Active Site Dynamics in Substrate Hydrolysis Catalyzed by DapE

Article

Active Site Dynamics in the Substrate Hydrolysis Catalyzed by DapE Enzyme and Its Mutants from Hybrid QM/MM Molecular Dynamics Simulation Debodyuti Dutta, and Sabyashachi Mishra J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b04431 • Publication Date (Web): 30 Jun 2017 Downloaded from http://pubs.acs.org on June 30, 2017

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The Journal of Physical Chemistry

Active Site Dynamics in the Substrate Hydrolysis Catalyzed by DapE Enzyme and its Mutants from Hybrid QM/MM Molecular Dynamics Simulation Debodyuti Dutta and Sabyashachi Mishra∗ Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur, India E-mail: [email protected]

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Abstract The mechanism of the catalytic hydrolysis of N-succinyl diaminopimelic acid by the microbial enzyme DapE in its wild-type form as well as three of its mutants (E134D, H67A, and H349A) is investigated employing hybrid quantum-mechanics molecular-mechanics (QM/MM) method coupled with molecular dynamics (MD) simulations, wherein the time evolution of the atoms of QM and MM regions are obtained from the forces acting on the individual atoms. The free-energy profiles along the reaction coordinates of this multi-step hydrolysis reaction process is explored using a combination of equilibrium and nonequilibrium (umbrella sampling) QM/MM-MD simulation techniques. In the enzyme-substrate complexes of wt-DapE and the E134D mutant, the nucleophilic attack is found to be the rate determining step involving a barrier of 15.3 kcal/mol and 21.5 kcal/mol, respectively, which explain satisfactorily the free energy of activation obtained from kinetic experiments in the wt-DapE-SDAP (15.2 kcal/mol) and the three orders of magnitude decrease in the catalytic activity due to E134D mutation. The catalysis is found to be quenched in the H67A and H349A mutants of DapE due to the conformational rearrangement in the active site induced by the absence of the active site His residues that prohibits the activation of the catalytic water molecule.

Introduction Among the most worrisome global health problems, bacterial infections attract the maximum attention. The rise in the number of multi-drug resistant bacteria and the consequent rise in the instances of severe and deadly bacterial infections has recently led the World Health Organization (WHO) to draw up a list of twelve most dangerous pathogens that need to be tamed with increased urgency. 1 The discovery of new antibiotics is the need of the hour in the fight against the pathogens that have become resistant to a large number of antibiotics, including some of the best available antibiotics. 2–6 In this aspect, the meso-diaminopimelate (mDAP)/lysine biosynthetic pathway of bacteria 2 ACS Paragon Plus Environment

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provides a good opportunity in discovery of new antibiotic targets. 7–12 Since this pathway is absent in human beings, targeting one of the enzymes operating in this pathway offers the additional benefit of reduced side effects. At the same time, the indispensability of this pathway for the survival of bacteria makes these targets potentially very effective. 13–15 In particular, the enzyme DapE (dapE-encoded N-succinyl-L-L diaminopimelic acid desuccinylase), which is operative at one of the later stages of the lysine biosynthetic pathway has been shown to be indispensable for bacterial survival to the extent that dapE deletion mutants are unable to survive in lysine supplemented media. 13,14,16 The fact that DapE has been identified in several pathogenic bacteria including all of the so-called ESKAPE pathogens that feature prominently in the high priority list of the twelve most dangerous pathogens declared by WHO, 1 makes DapE an attractive target for antibacterial research. The key to the discovery of potential antibiotics lies in the detailed understanding of the mechanism of action of this enzyme. Several research work have significantly enriched our understanding of the action of this enzyme 7–9,11,12,14,15,17–30 The X-ray crystal structure of DapE reveals its dimeric structure with each monomer exhibiting a dimerization domain and a catalytic domain (Figure 1a). The active site of the enzyme, hosted in the catalytic domain, carries two Zn centers coordinated by His, Asp, and Glu residues (Figure 1b). Computational studies of biomolecular systems provide a microscopic view of the physiological role of the biomolecular systems at atomistic and electronic levels. The computational research on the biochemical reactions are generally studied by hybrid quantum mechanics molecular mechanics (QM/MM) methods 31–33 that exploit the speed of molecular mechanics (MM) and chemical accuracy of quantum mechanics (QM). In QM/MM methods, the electronically important part (i.e., the site of the chemical reaction) of the system is treated with QM methods and the remaining part of the system is treated with MM methods. With this strategy, the structural and enthalpic aspects of intermediates and transition states are computed in terms of the critical points in the multi-dimensional



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potential energy surfaces which provide crucial information to the mechanistic aspects of the enzyme catalysis. A severe limitation of this class of computational methods is, however, the neglect of the conformational dynamics during an enzymatic reaction that takes place in physiological environment. Hybrid QM/MM method coupled with molecular dynamics (MD) treatment (QM/MMMD computational technique), on the other hand, overcomes this limitation by evaluating energy and forces (from the gradients of energy) within the QM/MM description, and by using the forces on each atom, the hybrid system is propagated in time by solving Newton’s equation of motion, thus accounting for the dynamic effects of the atoms both in the QM as well as in the MM regions. 34–37 While QM/MM-MD simulations can be more insightful compared to the static QM/MM methods, it has been rarely performed for large biological systems due to the facts that these simulations are computationally very expensive and that, various QM/MM-MD methodologies are still under development. There are only a few studies reported which employ QM/MM-MD methodology and a majority of them generally employ semi-empirical methods to reduce the computational cost. 38,39 On the other hand, density functional theory based QM/MM-MD simulations have been rare, especially for reactive biomolecular systems. 40–42 These studies have generally reported single step biological processes. To the best of our knowledge, a multi-step reactive biological process has not been studied using hybrid QM/MM-MD method. In this work, we employ hybrid QM/MM-MD technique to investigate the mechanism of the catalytic action of microbial enzyme DapE, which catalytically hydrolyzes N-succinyl diamino-pimelic acid (SDAP) to give rise to succinic acid and diaminopimelic acid. We also study the role of the active site residues by investigating the catalytic action in three mutants (E134D, H67A, and H349A) of DapE. The results from these simulations have been validated by comparing them with the results from experimental kinetic studies. 12,43,44


