NMR Dynamics of PSE-4 β-Lactamase: An Interplay of ps-ns Order and μs-ms Motions in the Active Site

Abstract

The backbone dynamics for the 29.5 kDa class A β-lactamase PSE-4 is presented. This solution NMR study was performed using multiple field ¹⁵N spin relaxation and amide exchange data in the EX2 regime. Analysis was carried out with the relax program and includes the Lipari-Szabo model-free approach. Showing similarity to the homologous enzyme TEM-1, PSE-4 is very rigid on the ps-ns timescale, although slower μs-ms motions are present for several residues; this is especially true near the active site. However, significant dynamics differences exist between the two homologs for several important residues. Moreover, our data support the presence of a motion of the Ω loop first detected using molecular dynamics simulations on TEM-1. Thus, class A β-lactamases appear to be a class of highly ordered proteins on the ps-ns timescale despite their efficient catalytic activity and high plasticity toward several different β-lactam antibiotics. Most importantly, catalytically relevant μs-ms motions are present in the active site, suggesting an important role in catalysis.

Introduction

The main resistance mechanism against penicillin-derived molecules (the β-lactams) is the production of enzymes, the β-lactamases, able to cleave the four-membered β-lactam ring (1). Enzymes from class A are the most often found (2), representing a diverse class of proteins in terms of substrate specificity. Moreover, these 30 kDa enzymes are highly effective catalysts, some with a diffusion-controlled specific activity (3).

Class A β-lactamases general mechanism is composed of two steps akin to that of serine proteinases (4). First, catalytic Ser⁷⁰ makes a nucleophilic attack on the carbonyl of the β-lactam ring. This leads to the hydrolysis of the β-lactam ring after acylation to the protein (1). The process is similar when β-lactam antibiotics inactivate their target, ending up in an inactive acyl-enzyme complex that stops bacterial cell growth and leads to cell death. The second step, a deacylation, which is virtually absent for DD-transpeptidases, consists of a nucleophilic attack by a H₂O molecule activated by the conserved residue Glu¹⁶⁶, part of the Ω loop (Arg¹⁶¹ to Asp¹⁷⁹) (1). This leads to the hydrolysis of the acyl-enzyme complex and release of the hydrolyzed β-lactam.

To attack the β-lactam ring, the catalytic Ser⁷⁰ must have its hydroxyl proton accepted by a general base. The identity of this activator is, however, controversial. One hypothesis involves Lys⁷³ as the general base whereas another involves Glu¹⁶⁶ (1). Other studies proposed the involvement of Ser¹³⁰ (5). A new model has emerged recently in which a duality of mechanisms was shown for tetrahedral formation (6), meaning that the activation process could depend on the β-lactamase/β-lactam combination. A deeper understanding of the structure/function relationship in β-lactamases may help in validating and reinforcing this hypothesis. More specifically, the knowledge of the motions arising in these proteins, especially near the active site, should provide a better mechanistic understanding and complement structural data. Several molecular dynamics (MD) studies have been performed to get insights into the function/structure/dynamics link of class A β-lactamases. These studies have focused on TEM-1.

NMR is a powerful tool for the study of protein dynamics. It allows atom-specific data to be gathered for movements as fast as side-chain rotations or hydrogen-bond formation, and as slow as protein folding. Studying movements of N-H bonds provides a specific probe for almost all residues. ¹⁵N spin relaxation rates depend mainly on the N-H bond reorientations with respect to the external magnetic field as a function of time (7), allowing the study of the information-rich ps-ns and μs-ms timescales. It is known that motions arising on the ps-ns timescale influence the thermodynamics of ligand binding, as well as the kinetics of catalyzed reactions (8). Moreover, motions on the μs-ms timescale are directly linked to enzyme catalysis (9).

As of today, only one class A β-lactamase, TEM-1, has had its backbone dynamics characterized by NMR. TEM-1 is the model enzyme for traditional class A β-lactamases. Savard and Gagné (10) demonstrated that TEM-1 is a very rigid protein on the ps-ns timescale. This rigidity is especially important near the active site, presuming that substrate binding should not trigger any important unfavorable loss in conformational entropy. In addition, μs-ms motions were observed around the active site and Ω loop. Further insights into TEM-1 dynamics were obtained by a study on the comparative dynamics of the wild-type enzyme with the mutant Tyr¹⁰⁵Asp (11). It was shown that this single point mutation could have long-range effects on the dynamics of the protein.

Here, we add to these two studies by presenting the backbone dynamics of the carbenicillin hydrolyzing class A β-lactamase PSE-4 as obtained by NMR. PSE-4 enzyme was originally found in Pseudomonas aeruginosa (12), an opportunistic pathogen, but was soon found in nonpseudomonal strains (13). It is the model enzyme for the subclass of carbenicillin hydrolyzing class A β-lactamases. The crystal structure of this 271-residue protein (29.5 kDa) was determined previously (14). Besides PSE-4 having a high sequence identity with TEM-1 (41.5%), its structure (composed of two domains: an all α- and an α/β domain) is also very close to that of TEM-1 with a backbone RMSD of 1.3 Å.

We supply data on PSE-4 dynamics from amide exchange as well as ¹⁵N spin relaxation data analyzed using the Lipari-Szabo model-free approach (15,16). Additionally, the assessment of data sets consistency, a prerequisite for multiple field data analysis, is discussed in the context of the data presented in this work.

Methods

NMR data acquisition

¹⁵N-labeled PSE-4 was produced as described previously (17). NMR samples were as follows: 0.5 mM PSE-4, 10% D₂O, 3 mM imidazole, and 0.1% sodium azide at pH 6.65. Chemical shift referencing was performed externally using a sample of 0.4 mM 2,2-dimethyl-2-silapentane-5-sulfonic acid (DSS) in 10% D₂O. Spectra were acquired at a temperature of 31.5°C (calibrated using MeOH) on a Varian INOVA 600 (in-house), and Varian INOVA 500 and 800 (Québec/Eastern Canada High Field NMR Facility, Montréal, Canada) spectrometers (corresponding to 60.8, 50.6, and 81.0 MHz nitrogen frequency, respectively) equipped with z axis, pulsed-field gradient, triple-resonance cold probes (except for amide exchange data at pH 7.85, which was acquired using a room temperature probe).

