Biapenem inactivation by B2 metallo β-lactamases: energy landscape of the post-hydrolysis reactions

Abstract

Background: The first line of defense by bacteria against β-lactam antibiotics is the expression of β-lactamases, which cleave the amide bond of the β-lactam ring. In the reaction of biapenem inactivation by B2 metallo β-lactamases (MβLs), after the β-lactam ring is opened, the carboxyl group generated by the hydrolytic process and the hydroxyethyl group (common to all carbapenems) rotate around the C5-C6 bond, assuming a new position that allows a proton transfer from the hydroxyethyl group to C2, and a nucleophilic attack on C3 by the oxygen atom of the same side-chain. This process leads to the formation of a bicyclic compound, as originally observed in the X-ray structure of the metallo β-lactamase CphA in complex with product.

Methodology/principal findings: QM/MM and metadynamics simulations of the post-hydrolysis steps in solution and in the enzyme reveal that while the rotation of the hydroxyethyl group can occur in solution or in the enzyme active site, formation of the bicyclic compound occurs primarily in solution, after which the final product binds back to the enzyme. The calculations also suggest that the rotation and cyclization steps can occur at a rate comparable to that observed experimentally for the enzymatic inactivation of biapenem only if the hydrolysis reaction leaves the N4 nitrogen of the β-lactam ring unprotonated.

Conclusions/significance: The calculations support the existence of a common mechanism (in which ionized N4 is the leaving group) for carbapenems hydrolysis in all MβLs, and suggest a possible revision of mechanisms for B2 MβLs in which the cleavage of the β-lactam ring is associated with or immediately followed by protonation of N4. The study also indicates that the bicyclic derivative of biapenem has significant affinity for B2 MβLs, and that it may be possible to obtain clinically effective inhibitors of these enzymes by modification of this lead compound.

Figure 1. CphA sustrates and products.

A. Two carbapenems: imipenem (left), biapenem (right). An asterisk marks the carbon atom that replaces the sulfur of penicillins. Biapenem differs from imipenem for the presence of a C-1β methyl group and a C-2 σ-symmetric (6,7-dihydro-5H-pyrazolo[1,2-a], , triazolium-6-yl)thio group. Notice the C6 hydroxyethyl group common to all carbapenems. B. Bicyclic derivative of biapenem bound in the active site of CphA (PDB entry 1X8I). His118, Asp120 and biapenem N4 are shown here as unprotonated, and thus the hydrogen bond pattern of Wat is undefined; the actual ionization state of these groups inside the bacterial cell may be different. Zn²⁺ coordination and hydrogen bonds are shown as thin yellow lines and dashed blue lines.

Figure 2. Formation of the bicyclic derivative of biapenem.

A. QM/MM optimized model of the active site of CphA in complex with hydrolyzed biapenem (“Conformation A” in the metadynamics analysis of the hydroxyethyl group rotations described later on). In the configuration shown here both N4 and the C6 carboxylate are protonated (atoms HN4 and HO7). A water molecule (originating from bulk solvent after the hydrolysis reaction is completed) is hydrogen bonded to Asp120 and loosely coordinated to Zn²⁺ (dashed yellow bond). Zn²⁺ has only five strong ligands, in agreement with spectroscopic data . A red arrow indicates the rotation of the C6 carboxylate and hydroxyethyl moieties (the latter only partially visible) required to generate the open-ring form shown in the next panel. B. Conformation of hydrolyzed biapenem that precedes the formation of the bicyclic compound (“Conformation B” in the metadynamics analysis of the hydroxyethyl group rotations). A blue arrow indicates the proton transfer from O62 to C2 required to generate the bicyclic compound. C. Active site of CphA in complex with the bicyclic derivative of biapenem. The C2–H2 and O62–C3 bonds formed during the rearrangement are shown as thin green lines. N4 is protonated.

Figure 3. PES of the non-enzymatic formation of the bicyclic derivative of biapenem when N4 is protonated.

The PES is defined by two reaction coordinates: the forming C2–H2 bond between the hydroxyl hydrogen and C2 and the forming C3–O62 bond between the hydroxyl oxygen and C3. The position of the only TS is marked on the surface. QM/MM energies are in kcal/mol. Colors on the PESs reflect the QM/MM energy levels, as represented in the reference bar on the side.

Figure 4. Free energy profiles of the cyclization reaction in solution.

