Molecular modeling was addressed to understand different substrate-binding modes and clarify the role of two positively charged residues of the penicillin G acylase active site – βR263 and αR145 – in binding of negatively charged substrates. Although the electrostatic contribution to productive substrate binding was dominated by βR263 rather than αR145, it was found that productive binding was not the only possible mode of substrate placement in the active site. Two extra binding modes – nonproductive and preproductive – were located by means of molecular docking and dynamics with binding affinities comparable with the productive one. A unique feature of nonproductive and preproductive complexes was that the substrate's acyl group did not penetrate the hydrophobic pocket, but occupied a patch on the protein interface spanning from βR263 to αR145. Nonproductive and preproductive complexes competed with each other and productive binding mode, giving rise to increased apparent substrate binding. Preproductive complex revealed an ability to switch to a productive one during molecular dynamics simulations, and conformational plasticity of the penicillin G acylase active site was shown to be crucial for that. Nonproductive binding observed at molecular modeling corresponded well with experimentally observed substrate inhibition in penicillin acylase catalysis. By combining estimated free energies of substrate binding in each mode, and accounting for two possible conformations of the penicillin G acylase active site (closed and open) quantitative agreement with experimentally measured KM values was achieved. Calculated near-attack conformation frequencies from corresponding molecular dynamics simulations were in a quantitative correlation with experimental kcat values and demonstrated adequate application of molecular modeling methods.
The importance of electrostatic interactions in penicillin acylase (PA) catalysis was first evidenced from experimental studies of the stereospecificity of PA-catalyzed hydrolysis of N-phenylacetylated amino acids . It was suggested that preferential binding of S enantiomers compared with R enantiomers was determined by specific electrostatic interaction of the substrate's carboxylic group with a positively charged active site residue of PA. This suggestion could not be verified until the X-ray structure of PA emerged [2, 3] and structural considerations became available. However, it appeared that at least two positively charged residues – βR263 and αR145 – were in proximity to the catalytic residue βS1, and a priori both could be involved in recognition of negatively charged substrate groups.
One suggestion based on a cocrystal structure (PDB ID: 1FXV) of inactive PA mutant with penicillin G (PG) assigned a major role to αR145 . Mutation to the oxyanion hole residue βN241A was applied to inactivate the enzyme because use of native PA crystals led to PG hydrolysis, preventing X-ray studies of enzyme–substrate (ES) complex. In the 1FXV structure, the PG molecule was shifted from the oxyanion hole towards the solution and its β-lactam moiety contacted with αR145, staying relatively far (~ 11 Å) from βR263.
Another suggestion based on a cocrystal structure of wild-type PA (wtPA) with penicillin G sulfoxide – a sluggishly hydrolyzed analogue of natural PA substrate penicillin G – assigned a crucial role in substrate binding to the residue βR263 . Because it followed from the structure (PDB ID: 1GM9), residue βR263 was much closer to penicillin G sulfoxide's carboxylic group (∼4 Å) than αR145 (∼ 10 Å).
These somewhat contradictory results have recently been reconsidered in our molecular modeling study , in which a number of protocols were used to refine wtPA–PG complex structure. It was shown that all trajectories started either from 1FXV, 1GM9, or substrate docked to the PA active site, converge to similar binding mode of PG, which was much closer to that in 1GM9 than in 1FXV. The obtained wtPA–PG complex corresponded to a productive Michaelis complex characterized by correct orientation of the substrate and enzyme catalytic residues in correspondence with the requirements of theoretical chemistry. Evidently, the electrostatic contribution of the productive substrate binding was dominated by βR263.
However, the role of both positively charged residues in the PA active site – βR263 and αR145 – in substrate binding seems to be more complicated and is not yet well explained by crystallographic and modeling studies. Experimentally characterized binding of PG to mutated PA (mPA), in which one of the positive charges (αR145) was switched off by mutation to leucine, clearly indicates an important role for the αR145 residue in ES interactions . We have therefore undertaken an experimental study combined with molecular modeling to clarify the situation.
