Comparison of formation of reactive conformers for the S_N2 displacements by CH₃CO in water and by Asp124-CO in a haloalkane dehalogenase

Abstract

The S_N2 displacement of Cl⁻ from 1,2-dichloroethane by acetate (CH₃CO) in water and by the carboxylate of the active site aspartate in the haloalkane dehalogenase of Xanthobacter autothropicus have been compared by using molecular dynamics simulations. In aqueous solution, six families of contact-pair structures (I–VI) were identified, and their relative concentrations and dissociation rate constants were determined. The near attack conformers (NACs) required for the S_N2 displacement reaction are members of the IV (CH₃COO⁻⋅ ⋅ ⋅CH₂(Cl)CH₂Cl) family and are formed in the sequence II→III→IV→NAC. The NAC subclass is defined by the —COO⁻⋅ ⋅ ⋅C—Cl contact distance of ≤3.41 Å and the —COO⁻⋅ ⋅ ⋅C—Cl angle of 157–180°. The mole percentage of NACs is 0.16%, based on the 1 M standard state. This result may be compared with 13.4 mole percentage of NACs in the Michaelis complex in the enzyme. It follows that NAC formation in the enzyme is favored by 2.6 kcal/mol. Because reaction coordinates from S to TS, both in water and in the enzyme, pass via NAC (i.e., S → NAC → TS), the reduction in the S → NAC barrier by 2.6 kcal/mol accounts for ≈25% of the reduction of total barrier in the S → TS (10.7 kcal/mol). The remaining 75% of the advantage of the enzymatic reaction revolves around the efficiency of NAC → TS step. This process, based on previous studies, is discussed briefly.

Xanthobacter autothropicus haloalkane dehalogenase (DhlA) catalyzes the S_N2 displacement of the halogen substituent from haloalkanes by Asp-CO. This reaction can be compared with the reaction in water with CH₃CO (AcO⁻) as a nucleophile (Scheme S1). The activation barrier (ΔG^≠) for the displacement of Cl⁻ from dichloroethane (DCE) is 15.3 kcal/mol for the enzymatic reaction (1) and ≈26 kcal/mol for the nonenzymatic counterpart in water (2). The first goal of this study is to devise means of determining the time-dependent mechanism of forming contact pairs from two separate reactants in water that satisfy the structural restraints of a near attack conformation (NAC). The second objective is to evaluate the contribution of NAC formation to the kinetic advantage of the DhlA reaction over the model reaction in water. These procedures can be generally applied to a study of various enzymatic catalysis over a water reaction.

Scheme 1.

Methods

Molecular Dynamics (MD) Simulation of 1,2-DCE and Acetate in Water.

To compare ground state structures of reactants in water with those in the enzyme active site, an MD simulation was performed on the system consisting of 1,2-DCE and an acetate ion (AcO⁻) in a box of TIP3P water (3). Standard charmm (version 27) force field was used for AcO⁻ although opls force field parameters were adopted for DCE. The torsional parameters for DCE were adjusted so that only one of the two gauche conformations was sampled. It is known that for the S_N2 displacement of Cl⁻, DCE should be in a gauche conformation (4–6). After the reactants were placed in a water box of size 20 × 20 × 20 ų, any TIP3P water molecule whose oxygen was within 2.6 Å from any atom of the reactants was deleted, and the system was energy-minimized by using a combination of the steepest descent (SD) and adopted basis Newton-Raphson (ABNR) methods (7). An MD simulation was performed on the energy-minimized system with the position of carboxyl carbon of the acetate fixed at the center of the box. A periodic boundary condition was used to simulate a continuous water pool. The shake algorithm was used to constrain bonds containing hydrogens to their equilibrium lengths (8). The Verlet leapfrog algorithm was used to integrate the equations of motion (9). A time step of 1.5 fs was used, and the nonbonded list was updated every 20 time steps. The nonbonded interactions were cut off at 10 Å. The Coulombic term was cut off by using a force shifting function, and the Lennard-Jones term was cut off with a switching function. The system was initially coupled to a 200 K heat bath for 15 ps by using a coupling constant of 5 s⁻¹. The system was subsequently coupled to a heat bath at 300 K for the rest of the simulation (23 ns) by using a coupling constant of 5 s⁻¹. The pressure was constantly maintained by a Berendsen algorithm (10) using an isothermal compressibility of 4.63 × 10⁻⁵ atm⁻¹ and a pressure coupling constant of 5.0 ps. Coordinates were saved every 100 time steps.

