Rate constants (s⁻¹) for individual steps in the cyclization reaction of hydrolyzed biapenem in solution and in the configurations of the enzyme listed in <b>Table 1</b>.

<p>Rate constants (s⁻¹) for individual steps in the cyclization reaction of hydrolyzed biapenem in solution and in the configurations of the enzyme listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-t001" target="_blank"><b>Table 1</b></a>.</p

Energetics of the rotation of the hydroxyethyl group of hydrolyzed biapenem in solution and in the enzyme (Configuration No. 4 in <b>Table 1</b> and <b>Fig. 6A</b>).

<p>ΔG values (kcal/mol) are the mean and standard deviation (in parenthesis) of two metadynamics simulations started respectively from conformation A (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g002" target="_blank"><b>Fig. 2A</b></a>) or B (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g002" target="_blank"><b>Fig. 2B</b></a>) of hydrolyzed biapenem. Values in bold highlight reactions that occur spontaneously.</p

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

<p>The reaction path corresponding to the red trace in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g004" target="_blank"><b>Fig. 4</b></a> 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.</p

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

<p>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.</p

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

<p>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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g002" target="_blank">Fig. 2</a>) 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#s4" target="_blank">Methods</a>) is shown in each panel below the color bar.</p

Free energy profiles of the cyclization reaction in the enzyme.

<p><b>A.</b> 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g004" target="_blank"><b>Fig. 4A</b></a>. 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>B.</b> Time course of the reaction corresponding to the magenta trace in panel A (enzyme configuration No. 2 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-t001" target="_blank"><b>Table 1</b></a>), starting from 100% hydrolyzed biapenem with N4 ionized (RS N4 in panel A).</p

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

<p>FESs for the hydroxyethyl group rotations occurring with hydrolyzed biapenem in the active site of CphA in the configuration No. 4 of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-t001" target="_blank"><b>Table 1</b></a> were calculated under the same conditions and for the same collective variables as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g008" target="_blank"><b>Fig. 8</b></a>. 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#s4" target="_blank">Methods</a>) is shown in each panel below the color bar.</p

Thermodynamic cycles for the cyclization reactions of hydrolyzed biapenem.

<p><b>A.</b> 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>B.</b> Intermediate step leading to the collapsed thermodynamic cycle shown in panel C. <b>C.</b> 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone-0030079-g006" target="_blank"><b>Figure 6</b></a>, 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.</p

CphA sustrates and products.

<p><b>A.</b> 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-5<i>H</i>-pyrazolo[1,2-<i>a</i>]<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone.0030079-Fisher1" target="_blank">[1]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone.0030079-Hall1" target="_blank">[2]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone.0030079-Frere1" target="_blank">[4]</a> triazolium-6-yl)thio group. Notice the C6 hydroxyethyl group common to all carbapenems. <b>B.</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.</p

Formation of the bicyclic derivative of biapenem.

<p><b>A.</b> 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 href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030079#pone.0030079-Sharma1" target="_blank">[29]</a>. 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>B.</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. <b>C.</b> 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.</p