Mechanistic insights into the dehalogenation reaction of fluoroacetate/fluoroacetic acid Sebastián Miranda-Rojas and Alejandro Toro-Labbé Citation: The Journal of Chemical Physics 142, 194301 (2015); doi: 10.1063/1.4920946 View online: http://dx.doi.org/10.1063/1.4920946 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/19?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A probability generating function method for stochastic reaction networks J. Chem. Phys. 136, 234108 (2012); 10.1063/1.4729374 Trends in C–O and C–N bond formations over transition metal surfaces: An insight into kinetic sensitivity in catalytic reactions J. Chem. Phys. 126, 194706 (2007); 10.1063/1.2734544 Effects of nonproductive binding on the kinetics of enzymatic reactions with patterned substrates J. Chem. Phys. 126, 035103 (2007); 10.1063/1.2428301 Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: Proton transfer in triosephosphate isomerase J. Chem. Phys. 124, 124516 (2006); 10.1063/1.2181145 Activation and protonation of dinitrogen at the FeMo cofactor of nitrogenase J. Chem. Phys. 123, 074306 (2005); 10.1063/1.2008227
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THE JOURNAL OF CHEMICAL PHYSICS 142, 194301 (2015)
Mechanistic insights into the dehalogenation reaction of fluoroacetate/fluoroacetic acid Sebastián Miranda-Rojas1,a) and Alejandro Toro-Labbé2 1
Chemical Processes and Catalysis (CPC), Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Avenida República 275, Santiago, Chile 2 Laboratorio de Química Teórica Computacional (QTC), Facultad de Química, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile
(Received 11 February 2015; accepted 29 April 2015; published online 15 May 2015) Fluoroacetate is a toxic compound whose environmental accumulation may represent an important contamination problem, its elimination is therefore a challenging issue. Fluoroacetate dehalogenase catalyzes its degradation through a two step process initiated by an SN2 reaction in which the aspartate residue performs a nucleophilic attack on the carbon bonded to the fluorine; the second step is hydrolysis that releases the product as glycolate. In this paper, we present a study based on density functional theory calculations of the SN2 initiation reaction modeled through the interaction between the substrate and the propionate anion as the nucleophile. Results are analyzed within the framework of the reaction force and using the reaction electronic flux to identify and characterize the electronic activity that drives the reaction. Our results reveal that the selective protonation of the substrate catalyzes the reaction by decreasing the resistance of the structural and electronic reorganization needed to reach the transition state. Finally, the reaction energy is modulated by the degree of stabilization of the fluoride anion formed after the SN2 reaction. In this way, a site-induced partial protonation acts as a chemical switch in a key process that determines the output of the reaction. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4920946]
I. INTRODUCTION
The environmental accumulation of organohalogen compounds represents a major pollution problem and dehalogenation reactions are the main way for degradation.1,2 Among these compounds, the fluorinated molecules are the hardest to eliminate due to thier strong C—F bond.3,4 Related to the latter, the fluoroacetate (FAc) is a compound commonly present in nature and has been found to be highly toxic for mammals because of its conversion into fluorocitrate, a precursor of a potent inhibitor of aconitase, enzyme involved in the citric acid cycle.5–7 Dehalogenases in general share the first step of the reaction mechanisms, which corresponds to a nucleophilic attack to the carbon Cα bonded to the halogen atom (see Fig. 1).8–10 In the particular case of the fluoroacetate dehalogenase (FAcD) enzyme, this key step represents a chemically interesting problem because the Cα under nucleophilic attack is adjacent to a carboxylate. The study of this SN2 step that initiates the catalytic reaction is the target of this paper. From the most recently available crystal structure of the FAcD enzyme,11 it is possible to identify key structural features that help to understand the way the FAcD enzyme acts. In this structure, the nucleophile (aspartate) was mutated into asparagine in order to capture the substrate before its conversion to product. Fig. 1(a) displays the available crystal structure,11 where the nitrogen from asparagine amide was replaced by a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2015/142(19)/194301/9/$30.00