Results and Discussion
Open and closed conformations of the PA active site
As shown by crystallographic studies, residues αR145 and αF146 in the PA active site can adopt two distinct conformations – so-called ‘closed’ and ‘open’ – differing in their secondary structure motif and side-chain orientations . The closed state is characteristic for binding specific ligands, in which the αF146 side chain tightly packs the ligand acyl moiety into the hydrophobic pocket, and residues αR145–αF146 comprise an α-helix motif. The open state is observed upon binding of nonspecific bulky ligands, when αF146 cannot screen the ligand hydrophobic moiety from the solvent, whereas αR145 is completely exposed to the solvent. The main chain conformation of αR145–αF146 in the open state is a less twisted π helix, and it has recently been shown that residues α142–α144 also change their secondary structure upon opening . It was suggested that the closed and open states of the PA active site might coexist in dynamic equilibrium with a preference towards the closed state in the free enzyme or specific enzyme–ligand complexes, and the open state in complexes with nonspecific bulky ligands.
To evaluate the contribution of the open state to the kinetic scheme, the thermodynamics of enzyme opening must be taken into account. In current molecular dynamics (MD) studies of the free enzyme, the closed state was observed for 60% of the free wtPA trajectory and ~ 50% of the free mPA trajectory. Thus, the estimated ΔG of the opening was ~ 0.3 kcal·mol−1 for the wtPA and 0 kcal·mol−1 for the αR145L mutant. Of course, precise estimation of such conformational equilibrium would ideally require ab initio calculations and much longer MD trajectories [9-11]. However, qualitatively obtained results seemed to be reasonable and consistent with experimental data. It should be noted that the αR145L mutant looks more prone for opening; qualitatively, this might contribute to the lack of specific interactions maintaining the closed state, such as hydrogen bonding between the guanidine group of αR145 and the main chain carbonyl oxygen of βQ23 in the wtPA.
Transition from the closed to the open state plays an important role in PA catalysis and substrate binding. As mentioned earlier, the closed conformation of the enzyme cannot directly bind substrate, because the size of the bottleneck at the PA hydrophobic pocket is smaller than the substrate phenyl ring . However, opening causes a shift in the side chains of αF146 and βF71 – residues determining the bottleneck size (Fig. 1). Thus, opening is a crucial prerequisite of substrate binding by PA, and must be included in the kinetic scheme.
Productive substrate binding
Analysis of the MD trajectories for four systems [wtPA–PG, wtPA–penicillin G methyl ester (PGE), mPA–PG and mPA–PGE] revealed that no significant conformational changes took place in the active site upon substrate binding. Moreover, all four systems demonstrated a similar binding pattern for the substrates (Fig. 2). Somewhat lower affinity of PG towards mPA (calculated as described in 'Materials and methods') may be qualitatively described by a small shift in αF146 towards the solution due to a smaller volume of leucine residue compared with arginine and a corresponding shift in the substrate, implying weakening of the H-bonds with an oxyanion hole (detailed statistics of H-bonds can be found in the Supporting information, see β69Ala and β241Asn columns). The smaller difference in PG and PGE binding energies may be explained by the fact that the substrate carboxylic group does not form a bidentate salt bridge with βR263, but rather forms a single H-bond, which is preserved even in case of ester substrate.
In this study, some of the ES complexes revealed opening upon MD simulations when launched from the closed conformation. These trajectories were relaunched for correct characterization of complexes in the closed state. However, because opening might contribute to the apparent KM value – KM is an integral kinetic parameter – additional characterization of ES binding in the open state and the thermodynamics of opening must be taken into account to reproduce experimentally measured Michaelis constants.
For this purpose, four ES complexes in the open state were constructed (as described in 'Materials and methods') with PDB structure 1FXV taken as a template. It appeared that all MD trajectories in the open state remained stable during 10 ns simulations, confirming that the open state could be viewed as an independent counterpart of the kinetic scheme describing substrate binding by PA.
Partial displacement from the oxyanion hole accompanied by H-bonding between the substrate's carbonyl oxygen and β1S hydroxyl group was observed in all open-state trajectories of ES (see Supporting information). This tendency was even more pronounced in the case of mPA, in which residue αF146 was further shifted towards the solution compared with the ES complexes of wtPA. Displacement from the oxyanion hole diminished the percentage of near-attack conformations (NAC) (discussed below), however, productive binding in the open state was even more energetically favorable than binding in the closed state (Table 1).