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Computational Methods The initial structure of the enzyme-substrate complex for wt-DapE and its three mutants, namely, E134D, H67A, and H349A, were obtained from the molecular dynamics (MD) trajectories reported in our earlier publication. 24 In brief, the substrate L,L-SDAP was introduced to the active site of DapE enzyme (in wild-type form (PDB ID: 3IC1)

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and

the three single point mutants) followed by heating (5 ns) and equilibration (5 ns) at 300 K so as to remove any bias that might have crept in docking. The MD simulations were carried out by Amber14 program 45 with AMBER force field 46 for protein and TIP3 potential 47 for water. Towards the end of the 5 ns of equilibration, the systems showed very little conformational changes in the active site, as can be seen from the RMSD of Cα atoms and the active site heavy atoms during heating and equilibration (Figure S1 in the supporting information). Four different snapshots were selected from the last nano-second of the equilibration MD simulations for the wild-type DapE, the wild-type DapE-SDAP complex, and each of its three mutants with substrate bound forms. The structural and energetic comparison of the selected snapshots are made in Tables S1 and S2 in the supporting information. These snapshots were then used as the starting structures of QM/MM-MD simulations. The substrate and the active site residues were treated quantum mechanically (QM layer), while the remaining part of the solvated enzyme-substrate complex was considered using molecular mechanics (MM layer). The side chains of H67 (or A67, in case of the H67A mutant), D100, E134 (or D134, in case of the E134D mutant), E135, E163, H349 (or A349, in case of H349A mutation), the two Zn ions, the substrate, and the catalytic water molecule were kept in the QM layer. In addition, nine other water molecules that showed hydrogen bonding interactions with one of the active site residue were also considered in QM layer. The total number of atoms treated quantum mechanically amounted to 88, 124, 121, 115, and all for DapE, DapESDAP, E134D-DapE-SDAP, H67A-DapE-SDAP and H349A-DapE-SDAP systems, respectively. For quantum mechanical treatment, the M06-2X functional 48 together with 6-31++G(d,p) basis set 49,50 was used. The atoms in the MM layer were described using Amber force field for protein and TIP3 potential for water molecules. The total energy of the hybrid QM/MM system is given by the sum of the energy of the



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QM layer, the MM layer, and the interaction energy between the atoms of the two layers. The QM-MM interaction energy is calculated using the so-called electronic embedding scheme, 51 wherein, the polarization of the QM layer caused by the atoms of MM layer are taken into account. Within this QM/MM framework the force acting on an atom in the hybrid system is obtained from the first derivative of the total energy with respect to the Cartesian coordinates of the concerned atom. 52 Using the forces evaluated from the above method, the coordinates of the hybrid system were propagated and corresponding QM/MM-MD trajectories were obtained, using the QM/MM-MD programme implemented in Amber14. 45 The QM/MM-MD simulations were carried out at constant temperature (300 K) and pressure (1 bar). The constant temperature was achieved by performing Langevin dynamics with Langevin thermostat 53 at 300 K and a collision collision frequency of 5 ps−1 , whereas the pressure was controlled by using Berendsen barostat 54 with a target pressure of 1 bar together with a relaxation time of 1 ps. The long-range electrostatic interactions between MM and MM atoms were treated by the particle mesh Ewald (PME) 55 method with a 10 ˚ A cutoff and the van der Waals interactions were truncated at a cutoff of 12 ˚ A, with a switch function activated starting at 10 ˚ A. Electronic embedding was used to consider the interaction between the atoms in QM and MM layers. For non-bonded interaction between QM and MM atoms, a cut off of 8 ˚ A was used. 52,56 This value of the cut off signifies that all MM atoms which are found within the 8˚ A shell around any atom of the QM layer would be included in the non-bonding list for all QM atoms. 52,56 While the hydrogen containing bonds in the MM layer were constrained with SHAKE algorithm, 57 the same was not applied to the bonds in the QM layer. This necessitated a smaller time step of integration (0.5 fs) employed in this work. Gaussian 09 58 was used for the QM calculations which was called as an external QM program in the AMBER14 module. One such QM/MM-MD simulation of 1 ps takes around 10 days on a sixteen (Intel E52695 V2 2.4 GHz) core CPU. Using the above described methodology, QM/MM-MD simulations were performed for the the hydrolysis of substrate SDAP catalyzed by DapE enzyme. The reaction was modelled along a general acid-base hydrolysis mechanism, 12,16,43,44 which involved (a) the activation of catalytic water molecule by Glu134, followed by (b) nucleophilic attack of the hydroxyl ion on the


