin protein-protein interactions. 1,2 NMR, and especially the relaxation dispersion method, is unique in being able to provide not only kinetic but also structural information about the conformational changes occuring during protein association. 3,4 In some cases, molecular dynamics (MD) simulations have been successfully paired with NMR experiments [5][6][7][8] to reveal the conformational dynamics in atomic detail. [9][10][11] However, despite numerous studies in which the mechanisms of specific protein-protein interactions are described in exquisite detail, [2][3][4][9][10][11] we still do not have a general understanding of the molecular determinants which enable some proteins to access their bound-like conformation before encountering their binding partners, while others undergo conformational change after recognising their ligands.
Local frustration, the existence of multiple favourable interactions which cannot be satisfied at the same time, has emerged as an important concept in rationalising why some regions in proteins undergo conformational changes in the absence of a binding partner. [12][13][14] Proteins are globally minimally frustrated and, thus, adopt well-defined native structures.
Nonetheless, the existence of a set of competing local interactions can establish a dynamic equilibrium between distinct conformational states. Locally frustrated interactions 15 are indeed more common in binding interfaces of protein complexes 12 and play an important role in determining which parts of the interacting molecules are flexible. However, relatively few studies 16,17 have analysed in atomic detail how frustration shapes conformational dynamics and, therefore, can enable protein association. This lack of understanding will hamper the exploitation of local frustration, and associated dynamic equilibria, as a design principle for synthetic molecular machines and switches.
To understand the role of frustration and dynamics we study the N-terminal domain of the transmembrane protein DsbD (nDsbD), a central oxidoreductase in the periplasm of Gram-negative bacteria. DsbD is a three-domain membrane protein (Fig. 1A) which acquires reductant from cytoplasmic thioredoxin and, through a series of thiol-disulfide exchange reactions (Fig. 1B), transfers this reductant to multiple periplasmic pathways (Fig. 1A). 18,19 nDsbD plays a critical role as the hub for reductant provision in the bacterial periplasm. 20 It interacts with the C-terminal domain of DsbD (cDsbD) to aquire the reductant provided by cytoplasmic thioredoxin and then also interacts with several globular periplasmic partners to provide reductant (Fig. 1A). All these reductant exchange steps involve close interactions between nDsbD and its binding partners, which are essential so that their functional cysteine pairs can come into proximity leading to reductant transfer. 21,22 X-ray structures show that the cap-loop region of nDsbD, containing residues D68-E69-F70-Y71-G72, plays a key role in the association reactions of nDsbD with its binding partners, cDsbD, DsbC, and CcmG. 21,23,24 The catalytic subdomain of nDsbD is inserted in the antigen-binding end of its immunoglobulin (Ig) fold with the two active-site cysteines, C103 and C109, located on opposite strands of a β-hairpin (Fig. 1C). For both oxidation states of isolated nDsbD (with and without a disulfide bond between C103 and C109), the active-site cysteines are shielded by the cap-loop region which adopts a closed conformation. 21,22,25,26 Strikingly, all structures of nDsbD in complex with its binding partners show the cap loop in an open conformation allowing interaction of the cysteine pairs of the two  (Trx) in the cytoplasm, via the three domains of DsbD to the other periplasmic pathways is shown. Trx red reduces the disulfide bond in tmDsbD ox , tmDsbD red then reduces cDsbD ox , and cDsbD red then reduces nDsbD ox . DsbC, CcmG and DsbG then accept reductant from nDsbD red . cDsbD, Trx, DsbC, CcmG and DsbG all have the thioredoxin fold, characteristic of thiol-disulfide isomerases. nDsbD, in contrast adopts an immunoglobulin fold. (B) Schematic representation of a thiol:disulfide exchange reaction (bimolecular nucleophilic substitution mechanism). (C) The structure of oxidised nDsbD is illustrated (PDB: 1L6P). The cap loop (residues 68-72) which covers the active site is highlighted in teal. The side chain of F70 (shown in a surface representation) shields the active-site disulfide bond (between C103 and C109, shown in yellow) in the closed cap loop conformation. (D) The cap loop of nDsbD adopts an open conformation in the complex of nDsbD and cDsbD (PDB: 1VRS). This allows the interaction of the cysteine residues of the two domains. cDsbD, shown in grey, has the thioredoxin fold typical of oxidoreductases. nDsbD is shown in pale cyan. proteins (Fig. 1D). 21,24,27 While these structures provide static snapshots of the closed and open states of the cap loop, they do not provide any insight into the mechanism of loop opening that is essential for the function of nDsbD. To understand the drivers of this conformational change, several hypotheses regarding the solution state of nDsbD need to be examined. (1) It is possible that the cap loop only opens when nDsbD encounters its binding partners, a mechanism consistent with the hypothesised protective role of this region of the protein. 25  in reduced nDsbD, so the possibility that nDsbD interacts with its partners via different loop-opening mechanisms depending on its oxidation state also needs to be considered. In this scenario, the disulfide bond would modulate the conformational ensemble of nDsbD ox as has been hinted at by structural bioinformatics. 28,29 Here we use both NMR experiments and MD simulations to describe different behaviours for the cap loop depending on the oxidation state of nDsbD. The atomic-scale insight afforded by these two methods reveals how the disulfide bond introduces local frustration specifically in oxidised nDsbD (nDsbD ox ), allowing the cap loop and active site in oxidised nDsbD to sample bound-like conformations in the absence of a binding partner. Our observations have implications not only for the function of DsbD, but broadly for the role of local frustration in ensuring optimised protein-protein interactions and, more generally, for the design of molecular switches.