Measurement of longitudinal (R₁) and transversal (R₂) relaxation rates as well as the steady-state heteronuclear nuclear Overhauser effect (NOE) proceeded with established pulse sequences (18,19). Details are available in the Supporting Material. For both R₁ and R₂ experiments, acquisition of relaxation data was made in an interleaved manner to prevent the effects of field and sample inhomogeneity as a function of time (20). NOEs were made in duplicate at 50.6 MHz. At 60.8 MHz, R₁ experiments were made in quadruplicate, R₂, in quintuplicate, and NOE, in triplicate, with some experiments recorded before and others after the recording of data at 50.6 and 81.0 MHz. This ensured that the sample was in the same state throughout the complete experimental scheme.

Amide exchange experiments proceeded from TROSY-HSQC spectra (BioPack, Varian, Palo Alto, CA) of lyophilized PSE-4 dissolved in D₂O. The TROSY implementation allowed smaller phase cycling so very short spectra could be acquired with limited baseline distortions. At the beginning, more frequent short spectra (with a low number of transients) were acquired, and at the end, fewer long spectra (with increasing transients) were acquired. To determine the exchange regime, amide exchange experiments were performed for 80 days at pH 6.65, and for six days at pH 7.85. In both situations, 60 spectra were recorded. Details can be found in the Supporting Material.

NMR data processing

NMR data were processed using the program NMRPipe (21). Details are available in the Supporting Material. Peak deconvolution proceeded using the macro nlinLS invoked from the script autoFit.tcl, both distributed within NMRPipe (21). R₁ and R₂, as well as amide exchange rates, were obtained with the program CURVEFIT (A. G. Palmer, Columbia University, New York, NY). Errors on these fits were obtained from either 500 Monte Carlo simulations or the Jackknife method, using the method that yielded the largest error. A correction was introduced for systematic errors not accounted for when a near-perfect fit was obtained from the R₁ and R₂ exponential curve-fitting. This was done only for model-free analysis where too small errors on experimental data can introduce overcomplex models. Thus, parameters with unrealistically small errors (smaller than the mean value) had their error scaled to the mean value. This is similar to what was done in Savard and Gagné (10). Finally, NOEs were calculated as the ratio of peak amplitude with and without proton saturation, and error propagation calculated from the noise.

Consistency test

Consistency between data sets acquired at different magnetic fields was assessed with the use of reduced spectral density mapping (22) within the program relax (Ver. 1.2.14) (23,24). The test consisted of calculating the field-independent function J(0) for each residue and then comparing results obtained at different fields. For these calculations, the ¹⁵N chemical shift anisotropy (CSA) was −172 ppm, and the vibrationally averaged effective N-H bond length (r_N–H) was 1.02 Å.

Model-free analysis

Model-free analysis of relaxation data was performed using the program relax (Ver. 1.2.14) (23,24) with a variant of the methodology for the dual optimization of the model-free parameters and the global diffusion tensor proposed recently (24) (see Fig. S4 in the Supporting Material). To avoid any artifact (resulting from under- or overfitting), only residues for which data were available at the three magnetic fields were analyzed. N-H vectors orientations were extracted from PDB 1G68 (14). Values for the CSA and r_N–H were the same as for the consistency test. This is as in Savard and Gagné (10), for comparison purposes with dynamics of the homologous protein TEM-1.

Five different diffusion tensors were tested (no global diffusion tensor with a local τ_m parameter for each residue, sphere, prolate spheroid, oblate spheroid, and ellipsoid). These were optimized using residues from well-defined secondary structures (determined using DSSP (25), see Table S3 in the Supporting Material) and selected by Akaike information criterion (AIC) (26). Selection of local model-free models (described in the Supporting Material) during iterations for diffusion tensor optimization was also done using AIC. This allowed the selection of complex models for residues difficult to fit, avoiding the diffusion tensor from being biased by those residues. After convergence of the different diffusion tensors and selection of that with the lowest AIC, local model-free models were minimized for all residues using this diffusion tensor, which was then held fixed. Then, the best model for each residue was selected using the small sample size-corrected (AIC_c) (27). This was done to minimize overfitting which could lead to overinterpretation of relaxation data. Finally, errors on the extracted local parameters were obtained by performing 500 Monte Carlo simulations. A flowchart of the model-free protocol used in this study is available in Fig. S4.

Sequence numbering

Using the Ambler numbering scheme (28), mature PSE-4 starts at residue 22 and ends, after 271 residues and three gaps (positions 58, 239, and 253), at residue 295.

Results and Discussion

Chemical shift referencing was done externally because DSS interacts weakly with PSE-4 (data not shown). In addition, samples did not contain any proteinase inhibitor cocktail because we also observed that some inhibitors bind to the active site (data not shown). Finally, no buffer was used because NMR data indicate that the phosphate buffer interacts weakly with TEM-1's active site (P.-Y. Savard and S. Gagné, personal communication, 2006), despite its ubiquitous use in many kinetics studies of β-lactamases. Therefore, samples were prepared to minimize any unwanted interaction that could bias our study because relaxation experiments are extremely sensitive.

As for the homologous TEM-1 (10), spectra were of very high quality despite PSE-4 molecular weight (Fig. S1). Backbone resonance assignments for PSE-4 (BMRB No. 6838) (17) allowed for the extraction of atom-specific data. Hence, no information could be extracted for residues Ser²², Ser²³, Ser²⁴, Ser⁷⁰, and Ala²³⁷ for which assignments are unavailable; Ser²², Ser²³, and Ser²⁴, probably because of fast solvent exchange; and Ser⁷⁰ and Ala²³⁷, certainly because of very broad and/or highly overlapped resonances. In addition, residues that overlapped severely were excluded from further analysis (see Table S2, Table S3, and Table S4). Hence, a total of 230 residues were characterized with data at the three magnetic fields (N = 231 at 50.6 MHz, 232 at 60.8 MHz, and 238 at 81.0 MHz).