Table 1. Substrate-binding energies (kcal·mol−1) in productive, nonproductive and preproductive binding modes with both closed and open states of PA estimated from molecular dynamics
a Free energy of substrate binding in this conformation was estimated to be more than 3 kcal less favorable. b Transition to productive binding was observed in corresponding MD trajectory, binding energy was not estimated. c Corresponding complex could not be located by docking.
We were very interested in qualitative interpretation of the phenomena observed from kinetic experiments (see 'Materials and methods') – worsening of substrate binding when charge–charge interactions were switched off (either by enzyme αR145L mutation or esterification of the substrate carboxylic group), while retaining affinity when both enzyme and substrate charges were neutralized. Some extra aspects of ES interactions had to be considered for the correct interpretation of experimental KM values and a consistent description of the substrate-binding process and catalysis. Might some alternative and as yet unknown ES interactions have taken place and had an impact on the apparent KM value?
It is known from previous experimental studies conducted in our laboratory that PG hydrolysis by PA is complicated by substrate inhibition at high PG concentrations [12, 13]. This means that at least two PG molecules can bind to PA: one specifically in the productive conformation in the active site, and the other somewhere else on the enzyme surface, although not far from the first molecule, so that it might influence the catalytic properties of the enzyme. Binding of the two molecules can be discriminated by stationary kinetic studies, however, competition between two (or more) binding modes for the same (or overlapping) patch(es) on the enzyme interface cannot be deduced from stationary kinetics.
Exhaustive docking localized two new binding modes of the substrate, in addition to the already characterized productive binding. In the first, the substrate phenylacetyl group was in contact with residues α145–α146 and the β-lactam moiety was in contact with βR263, whereas in the second, orientation of the substrate acyl and amid portions was flipped. Both alternative positions overlapped with the productive binding mode, thus competing with each other.
Subsequent MD studies revealed that the first complex could undergo a reversible transition to productive binding, whereas the second was disconnected from the pathways leading to other binding modes. Because of this obvious physical interpretation, the former complex was annotated as preproductive, and the latter as nonproductive.
Analysis of nonproductive binding mode
In this complex, the substrate leaving group contacts residue α145, and an electrostatic interaction stabilizes the wtPA–PG complex. In mPA, the electrostatics is switched off, however, weak hydrophobic and Van der Waals' contacts may be formed with the ester group of PGE. Particularly stable is the complex of PGE with mPA in the closed state, where a leucine residue forms a complementary hydrophobic cavity for the substrate methyl group (Fig. 3). In the open conformation of mPA, the nonproductive binding site is too large for PGE, which is reflected by the lower binding energy (Table 1).
The absence of nonproductive complexes wtPA–PGE and mPA–PG can be qualitatively explained by the noncomplementarity of interactions between the substrate leaving group (which is either ester or carboxylic) and residue α145 (which is either charged or hydrophobic). Starting from docked and energy minimized conformations, these molecular systems revealed substrate dissociation during an unconstrained MD run.
Upon nonproductive binding, the acyl group of the substrate forms hydrophobic contacts with residues βF254 and βW238, and H-bonds with βR263 and βN388 (Fig. 3). Poorer stability of the mPA–PGE nonproductive complex compared with wtPA–PG can be explained by lesser geometric complementarity: hydrophobic interactions between an ester group and leucine residue pull the substrate towards the solution slightly, weakening H-bonding with βR263 and βN388. In addition, the H-bond with βS386 becomes weaker because of the reduced polarity of the ester compared with carboxylate.
Analysis of the preproductive binding mode
Upon preproductive binding, substrate occupies mostly the same patch on the enzyme surface, however, its orientation is flipped compared with nonproductive binding: the acyl group of the substrate contacts residues α145–146, while the leaving group is oriented towards residue βR263. Obviously, in the case of mPA, interactions with either PG or PGE are more favorable compared with wtPA because of the complementary hydrophobic contacts (Fig. 4).
Some of the modeled preproductive complexes revealed conformational transition during MD simulations and switched to the productive binding mode (Table 1). This was particularly characteristic of open conformations of the enzyme, because the bottleneck was large enough to let the substrate move inside the acyl-binding site. Conversely, preproductive complexes formed by the closed enzyme were stable in MD trajectories. This might be due to steric obstructions limiting the mobility of the αF146 residue, which restricts the size of the hydrophobic pocket bottleneck in the closed state, preventing direct switching to a productive substrate-binding mode.