Construction of plasmids
Plasmids used in this study are listed in Table S1. The plasmid pDzn3, described in previous work, 30,31 encodes isolated wild-type (WT) nDsbD (L2-V132) bearing a thrombincleavable C-terminal polyhistidine tag. This construct was used as a template to produce a cap-loop deletion variant of nDsbD (∆loop-nDsbD), where residues H66-K73 were replaced by the amino acid sequence A-G-G. Site-directed mutagenesis (QuikChange, Qiagen) was performed using oligonucleotides 5'-(AGGAAGCGAGATTTACCGCGATCGGCTG)-3' and 5'-(CCGGCCCAGACGC CTTGCGGCAGCTGC)-3'; the resulting plasmid was named pDzn8. DNA manipulations were conducted using standard methods. PCR was performed with KOD Hot Start DNA polymerase (Novagen) and oligonucleotides were synthesized by Sigma Aldrich.

Protein production, purification and characterization
Isolated WT nDsbD and ∆loop-nDsbD were expressed using BL21(DE3) cells (Stratagene) and were purified from periplasmic extracts of E. coli using a C-terminal polyhistidine tag.
Thrombin cleavage of the affinity tag was performed using the Sigma Thrombin CleanCleave Kit (Sigma) according to the manufacturer's instructions. Production and purification of all protein samples was carried out as described previously. 30,32 NMR spectroscopy NMR experiments were conducted using home-built 500, 600 and 750 MHz spectrometers equipped with Oxford Instruments Company magnets, home-built triple-resonance pulsedfield gradient probeheads and GE/Omega data acquisition computers and software. All experiments were conducted at 25 • C and at pH 6.5 in 95% H 2 O/5% D 2 O, unless stated otherwise. Spectra were processed using NMRPipe 33 and analysed using CCPN Analysis. 34,35 6 Residual dipolar couplings (RDCs) were measured using Pf1 phage purchased from ASLA BIOTECH Ltd. (Riga, Latvia). RDCs were measured at 600 MHz for 0.5 mM nDsbD with 10 mg/ml Pf1 phage, 2 mM K 2 PO 4 , 0.4 mM MgCl 2 , 0.01 % NaN 3 and 10 % D 2 O.
Measurements were carried out for isotropic solutions prior to the addition of the Pf1 phage.
Separate samples were used for oxidised and reduced nDsbD. RDCs were measured using the InPhase-AntiPhase (IPAP) approach. 36 The F 2 ( 1 H) and   eight and ten 10 ns trajectories were run for nDsbD red and nDsbD ox , respectively. Missing side-chain atoms were added using the WHAT-IF Server. 51 The histidine side chains were protonated and the cysteine side chains (C103 and C109) in the active site of nDsbD red were represented as thiols; these choices were based on pH titrations monitored by NMR. 30 The protein was embedded in rhombic dodecahedral boxes, with a minimum distance to the box edges of 12 Å at NaCl concentrations of 0.1 M. Trajectories using a larger distance of 15 Å to the box edges showed no significant differences. The CHARMM 22 force field 52 with the CMAP correction 53 and the CHARMM TIP3P water model was used. Electrostatic interactions were calculated with the Particle Mesh Ewald method (PME). 54 The Lennard-Jones potential was switched to zero, between 10 Å and 12 Å. 55 The length of bonds involving hydrogen atoms was constrained, using the PLINCs algorithm. 56