When analyzing the trajectory, a configuration of AcO⁻ and DCE is classified as a contact pair when the closest intermolecular distance is within the van der Waals distance between two interacting atoms. The van der Waals radii used are 1.92 Å for sp³ carbon, 1.76 Å for sp² carbon in acetate, 1.49 Å for acetate oxygen, and 1.75 Å for chlorine (11).

Results

Interactions between AcO⁻ and DCE (0.214 M for each) were investigated in water by using 23 ns MD simulation. The following results are based on the analysis of structures at every 0.15 ps of this MD trajectory. Reported numerical values in this paper are based on the correction to a 1 M standard state of both reactants.

Structures of Contact Pairs (AcO⁻⋅DCE) in Water.

In a 1 M aqueous solution of AcO⁻ and 1,2-DCE, collision dimers are present 43% of the time. Once these dimers form, the partners remain together for ≈25 ps on average and in few cases up to ≈80 ps. During this ≈25- to 80-ps time, the type of contact changes every few picoseconds. Fig. 1 shows structures of the various dimers.

Figure 1.

Six contact pairs of ClCH₂CH₂Cl and CH₃CO. NAC is subspecies of IV where the angle of approach —COO⁻⋅ ⋅ ⋅ C—Cl is within the range of 157–180°. Atoms are colored by using standard atom representation: O (red), C (gray), H (white), Cl (green).

The formation of six contact pairs can be observed to occur at a frequency in the decreasing order of I, II ≫ III, IV > V, VI (Table 1). In ≈85% of the dimeric states (I and II), the acetate-COO⁻ points away from the partner DCE. In these cases, there is little preference in choosing the complexing moiety of DCE (—CH₂ or —Cl). The slight preference to DCE-Cl (I) over DCE-CH₂ (II) may be due to the larger surface area of the —Cl. When acetate-COO⁻ is involved in a contact, the preference for the contact is with DCE-CH₂ (III, IV) over DCE-Cl (V, VI) due to the negative electrostatic interaction of acetate-COO⁻ and DCE-Cl. The atomic charges for the DCE methylene C is −0.06 electronic unit (e.u.), and the charge for —Cl is −0.20 e.u. For IV and VI, it should be noted that the mole factions are obtained by counting contacts involving either O of the carboxylate ion. Thus, the probability to be involved in forming a dimer for each O is the half of the values listed in Table 1.

Table 1.

Mole fraction of contact pairs of DCE and CH₃CO and the first-order rate constants for disappearance of each contact pair

Contact pairs	Symbol	Mole fraction, %	kdiss × 1012, s−1
—O2CCH3⋅ ⋅ ⋅CICH2CH2CI	I	43	3.6
—O2CCH3⋅ ⋅ ⋅CH2(CI)CH2CI	II	41	4.3
H3CCO⋅ ⋅ ⋅CH2(CI)CH2CI	III	6	6.4
H3CCOO−⋅ ⋅ ⋅CH2(CI)CH2CI	IV	6	23
H3CCO⋅ ⋅ ⋅CICH2CH2CI	V	2	11
H3CCOO−⋅ ⋅ ⋅CICH2CH2CI*	VI	1	20

The DCE is present as one of two equivalent gauche conformers. 

^*Mole fraction of conformer IV and VI are calculated by counting contacts involving either O of the carboxylate. 

From MD trajectories, one can also study the kinetic stability of each contact pair by calculating the first order rate constants for its dissociation (k_diss). The k_diss for contact pair decomposition was obtained from the statistics of the length of time for each contact pair to remain before it dissociates or rearranges into another contact pair. The first order plots of log (concentration of the contact pair) vs. time are shown in Fig. 2, and the slopes of each plot (k_diss, ×10¹² s⁻¹) are summarized in Table 1. All of these k_diss are within the range of 10¹² s⁻¹. The half-life (log (2)/k_diss) of each contact pair is in the decreasing order of I, II > III, V > IV, VI. This finding is comparable to the trend observed in the relative concentrations of contact pairs at equilibrium (I, II > III, IV > V, VI). I and II are the most probable contact pairs and dissociate most slowly. The differences between the order of the half-life and the order of concentration at equilibrium are in IV and V. The somewhat faster dissociation of IV reflects an energetic cost in desolvating the acetate-COO⁻ when forming a contact with DCE, which will be discussed further (see below). It was observed from our simulation that formation of dimers involving the acetate-COO⁻ (III and V) do not require desolvation. This finding may explain their relatively longer half-lives compared with IV and VI, even though III and V appear less frequently than IV and VI.