The only preproductive complex that could not be located for the closed enzyme state was wtPA–PGE. It is possible that there was not enough space in the wtPA active site to enclose the ester substrate, because an arginine residue occupies more space than leucine in the αR145L mutant, and in the closed state the patch available for pre- or nonproductive binding is smaller than in the open state. In addition, PGE is slightly bigger than PG. This suggestion is confirmed by the fact that nonproductive complex wtPA–PGE in the closed state was not observed as well.
Results of all the MD simulations performed are summarized in Table 1.
Mechanism of substrate binding by PA and its formal kinetic scheme
Analyzing the energies of substrate binding in productive, nonproductive and preproductive conformations, we can conclude that some of these complexes contribute significantly to the observable KM, whereas others may be omitted from the formal kinetic scheme because their contribution to KM is negligible. However, some of the observed complexes, for example, preproductive ones corresponding to the open conformation of the enzyme, cannot be omitted from the kinetic scheme because they are located within the most probable trajectory of substrate penetration into the active site in the productive mode. As discussed earlier, substrate cannot squeeze into the acyl-binding site of the enzyme to form a productive Michaelis complex because of geometric constraints imposed by the hydrophobic pocket bottleneck. Thus, active site opening must take place in the final stage of productive substrate binding. When the enzyme is in the open state, there is a distinguishable complex that the substrate forms on its way to productive binding mode. This intermediate ES complex is not as energetically favorable as the Michaelis complex, but its formation facilitates penetration of the substrate into the active site. This is used upon substrate binding by PA to reduce the diffusion limitations in a quite specific and rational manner.
Substrate binding by the enzyme in its closed state may also assist productive binding because it seems probable that preproductive ES complex in the closed state is in conformational equilibrium with the open state (at least there are no suggestions to the contrary). Thus preproductive complexes, being less energetically favorable than productive complexes, must be considered as an integral part of the PA kinetic scheme. By contrast, nonproductive complexes seem not to be related to productive binding, e.g. the substrate must first dissociate from the nonproductive binding site, so that it is possible to form preproductive complex first (during the next approach to the enzyme), and then to flip to productive binding. For systems such as wtPA–PGE and mPA–PG, these complexes are relatively unfavorable and might easily be omitted from the kinetic scheme without missing qualitative traits of substrate binding.
Evaluation of Michaelis constants from MD simulations
Calculated free energies of ES binding can be transformed to KM values assuming that: (a) the Michaelis scheme is applicable, and (b) the catalytic transformation step is much slower than dissociation. With these assumptions, it may be stated that KM = 1/KS (where KS is a binding constant calculated directly from estimated binding energy). Correlation of KM values calculated assuming only productive binding in a closed state (Table 2, column 1) with experimental data (Table 2, last column) can be regarded as generally acceptable for computational chemistry. Because the overall accuracy of currently available scoring functions is ∼1–2 kcal·mol−1, this corresponds to a one order of magnitude error in binding constant estimation. However, comparing a series of four closely related ES complexes (two very similar ligands and enzymes differing by single amino acid substitution) a better correlation might be anticipated.
Table 2. Comparison of theoretically calculated and experimentally measured Michaelis constants. Columns 1–3 correspond to theoretically calculated KM values according to different kinetic schemes (corresponding equations relating KM and individual binding constants can be found in Scheme 1), 1, Only productive binding with the closed state of the enzyme was considered; 2, productive binding with both closed and open states of the enzyme were considered; 3, productive, nonproductive and preproductive binding with both closed and open states of the enzyme were considered. The last column corresponds to experimentally measured KM values
KM values presented in Table 2, column 2 were calculated by combining estimated constants of substrate binding in the closed and open states and taking into account the interstate equilibrium constant, according to the kinetic scheme. As shown, theoretically calculated KM values still demonstrate qualitative disagreement with experimental ones.