¹⁵N spin relaxation data

¹⁵N spin relaxation data consisted of three sets of experiments: ¹⁵N-R₁, ¹⁵N-R₂, and {¹H}¹⁵N - NOE. Data at more than one magnetic field being required for overdetermination of model-free parameters, we acquired data at 11.7, 14.1, and 18.8 T (respectively, 50.6, 60.8, and 81.0 MHz nitrogen frequency). To confirm that the sample did not change during the experimental scheme, we recorded one set of NOE, three complete sets of R₁, and two complete sets of R₂ at 60.8 MHz before recording data at 50.6 and 81.0 MHz. After data acquisition at 50.6 and 81.0 MHz, we recorded two sets of NOE, one complete set of R₁, and three complete sets of R₂ again at 60.8 MHz. Moreover, it allowed us to verify that error on spin relaxation data was neither under- nor overestimated using Jackknife and Monte Carlo methods (data not shown). For example, the four different R₁ data sets recorded at 60.8 MHz gave rates that, within estimated errors, were reproducible for most residues. Mean relative errors for these data sets were as follows: 2.77%, 2.91%, 2.77%, and 3.28%. On the other hand, mean error for the combined data sets was 2.47%, reflecting the improvement obtained when using more data points. Data sets recorded at 50.6 and 81.0 MHz were not repeated as for 60.8 MHz (except for NOE at 50.6 MHz), but displayed errors of the same range. Finally, even though R₂ values obtained at 60.8 MHz were extracted from experiments with two different RF fields (5.2 and 6.0 kHz), this difference did not affect rates, which fell within respective errors (data not shown). ¹⁵N spin relaxation data for PSE-4 have been deposited in the Biological Magnetic Resonance Data Bank (BMRB) (6838).

Statistics for the 2103 observables are available in Table S1. Mean errors for the recorded parameters vary between 2 and 4% before scaling (see Methods). Except for the five C-terminal residues, PSE-4 dynamics seems to be quite homogeneous, as is the case for TEM-1 (10). This points to a unique diffusion core for this enzyme.

Data sets consistency

To extract high quality information from multiple field experiments, it is important that data sets share a high degree of consistency. Inconsistencies can arise from several factors, including variations in sample viscosity (caused by changes in temperature, concentration, etc.) and water saturation during acquisition (which influences N-H moieties as a function of the exchange rate with the aqueous solvent). In this study, the field-independent function J(0) (the spectral density at the zero frequency) (22) was used to assess data sets consistency.

Results from this consistency test demonstrate the good quality of the three data sets (Fig. S3). The 50.6 and 60.8 MHz data display especially high consistency, whereas 81.0 MHz consistency with 50.6 and 60.8 MHz data is good. The somehow wider distributions seen for data at 81.0 MHz were assessed further (see model-free analysis, below).

Model-free analysis

The model-free formalism (15,16,23,29) is the preferred approach for spin relaxation data analysis. Using this formalism, two main parameters, S² and τ, account, respectively, for the restriction of the motion for one vector (e.g., the N-H bond) and the effective upper limit for the timescale of this motion (normalized by S²). Moreover, the R_ex parameter can account for slow motions on the μs-ms timescale contributing to the observed R₂. Several programs have been developed for the optimization of the model-free parameters. We used the open source program relax (23,24) with the protocol presented in Fig. S4.

A reanalysis of TEM-1's spin relaxation data (10) using the same approach as the one used here for PSE-4 has been performed recently and will be presented elsewhere. In this study, data were also reanalyzed using the same approach as in Savard and Gagné (10), but with ModelFree-4.20 (30,31) to avoid problems present in the preceding versions of the program (23). In the following discussion, results obtained for PSE-4 will be compared with those for TEM-1 in either publication, especially when differences arise.

Since the consistency test revealed some inconsistency in the 81.0 MHz data, an in-depth look at the data was done. We found out the R₂ data at 81.0 MHz were causing this inconsistency and did not use it for model-free analysis. Because the inconsistency was detected, it does not affect the quality of the extracted information. Details are available in the Supporting Material.

Description of global diffusion

The diffusion of PSE-4 is homogeneous. This is confirmed by the derivation of model-free parameters using a local diffusion tensor for each N-H vector. Indeed, the mean local τ_m is 12.70 ± 0.87 ns (excluding the three C-terminal residues) with only a few dispersed outsiders, thus with no region in the three-dimensional structure showing differential diffusion (data not shown).

Table 1 shows a summary of the optimization results for the different diffusion tensors tested. The best model consists of an ellipsoid described by the isotropic component of diffusion D_iso = 13.141 (± 0.024) × 10⁶ s⁻¹, the anisotropy of diffusion D_a = 3.75 (± 0.19) × 10⁶ s⁻¹, the rhombicity D_r = 0.080 (± 0.022) s⁻¹, the global correlation time τ_m = 12.683 (± 0.024) ns, and the diffusion constants for the three principal diffusion axes D_x = 11.59 (± 0.10) × 10⁶ s⁻¹, D_y = 12.19 (± 0.11) × 10⁶ s⁻¹, and D_z = 15.64 (± 0.13) × 10⁶ s⁻¹. A representation of this diffusion tensor, and of the orientations of the N-H vectors used for its optimization, is available in Fig. S5. These parameters are close to the prolate description of TEM-1 presented in Savard and Gagné (10), where D_‖/D_⊥ was equal to 1.23. Indeed, for PSE-4, D_‖/D_⊥ = D_z/((D_x + D_y)/2) = 1.32. Anisotropy for PSE-4 extracted from the model-free analysis agrees with the shape from the crystal structure (14), the relative moments of inertia being 1.00, 0.89, and 0.59 as determined using the program pdbinertia (A. G. Palmer, Columbia University, New York, NY).

Table 1.

Summary of the diffusion tensor optimization

Diffusion model	AIC	τm (ns)	D‖/D⊥	θ (°)	ϕ (°)	ψ (°)
Local τm	1442.1	—	—	—	—	—
Sphere	1492.2	12.39	1	—	—	—
Prolate spheroid	1391.3	12.67	1.33	147.5	50.1	—
Oblate spheroid	1475.6	12.45	0.92	38.9	27.2	—
Ellipsoid∗	1385.1	12.68	1.32	166.2	146.8	131.6

We used 134 residues in regular secondary structures with relaxation data at three fields.

^∗Lowest AIC: selected description.