Figure 2.

First order kinetics of contact pairs I (♦), II (+), III (□), IV (×), V (▵), and VI (*). The coefficients of correlation are >9.5 for all of the contact pairs.

Mechanism of NAC Formation in Water.

Among the various contact dimers in water (Fig. 1), only those in which acetate-COO⁻ contacts (IV) the back side of CH₂-Cl can undergo an S_N2 displacement of Cl⁻. Therefore, our definition of the NAC is the —COO⁻⋅ ⋅ ⋅C—Cl distance ≤3.41 Å and the angle of attack given by —COO⁻⋅ ⋅ ⋅C—Cl being within ±15° deviation from the angle in the TS. We first discuss the mechanism of IV formation, followed by discussion on the character of the approach angles in IV and the NAC formation.

Dimers involving the AcO⁻⋅⋅⋅CH₂(Cl)CH₂Cl (IV) contact are disfavored. A dimer IV is not formed frequently (6% of total dimers), and even once formed it rapidly dissociates or rearranges into another contact pair (dissociation rate constant is 23.4 × 10¹² s⁻¹; Table 1). The instability of IV reflects an energetic cost in desolvating the AcO⁻ when forming a contact with DCE. Based on the observation of the hydration shell structures, the following picture is proposed (Scheme S2). With AcO⁻ in water, there are three water molecules associated with each O of the carboxylate, and one water molecule is held between them. This bridging water molecule is bound more strongly to one of the AcO⁻ oxygens and then moves to the other oxygen. For acetate, when complexed with DCE, the complexing O is hydrated by three water molecules and the noncomplexing O hydrated by three or four water molecules. These pictorial descriptions are supported by the time-average number of water molecules whose H is within 2.4 Å distant from O of AcO⁻ in free and in complexed states. In a free state, there are 3.5 water molecules within the sphere (r = 2.4 Å) around each O of the carboxylate, whereas in a complex IV, there are 3.0 water molecules for the complexing O and 3.6 water molecules for the noncomplexing O. Thus, desolvation required in formation of IV is equivalent to breaking of ≈0.5 water–hydrogen bond (Scheme S2).

Scheme 2.

It was observed that the desolvation of the complexing O of AcO⁻ is achieved not by a direct collision between two molecules, but via a formation of series of other contacts, which do not require a disruption of hydrogen bonds between water and the solutes. Statistics of contact pairs forming before IV shows that II → III → IV is the most probable path leading to IV, with the same carbon center of DCE involved in II, III, and IV contacts (Scheme S3). This characteristic of having a specific path to form IV is a distinct feature of IV compared with other contact pairs such as I or II. The path in Scheme S3 is obtained in the following manner. Throughout the trajectory, whenever the contact-pair IV is formed, the types of contact pair occurring for the time of τ just before the formation of IV were sampled. These statistics were repeatedly obtained with varying τ (1.5, 3.3, 5.0, 10.0, and 15.0 ps) to trace the time-evolution pattern of the contact-pair just before IV (Fig. 3). The same procedures were repeated for the I and II contact pairs for a comparison purpose. Among the structures (Y) preceding the X (X = IV, I, or II) contact, the contact pair Y is designated by Y′ if the complexing —CH₂Cl of DCE is different from that in X (i.e., if transition of Y → X involves a 1,2-migration). In Fig. 3, the dimer statistics just before X = IV, I, and II approximately reflect the general feature of the probability of each dimer shown in Table 1; i.e., I, I′, II and II′ occur more often than III-VI′. However, three following features are seen in the statistics of X = IV, which distinguish from X = I or II. First, the number of contacts for X = IV is greater than for X = I or II regardless of the type of Y during the same sampling period τ. This result implies that IV prefers to form via other dimeric state(s) rather than by a direct collision. Second, the number of contact Y = III before X = IV becomes even larger than Y = I, I′, or II′ when decreasing the sampling period τ. This result suggests that III is most likely followed by X = IV. Third, among Y = I, I′, II and II′, there is a stronger preference for II rather than I, I′ or II′. This feature also becomes pronounced when decreasing τ, implying II also occurs just before IV with high probability. Between II and III, formation of II might precede formation of III because, as τ gets smaller, the population of II decreases more rapidly than does III. All of these features are not seen in the statistics of X = I or II. In fact, the dimer statistics just before X = I (Fig. 3B) and X = II (Fig. 3C) are similar to the relative population of each conformer when sampled throughout the whole trajectory (Table 1). This result implies that there is no correlation between X (I or II) and Y (conformers formed just before X). These observations establish the proposed scenario of II → III → IV (Scheme S3).