oxygen to represent the aspartate, nucleophile of the SN2 reaction. From the reactant conformation displayed in Fig. 1(a), it can be noticed that the Cα—F bond is practically coplanar to the carboxylate. However, according to previous theoretical studies,12 the preferred transition state for this type of SN2 reaction in vacuum situate the Cα—F bond out of the plane of the carboxylic moiety. This was explained by the stabilizing interaction between the π-bond of the carboxylate group with the orbitals involved in the reaction axis.12 Fig. 1(b) shows the conformation of the product of the SN2 reaction and intermediate of the whole catalytic process, where the orientation of the carboxylate barely changed with respect to the reactant. Consistency between the crystal structure of the reactants, transition state, and intermediate described above would imply an internal rotation of the CH2—F group along the Cα—C bond that should involve important structural work. Then, two probable scenarios are possible, the first where the transition state actually changes its conformation from the reactant situating the Cα—F bond out of the plane of the carboxylate moiety; and the case where the transition state has a similar conformation with reactant and product. Therefore, these scenarios open the question about the relevance of the conformation of the transition state of the SN2 reaction. On the other hand, the close interaction of the carboxylate from the substrate with two arginines and a tyrosine, also depicted in Fig. 1, may allow a partial proton transfer that could modify the behavior of the reaction. Something that have not received much attention is that experimental evidence reported in the mid forties suggested that FAc is more reactive toward nucleophilic substitution when its carboxylic acid is in the protonated
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FIG. 1. Crystal structure of the complex formed between the substrate (FAc) and the nucleophile (aspartic acid) in the reactant (a) and product (b) states.11 Here are depicted the main interactions between the carboxylate moiety of the substrate with the binding site. The red ellipse encloses the reduced reaction model that is used in this study and the black arrow connects the atoms involved in the nucleophilic attack.
form,13 results that motivated this research. Experimentally, it is difficult to characterize the effect of a selective protonation of the substrate in solution without affecting the nucleophile since both have a carboxylic acid and a very low pH solution will protonate the two reactants, and not only the substrate as needed. However, the description of the behavior of this reaction in solution is possible by computational methods, thus helping to understand the features that the enzyme can exploit in order to reach its catalytic proficiency. The only insights about the activation of this catalytic step are associated to the interaction of the halogen with His155, Trp156, and Tyr219 (numbering according to PDB ID 3R3U from Rhodopseudomonas palustris11) which may facilitate the Cα—F bond dissociation.11,14,15 Nevertheless, there are intrinsic properties of the ligand that we will expose in this article that may be affected by the enzyme environment, which have not been explored and would help to explain how the enzyme decreases the energy barrier for this process. Moreover, we obtained new insights from the analysis of the electronic structure along the reaction coordinate that provides a deeper understanding of the behavior of FAc during the SN2 reaction. In this context, the effect of the conformational change of the transition states and the protonation of the substrate in the SN2 reaction without explicitly considering the enzyme environment are key issues that are going to be addressed in this study. We present a detailed study of the reaction using the model system enclosed within the ellipse displayed in Fig. 1. In Fig. 2 are displayed the key conformations of the three reactions under study. To characterize the effect that the protonation state of the carboxylic acid from the substrate has in the reaction mechanism, it was studied as a carboxylic acid (protonated form) and as a carboxylate (deprotonated form), reactions R1 and R2, respectively (Fig. 2). From this point, we will refer as protonated substrate when we need to discuss about the substrate with the protonated carboxylic acid, and deprotonated substrate when we need to refer to the substrate with the carboxylate anion. The possibility of the catalytic
site to change the conformation of the transition state was also studied, where comparison of reactions R1 and R3, both involving the protonated substrate, addresses this issue. All three reactions displayed in Fig. 2 were analyzed within the framework of the reaction force analysis16–21 and the reaction electronic flux,20,21 this to characterize the electronic activity taking place during the reaction.