Finally, diffusion description from model-free analysis is close to that estimated from hydrodynamics calculations using HYDRONMR (32) (with parameter a, the effective radius of the atomic element, set to 2.6 Å, as in Hall and Fushman (33)). In fact, using this approach, D_a = 3.82 × 10⁶ s⁻¹, i.e., within 2% of model-free derived D_a. Moreover, values of the diffusion constant for the three principal axes of the diffusion were within 4% of the model-free derived values, with D_‖/D_⊥ = 1.30. A similar analysis for TEM-1 is in agreement with PSE-4 having a higher anisotropy than TEM-1 and endorses model-free results for global tumbling.

Description of local motions

Fig. S6 shows the optimized residue-specific model-free parameters. Even though parameters are far more important than model listing, we can summarize PSE-4 local model-free models as follows: m0 (1), m1 (129), m2 (46), m3 (28), m4 (3), m5 (19), m6 (3), m7 (0), m8 (0), and m9 (1), for a total of 230 N-H vectors analyzed. As is seen here, most residues (77%) are fitted with simple models m1 and m2. Local model-free parameters for PSE-4 have been deposited in the BMRB.

Order parameters

The mean order parameter (S²) of PSE-4 backbone amides is 0.861 ± 0.087 (0.868 ± 0.051 excluding the three C-terminal flexible residues). Additionally, the mean S² for the secondary structure core (0.879 ± 0.035) is slightly higher and less dispersed than that for the loops and very short helices (0.834 ± 0.125; 0.852 ± 0.066 excluding the flexible C terminus). Clearly, PSE-4 is a highly ordered protein on the ps-ns timescale, displaying S² > 0.85 (the typical value for regular secondary structures, equivalent to motion on a cone of semiangle θ = 19° (15)) for 70% of its amides (Fig. 1 A). The most rigid amides are located around the active site and Ω loop, as was the case for TEM-1 (10). Only some solvent exposed loops are less rigid, with just five residues (Asn⁵³, Ser²⁹², Gln²⁹³, Ser²⁹⁴, and Arg²⁹⁵) possessing an order parameter below 0.70, indicating the absence of high amplitude backbone motions in PSE-4, similar to previous observations for TEM-1. This high rigidity might be related to the low thermal stability of both TEM-1 and PSE-4, which precipitate in vitro at temperatures >41°C (data not shown).

Figure 1.

Motions extracted from model-free analysis. (A) Backbone amide ps-ns timescale generalized order parameter (S²). (B) Residues fitted using a conformational exchange term (R_ex, model-free models m3, m4, m7, m8, or m9). In all insets, gray cartoon is used for residues without data (prolines, overlapped and unassigned) whereas, in the R_ex inset, white cartoon representation is used for absence of the parameter in the model fitted. Active site residues (Ser⁷⁰, Lys⁷³, Ser¹³⁰, Glu¹⁶⁶, and Arg²³⁴) are shown in the stick representation. Missing residues in the crystal structure (Ser²², Ser²³, Gln²⁹³, Ser²⁹⁴, and Arg²⁹⁵) were added for visualization of their fitted parameters (refer to electronic figure for color representation).

When comparing TEM-1's model-free order parameters with those of PSE-4, TEM-1 appears slightly more rigid than PSE-4 (Fig. S8). Differences seem to be smaller for the Ω loop where order parameters agree more than for other loops, pointing to a conservation of order for this important part of the enzyme. This similarity of backbone dynamics on the ps-ns timescale might hide important differences for side-chain motions, as is the case for calmodulin (34). However, this is beyond the scope of this article.

Conformational exchange

Fig. 1 B shows residues for which a contribution to R₂ from μs-ms motions had to be accounted for. R_ex parameters depend on several factors (timescale of exchange, populations of either states, and chemical shift difference). Conformational exchange can be detected either for a moving N-H moiety or for a rigid vector with a moving neighbor modulating its chemical shift but can be invisible for certain combinations of timescales, populations, and chemical shift changes. R_ex parameters are scaled quadratically with the magnetic field and are presented in this study for an effective magnetic field of 60.8 MHz. Thus, R_ex values for TEM-1 (10) are rescaled from their originally associated field (50.6 MHz) for comparison purposes.

In PSE-4, 32 residues have a nonnull R_ex parameter. Of these, five are particularly important because of both their elevated R_ex parameter and localization on the protein three-dimensional structure. These are residues Thr¹²⁸, Leu²²¹, Arg²³⁴, Ser²³⁵, and Gly²³⁶, which are located 4.5–12.5 Å from the active site. This is consistent with two nearby residues (Ser⁷⁰ and Ala²³⁷) not being observed, probably because of their extreme broadening arising from important μs-ms motions. Since these motions are near the surface of the active site cavity, conformational exchange could arise because of a ligand moving in and out of the cavity. A potential candidate for this motion could be a structural water molecule moving slowly between residues Asn²¹⁴, Arg²³⁴, and Ser²³⁵, as seen in a 5-ns MD simulation of TEM-1 (35). This would point to a conservation of slow motions in the active site for both TEM-1 and PSE-4. The motion of this water molecule would also affect residues Ser⁷⁰ and Ala²³⁷ (extremely broadened), both being on the path which the ligand would take to possibly access residues Asn²¹⁴, Arg²³⁴, and Ser²³⁵. The R_ex for Gly²³⁶ could be explained in the same way. The same is valid for TEM-1, where R_ex parameters arise near the active site and Ala²³⁷ could not be assigned.

Active-site residues

TEM-1's active site has been shown to be extremely ordered on the ps-ns timescale with several residues displaying order parameters >0.94 (10). This was consistent with active site residues displaying lower than average B-factors for TEM-1 in the presence of a sulfate ion in the active site (36). In PSE-4, the most rigid residues on the ps-ns timescale are also located in the active site, pointing to a meaningful conservation of this feature which could also be foreseen from backbone amide B-factors (14) (Fig. S7).

Ser⁷⁰: N-H correlation for Ser⁷⁰ is not observed. In TEM-1, it is severely overlapped and broadened, thus unusable. This strongly supports the existence of motions on timescales slower than global tumbling (e.g., μs-ms) also affecting other residues in the vicinity that display broadened backbone (Ala237) or side-chain (Lys⁷³) resonances.