Analysis of the MD simulations
To validate our MD simulations, amide order parameters (S 2 ) and residual dipolar couplings (RDCs) were calculated from them. Before calculating S 2 and RDCs we removed the overall tumbling from the simulations by aligning each frame to a reference structure. Order parameters were calculated in 5 ns blocks from the MD trajectories 59 with S 2 given by where α and β denote the x,y,z components of the bond vectorμ.
To calculate RDCs, the principle axes of the reference structure were aligned with the experimentally determined alignment tensor. The use of a single reference structure is justified given the stability of the overall fold of nDsbD in the simulations. The RDC for a given residue in a given structure is then calculated using where κ depends on the gyromagnetic ratios γ I γ S , the magnetic permittivity of vacuum µ 0 and Planck's constanth and is defined as κ = − 3 8π 2 γ I γ S µ 0h . R is the bond length and is uniformly set to 1.04 Å. The angles θ 1 , θ 2 and θ 3 describe the orientation of the individual bonds with respect to the three principal axes of the alignment tensor. A x , A y and A z are the principal components of the alignment tensor.

Results and Discussion
The solution structure of nDsbD as probed by NMR NMR experiments demonstrate that the cap loop has an important protective role in shielding the active-site cysteines of nDsbD. For nDsbD ox , we showed previously that reduction of the disulfide bond by dithiothreitol (DTT) is very slow, indicating that the cap loop shields C103 and C109 from the reducing agent. 22 NMR spectra for nDsbD red collected between pH 6 and 11 show no change in cysteine C β chemical shifts. This indicates that the pK a of C109, the cysteine residue thought to initiate reductant transfer, 23  circles while RDCs calculated by fitting the alignment tensor to the X-ray structure (PDB:3PFU for reduced and PDB:1L6P for oxidised nDsbD) are indicated by the solid line. The small RDCs measured for residues 1-8 and 126-135 in both redox states are likely to indicate conformational dynamics leading to averaging of these RDCs; values for most of these residues cannot be predicted from the X-ray structures because electron density is not observed before residue 8 and after residue 125 in the structures. For most residues very similar RDCs were measured for reduced and oxidised nDsbD. Experimental RDCs are compared with RDCs calculated from MD simulations for (C) reduced and (D) oxidised nDsbD. 12 to 122 of less than 0.15 Å. To probe the solution structure of oxidised and reduced nDsbD, we measured 1 H-15 N residual dipolar couplings (RDCs), which are sensitive reporters of protein structure ( Fig. 2 and Table S2). The RDCs for N-and C-terminal residues do not agree well with those predicted from the X-ray structures. The measured RDCs for most of these residues are close to 0 Hz suggesting they are averaged due to conformational disorder. By contrast, the RDCs for the core β-sandwich are predicted very well by the X-ray structures; Q values of 0.21 and 0.17 are obtained for oxidised and reduced nDsbD, respectively (Table S2). When fits are carried out for residues 12-122, which includes the core β-sandwich and the active-site/cap-loop residues, Q values of 0.24 and 0.19 are obtained for oxidised and reduced nDsbD, respectively. The similar Q values for the two sets of RDCs suggest that the orientation of the active-site/cap-loop residues relative to the core β-sandwich of both oxidised and reduced nDsbD in solution is well-described by the X-ray structures in which the cap loop adopts a closed conformation. Nevertheless, the cap loop must open to expose the active site in order for nDsbD to carry out its biological function.