Scheme 3.

Figure 3.

Statistics of contact pairs (Y) formed for τ (ps) just before formation of X. τ is varied from 1.6 ps (red bar), 3.3 (violet), 5.0 (light yellow), and 10.0 (light blue) to 15.0 ps (dark blue). Notice that the contact pair whose type is the same as X is excluded in the statistics of Y.

Five percent of IV satisfies the attack-angle criterion of NAC (—COO⁻⋅⋅⋅C—Cl ≤ 157–180°). Examination of angles of approach to form IV shows that the population is distributed as a normal sine curve along the angle of approach, with the most configurations populating at 90–120° (gray bars in Fig. 4). Mathematically the number of possible configurations at a certain angle of approach is a sine function of the angle of approach. Thus, a perfect sine distribution establishes no preference to a configuration of a certain angle of approach. For the case under inspection, the curvature is not completely symmetric due to the electrostatic repulsion between AcO⁻ and DCE-Cl at small angles of approach.

Figure 4.

Statistics of angle of approach —COO⁻⋅ ⋅ ⋅ C—Cl in water (gray bars) and in enzyme (black bars).

Discussion

Kinetic/Thermodynamic Properties of Contact Pairs (AcO⁻⋅DCE) in Water.

The present work establishes methods to study behaviors of two reactants in water and compare this with a behavior of substrate in the enzyme. A behavior of ground state in water can be studied by examining various contact pairs. Six contact pairs of AcO⁻⋅DCE (I, II, III, IV, V, and VI in Fig. 1) have different populations and half-lives, depending on the nature of solute–solute interactions and solute–water interactions. The trend in both the population and the half-life follow the order of I, II ≫ III, IV > V, VI (Table 1). It was observed that formation of IV (CH₃COO⁻⋅ ⋅ ⋅CH₂(Cl)CH₂Cl) and VI (CH₃COO⁻⋅ ⋅ ⋅ClCH₂CH₂Cl) requires desolvation of AcO⁻.

The Mechanism of NAC Formation in Water.

Due to the requirement of desolvation of the acetate-COO⁻, formation of IV in water does not occur via random collision of AcO⁻and DCE. There is a specific path that is favored in IV formation (Scheme S3). First, AcO⁻ and DCE form a complex, which most frequently involves contact between the acetate-CH₃ and either DCE-Cl (I) or DCE-CH₂ (II). The two contact structures I and II are formed without breaking hydrogen bonds to the waters solvating the two carboxylate oxygens of AcO⁻. I or II frequently rearrange by rotation and translation of the DCE and AcO⁻ components relative to the other while retaining the dimeric state for ≈25–80 ps. From the statistics of contact pairs present just before IV (Fig. 3), we propose the series of II → III → IV as a time-dependent mechanism of IV formation (Scheme S3). In this series of dimer formation, the —CH carbon center of DCE, which is involved in IV, is the same carbon that is in contact with AcO⁻ in the preceding II and III (Scheme S3). Desolvation of water occurs in the last step of III → IV. The number of water hydrogen bonds formed at the contact O of AcO⁻ is 3.5(II) → 3.5(III) → 3.0(IV).