Lys⁷³: Lys⁷³ is suspected of being involved in the first catalytic step (acylation), where its side-chain N_ζ group could activate Ser⁷⁰ by accepting a proton from the side-chain hydroxyl group (2.8 Å away) (1). Lys⁷³ was fitted to model m1 with one of the highest order parameters throughout PSE-4 (0.94 ± 0.01). This contrasts with the low intensity of its N-H cross-peak, which suggests that chemical exchange broadening may be present. Indeed, Lys⁷³'s C_α is the weakest of all lysine C_α (data not shown). Moreover, we were unable to see Lys⁷³'s side chain further than the C_β, thus preventing the titration of the side-chain N_ζ group. These, again, indicate important μs-ms motions nearby. These motions could be similar to those presumably affecting Ser⁷⁰, located <6 Å away (N-H to N-H). If rejecting model m1 because of these evidences of slow motions arising nearby, the second lowest size-corrected AIC score for Lys⁷³ within PSE-4 is model m3 with an R_ex parameter of 0.7 ± 0.5 s⁻¹. Compared with the R_ex parameters for other residues, this R_ex would be the lowest and the one with the highest relative error. Hence, the possibility for Lys⁷³ N-H to be fitted using an R_ex parameter is questionable, although strong signs of conformational exchange are present, especially for the side chain. The situation in TEM-1 was very similar, and Lys⁷³ fitted model m1 with a S² of 0.95 ± 0.02. These data indicate Lys⁷³'s side chain could be affected by motions in the slow- or intermediate-exchange regime. Under certain conditions, R_ex does not scale quadratically with the magnetic field (37). This could explain the low R_ex with high error obtained for Lys⁷³ when using model m3, where the model-free fitting procedure scales the R_ex quadratically for multiple field data. Incorporating the parameter α from Millet et al. (37) in the fitting procedure could potentially alleviate this problem. Finally, if present, these motions could explain the extreme broadening of Lys⁷³'s side chain, as well as Ser⁷⁰ and Ala²³⁷ amides. Such very slow motions will, in the future, be probed by relaxation dispersion experiments.

Tyr¹⁰⁵: Tyr¹⁰⁵ displays a correlation time of 1008 ± 188 ps in conjunction with an S² of 0.80 ± 0.02 using the two-timescale model m5. In TEM-1, this residue was one of the most flexible (10) and the selected model did not incorporate this kind of two-timescale motion as in PSE-4. This could be of significant importance in regard to substrate recognition and specificity. The motion detected here could, however, be artefactual because model m2 also fits relatively well the experimental data: with a higher S² (0.85 ± 0.01), but with a correlation time of 26 ± 4 ps, similar to the case in TEM-1. On the other hand, model m5 could suit data almost as well in TEM-1, yielding a similar S² (0.79) but with a τ_s of ∼500 ps.

In another work, Doucet et al. (38) discussed the importance of this residue for substrate specificity and proposed that steric restriction of the active site by residue Tyr¹⁰⁵ side chain could allow the correct positioning and stabilization of substrates within the active site, thus facilitating catalysis. This gate-keeping function was further investigated and the side chain of Tyr¹⁰⁵ was shown to adopt two conformations: one in which the side chain points toward Val²¹⁶ (open state, rotamer t) and one in which the side chain points toward Glu¹⁰⁴ (closed state, rotamer m, only visible in inhibitor-bound TEM-1) (39). This motion seen for TEM-1 could influence the dynamics of the backbone N-H moiety of Tyr¹⁰⁵ in PSE-4 where rotamer t is present, with only minor electronic density toward the position of rotamer m. Using SHIFTS (Ver. 4.1.1) (40), chemical shifts for the two rotamers discussed in Doucet et al. (38) were predicted. Based on these results, only two residues would have their backbone ¹⁵N chemical shift modified by such a transition between the two rotamers t and m. Of course, Tyr¹⁰⁵ amide nitrogen has a different chemical shift in both rotamers, although the difference is very small (12 Hz at 60.8 MHz) and would not give rise to a significant R_ex. Ser¹⁰⁶ would be more affected with a difference in ¹⁵N chemical shift of 286 Hz at 60.8 MHz between the two rotamers. This would be expected to give rise to an R_ex term, although no such parameter was observed in the model-free minimization. A possible explanation for this situation is that the timescale for this conversion from rotamer t to rotamer m would be on the subnanosecond timescale as proposed by the selected model for Tyr¹⁰⁵. If so, it would not influence transverse relaxation of Ser¹⁰⁶ and would only be probed by Tyr¹⁰⁵ itself.

Ser¹³⁰: Residue Ser¹³⁰ has been proposed to participate in the catalytic process (5) and was shown to be of clinical importance for enhanced resistance (41). In the crystal structure by Lim et al. (14), the hydroxyl group of Ser¹³⁰ displays two alternative positions. Such alternative positions with a shared occupancy of 0.5 between two conformations are seen for eight other residues in the crystal structure (14). From model-free analysis, Ser¹³⁰ fits model m1 (as other residues we could observe with atoms displaying shared occupancy of 0.5) with an S² of 0.95 ± 0.02. The movement of its side chain might not influence the amide transversal relaxation of Ser¹³⁰, but, depending on the timescale, could be the cause of such conformational exchange effects seen for nearby residues Ser⁷⁰ (not observed, broadened), Thr¹²⁸, Arg²³⁴, Ser²³⁵, Gly²³⁶, and Ala²³⁷ (not observed, broadened), all within 5 to 8 Å from the side chain of Ser¹³⁰. In TEM-1, no model-free parameter could be extracted (10). As for Lys⁷³, Ser¹³⁰ order parameter in PSE-4 is very high. This is also the case for other residues of the conserved Ser¹³⁰-Asp¹³¹-Asn¹³² (0.95 ± 0.02, 0.92 ± 0.01, and 0.97 ± 0.01, respectively) structural motif (known as the SDN loop).