NMR spin-relaxation experiments and model-free analysis
To investigate whether the cap loop is flexible in solution, opening and closing frequently, and whether the dynamic behaviour of the loop differs in the two oxidation states, we studied the fast time-scale (ps-ns) dynamics of nDsbD using NMR relaxation experiments. 15 N relaxation experiments, analysed using the "model-free" approach, 42,43 showed that most of the protein backbone is relatively rigid. The majority of order parameters (S 2 ) for the backbone amide bonds are above 0.8 (Fig. 3). The N-and C-terminal regions of nDsbD gave very low S 2 values and are clearly disordered in solution, confirming the interpretation of the RDC data. Other residues with order parameters below 0.75 are located in loops and at the start or end of elements of secondary structure but are not found to be clustered in a specific region. For example, lower order parameters are observed for residues 57 and 58 in both redox states. These residues are located in a long 'loop' parallel to the core β-sandwich In nDsbD ox , seven residues between V64 and G72 have NOE values at or below 0.7 while in nDsbD red there is only one residue with an NOE value below 0.7 ( Figure S1 and Table   S3). The consequence of this difference is that the majority of residues in this region in nDsbD ox require a more complex model (with the τ e parameter ranging from ∼ 50 to 350 ps) to obtain a satisfactory fit in the analysis while the majority of residues in nDsbD red can be fitted with the simpler S 2 -only model which assumes a τ e value of faster than ∼ 10 ps. Therefore, although the amplitude of motions of cap-loop residues is limited and does not appear to differ very much between the two oxidation states, the timescale of the fast dynamics, as described by the approach of Lipari & Szabo, may differ.

Molecular dynamics simulations
To understand the differences between reduced and oxidised nDsbD and their conformational dynamics at atomistic resolution, molecular dynamics (MD) simulations were employed. To track the orientation of the cap loop relative to the active site in the MD trajectories, the distance between the centre of the aromatic ring of F70 and the sulfur atom of C109 was calculated. Multiple simulations, for a total of 1 µs, were started from the X-ray structure of reduced nDsbD (3PFU). The distance between F70 and C109 remained close to the value in the X-ray structure of nDsbD red , as shown for example trajectories in Fig. 4A,B. Opening of the cap loop in nDsbD red was not observed in 1 µs of simulation time (Fig. 4D). This confirms that the cap loop protects the active-site cysteines of nDsbD red from the oxidising environment of the periplasm The spontaneous loop opening of nDsbD ox and the relative stability of partially open conformations observed in our MD simulations (Fig. 4H) marks a clear difference between the conformational ensembles sampled by oxidised and reduced nDsbD (Fig 4D,H).
We have also employed MD to probe the behaviour of the cap loop in simulations start- ing from an open conformation of nDsbD observed in the 1VRS X-ray structure of the nDsbD/cDsbD complex. 23 Five of eight trajectories for nDsbD red started with an open loop conformation closed within 10 ns (Fig. 4C). Simulations of nDsbD ox , started from a fully open 1VRS oxidised structure, closed within 10 ns in three out of ten trajectories (Fig. 4G).
These simulations demonstrate that in both reduced and oxidised nDsbD the cap loop can close rapidly in the absence of a bound interaction partner.

Comparison between MD simulations and NMR
To validate the MD simulations we used the trajectories to predict 1 H-15 N RDC and S 2 values and to compare these to our experimental values. RDCs provide information about the average orientation of peptide bonds and are therefore well-suited for comparison with MD simulations (Fig. 2C,D). For nDsbD red , the agreement between calculated and experimental RDCs improved (Q = 0.23 for residues 8-125) for the 1 µs MD ensemble compared to the 3PFU X-ray structure (Q = 0.38). For nDsbD ox , agreement also improved (Q = 0.26 for residues 8-122) for the MD ensemble compared to the 1L6P X-ray structure (Q = 0.34).
Thus the simulations provide a better representation of the average backbone conformation in solution because they capture the flexibility of the N-and C-termini, which gave poor agreement when using the static X-ray structures. It is also interesting to note that the RDCs for residues 106 and 108, which gave poor agreement in the fits to the static X-ray structures due to crystal contacts, agree well with the values predicted from the MD simulations.
The extent of the fast-time scale (ps-ns) dynamics observed experimentally by NMR is on the whole correctly reproduced by the MD simulations (Fig. 3). The root mean-square deviation (RMSD) between the order parameters (S 2 ) detemined from model-free analysis and from the simulations is 0.08 for both reduced and oxidised nDsbD. The N-and C-termini were very flexible, but most residues in the folded segments of nDsbD were well ordered with