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substrate, which leads to (c) the cleavage of the peptide bond of the substrate accompanied by a proton transfer from Glu134 to the substrate (Figure 1c). Each of the three steps was studied using 5 ps of equilibrium QM/MM-MD simulation starting from each of the four snapshots (vide supra) taken from the MD simulations of wt-DapE and enzyme-substrate complex of wt-DapE and its three mutants (Table 1). However, when the desired reaction step does not take place during the stipulated (5 ps) QM/MM-MD simulation time, due to large underlying activation energy barrier, a non-equilibrium QM/MM-MD sampling method was used to overcome this barrier. For non-equilibrium QM/MM-MD sampling, we have used a combination of steered molecular dynamics (SMD) and umbrella sampling techniques, wherein, a particular step is first driven along a chosen reaction coordinate using QM/MM-SMD technique to generate the path of the reaction step. Snapshots at regular interval from the traversed path in the QM/MM-SMD trajectory were then chosen to carry out QM/MM umbrella sampling simulations. We carried out QM/MM umbrella sampling simulations 59 using harmonic umbrella potentials with a window spacing of 0.1 ˚ A along the chosen reaction coordinate. With each biased umbrella potential, 200 steps (100 fs) of QM/MM-MD simulations were carried out and the resulting umbrella sampling trajectories were analyzed using the weighted histogram analysis method (WHAM) 60,61 to obtain the the free energy profiles corresponding to the reaction step. The convergence of the free-energy profiles obtained from umbrella sampling technique were established (a) by varying the force constants (100, 120, 150, and 200 kcal/mol/˚ A2 ) associated with the applied umbrella potentials, and (b) by varying the number of QM/MM-MD steps with each umbrella potential (100 steps and 200 steps).

Results and Discussion Unbiased QM/MM-MD Simulation of the Activation of Water Molecule Four snapshots were randomly selected from the equilibration MD simulation of DapE and SDAP bound DapE in its wild-type form as well as E134D, H67A, and H349A mutants. Each of



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these snapshots were used as the initial geometry for 5 ps of QM/MM-MD simulations. During the 5 ps of QM/MM-MD simulations, the activation of the catalytic water molecule by Glu134 residue is seen to take place at different lengths of simulation time in different trajectories in wt-DapE-SDAP. The time evolution of the proton transfer from the catalytic water molecule to Glu134 side chain is shown in Figure 2a in terms of the distance between the oxygen atom of the catalytic water molecule and its hydrogen atom that gets transferred to Glu134, and the distance between this hydrogen atom and the proton accepting oxygen atom of Glu134 in the four QM/MM-MD trajectories of wt-DapE-SDAP system. It can be seen that the breaking of the O-H covalent bond in water and the formation of O-H bond in Glu134 occurs simultaneously and that, the proton transfer process is complete between 1.5 ps to 3.5 ps in all four QM/MM-MD trajectories (Figure 2a). The conformations encountered in the above mentioned QM/MM-MD trajectories were further analyzed by selecting 20 snapshots from the four trajectories and by carrying out the natural bond order (NBO) analysis of the atoms in the QM layer. Figure 2b shows the relation between the bond-order of the O-H bond of water against its bond distance. If the O-H bond order is found to be greater than 0.9 (corresponds to the O-H bond distance less than 1.15 ˚ A in Figure 2b), this bond is considered to be covalent and consequently, if the O-H bond of water is longer than 1.15 ˚ A, the water is considered to be deprotonated. Going by this argument, in 53% of the total frames in the four QM/MM-MD trajectories of wt-DapE-SDAP complex, the catalytic water is deprotonated, which directly gives an estimation of the efficiency of Glu134 to deprotonate the catalytic water. While all four trajectories of wt-DapE-SDAP complex show activation of the catalytic water molecule during 5 ps of QM/MM-MD simulation, only two of the four trajectories of E134DDapE-SDAP system show proton transfer from water to Asp134 during 5 ps of QM/MM-MD simulation (Figure 2c). Overall, we find that in 46% of the frames in the QM/MM-MD trajectories of E134D mutant, the water is deprotonated, as compared to 53% in the wt-DapE-SDAP during the same amount of simulation time. Hence, Asp134 in the E134D mutant is less efficient in activating the catalytic water molecule than Glu134 in the wt-DapE, due to the shorter side chain length of Asp134 compared to Glu134 (Figure 1c).


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In wt-DapE, His67 is coordinated to Zn1 atom through the epsilon nitrogen (Figure 1b). When His67 is mutated to alanine there arises a vacancy in the coordination sphere of Zn1 since alanine contains no suitable atom to coordinate to Zn1. Furthermore, alanine, with a comparatively smaller side chain remains far from Zn1, thus creating a vacant space around Zn1. The creation of the empty space and the vacancy in the coordination sphere of Zn1 induces a conformational change in the side chain of Glu134, which exhibits a coordination with Zn1 with one of its carboxyl oxygen atoms. This Zn1-E134 coordination remains intact through out the QM/MM-MD simulation in all four trajectories of H67A-DapE-SDAP system (Figure S2a, in the supporting information). Due to the Zn1-Glu134 coordination in H67A-DapE-SDAP, the Glu134 residue is no longer available for activation of the catalytic water molecule, as a result of which, the deprotonation of the water does not take place during the QM/MM-MD simulation in H67A-DapE-SDAP system (Figure S2a, in the supporting information). Since the deprotonation of water constitutes the first step of the catalytic reaction, the H67A mutation renders the enzyme inactive. For similar reasons, when His349 (coordinated to Zn2 through epsilon nitrogen) is mutated to alanine, the Glu134 residue shows strong coordination with the Zn2 metal center and is unable to deprotonate the catalytic water (Figure S2b, in the supporting information), which accounts for the inactivity of the enzyme in H349A mutant. 43 To investigate the role of the substrate in the activation of the catalytic water molecule, we carried out four QM/MM-MD simulations for DapE, where the substrate SDAP is absent. These simulations show that, unlike in the substrate bound DapE (DapE-SDAP complex), Glu134 residue in DapE is unable to completely accept the proton from the catalytic water molecule, despite being suitably positioned near the active site to deprotonate the water. Although in 38% of the total frames the O-H distance in the catalytic water is more than 1.15 ˚ A (Figure 2d), we do not observe a permanent deprotonation of the catalytic water molecule. Instead, the hydrogen atom of the catalytic water molecule moves back and forth between the two oxygen centers (the oxygen atom of water and the carboxyl oxygen of Glu134). In the absence of the substrate in the active site, the catalytic water bridges the two Zn atoms via its oxygen atom and, at the same time, is hydrogen bonded to Glu134. 16 Since the bridging catalytic water molecule in DapE is under the influence of two metal centers, its degrees of freedom is somewhat restricted and the