II. THEORETICAL BACKGROUND A. Reaction force
The intrinsic reaction coordinate (IRC)22,23 procedure has become an extremely useful tool to follow the mechanistic events associated to a chemical reaction, it provides the minimum energy pathway that connects along a reaction coordinate (ξ = IRC), the transition state with reactants and products. Despite the relevance of the energy profile, which provides the kinetic and the thermodynamic information of the reaction, it is not able to provide information about the mechanism of a chemical reaction. The reaction force analysis provides a useful framework to characterize reaction mechanisms, it is defined as the negative derivative of the energy with respect to ξ,16–21 the reaction coordinate F(ξ) = −
dE . dξ
(1)
For any elementary step in which the products are separated from the reactants by an energy barrier, the reaction force profile presents two critical points, ξ1 and ξ2. The first critical point ξ1 is located somewhere between the reactants (ξR) and the transition state (ξTS); ξ2 is located between the ξTS and the products (ξP). This entails a natural division of the reaction coordinate into three reaction regions (RR); it has been observed in many different kinds of reactions that each RR is mostly associated to specific processes that drive the reaction until the final chemical product.18,24–27 First, the reactant region (ξR ≤ ξ ≤ ξ1), is generally dominated
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FIG. 2. Schematic representation of the reactant, transition state, and product of reactions R1-R3. In R1 the carboxylic acid is perpendicular to the axis of reaction (red dashed arrow); R2 represents the completely deprotonated reaction, and in R3 the carboxylic acid is parallel to the axis of reaction at the transition state.
by structural rearrangements that activate the reactant. Then follows the transition state region (ξ1 ≤ ξ ≤ ξ2), where most of the electronic reorganization occurs, in this region most of the bond formation and bond breaking processes take place. Finally, the product region (ξ2 ≤ ξ ≤ ξP) is mostly characterized by structural relaxation that accompanies the change from the transition state to the product. This partitioning scheme of ξ allows expressing both, the reaction and the activation energies (∆E ◦ and ∆E ,), in terms of reaction works (Wi ) linking specific amounts of energy with the different stages of the reaction. The reaction works are defined as the integrals of the reaction force within the specific regions ξ1 ξTS W1 = − F(ξ)dξ > 0, W2 = − F(ξ)dξ > 0, ξR
W3 = −
ξ2
ξ TS
ξ1
F(ξ)dξ < 0,
W4 = −
ξP
ξ TS
(2) F(ξ)dξ < 0.
Note that although W2 and W3 are reaction works belonging to the transition state region, they have been defined separately for a better characterization of the activation energy ∆E ,. The positive sign of W1 and W2 points out that there is a resistance to the activation process, whereas the negative sign of W3 and W4 indicates the spontaneity of the relaxation process. Since the reaction works are associated
to separated regions where the different effects, structural reordering or electronic activity, may prevail over the other, its physical nature can be characterized as being mostly structural {W1, W4} or electronic {W2, W3}. In this context, the reaction energy (∆E ◦) and the activation barrier (∆E ,) obey the following expressions:16,18–21 ∆E ◦ = [E(ξ P ) − E(ξ R )] = W1 + W2 + W3 + W4,
(3)
∆E , = [E(ξT S ) − E(ξ R )] = W1 + W2.