Glu¹⁶⁶: Residue Glu¹⁶⁶ is directly involved in catalysis, probably for both acylation and deacylation steps (1). As was the case for the two catalytic residues Lys⁷³ and Ser¹³⁰, residue Glu¹⁶⁶ fits model m1 with a fairly high order parameter (0.91 ± 0.02). In the reanalysis using ModelFree-4.20 for TEM-1, Glu¹⁶⁶ fitted model m1 with S² = 0.94 ± 0.02, in contrast with model m4 in the original work (10). Using relax, this residue was assigned model m2 with S² = 0.93 ± 0.02 and τ_e = 47 ± 24 ps. This is not surprising, as the R_ex first detected was of low significance and, thus, m4 could simplify to m1 or m2. Rigidity for Glu¹⁶⁶ thus seems similar in TEM-1, although a bit higher as for many other residues.

Arg²³⁴: In carbenicillin-hydrolyzing β-lactamases such as PSE-4, residue 234 is an arginine. In other class-A β-lactamases, it is a lysine. Arg²³⁴ first fitted model m2 with an average S² of 0.88 ± 0.02. However, the value measured for R₂ at 50.6 MHz is most likely underestimated and erroneous, because of the partial overlap with residue Lys¹⁹², a result of the poorer resolution at the lower field. Indeed, Arg²³⁴ has one of the highest R₂ values at both 60.8 and 81.0 MHz, whereas at 50.6 MHz the measured R₂ is much lower than for surrounding residues. Hence, when excluding R₂ at 50.6 MHz, the selected model becomes m3 with an unchanged order parameter of 0.88 and an R_ex parameter of 4.2 ± 1.6 s⁻¹. This is much more logical for this residue, because the majority of surrounding residues display signs of conformational exchange. Moreover, for TEM-1, presence of R_ex was also found using either ModelFree-4.20 or relax, both with an R_ex of 1.9 ± 0.4 s⁻¹ and a high S² of 0.94 ± 0.02. Thus, order on the ps-ns timescale would be higher in TEM-1, but the presence of slow μs-ms motions would be similar, again indicating the presence of conserved μs-ms motions near the active site.

Ω loop: A 19-residue loop is located below the active site of class-A β-lactamases (residues Arg¹⁶¹ to Asp¹⁷⁹). This loop is an Ω loop, a nonregular secondary structure found in many proteins (42). It was shown in two different studies to be flexible in TEM-1 using in silico approaches (35,43). Indeed, in a 5-ns simulation (35), a flaplike motion of the Ω loop was present for TEM-1 in the absence of a ligand. The timescale was undefined in this study because this phenomenon was only seen once, the loop keeping its new position after the movement had happened. No such motion had been seen in the 1-ns simulation by Díaz et al. (44); these inconsistencies could either be a result of the short simulation length in the Díaz et al. (44) study or of simulation artifacts in the study of Roccatano et al. (35). Nevertheless, in TEM-1, using NMR, the Ω loop was shown to be very rigid on the ps-ns timescale, although displaying the presence of some μs-ms motions (10). This seems to unite short simulations results showing limited motions with longer simulations pointing to slow high-amplitude motions. Indeed, movements on the order of the μs-ms timescale are hardly defined using currently available MD simulations.

Our results for PSE-4 confirm this observation, although differently from what was seen in TEM-1 using NMR. In fact, only two residues within PSE-4 Ω loop display signs of conformational exchange (i.e., Arg¹⁶¹ and Arg¹⁷⁸). These residues are located at the extremities of the Ω loop, where it narrows (with N-H moieties separated by ∼8 Å). Arg¹⁷⁸ could represent the hinge of a movement similar to that stated above, which could allow Gly¹⁷⁵ (Asn¹⁷⁵ in TEM-1) to reach Arg⁶⁵ to form the hydrogen bond discussed by Roccatano et al. (35) (Fig. 2). This would correspond to a movement of ∼5 Å, Arg⁶⁵ carbonyl being 7.1 Å from Gly¹⁷⁵ amide nitrogen in the steady-state crystal structure. This motion would fill the cavity between the Ω loop and the protein core present in both TEM-1 and PSE-4 (Fig. 2 D). With this cavity closed, the structure would be better packed, possibly transiently stabilizing Glu¹⁶⁶ in a catalytically relevant position. The absence of R_ex for residues Asp¹⁷⁶ and Leu¹⁷⁷ does not counterindicate this possibility, as the N-H moiety of Leu¹⁷⁷ would point toward the solvent in both conformations and hydrogen bonding of Asp¹⁷⁶ N-H group with the carbonyl of residue Lys¹⁷³ would also be present in both conformations. Unfortunately, because of overlapped resonances, no spin relaxation data are available for residues Lys¹⁷³ and Leu¹⁷⁴, which could sense this movement because they are closer to the protein core. However, these residues both display normal amplitude N, H^N, C_α, and C_β resonances, which could contradict their involvement into conformational exchange. Hence, current observations support the slow motion of the Ω loop proposed by Roccatano et al. (35). Because of the implications of movements of the Ω loop in terms of catalysis, it will be very important to get more insights into this part of the enzyme. In fact, if a movement such as the one discussed above exists, it would allow Glu¹⁶⁶ to stay close to Ser⁷⁰ and potentially act during the acylation step (35).

Figure 2.

Cavity-filling motion for residues Glu¹⁷¹-Leu¹⁷⁷ of the Ω loop. (A) Order parameters (S² colored as in Fig. 1A). (B) Conformational exchange (R_ex colored as in Fig. 1B). (C) Apparent free energies of exchange (ΔG_HX, colored as in Fig. 3). (D) The cavity between the Ω loop and the protein core that the motion of residues Glu¹⁷¹-Leu¹⁷⁷ (yellow) would fill is shown in gray surface. Residues from the hinge (Arg¹⁶¹ and Arg¹⁷⁸) are colored red and shown in the stick representation as well as residues Arg⁶⁵ and Gly¹⁷⁵ (orange), which would form a hydrogen bond once the motion (black arrow) is completed. Catalytic Glu¹⁶⁶ is also shown in the stick representation. A stereo version is available in the Supporting Material.