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oxygen center of water molecule shows an increased electronegativity. This makes it difficult for Glu134 to deprotonate the water in DapE. On the other hand, in the DapE-SDAP complex, the water no longer bridges the two Zn centers since the substrate binding pushes the water molecule towards Zn1 center while establishing a strong substrate-Zn2 coordination (Figure 1c). As a result, in DapE-SDAP complex, the oxygen atom of water molecule is less electronegative and has greater translational degrees of freedom compared to the oxygen atom of the catalytic water molecule in DapE. This facilitates the activation of the catalytic water molecule in DapESDAP complex which suggests that the presence of the substrate in the active site of the enzyme accelerates the deprotonation of the catalytic water molecule. The free-energy profile along the proton-transfer coordinate (r, the O-H distance of catalytic water) has been estimated from the probability distribution P (r) in the QM/MM-MD simulation using the Boltzmann relation ∆G(r) = −kB T ln P (r),

(1)

where kB is the Boltzmann constant and T is the temperature (300 K). The free energy profiles are shown in Figure 3. In DapE, we observe that although the O-H bond of water is longer (1.18 ˚ A) due to the influence of Glu134, the water is never completely deprotonated as reflected by a single-well free-energy profile (Figure 3). On the other hand, for wt-DapESDAP and E134D-DapE-SDAP, there are substantial fraction of snapshots with deprotonated catalytic water molecule, as evident from the wide free-energy basin around O-H distance of 1.5 ˚ A (Figure 3). The free-energy profiles show an activation energy barrier of about 3 kcal/mol for both wt-DapE-SDAP and E134D-DapE-SDAP system for the activation of catalytic water molecule (Figure 3). Similar to DapE, the free-energy profiles of H67A and H349A mutant of DapE-SDAP complex show a single-well free-energy profile due to the absence of proton transfer reaction in these two systems (Figure S3, supporting information).


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Non-equilibrium QM/MM-MD Simulation of the Nucleophilic Attack From the above QM/MM-MD simulations, we observed that only in wt-DapE-SDAP and E134D-DapE-SDAP, a substantial concentration of the hydroxyl nucleophile is formed due to the deprotonation of the catalytic water molecule. Therefore, the substrate hydrolysis reaction was further pursued only for these two systems. After the activation of the water molecule, the formed hydroxyl ion undergoes a nucleophilic attack on the carbonyl group of the substrate (Figure 1c). However, our earlier calculations suggested that the nucleophilic attack involves a barrier of 20 kcal/mol, 21 which is too high a barrier to be surmounted by equilibrium QM/MM-MD simulation. Therefore, we adopted non-equilibrium QM/MM-MD simulation technique to study this step of the reaction. Starting from a QM/MM-MD snapshot of wt-DapE-SDAP system where the catalytic water molecule is deprotonated, four steered MD (SMD) simulations were performed, wherein the oxygen atom of the hydroxyl ion was moved towards the carbonyl carbon atom of SDAP by ˚2 ) along the chosen reaction applying four different forces (100, 120, 150, and 200 kcal/mol/A coordinate. The distance between the nucleophile and the electrophile was an obvious choice as the reaction coordinate for the nucleophilic attack and the charge difference between the two centers obtained from NBO calculation supported the choice. For example, the NBO charge difference of the oxygen of the hydroxyl ion and the carbonyl carbon of SDAP was found to be largest after the catalytic water was deprotonated. With the progress of the SMD simulations, as the hydroxyl ion moves closer to the carbonyl center of SDAP, the protonated Glu134 also approaches the substrate SDAP, as it is hydrogen bonded with the hydroxyl ion. This can be seen from the time evolution of the corresponding distances (Figure 4a). Thus, at the end of SMD simulation, the hydroxyl group forms a covalent bond with the carbonyl carbon center of SDAP and the carbonyl (C=O) double bond becomes a single bond (Figure 4a and Figure S4 in the supporting information). An NBO analysis of the last structure of the SMD trajectory confirms that the hybridization of the carbon center (the site of the nucleophilic attack), changes to sp3 from an initial sp2 hybridization. From Figure 4a, we see that the carbonyl double bond