(4)
This is a very important result since the reaction and activation energies might be rationalized in terms of structural {W1, W4} and electronic {W2, W3} contributions, thus producing valuable information about their physical nature. Indeed, the physical nature of ∆E , will be determined by the relative weight of W1 and W2. B. Reaction electronic flux
In order to get a deeper insight about the mechanism of a chemical reaction, the reaction electronic flux (REF) is used to identify and characterize the electronic activity taking place during the reaction, it is defined as follows:20,21,28–30 ( ) dµ J(ξ) = − . (5) dξ
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Explicitly, the REF describes the rate of change of the electronic chemical potential (µ) along ξ. Its usefulness comes from the fact that the chemical potential defines the tendency of electrons to escape from an equilibrium state, thus producing electronic activity. The electronic chemical potential,31 was found to be the negative of the electronegativity ( χ)31–36 and it is defined as the energy derivative with respect to the total number of electrons (N) keeping the external potential (v(r)) constant31 ) ( dE = − χ. (6) µ= dN v(r ) Working formulae for µ can be obtained by using the finite difference approximation31,35,37,38 and the Koopmans theorem,39 thus obtaining ( ) dE 1 1 µ= ≈ − (I P + E A) ≈ (ε H + ε L ) , (7) dN 2 2 where I P and E A are the first ionization potential and electron affinity, respectively; ε H and ε L correspond to the energy of the frontier molecular orbitals HOMO and LUMO. Positive values of REF afford for spontaneous electronic reordering driven by bond strengthening and/or bond formation processes, whereas the negative values indicate non spontaneous electronic activity driven by bond weakening and/or bond breaking processes.20,28
III. COMPUTATIONAL DETAILS
To establish the starting geometry for the transition state optimization, the crystal structure of the complex between FAcD and the substrate was used as a Ref. 11, Fig. 1(a). The model system under study is confined within the elliptic frames in Fig. 1, it consists in the substrate FAc and the nucleophile propionate anion as a model for the aspartate residue. All transition states were optimized with density functional theory by using the Becke340 and the Lee-Yang-Parr41–43 (B3LYP) as the exchange and correlation functionals, and the 6-311g(d,p) basis set. Frequency calculations were carried out for the optimized structures of critical points across the reaction coordinate, namely, reactant, transition state, and product, to verify their nature as stable minima or transition states. Once the transition state was converged, an IRC calculation was performed at the same level of theory for each system in order to obtain the minimum energy path between reactant and products. The Polarizable Continuum Model (PCM) was included in all calculations, either optimization and IRC calculations, in order to consistently consider the solvent effect in every stage of the reaction mechanism when the substrate is outside the enzyme environment. All calculations were carried out by using the Gaussian 09 software.44 To explore the changes on the electronic distribution along the reaction coordinate, the NPA analysis was used.45 With the purpose of facilitating the comparative analysis of the reactions under study, the IRC calculations will be represented using a reduced reaction coordinate going from 0 at the reactants (ξ R ) to 1 at the product (ξ P ). Each point along the reduced reaction coordinate was obtained according to the
J. Chem. Phys. 142, 194301 (2015)
following expression: ξ∗ =
(ξ − ξ R ) . (ξ P − ξ R )
(8)
IV. RESULTS AND DISCUSSION
Two transition states (TS) were obtained for the protonated substrate and one for the deprotonated substrate. Each transition state led to its corresponding reactant and product after the IRC calculation, thus defining reactions R1, R2, and R3; the geometries of their reactants, TS and products are presented in Fig. 2. The reaction R1 exhibits a TS structure in which the plane of the carboxylic acid is perpendicular to the imaginary axis of the reaction coordinate (red arrows); R1 will be considered the reference reaction as the conformation of its protonated TS represents a base line for the theoretical and experimental data discussed above.12,13 The TS in reaction R2 is analogous to that of R1, but with the deprotonated substrate. It is relevant to mention that for R2, only the perpendicular conformation of the TS was obtained regardless of the starting geometry. The protonated substrate of reaction R3 presents a TS structure in which the carboxylic group is parallel to the reaction axis forming an intramolecular hydrogen bond between the fluoride and the proton from the carboxylic acid, required to obtain the TS in this conformation. The comparison between R1 and R3 will shed light into the relevance of the conformation of the transition state, while between R1 and R2 will allow to determine if the partial protonation of FAc may have a role in the reaction mechanism. A. Structural rearrangements during the reaction