NMR relaxation dispersion experiments
The 15 N relaxation experiments (ps-ns) and MD simulations (ps-ns and sub µs) described above, which focus on fast motions, showed that the cap loop is rigid and closed in nDsbD red but undergoes more complex dynamics in nDsbD ox . To determine whether the protein also undergoes oxidation-state-dependent motions on the slower µs-ms timescale, we extended our studies using 15 N NMR relaxation dispersion experiments. 1,47 As before, we detected a difference in the behaviour of nDsbD in its reduced and oxidised states. For nDsbD red , no evidence for µs-ms dynamics in the cap loop ( Fig. 5A-C)   five temperatures yielded a detailed description of the thermodynamics and kinetics of the exchange process (Fig. S2B). The minor "excited" state is enthalpically but not entropically more favourable than the major ground state of nDsbD ox . The fits also demonstrated that no enthalphic barrier separates the ground and excited state of nDsbD ox . The absence of an enthalpic barrier between the two states might mean that no favourable interactions have to be broken in the transition state, but that the diffusion process itself may limit the speed of the transition. 63 The relaxation dispersion experiments also provided insight into the differences in struc- N chemical shift differences between the major and minor states do, however, resemble the chemical shift differences between the oxidised and reduced isoforms of nDsbD (Fig. 6C). 30 The conformation adopted by the cap loop in the minor state of nDsbD ox might therefore be similar to the conformation adopted in nDsbD red . However, the correlation in Fig. 6C is not perfect; the differences between the chemical shifts of the minor state of nDsbD ox and those of nDsbD red might reflect the local electronic and steric differences between having a disulfide bond (in the minor state of nDsbD ox ) and two cysteines (in nDsbD red ) in the active site. Importantly, the sign of the chemical shift differences between the major and minor state, which could be determined experimentally for E69, Y71 and K73, further suggested that the minor state structure of the cap loop of nDsbD ox is not disordered (Fig. 6D) but instead may be similar to that adopted in nDsbD red (Fig. 6E).

Coupling between the active site and the cap loop
Both NMR experiments and MD simulations show differences in the dynamics of the cap loop in the oxidised and reduced states of nDsbD. X-ray crystallography and solution NMR show that their respective average structures in these two states are very similar. The only major difference between the two states is the presence of a disulfide bond in the active site of nDsbD ox and a pair of thiol groups in nDsbD red . Therefore, coupling between the active-site cysteines and the cap-loop region that is responsible for the oxidation-state dependence of the cap-loop dynamics must exist.
To understand this coupling, we examined the side-chain conformations of C103/C109 and cap-loop residue F70 in the MD simulations (Fig. 7). The side chains of C103 and C109 both adopt a trans conformation (χ 1 ≈ 180 • ) in the X-ray structure of nDsbD red . This conformation is maintained throughout the MD simulations of nDsbD red with only very rare excursions of χ 1 for one or the other, but never both, cysteines to a gauche-conformation (χ 1 ≈ −60 • ) (Fig. 7C), suggesting that the conformation of the cysteines in the 3PFU X-ray By contrast, F70 can adopt two different conformations in nDsbD ox as revealed by MD and NMR In nDsbD ox , the side chains of C103 and C109 adopt gauche-conformations (χ 1 ≈ −60 • ) in X-ray structures and this conformation is maintained throughout the MD simulations. Only rare excursions of χ 1 for one or the other, but never both, cysteines to a trans conformation (χ 1 ≈ 180 • ) (Fig. 7F) are observed. The C103-C109 disulfide bond in nDsbD ox provides a flat binding surface for the phenyl ring of F70. As a consequence, the aromatic ring of F70 switches between gauche-and trans orientations (Fig. 7E), leading to approximately equal populations of the two orientations (Fig. 7D).  (Fig. 5H). Importantly, the amide peaks for C103 and C109, which are invisible in the wild-type oxidised protein, can be detected for ∆loop-nDsbD ox . 15 N relaxation dispersion profiles for C103 (C98) and C109 (C104) are also flat (Fig. 5I). Thus, truncation of the cap loop alters the µs-ms dynamics of the cap-loop region and the active-site cysteines.

Conclusion
We Importantly, combining NMR experiments and MD simulations, we showed how local frustration 12,13 in nDsbD ox , but not in nDsbD red , gives rise to these differences in the dynamics of the two redox isoforms. Local frustration has been highlighted in the interaction interfaces of many protein complexes. 12 Tables S1 to S4  Supporting Information reference  The transition state appears to be more enthalphically favourable than the ground state. There is, however, a sizeable free energy barrier as the transition state is lower in entropy than the ground state. Note that ΔS ‡ and hence ΔG ‡ depend on the transmission coefficient κ that is used in eqn. 1.     106.2 * 106/108 were excluded due to crystal contacts in the X-ray structures which may distort conformation leading to poor fits; core means α1, β-sandwich and tight turn(s); active site means α2, β-strands but not loop (69-71). 7