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(C=O) of SDAP gradually lengthens to form a C-O single bond as the nucleophile approaches the carbonyl carbon center of SDAP. As the hydroxyl group forms the covalent bond in the tetrahedral intermediate, its hydrogen bonding interaction with protonated Glu134 is seen to decrease (Figure 4a). From the above mentioned SMD simulations, the path traversed by the nucleophile for the nucleophilic attack was obtained. Twenty-four equi-spaced snapshots from each of the four SMD trajectories were collected. These 24 structures differ from each other in terms of the distance between the nucleophile and the substrate. On each of these snapshots an umbrella potential was applied along the nucleophile-substrate distance and 200 steps (100 fs) of umbrella sampling simulation was carried out. This process was repeated for all four SMD trajectories. The sampling of the reactive coordinate by the applied umbrella potentials are summarized in Figure S5 in the supporting information. The resulting umbrella sampling trajectories were analyzed using WHAM 60,61 and the corresponding free-energy profiles are shown in Figure 5. The free energy profiles from the WHAM analyses estimate the activation energy for the nucleophilic step as 13.9, 15.1, 15.7, and 16.1 kcal/mol in the four umbrella sampling simulations, with an average value of the activation energy barrier as 15.2 kcal/mol (Table 2). Similar to the wt-DapE-SDAP, the nucleophilic attack in E134D-DapE-SDAP system was studied by carrying out four QM/MM-SMD simulations with four different pulling forces (100, 120, 150, and 200 kcal/mol/˚ A2 ) along the distance between the nucleophile and the C atom of the carbonyl group of the substrate. The nucleophilic attack was complete by the end of the QM/MM-SMD simulation, where the tetrahedral intermediate was produced (Figure 4b). NBO calculations were performed on the last snapshot showing tetrahedral intermediate with the carbonyl carbon atom (sp2 hybridized at the beginning of the reaction step) in SDAP showing sp2.92 hybridization in the E134D-DapE-SDAP system, which ascertains the tetrahedral nature of the carbon atom. The distance between the Asp134 residue and the hydroxyl ion is observed to be longer in the E134D-DapE-SDAP compared to that between Glu134 and the hydroxyl group in wt-DapE-SDAP. In wt-DapE-SDAP, the hydrogen bond interaction between Glu134 and hydroxyl group is stronger which is reflected from the to-and-fro movement of the hydrogen atom between the oxygen centers of the newly formed hydroxyl ion and Glu134 (Figure 4a).


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This phenomenon stops once the hydroxyl group is sufficiently close to the SDAP (Figure 4a and Figure S4 in the supporting information). However, in E134D-DapE-SDAP, due to reduced chain length of Asp134 (compared to Glu134), the interaction between Asp134 and hydroxyl group is weaker (Figure 4b). Thirty equi-spaced snapshots were taken from each of the four QM/MM-SMD trajectories of E134D-DapE-SDAP and umbrella sampling simulations were carried out on each of the snapshots, as discussed above. The free-energy profiles obtained from WHAM analysis of the umbrella sampling trajectories show activation free energy barrier of 20.5, 21.0, 22.0, 22.1 kcal/mol (see Figure 5), with an average activation free energy barrier of 21.5 kcal/mol in E134D-DapESDAP (Table 2). The difference in the activation energy barrier between the wt-DapE-SDAP and E134D-DapE-SDAP systems can be attributed to the shorter side chain length of Asp134 in E134D-DapE-SDAP compared to that of Glu134 in wt-DapE-SDAP. The active site residue Glu134 or Asp134 (in E134D mutant) remains hydrogen bonded to the hydroxyl ion as it approaches SDAP. Due to shorter side chain, it is more difficult for Asp134 to get continue to remain hydrogen bonded to the nucleophile as compared to Glu134. This in turn increases the activation energy in case of the E134D-DapE-SDAP system as compared to wt-DapE-SDAP.

QM/MM-MD Simulation of the Cleavage of the Peptide Bond After the formation of the tetrahedral intermediate, the substrate hydrolysis reaction progresses via a proton transfer from the Glu134 to the nitrogen atom of the peptide group of SDAP, which then leads to the weakening of the peptide bond resulting in the substrate hydrolysis. The initial structure of the tetrahedral intermediate of the wt-DapE-SDAP was obtained by taking a snapshot from the last window of the umbrella sampling simulations of the nucleophilic attack in wt-DapE-SDAP system and by removing the biased umbrella potential. In the initial snapshots, the distance between the carboxylate proton of Glu134 and the nitrogen was found to be around 2.00 ˚ A and by performing 5 ps of equilibrium QM/MM-MD simulations, proton transfer from Glu134 to the nitrogen of SDAP was observed (Figure 6a). Four such simulations were carried out starting from four different initial structures obtained from the last step of the four umbrella sampling simulation of the nucleophilic attack in wt-DapE-SDAP system. In