The main conformational changes along each reaction, R1, R2, and R3 are displayed in Fig. 2. The chemical events taking place in R1 can be sequentially described from the reactant complex starting with an interaction distance of 3.21 Å defined between the attacking oxygen from aspartate and the Cα from the FAc moiety (Asp—O · · · Cα—FAc). This distance gets shortened by 1.33 Å reaching a value of 1.88 Å at the TS indicating the beginning of the Cα—O bond formation process that comes along with an elongation of the Cα—F bond from 1.40 Å at the reactant complex to 1.89 Å at the TS conformation. After the product is obtained, an O—Cα bond of 1.45 Å between Asp and FAc was finally formed. Because of the high reactivity of the fluoride anion, instead of leaving the substrate it attacks the vicinal carbon of the carboxylic acid, which is in the proper orientation, forming a bond 1.61 Å long with a tetrahedral carbon as a product. In this particular case, the electrophilicity of the carboxylic carbon is increased by the protonation of the substrate. The R2 reaction between the Asp and the negatively charged FAc starts with the two reactants at 3.44 Å (0.23 Å longer than R1) followed by the transition state with an O—Cα distance of 1.87 Å, indicative of the bond formation process. Meanwhile, the Cα—F bond is elongated from 1.42 to 2.01 Å, exposing the corresponding bond weakening process taking place mainly at the transition state region. Despite that the R1 and R2 transition states are quite similar, the Cα—F bond
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TABLE I. Reaction energies, energy barriers, and reaction works associated to reactions R1-R3.a Model
∆G◦
∆E◦
∆E,
W1
W2
W3
W4
R1 R2 R3
10.9 17.8 −19.1
6.5 15.1 −20.0
22.3 31.1 21.4
15.0 20.7 16.3
7.3 10.5 5.1
−5.7 −4.2 −18.3
−10.1 −11.8 −23.2
a All
values are in kcal/mol.
distance is longer in R2 due to the fact that in R2 the fluoride is completely eliminated, as shown in the product of the reaction. Reaction R3 presents structures along the reaction pathway that are notably different from the other two reaction models. The interaction distance of the reactant complex was 3.41 Å, 0.20 Å longer than R1 and very similar to R2 exposing that the difference observed between R1 and R2 is not completely due to electrostatic repulsion. Then, the O · · · Cα interaction distance decreased to 2.03 Å at the transition state, 0.15 Å longer than in R1. In R3, where the carboxylate is parallel to the axis of reaction, the fluoride leaves the substrate after the formation of the Cα—O bond, and then it captures the proton from the carboxylic acid making a hydrogen bond (F—H · · · O) with the carboxylate moiety. B. Minimun energy pathway
Reaction and activation energies, as well as their related reaction works are listed in Table I. The calculated energy barriers for R1, R2, and R3 were of 22.3, 31.1, and 21.4 kcal/mol, respectively. The activation energy of R1 is in good agreement with the value obtained using a model similar to R1 previously reported (18.7 kcal/mol).14 The comparison of R1 and R3, both protonated forms of FAc, with R2 showed that the protonation of the carboxylic moiety causes a reduction of the energy barrier of 8.8 and 9.7 kcal/mol for R1 and R3, respectively. These results indicate that R1 and R3 are kinetically similar and that the protonated form of the carboxylic acid from the substrate provides an important catalytic effect for the nucleophilic attack to the Cα, completely independent of the conformation of the TS. The reaction energies were very different among the studied models. To correctly assess the thermodynamic behavior of the three reaction models, we performed thermal correction to the energies in order to provide the Gibbs free energies (data listed in Table I). The Gibbs free energies of R1 and R2 exposed that both reactions have endergonic behavior. For the case of R1, it is able to partially stabilize the negative charge of the fluoride formed during the reaction, by intramolecularly reacting with the anion as described above (Sec. IV A). This allows to decrease the energy difference between reactants and products in R1. Meanwhile, the inability of R2 to somehow stabilize the fluoride anion formed as a product led to a highly endergonic reaction. On the other hand, R3 was exergonic by 19.1 kcal/mol, inferring that the protonation of the fluoride has also an important role in the stabilization of the anion. Then, the thermodynamic behavior depends on the mechanism in charge of the stabilization of the fluoride formed as a product. According to our findings, this anion is highly unstable in absence of proton donors in the vicinity, which are necessary to stabilize its charge.