Relying upon the described calculations of probable ES complexes differing by the active site conformation (closed or open) and the mode of substrate binding (productive, non- or preproductive) the entire picture of substrate binding by PA can be constructed, giving rise to formal kinetic scheme and corresponding expression for observable KM. To illustrate the qualitative and quantitative aspects of substrate binding for each of four studied systems (wtPA–PG, mPA–PG, wtPA–PGE, mPA–PGE) kinetic schemes are provided (Scheme 1) in which: (a) energetically unfavorable complexes are depicted in light gray; (b) improbable transitions (such as single-step transition from preproductive binding to productive in the closed conformation of the enzyme) are crossed out; and (c) transitions that are likely to occur, but were not observed in our MD trajectories, are depicted by dashed arrows. Expressions of observable KM corresponding to each scheme are also presented. Finally, taking into account all possible binding modes of substrate binding and both closed and open enzyme states, we obtained calculated KM values quite close to those obtained experimentally (Table 1, column 3).
Evaluation of catalytic constants from MD trajectories
In addition to data concerning the structure of ES complexes and their corresponding binding energies, MD simulations can provide valuable information on relative reaction rates. The link between the catalytic constant describing the enzymatic transformation of the substrate and the MD trajectory of the corresponding ES complex can be established by calculating the frequency of NACs that are observed in the MD trajectory. The notion of a NAC introduced by Lightstone & Bruice  concerns intuitively defined geometrical criteria that characterize the complex of reagents that can undergo chemical transformation per se, e.g. without major structural rearrangements. Qualitatively, NAC is in a vicinity of the transition state geometry, so that only a slight movement along a few reaction coordinates is needed to push the reagents through the activation barrier (Fig. 5).
Using criteria defined in the 'Materials and methods', the frequency of NAC was calculated from the available MD trajectories. Assuming that NAC frequency is proportional to the substrate reactivity, which is kcat (because the enzyme acylation step is rate limiting ), substrates can be quantitatively ranked by their catalytic constants.
The formula for converting NAC frequencies into kcat is given by the following equation:
where denotes the ‘reference’ catalytic constant, which, by our approximation, has the same value for both PG and PGE hydrolysis (and is equal to kcat when NAC frequency = 1), and α(ESpro) denotes the fraction of productive ES complexes (relative to the total concentration of all enzyme forms) in closed and open states.
Having calculated NAC frequencies for wtPA–PG, wtPA–PGE, mPA–PG and mPA–PGE complexes, and taking the values of two experimentally determined catalytic constants (for PG hydrolysis by wtPA and by mPA) as references, the residual catalytic constants (as well as ‘reference’ catalytic constants) can be determined using a least square fitting procedure.
As shown in Table 3, experimentally determined catalytic constants are in good quantitative agreement with those calculated from NAC frequencies. The estimated ‘reference’ catalytic constant for mPA is approximately two times smaller than for wtPA, qualitatively reflecting the lower reactivity of the mutant enzyme, which may also relate to differences in the equilibrium between the open and closed states, because the reaction apparently occurs through the closed enzyme state. Obviously, careful application of NAC methodology can significantly enrich molecular modeling studies of enzyme specificity.
Table 3. Comparison of theoretically calculated and experimentally measured catalytic constants
a Experimental value. b 'Reference' catalytic constant corresponding to NAC = 1.0. c Catalytic constant calculated via Eqn (1).
Current kinetic studies of αR145L mutant revealed that enzyme specificity towards negatively charged substrates cannot be explained by assuming that only βR263 residue contributes to their binding. In this study, we show that switching off one of the charges – either on active site residue αR145 (by mutating it to leucine) or on the substrate carboxylic group (by converting it to ester) – substantially suppresses the formation of ES complex. Simultaneous neutralization of these two charges, however, does not lead to summation of their negative contributions (as might be expected if αR145 does not form a contact with PG carboxylic group). Evidently, representation of PG binding to PA by single productive Michaelis complex is somewhat oversimplified.
Molecular modeling studies of the role of positively charged residues αR145 and βR263 in PA catalysis led to the conclusion that conformational plasticity of the enzyme (at least its active site) and several substrate binding modes have to be taken into account for consistent description of interactions between enzyme and substrate.
Substrate binding by wtPA (in both closed and open states) is characterized by highly efficient formation of productive, nonproductive and preproductive enzyme–PG complexes. Nonproductive and preproductive complexes formed by the closed enzyme conformation contribute to apparent binding energy, whereas the corresponding complexes formed by the open state are far less stable and do not make significant impact.
Substrate binding by αR145L mutant is not complicated by nonproductive interactions; however, formation of productive ES complex is less energetically favorable.