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these simulations, simultaneous breaking of the O-H covalent bond of the protonated side chain of E134 and formation of the N-H covalent bond was observed, resulting the transfer of proton from Glu134 to the nitrogen of SDAP (Figure 6a). The proton transfer results in a slightly elongated C-N bond (Figure 6a), which leads to the formation of the final product, namely DAP and succinic acid. From the time series of N-H and C-N distances in the QM/MM-MD trajectories in wt-DapE-SDAP (Figure 6a and Figure S6a-c in the supporting information), it is clear that the third step of the reaction is initiated by the proton transfer from Glu134 to substrate N atom which then leads to the weakening of the C-N bond. Since the cleaved product molecules are surrounded by protein environment in all directions, they are unable to move much apart. In the present QM/MM-MD simulations for wt-DapE-SDAP, the distance between the atoms of the cleaved peptide bond, the C and N atoms is found to be around 1.6 ˚ A. An NBO analysis on the last snapshot of the QM/MM-MD trajectory clarifies that the C-N bond is indeed cleaved. The free-energy profile along the proton transfer coordinate (obtained using Equation 1) shows an activation energy barrier of 2.5 kcal/mol for the proton transfer from Glu134 to SDAP (Figure 6c). Unlike in the wt-DapE-SDAP system, the QM/MM-MD simulations starting from the tetrahedral intermediate geometry in the E134D-DAPE-SDAP complex did not show the proton transfer from Asp134 to SDAP during the 5 ps of QM/MM-MD simulations. This can be understood from the fact that the distance between the proton donor and proton acceptor atoms in E134D-DapE-SDAP is longer than that in the wt-DapE-SDAP due to shorter side chain of Asp134 in the mutant. To study this reaction step, four different QM/MM-SMD simulations (with four different forces 100, 120, 150, 200 kcal/mol/˚ A2 ) were performed along the distance between the proton of the side chain of D134 and the nitrogen center of SDAP. This choice of the reaction coordinate is inspired from the wt-DapE QM/MM-MD trajectories where the cleavage of C-N bond was seen to be initiated by the proton transfer from Glu134 to substrate N atom (Figure 6a and Figure S6a-c in the supporting information). By the end of the QM/MM-SMD simulations, the proton transfer step was complete (Figure 6b). Twenty snapshots were taken from each of the four QM/MM-SMD simulations that served as the starting points for the biased umbrella sampling simulations. The WHAM analysis of the resulting umbrella sampling


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trajectories yielded the free-energy profiles along the umbrella coordinate that show activation energy barriers of 8.4, 8.7, 9.0, and 9.4 kcal/mol (Figure 6d), with an average value 8.9 kcal/mol of the activation energy barrier (Table 2). The higher activation energy barrier in the E134D mutant is a direct consequence of the shorter side chain length of Asp134, which explains the reason behind non-occurrence of the proton transfer reaction during equilibrium QM/MM-MD simulations. To investigate the the feasibilty of other coordinates as plausible reaction coordinate for the C-N bond breaking in E134D-DapE-SDAP system, two additional QM/MM-SMD simulations were carried out with two different choices of reaction coordinates, namely, (a) elongation of C-N distance and (b) linear combination of C-N bond elongation and N-H bond formation. The corresponding QM/MM-SMD trajectories are given Figure S9 in the supporting information. In both the QM/MM-SMD trajectories, elongation of the C-N bond is observed whereas the desired product is not formed due to the absence of the accompanying proton transfer from Glu134 to substrate. This indicates, as observed from the unbiased QM/MM-MD simulations in the wt-DapE-SDAP system (Figure 6a and Figure S6a-c in the supporting information), the proton transfer from Glu134 to substrate N atom initiates the cleavage of the C-N bond.

Overview of the Catalytic Action by DapE Enzyme From the present study, the nucleophilic attack is found to be the rate determining step in the catalytic hydrolysis reaction by DapE enzyme, both in wt-DapE-SDAP and E134D-DapE-SDAP complexes. The estimated activation energy barrier of 15.2 kcal/mol is in exact agreement with the experimentally determined barrier (15.2 kcal/mol, kcat = 140 s−1 ). 12,43,44 The results from the present QM/MM-MD simulation compares better to the experimental kinetics as against the results from (static) QM/MM method, where the activation energy barrier (estimated as 20 kcal/mol) was obtained from optimization of the reactants, intermediates and transition states. 21 In the so-called static QM/MM method, the effects of temperature and pressure and the role of active site dynamics in the overall enzymatic action are ignored, which resulted in an overestimation of the activation energy barrier. Unlike (static) QM/MM methods, the QM/MM MD simulations treat the biological molecules at finite temperature and pressure. Explicit solvent



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molecules as well as finite ionic concentration and the use of periodic boundary conditions reproduce the state of the biological molecule in the condensed phase in cellular environment. This has resulted an accurate estimation of the activation energy barrier. The kinetic experiments in E134D mutant of DapE found that the enzyme activity kcat in E134D mutant (0.13 s−1 ) decreases by nearly three orders of magnitude compared to the wt-DapE. 12,43,44 This decrease in the value of kcat amounts to an increase in the activation energy barrier by 4.2 kcal/mol at room temperature. This increase in activation is well reproduced in the present QM/MM-MD calculations, where the activation energy barrier in E134D mutant of DapE is found to be 6.3 kcal/mol higher than that of the wt-DapE. Apart from accurately reproducing the experimental kinetic results, the present QM/MM MD method also brings new insight to the mechanism of action of the enzyme. Earlier experimental studies have proposed a multi-step mechanism of catalytic action by DapE enzyme. 12,16,43,44 In the present study, we carried out an equilibrium QM/MM-MD simulation of the enzyme-substrate complex and observed the de-protonation of the catalytic water molecule by Glu134 during the equilibrium simulation. The nucleophilic attack of the resulting hydroxyl ion is a much slower process (rate determining step involving a barrier of 15 kcal/mol) which was not observed during pico-second scale QM/MM-MD simulations. The second step was modelled (by umbrella sampling), only after the catalytic water was deprotonated by Glu134. Therefore, the present work establishes that the reaction is indeed a multi-step reaction, as has been proposed in earlier experimental and computational studies. 12,16,21,43,44 Based on these facts, the present study finds a complete agreement with the previously reported mechanism of catalytic action by DapE enzyme. 12,16,43,44

Conclusions In this work, the mechanism of substrate hydrolysis by DapE enzyme and its three mutants are investigated using hybrid QM/MM-MD method, in which the time evolution of the reactive coordinates are studied by dividing the large enzyme-substrate complex to a chemically relevant part (treated by quantum mechanics) and the remaining part (treated by force field based molecular mechanics).