A. The profile of the reaction with N4 protonated (corresponding to the PES of Fig. 3 ) is shown in the upper quadrant as a blue line. The reaction coordinate axis is in arbitrary units and the reactant and product states are marked as RS NH4 and PS NH4, respectively. The profile of the reaction with N4 deprotonated is shown as a red line in the upper quadrant. The actual reactant and product states of the cyclization reaction (corresponding to PES II in Fig. 5 ) are marked as RS N4 and PS N4, respectively. In order to place this reaction on the same energy scale as the reaction with N4 protonated, two additional steps were calculated representing the protonation of RS N4 to RS NH4 (PES I in Fig. 5 ), and the protonation of PS N4 to PS NH4 (PES III in Fig. 5 ). Circles on the profiles mark the positions along the reaction coordinate (TSs and stationary points) where thermochemical properties were calculated with a vibrational analysis. All other values reflect only a shape-preserving interpolation between the calculated points. Changes in the entropic contribution (−T*S) to the free energy curves are shown in the lower quadrant with red and blue dashed lines and square markers for the NH4 and N4 pathways, respectively. B. Time course of the reaction corresponding to the red trace in panel A, starting from 100% hydrolyzed biapenem with N4 ionized (RS N4 in panel A). The almost instantaneous (between 0 and 10⁻⁵ s) protonation of RS N4 to RS NH4 (due to the very low barrier at TS1) is not shown.

Figure 5. PESs of the non-enzymatic formation of the bicyclic derivative of biapenem when N4 is deprotonated.

The reaction path corresponding to the red trace in Fig. 4 spans three separate PESs: red vertical lines connect the equivalent phase-space points of each PES (the jump points from one PES to another). PES I corresponds to a proton transfer (TS1) from N4 of hydrolyzed biapenem to a hydroxide ion. PES II corresponds to the proton transfer from the hydroxyl oxygen to C2 (TS2) and the formation of the C3–O bond (closure of the 6-membered ring, TS3). PES III corresponds to the reprotonation of N4 from water (TS4). QM/MM energies are in kcal/mol. Colors on the PESs reflect the QM/MM energy levels, as represented in the reference bars on the side of each PES.

Figure 6. Free energy profiles of the cyclization reaction in the enzyme.

A. The free energy profiles for the formation of the bicyclic compound in four configurations of the enzyme∶hydrolyzed biapenem complex (continuous lines and colored circles) are superimposed on the profiles of the same reaction in water with protonated and unprotonated N4 (blue and red lines, respectively), as already shown in Fig. 4A . All the profiles have their origin coincident with that of protonated reactant in solution (clear square on the left side). The difference in the free energy of the protonated product (PS NH4) between the catalyzed (cyan, magenta, yellow, and green circles) and the uncatalyzed reactions (clear square on the right side) reflects the difference in the free energy of binding (ΔG^bind) of the reactant versus the product. Changes in the entropic contribution (−T*S) to the free energy curves are shown in the lower quadrant with dashed lines and square markers of the corresponding color. B. Time course of the reaction corresponding to the magenta trace in panel A (enzyme configuration No. 2 in Table 1 ), starting from 100% hydrolyzed biapenem with N4 ionized (RS N4 in panel A).

Figure 7. Thermodynamic cycles for the cyclization reactions of hydrolyzed biapenem.

A. Thermodynamic cycle relating the energy of the cyclization reaction in solution with the energy of the same reaction in the enzyme active site. E•R and E•P are the enzyme∶reactant and the enzyme∶product complexes, respectively. B. Intermediate step leading to the collapsed thermodynamic cycle shown in panel C. C. Collapsed thermodynamic cycle in which the same energy quantity (ΔG^bind _R) has been subtracted from the vertical legs of the cycle shown in panel A. The difference between the catalyzed (lower branch) and the uncatalyzed reaction (upper branch) reflects the difference in the free energy of binding (ΔG^bind) of the product versus the reactant (vertical leg). While this cycle does not represent a real physical entity, it provides a rationalization for the convention adopted in Figure 6 , according to which all the free energy profiles of the reaction in the enzyme were placed with their origin coincident with that of the reaction in solution.

Figure 8. Free energy surfaces (FESs) of the hydroxyethyl group rotations in solution.

FESs were calculated under four conditions corresponding to 1) deprotonated N4 and C6 carboxylate (FES I), 2) deprotonated N4 and protonated C6 carboxylate (FES II), 3) protonated N4 and deprotonated C6 carboxylate (FES III), 4) protonated N4 and C6 carboxylate (FES IV). The collective variables (CV) sampled in the metadynamics simulations were the dihedral angle defined by atoms N4-C5-C6-C61 (see Fig. 2) or “Dihedral CV1”, and the dihedral angle defined by atoms C5-C6-C61-O62 or “Dihedral CV2”. The ranges of Dihedral 1 values corresponding to Conformation A and Conformation B are highlighted in red and green, respectively, in the FES I panel. The start point for all simulations was conformation B. The average error ε (kcal/mol) of the FES, as calculated from equation (4) (see Methods) is shown in each panel below the color bar.

Figure 9. Free energy surfaces (FESs) of the hydroxyethyl group rotations in the enzyme.

FESs for the hydroxyethyl group rotations occurring with hydrolyzed biapenem in the active site of CphA in the configuration No. 4 of Table 1 were calculated under the same conditions and for the same collective variables as in Fig. 8 . The start point for all simulations was conformation B. The start point for all simulations was conformation B. The average error ε (kcal/mol) of the FES, as calculated from equation (4) (see Methods) is shown in each panel below the color bar.