Two positively charged residues in PA active site – βR263 and αR145 – play very important roles in different substrate-binding modes which is especially important for enzyme specificity to negatively charged substrates.
Materials and methods
The wtPA was purified as described earlier . Absolute concentrations of both wtPA and mPA active sites were determined by titration with phenylmethanesulfonyl fluoride . PGE was donated by E. de Vroom (DSM-Gist, Delft, Netherlands); αR145L mutant of PA was provided by D.B. Janssen (Groningen, Netherlands). All other chemicals including PG, 6-aminopenicillanic acid (6-APA), phenylmethanesulfonyl fluoride, phenylacetic acid, buffer components and chromatography solvents of higher quality were purchased from Sigma-Aldrich (St Louis, MO, USA).
A Perkin–Elmer Series 200 HPLC system was used for analysis of enzymatic hydrolysis reaction samples. A mixture of acetonitrile and 0.01 m phosphate buffer with pH 3.0 (30 : 70) was used as the eluent and stop-buffer for enzymatic reactions. A reversed-phase Varian Chromsep SS 150 × 4.6 mm Nucleosil 100-5 C18 HPLC column was used as stationary phase. Analysis was carried out at 0.8 mL·min−1 eluent flow with photometric detection at 210 nm.
For preparation of buffer solutions pH-sensitive electrode Hamilton Slimtrode was used.
Assay of enzymes kinetic parameters
Kinetic parameters (kcat and KM) of the enzymatic hydrolysis of PG and PGE by wtPA and mPA were obtained by initial reaction rate analysis. Enzymatic hydrolysis was carried out in thermostated cells at 25 °C. Reactions were started by the addition of a small amount of enzyme to a premixed substrate and buffer solution (0.01 m phosphate buffer, pH 7.5). The reaction mixtures were sampled periodically into chromatographic eluent mixture to stop the reaction. Samples were later analyzed by HPLC. Total substrate conversion in all the experiments did not exceed 10%.
HPLC with spectrophotometric detection of hydrolysis products (phenylacetic acid, 6-APA and methyl ester of 6-APA) at 210 nm was used to measure changes of enzymatic reaction product concentrations over time. The obtained experimental dependences of initial hydrolysis rates on substrate concentrations were fitted to the Michaelis–Menten equation by nonlinear regression analysis using the Levenberg–Marquardt algorithm.
The obtained constants are shown in Tables 2 and 3.
Protein structure preparation
Productive ES complexes (for both PG and PGE) were prepared from PDB structures 1GM9 and 1FXV representing closed and open conformation of the enzyme correspondingly. Structure 1FXV was corrected by replacing βA241 residue with N (oxyanion hole residue) to render fully functional conformation of the native enzyme. Starting from closed and open conformations of the native enzyme, two corresponding structures of αR145L mutant enzyme were prepared. Further details of protein structure preparation for modeling (including addition of hydrogen atoms and water molecules) can be found in the Supporting information.
All MD calculations were performed with the gromacs package [18-20] in all-atom OPLS force field  and TIP3P  water box with periodic boundary conditions. Integration of the motion equations was performed with a 4-fs time step (achieved by using dummy atom constructions to describe motions of methyl and free amino groups, and mass redistribution between atoms, to which hydrogen atoms were attached ). Simulations were performed at a constant volume and at 300 K using a Berendsen thermostat with 0.1-ps relaxation time. Bond lengths were constrained using the LINCS algorithm . Forces were calculated with the twin range cut-off at 9 Å to account for short-range interactions and 15 Å for long-range interactions. The long-range list was updated every five integration steps. Electrostatics was treated via reaction field methodology  with a dielectric permeability of 80 and a 15 Å cut-off; Van der Waals' interactions were smoothly set to 0 at 9 Å distance. Before unconstrained MD in solution was run, the system was subjected to several pre-equilibration steps (as described in the Supporting information).
During unconstrained MD runs in explicit aqueous medium, all constructed systems revealed stable behavior. RMSD form the protein starting coordinates reached 1.5 Å in ∼1.5 ns and atomic RMSF stayed at 0.5 Å; solution-exposed residues contributed mostly to the observed mean deviation and fluctuation magnitudes (see Supporting information), confirming the overall adequacy of the MD simulations.