Limits in the analytical approach

Many factors limit interpretation of results extracted using the model-free approach (23,24). Here, we will concentrate on three specific limitations: variations of the CSA and r_N–H for different N-H moieties, and lack of well-defined N-H vector orientations in crystal structures. In this study, the CSA was held fixed with a value of −172 ppm. This allowed comparison with dynamics data for TEM-1 (10). As for the CSA, r_N–H was held fixed with a value of 1.02 Å, which allowed comparison with dynamics data for TEM-1 (10). Further discussion on CSA and r_N–H is available in the Supporting Material. Crystal structure 1G68 (14) has a 1.95 Å resolution, which does not allow the visualization of protons. Hence, derived N-H vector orientations may be erroneous from their actual average position, potentially having an effect on the model-free models selected because goodness of fit depends on N-H vector orientation compared to the diffusion tensor orientation. Moreover, for residues potentially involved in crystal contacts, orientations might be slightly off, which could also bias model-free analysis. This situation could be assessed by allowing variation of N-H bond orientations during model-free minimization. However, we chose not to introduce such variable into our analysis.

Amide exchange

Steady-state amide exchange experiments allow the study of higher energy states, difficult to detect with techniques reporting on ensembles. They can probe the presence of partially unfolded states, intermediates of which could be of importance for catalysis. Two limit cases for amide exchange exists: EX1 and EX2 (45). In the EX2 regime, insights into the thermodynamics of the opening reaction for the structure protecting the N-H group from exchange (transient unfolding processes) can be obtained. The equilibrium constant of exchanging sites K_op = 1/SF = k_open/k_close, where SF is the protection factor, and k_open and k_close the opening and closing rates, respectively, is calculated from K_op = k_ex/k_c, where k_ex is the exchange rate, and k_c is the expected unprotected exchange rate (intrinsic rate) (46,47). Moreover, the apparent stabilization free energy of the protecting structure is obtained from ΔG_HX = – RT ln K_op.

In the EX2 regime, exchange rates are pH-dependent, whereas in the EX1 limit, they are not affected by pH. Exchange was faster at pH 7.85 for all residues for which data were available, hence confirming the EX2 regime at pH 6.65 (see Table S4 and Fig. S9). A change of pH from 6.65 to 7.85 would theoretically cause effective rates to increase by a factor of 16. The mean increase of k_ex, in our case, was of 11 ± 7 (not including amides exchanging too fast to be observed at pH 7.85). This lower value could be a result of some amides entering the EX1 regime at a pH slightly below 7.85. Of the 226 residues with available data at pH 6.65, 101 exchanged very rapidly and were already unobservable in the first time point (i.e., after only 32 min, with k_ex > 1 × 10⁻³ s⁻¹). Therefore, 125 residues had a measurable exchange rate ranging from 2 × 10⁻³ s⁻¹ to 3 × 10⁻⁸ s⁻¹. ΔG_HX, as well as K_op and SF, were calculated using an Excel spreadsheet from S. W. Englander (University of Pennsylvania, Philadelphia, PA) and are displayed in Table S4. Moreover, ΔG_HX values are shown in Fig. 3. These data have been deposited in the BMRB (6838).

Figure 3.

Apparent stabilization free energies of the protecting structures (ΔG_HX). The value k_ex is shown for residues for which exchange was too fast for being quantified (k_ex > 1 × 10⁻³ s⁻¹). Important active site residues (Ser⁷⁰, Lys⁷³, Ser¹³⁰, Glu¹⁶⁶, and Arg²³⁴) and the disulfide bond (between Cys⁷⁷ and Cys¹²³, connecting two helices of the α-domain) are shown in the stick representation. Missing residues in the crystal structure (Ser²², Ser²³, Gln²⁹³, Ser²⁹⁴, and Arg²⁹⁵) were added for visualization of their parameters.

Globally, free energies of opening are ∼6–11 kcal mol⁻¹ for most residues within secondary structures, and are slightly higher in the α/β domain where many residues have ΔG_HX > 8 kcal mol⁻¹. Hence, this domain is more stable than the all α-domain. This is contrary to what was proposed for TEM-1 (10), that the α-domain might be the most stable. This hypothesis was speculative, as no amide exchange rate had been extracted, nor verification of EX2 regime done. For TEM-1, the slowest exchanging amides were those from the all α-domain and the authors concluded that this domain is more stable than the α/β domain because of the presence of the disulfide bond between Cys⁷⁷ and Cys¹²³, as proposed by Vanhove et al. (48). Here, we postulate the contrary for PSE-4 based on EX2 exchange data. In PSE-4, though the disulfide bond between Cys⁷⁷ and Cys¹²³ stabilizes the local structure (surrounding residues with ΔG_HX between 4 and 8 kcal mol⁻¹), the protection from the solvent in the α-domain is globally lower than in the α/β domain. One might argue that the disulfide bond in the PSE-4 sample is not formed. However, this is ruled out by C_β chemical shifts (49) for Cys⁷⁷ (41.6 ppm) and Cys¹²³ (42.0 ppm) (17), which show that both Cys are oxidized. The most stable domain in PSE-4 is the α/β domain, whereas it could be the α-domain in TEM-1. Indeed, theoretical free energy of folding calculated using VADAR (50) shows that the all α-domain in TEM-1 would be more stable than in PSE-4, whereas the inverse is predicted for the α/β domain (data not shown). These could indicate some thermodynamics differences between the two domains of these homologs. However, to confirm this hypothesis, analysis of data in the EX2 regime is required for TEM-1.

As expected, the first protons to exchange with the solvent were those within loops as well as most key residues from the active site (Fig. 3). Moreover, all glutamine and asparagine side chains were exchanged rapidly. These N-H moieties being all located at or near the protein surface, their exchange is too fast for steady-state exchange experiments and would require approaches such as pulse labeling (45). It is interesting to note that all residues from the Ile⁹⁷ to Gln¹¹⁵ region exchange fast, as well as residues Asn¹³² to Ile¹³⁷ from the adjacent α-helix. This region of PSE-4 could have a nonnegligible population existing as a partially unfolded state (probably with ΔG_HX < 4 kcal mol⁻¹, k_ex values all being >1 × 10⁻³ s⁻¹, despite 17 amides out of 24 having null ASA, as calculated using VADAR (50)). Indeed, ΔG_HX below 4 kcal mol⁻¹ would correspond to populations of partially unfolded states for >0.1%. Thus, the subdomain formed by residues Ile⁹⁷ to Gln¹¹⁵ and Asn¹³² to Ile¹³⁷ could be the driving force for the lower stability of the close by α-domain. Hence, local unfolding could arise near the active site, including residue Tyr¹⁰⁵, for which motions were discussed above. These local unfolding events, from both their population and their possible timescale and location could have a profound impact on PSE-4 catalysis and might be the cause of some of the observed R_ex.