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The substrate hydrolysis progresses via a general acid-base hydrolysis mechanism, where a catalytic water molecule present is the active site gets activated by Glu134 of DapE. This reaction step was modelled using equilibrium QM/MM-MD simulation technique, which resulted in an activation energy barrier of 2.9 kcal/mol in the wt-DapE-SDAP. Upon E134D mutation, the rate of this reaction was seen to marginally slow down which involved an activation energy barrier of 3.2 kcal/mol. On the other hand, in the H67A-DapE-SDAP and H349A-DapE-SDAP, the absence of His residues near the active site caused a change in the active site conformation that leads to a coordination of Glu134 residue with the Zn metal centers. The Zn-E134 coordination disfavors the activation of catalytic water molecule, thus terminating the catalytic hydrolysis. Comparison of the active site dynamics of DapE and DapE-SDAP complex reveals that, the presence of the substrate SDAP in the complex is essential to induce the activation of the catalytic water molecule by Glu134. The activation of the catalytic water molecule results in the hydroxyl ion, which undergoes a nucleophilic attack to the substrate to give rise to a tetrahedral intermediate. From transition state optimization calculations, the activation energy barrier for this step was estimated to be 20 kcal/mol in the wt-DapE-SDAP. 21 The high activation energy barrier makes this reaction step unsuitable to be studied by equilibration QM/MM-MD method. To overcome this barrier, a non-equilibrium QM/MM-MD sampling technique (umbrella sampling) was adapted with which the reaction was driven along the reaction coordinate by applying external force. The free-energy profiles associated with the umbrella sampling simulations, estimated from weighted histogram analysis method, show a barrier of 15.2 kcal/mol for the wt-DapE-SDAP and 21.5 kcal/mol for E134D-DapE-SDAP. The tetrahedral intermediated formed at the end of the nucleophilic attack undergoes a proton transfer from Glu134 to substrate which results in the cleavage of the peptide bond. While this reaction step could be studied using equilibrium QM/MM-MD simulation in the wt-DapE-SDAP (estimated activation energy barrier of 2 kcal/mol), non-equilibrium umbrella sampling technique was needed for this reaction step in E134D-DapE-SDAP which involves a barrier of 8.9 kcal/mol. The increased barrier in case of E134D-DapE-SDAP is due to the small alkyl side chain in Asp134 residue (in E134D mutant) which makes the proton donation from



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Asp134 to substrate more difficult. The present work demonstrates that with the combination of equilibrium and non-equilibrium QM/MM-MD simulation techniques, the mechanism of enzymatic action can be successfully elucidated and a quantitative comparison to the experimental kinetic results can be made. It is shown that capturing the dynamics in the active site of the enzyme is crucial in successfully explaining the enzymatic action. With a detailed understanding of the catalytic hydrolysis of the natural substrate of DapE achieved in this work, future application of the present strategy in studies involving the action of potential small molecule inhibitors of this important class of enzyme will pave the way for rational design of new inhibitors.

Acknowledgement SM thanks DST-India, New Delhi for Ramanujan Fellowship and IIT Kharagpur for ISIRD grant.

Supporting Information Available Supporting information available with additional tables and figures.

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Table 1: The details of the QM/MM-MD simulations. system DapE wt-DapE-SDAP

step 1a 4 snapshots X 5 ps 4 snapshots X 5 ps

E134D-DapESDAP

4 snapshots X 5 ps

H67A-DapE-SDAP H349A-DapESDAP

4 snapshots X 5 ps 4 snapshots X 5 ps

step 2b

step 3

4 snapshots X 24 umbrella potentials X 0.1 ps 4 snapshots X 30 umbrella potentials X 0.1 ps

4 snapshots X 5 psa

4 snapshots X 20 umbrella potentials X 0.1 psb

a

Equilibrium QM/MM-MD simulation. b Umbrella sampling simulation. During umbrella sampling, the four snapshots were treated with umbrella potentials of four different force constants, namely, 100, 120, 150, and 200 kcal/mol/˚ A2 . Table 2: The activation free energy barriers (∆G† in kcal/mol) for different steps of the reaction and comparison with experimental results. ∆G† (step 1) ∆G† (step 2) ∆G† (step 3) kcat (expta ) ∆G† (expta ) ∆G† (calcb ) a

wt-DapE-SDAP 2.9 15.2 2 140 s−1 15.3 15.2 Reference. 12,44

b

E134D-DapE-SDAP 3.2 21.5 8.9 0.13 s−1 19.5 21.5

This work.


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(a)

(b) (c) Figure 1: (a) DapE enzyme in cartoon representation with the active site in the catalytic domain. (b) The active site of DapE with SDAP after 5 ns of equilibration at 300 K. The peptide bond to be hydrolyzed is shown by the arrow. (b) Putative mechanism of the hydrolysis of L,L-SDAP by DapE.