PG parameterization for MD
Molecular-mechanical parameters of the PG were adapted from ab initio quantum chemical calculations performed on the analogous compound, N-acetyl-6-aminopenicillanic acid. An equilibrium geometry search, single-point calculations and electrostatic potential evaluation were performed at the restricted Hartree–Fock level in 6-31G* basis using PC gamess software [26, 27]. Partial atomic charges were assigned based on ab initio calculations within the scopes of RESP methodology  and previously derived set of charges for 6-APA . Special care was taken while assigning torsion parameters, standing for the rotation around C–N bond, connecting the β-lactam ring and the amide group of penicillin. Details of quantum chemical calculations and a complete set of derived molecular-mechanical parameters can be found in the Supporting information.
Construction of ES complexes was performed by automatic substrate (PG or PGE) docking to the preliminary prepared enzyme structures (wtPA and αR145L in closed and open conformations). To trap all possible conformations of ES complex the patch on the protein interface for substrate docking was chosen to be quite large (10 Å in each direction from Cz of βR263) compared with standard docking simulations. lead-finder® software was used for docking calculations . Solutions obtained by multiple docking experiments were clustered by RMSD criteria (< 0.8 Å within cluster) resulting in: (a) four clusters corresponding to productive substrate binding with closed conformation of the enzyme; (b) four clusters corresponding to productive substrate binding with open conformation; and (c) a number of clusters with relatively good substrate-binding energies, but not corresponding to productive binding. The latter structures were further assigned to preproductive and nonproductive binding modes (see Results and Discussion) and were used for MD studies as well as productive ES complexes.
To search for alternative substrate-binding modes, exhaustive docking was used to find low-energy substrate placements in the region spanning the active site funnel of 20 Å in diameter. Docking results were filtered to retain substrate conformations characterized by binding energy lower than −4 kcal·mol−1 and geometric overlap with the productive binding site.
Binding energy calculations
Docking methods are known to overestimate binding properties of fake substrates, giving rise to false positives. Therefore, to prove that the observed ES complexes were not docking artifacts, all discovered systems were subjected to unconstrained MD simulations. Each of the 16 systems – two complexes (preproductive and nonproductive) for each of the four ES systems in two possible states (closed and open) – was constructed by molecular docking, energy optimized and subjected to 10 ns of unconstrained MD simulations.
For each system under consideration (with either PG or PGE as a substrate, wtPA or mPA as an enzyme being either in closed or open state), the free energy of substrate binding was estimated by averaging single-point binding energies over the corresponding MD trajectory using the following procedure. An ensemble of ES complex structures was collected from the MD run by saving coordinates every 16 ps. Then, for each structure from the ensemble, the substrate-binding energy was estimated by means of a semiempirical molecular-mechanical function implemented in lead® software. The obtained binding energies were averaged over the ensemble of ES structures. Details of binding energy estimation using the molecular-mechanical function of lead-finder® are provided in the Supporting information.
Statistics of NACs
Following the notion of NACs  and details of the catalytic mechanism of PA recently validated by ab initio quantum chemical calculations , the following NAC criteria were chosen: (a) distance between the carbonyl carbon of the substrate and hydroxyl oxygen of βS1 is < 3.5 Å; (b) angle of nucleophilic attack, i.e. angle between the plane of the substrate amide bond and the bond introduced in (a), is > 75°; (c) hydrogen bonds exist between the substrate carbonyl oxygen and the oxyanion hole formed by main chain NH of βA69 and side chain NH2 of βN241. The percentage of NAC calculated over a MD trajectory for each ES complex was used to estimate the corresponding catalytic constant.
The introduced structural criteria for NAC have a straightforward interpretation: for the reaction (namely, the rate-limiting stage of enzymatic reaction, i.e. the acylation step) to take place, it is necessary that: (a) the reacting atoms (substrate carbonyl carbon and serine hydroxyl oxygen) remain close, (b) the angle of nucleophilic attack must be close to the optimal value of 90°, and (c) specific solvation of the transition state by means of hydrogen bonding with the oxyanion hole must take place. The final criterion may not seem evident, however, quantum chemical calculations show that hydrogen bonding contributes ∼10 kcal·mol−1 to transition state stabilization , and experimental evidence shows that the βN241A mutant is inactive .
This work was supported by the Russian Ministry for Science and Education (contract 16.512.11.2254).