NACs are subspecies of IV in which the attack angle of —COO⁻⋅ ⋅ ⋅C—Cl is within ±15° deviation from the bonding angle in the TS for the S_N2 displacement of Cl⁻. The mole fraction of all dimeric species (I, II, III, IV, V, VI) present at any time that are NACs is calculated to be 0.16%. This result can be compared with 13.4% of the mole percentage of DhlA⋅DCE conformers present as NACs in the Michaelis complex (12).

Comparison of Reaction Coordinates in Water and in Enzyme: Energy Contribution of NAC Formation to Free Energy of Activation.

By using the mole fraction of NAC found in the MD simulations, the free energy difference in forming a NAC in water and in the enzyme can be quantitatively compared. Both reaction coordinates start from the same standard 1 M concentration of the DCE, AcO⁻ and enzyme in aqueous solution (Scheme S4). From the literature, 1/K_m for the formation of DhlA⋅DCE complex is 2,000 M⁻¹ (ΔG° of substrate binding to DhlA = −4.5 kcal/mol; ref. 13). We have shown that 13.4% of this DhlA⋅DCE complex is represented by DhlA⋅NAC with all of the enzyme-bound DCE in gauche forms. Therefore, on average DhlA⋅NAC is 1.2 kcal/mol above the average energy of DhlA⋅DCE Michaelis complex. Now the reaction coordinate for the reaction in water can be assembled. Computational study by Jorgensen et al. (14) has shown that either of the two degenerate gauche forms is 0.62 kcal/mol more stable than the trans form in water. This result gives gauche-DCE [DCE(g)] being 0.1 kcal/mol above the total ground state. Formation of the AcO⁻⋅DCE(g) complex in which the —CH₃ moiety of AcO⁻ is in contact with the DCE carbon center (I or II) is 0.5 kcal/mol above the free energy of 1 M solution of DCE(g) and AcO⁻. This complex is equivalent to DhlA⋅DCE complex in the enzymatic reaction. We show that the aqueous NAC resides 3.2 kcal/mol above the AcO⁻⋅DCE(g) complex. In summary, the free energy difference between the NAC and the ground state of AcO⁻ and DCE at 1 M concentration is 3.8 kcal/mol, whereas the free energy difference between DhlA⋅DCE and DhlA⋅NAC is 1.2 kcal/mol. The activation energy is 26 kcal/mol in water (2) and 15.3 kcal/mol at the enzyme active site (1). Thus, the free energy difference in formation of NAC (2.6 kcal/mol) accounts for ≈25% of the advantage of the enzymatic reaction (ΔΔG^≠ = 11 kcal/mol).

Scheme 4.

*, Experimental.

The remaining 75% of the kinetic advantage of the enzyme over water stems from the ability of the enzyme to facilitate the reaction from NAC to TS. We have previously examined the E⋅NAC and E⋅TS structures by MD simulations (12). The enzyme reaction has also been explored by AM1/MM in which AM1 Hamiltonian was recalibrated to reproduce the energetics and geometries along the S_N2 reaction path for nucleophilic attack of AcO⁻ at DCE (15). A good portion of this advantage can be explained by the half-polar and half-hydrophobic surrounding of S and TS (Fig. 5), which assures both proton dissociation from nucleophilic Asp-124-COO⁻ and the advantage of a low dielectric for such an S_N2 displacement (16). Additional factors in catalysis are the movement of water molecules away from the active site on formation of TS and the assistance to departure of Cl⁻ in the TS by Trp-125 and Trp-175 (12). Quantitation of the importance to the energetics of NAC → TS of the heterogeneous active site, desolvation of nucleophile, and assistance to departure of the leaving group is presently impossible.

Figure 5.

Corey–Pauling–Koltun view of the hydrophobic pocket of DhlA with substrate DCE bound to it. Residues (gray) surrounding the substrate DCE form extensive van der Waals contacts with DCE. (A) View from the side of —CH₂Cl (gray at C and green at Cl) that is being attacked by Asp-124-COO⁻ (red at O). Only one water molecule (blue) is hydrogen bonded to the attacking O of Asp-124. This water molecule has moved away in the TS. (B) The dissected view of the structure in A. The carbon center shown is the nonelectrophilic C (gray), and Cl (green) is the nonleaving Cl.

Abbreviations

DhlA

Xanthobacter autothropicus haloalkane dehalogenase

DCE

dichloroethane

AcO⁻

acetate

NAC

near attack conformer

MD

molecular dynamics