The fact that the amide of Glu¹⁶⁶ and a few other amides from the Ω loop are protected from exchange with ΔG_HX between 6 and 8 kcal mol⁻¹ points toward some motional restriction of this long loop, preventing the disruption of the network of hydrogen bonds and the exposure of amide moieties to solvent. This argues against μs-ms motions proposed for TEM-1 in Savard and Gagné (10), where residues Arg¹⁶⁴, Glu^166, and Leu¹⁶⁹ possessed a R_ex parameter, these three residues displaying ΔG_HX of 7.3, 7.6, and 6.1 kcal mol⁻¹, respectively, within PSE-4. However, this is in agreement with the motion proposed by Roccatano et al. (35) and discussed in the model-free analysis, above, where residues Glu¹⁷¹-Leu¹⁷⁷ (with k_ex > 1 × 10⁻³ s⁻¹) could move toward the protein core without affecting residues Arg¹⁶¹-Glu¹⁷⁰ (with mean ΔG_HX ∼6.7 kcal mol⁻¹), as shown in Fig. 2. Indeed, this motion could transiently position the Ω loop so Glu¹⁶⁶ is in the vicinity of Ser⁷⁰ (35). Moreover, the loop could be protected against complete hydration. In fact, as stated before, at the location where residues Glu¹⁷¹-Leu¹⁷⁷ are proposed to translate by this motion, a cavity is present (Fig. 2 D). This available space would be filled in the closed state. The same cavity being also present in TEM-1, the conservation of this motion among class A β-lactamases is plausible, in agreement with observations from Roccatano et al. (35), as well as with recent simulations of both TEM-1 and PSE-4 which show motions of a different nature for the Ω loop, also consistent with our experimental data (O. Fisette and S. Gagné, personal communication, 2008). Finally, the fact that this motion was only seen once during the 5-ns simulation is consistent with a much slower effective timescale, as suggested by R_ex parameters extracted from model-free analysis.

Finally, during model-free analysis, Ser²³⁵ and Gly²³⁶, which both exchange with rates faster than 1 × 10⁻³ s⁻¹, were fitted with high R_ex parameters (7.5 and 4.5 s⁻¹, respectively). These data, in addition to null ASA for these amides, support the presence of μs-ms motions near the active site, potentially severely broadening amide cross-peaks of residues Ser⁷⁰ and Ala²³⁷, as discussed before. Once again, these motions might be important for catalysis since k_cat for hydrolysis of β-lactams by β-lactamases is ∼1 ms⁻¹.

Conclusions

This work is the first NMR characterization, to our knowledge, of the dynamics of a class A carbenicillin hydrolyzing β-lactamase. It follows the study of Savard and Gagné (10), which explored the dynamics of another class A β-lactamase, TEM-1.

Linking results from the different techniques used here to PSE-4 catalytic activity is not straightforward (51). The global picture of PSE-4 depicted in this report shows a very rigid protein on several timescales. Indeed, ps-ns timescale order parameters are elevated, almost as much as in the case of the homologous TEM-1. Moreover, overall stability is also quite elevated, with apparent free energies of opening (from amide exchange experiments) reaching 11 kcal mol⁻¹ for several residues in the β-sheet of the α/β domain. These results contrast with the low thermal stability of both TEM-1 and PSE-4 and with the presence of slow μs-ms motions.

Rigidity on the ps-ns timescale could be a characteristic of all class A β-lactamases. As stated before, the catalytic efficiency of some of the class A β-lactamases is diffusion controlled (3). This high efficiency supplemented by a high plasticity toward different types of β-lactams contrasts with the restricted motions in the catalytic site, at least on the ps-ns timescale. Longer timescales might be populated by important conserved motions as shown for many active site residues displaying conformational exchange terms (R_ex) reporting on the μs-ms timescale, the timescale of enzyme catalysis (e.g., PSE-4's k_cat against ampicillin and carbenicillin is ∼1.2 ms⁻¹ (52)). Moreover, the absence of detectable high amplitude motions on the faster timescales might show that the active site of class A β-lactamases adapts its shape on substrate approach, thus pointing to motions present during some steps of the catalytic process. To further understand this feature, it will be interesting to get insights into those longer timescales and to study dynamics of TEM-1 and PSE-4 mutants. Moreover, it will be critical to obtain data regarding dynamics during catalysis (see below).

We are aware that backbone dynamics can be decoupled from side-chain motions (34). The apparent lack of motions seen for backbone N-H moieties on the ps-ns timescale could be coupled to important side-chain motions on the same timescale. In addition, the apparent dynamics similarity between TEM-1 and PSE-4 might also prove limited to backbone amides with side chains potentially displaying different motional patterns. Hence, a side-chain dynamics study might prove very insightful. Moreover, we are mindful about the lack of data for a bound form of PSE-4 either with a β-lactam or an inhibitor. However, as highlighted by Savard and Gagné (10), this proves to be very difficult, considering the high catalytic efficiency of these enzymes. Finally, we are aware that conformational exchange indications showed here are qualitative and extracted from the transversal relaxation rates variations over a restricted range of magnetic field strengths. Hence, the μs-ms timescale will be an interesting target for further studies to better quantify the slow motions detected here, especially for what concerns motions around the Ω loop and active site cavity. This will be quite interesting, as this timescale is where the cleavage of the β-lactam ring occurs. Thus, the recording of relaxation dispersion data will certainly shed light onto the conformational exchange processes suspected to arise near the active site. Here, some residues (e.g., Lys⁷³), although rigid on the ps-ns timescale, display broadened resonances, in addition to some resonances even being invisible, as a result of peak broadening (e.g., Ser⁷⁰).

Finally, the detailed backbone dynamics data gathered for PSE-4 will join those from TEM-1 in enabling in-depth MD simulations. A comparative study of PSE-4 backbone dynamics characterized by MD and NMR is currently underway. This will permit better in silico studies of the dynamics of class A wild-type and mutant β-lactamases in the presence of substrate, experiments which are impossible using NMR because the turnover rate of relevant β-lactams is tremendously fast with respect to NMR experiments being quite long.