2 1.8 1.6

0.8

1

1

2

3

4

5

2 1.8 1.6

-

H(Wat)-COO (E134) (Å)

O-H (wat) bond order

1.2

0

0.4

1.2 1

0

1

4 2 3 Time (ps) (1 step=0.5 fs)

0

5

H(wat)-O(Wat) (Å)

E134D-DapE-SDAP S1

1.8 1.6 1.4 1.2 1

2

3

4

5

1.8

-

1.6 1.4 1.2 1 0

1.1

1.4 1.2 1.3 O-H (Wat) distance (Å)

1.5

1.6

2

2

1 0 2

1

(b)

H(Wat)-COO (E134) (Å)

H(Wat)-O(Wat) (Å) -

0.6

0.2

1.4

(a)

(c)

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1

QM/MM-MD trajectory 1 QM/MM-MD trajectory 2 QM/MM-MD trajectory 3 QM/MM-MD trajectory 4

1.4

H(Wat)-COO (D134) (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

H(Wat)-O(wat) (Å)


1 4 2 3 Time (ps) ) (1 step=0.5 fs)

5

(d)

1.8 1.6 1.4 1.2 1

0

1

4

5

4 2 3 Time (ps) (1 step=0.5 fs)

5

2

3

2 1.8 1.6 1.4 1.2 1

0

1

Figure 2: Time evolution of the reactive coordinates during the activation of catalytic water molecule obtained from QM/MM-MD simulations of (a) wt-DapE-SDAP (c) E134DDapE-SDAP and (d) wt-DapE. (b) The relation between bond order and bond distance of the O-H bond of the catalytic water molecule obtained from NBO calculations carried out with the snapshots from the QM/MM-MD simulations of wt-DapE-SDAP.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Free energy (kcal/mol)

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apo-DapE wt-DapE-SDAP E134D DapE-SDAP

4 3

2 1 0

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

O-H distance (Å) Figure 3: Free-energy profile along the proton transfer coordinate obtained from the QM/MM-MD simulations of wt-DapE, wt-DapE-SDAP, and E134D-DapE-SDAP systems using Equation 1.



5

5 O(Wat)-C(SDAP) H(E134)-O(wat) H(E134)-O(E134) C(SDAP)-O(SDAP)

O(Wat)-C(SDAP) H(D134)-O(Wat) H(D134)-O(D134) C(SDAP)-O(SDAP)

4 Distance (Å)

4 Distance (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 33

3

3

2

2 1

1 0

(a)

0.25 0.50 0.75 1.0 Time (ps) (1step = 0.5 fs)

0 0

(b)

0.25 0.5 0.75 1.0 Time (ps) (1 step = 0.5 fs)

1.25

Figure 4: Time evolution of the reactive coordinates during QM/MM-SMD simulation of (a) wt-DapE-SDAP (b) E134D-DapE-SDAP steered along the distance between the nucleophile (hydroxyl ion) and carbonyl carbon atom of substrate with a pulling force of 100 kcal/mol/˚ A2 . The results from the pulling forces of 200, 150, and 100 kcal/mol/˚ A2 are shown in Figure S4 in the supporting information.


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25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25

(a)

20

20

15

15

10

10

5

5

0

4

3

1

2

0

(b)

4

3

2

1

umbrella coordinate (Å) Figure 5: Free-energy profiles obtained from the weighted histogram analysis of the umbrella sampling trajectories obtained with biased umbrella potential (of force constants 200, 150, 120, and 100 kcal/mol/˚ A2 ) along the umbrella coordinate represented by the distance between the nucleophile (hydroxyl ion) and carbonyl carbon atom of substrate for (a) wt-DapE-SDAP (left panel) and (b) E134D-DapE-SDAP.



6

3 C-N(SDAP) H(E134)-N(SDAP) H(E134)-O(E134) H-N(SDAP)

5 Free energy (kcal/mol)

Distance (Å)

2.5

2

1.5

4 3 P TD

2 1

1 0

(a)

1 4 2 3 Time (ps) (1 step = 0.5 fs)

0 2.5

5

(b)

C(SDAP)-N(SDAP) H(D134)-N(SDAP) H(D134)-O(D134) H(SDAP)-N(SDAP)


2.5

2

1.5

1 0

(c)

1.5 2 H(E134)-N(SDAP) (Å)

1

10

3

Distance (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 33

8 6 4 2 0

0.25 0.50 Time (ps) (1 step = 0.5 fs)

3

0.75

(d)

2.5

2

1.5

1

umbrella coordinate (Å)

Figure 6: (a) Time evolution of the reactive coordinates during QM/MM-MD simulation of wt-DapE-SDAP with initial structure containing the substrate in the tetrahedral intermediate form. The trajectory shows the transfer of a proton from Glu134 to the N atom of substrate SDAP. The results from three other trajectories are given in Figure S6 in the supporting information. (b) The free-energy profile (obtained by using Equation 1) along the proton transfer coordinate from the QM/MM-MD trajectories. (c) Time evolution of the reactive coordinates during QM/MM-SMD simulation of E134D-DapE-SDAP starting from the tetrahedral intermediate structure of E134D-DapE-SDAP system using pulling force of 100 kcal/mol/˚ A2 . The results from the pulling forces of 200, 150, and 2 120 kcal/mol/˚ A are shown in Figure S7 in the supporting information. (d) Free-energy profiles obtained from the weighted histogram analysis of the umbrella sampling trajectories for E134D-DapE-SDAP system obtained with biased umbrella potential (of force constants 200, 150, 120, and 100 kcal/mol/˚ A2 ) along the umbrella coordinate represented by the proton transfer coordinate between Asp134 and N atom of substrate.


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Table of Contents Graphics


Active Site Dynamics in Substrate Hydrolysis Catalyzed by DapE

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