It is important to mention that a partial or complete selective protonation of the substrate can be easily achieved in the enzymatic catalytic site, but not in solution, in which case it is only possible to get either both reactants protonated or both deprotonated. To support our proposal about the need of a selective protonation we calculated the energy profile for the doubly protonated system, meaning that the carboxylic acid from the substrate and the nucleophile in their protonated forms. The resulting energy barrier was of 36.3 kcal/mol, 5.2 kcal/mol higher than the model completely ionized, being this the less favored mechanism. C. Reaction force analysis
The reaction force profiles of R1, R2, and R3 are displayed in Fig. 3. It can be observed that R1 showed no activity until approaching the transition state region. Meanwhile, R2 presented a small amount of work in the reactant region indicating early structural rearrangements to adopt the necessary conformation to reach the TS. As a consequence, R2 has the highest value of W1, which is 5.7 and 4.4 kcal/mol higher than the corresponding values of R1 and R3, respectively. The activity showed by R3 in the reactant region, which is gradually increasing until entering the TS region, is mainly associated to the difficulty to elongate the Cα—F bond due to the intramolecular hydrogen bond between the halogen and the proton from the carboxylic acid that reinforces and restricts the spatial position of the F atom. This explains the slightly higher value of W1 of R3 with respect to R1. Once in the transition state region, R2 showed the highest value of W2, work mostly associated to the electronic activity necessary to reach the transition state, which seems to be more difficult when the carboxylic group is deprotonated than protonated. This highlights that the energy barrier of R2 involves larger structural and electronic works when compared to R1 and R3. The fact that R3 presented the lowest value of W2 can be explained by the polarization of the fluoride atom at the reactant region caused by the interaction with the proton that acts as a charge acceptor. This induces a polarization of the electronic density in the Cα—F bond when compared to R1, similar to what can be expected from the interactions with the residues of the halogen binding site, but in a smaller scale. Despite the fact that in R3 the bond Cα—F should be weaker, as inferred from the lower electronic work involved in reaching the TS, the longer O—Cα and shorter Cα—F interaction distances at the TS structure (Fig. 2) reveal that the hydrogen bond with the fluoride also demands structural work at this point, due to conformational strain. The latter work can be decreased by the enzyme machinery aiding to lower the energy barrier by this means. Interestingly, the W1/W2 ratio in R1 and R2 is about 2, whereas it goes up to 3.2 in R3. First, this exposes that the work associated to the electronic reorganization is always smaller than that associated to the structural changes, which predominates in all three reactions. Second, the intramolecular hydrogen bond in R3 demands a major structural work and a low electronic work in order to reach the transition state
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FIG. 3. Reaction force profiles for reactions R1-R3. The plots at the right show the individual behavior of the force profiles, which are divided into reactant (R), transition state (T S), and product (P) regions.
structure. The latter is exposed by the magnitude of W1 which triplicates the value of W2. The final balance between the bond formation and breaking together with the stabilization of the fluoride resulted in larger negative values of W3 and W4 for R3. This can be rationalized as a lower resistance towards electronic and structural modifications to arrive the product configuration as reflected by its exergonic behavior. D. Reaction electronic flux
The REF profile was calculated to characterize the main chemical events taking place along the reaction coordinate, and it is shown in Fig. 4. This allows to identify the regions of the reaction coordinate where electronic activity associated to bond formation and/or bond strengthening and bond breaking and/or bond weakening is occurring. The REF of R1 slightly increases at the reactant region at the very beginning of the reaction. This can be attributed to the strengthening of the Cα—H bonds and the polarization induced by conformational changes, Cα changes from a tetrahedral sp3 to a planar sp2. Then, a small peak of negative activity associated to a slight weakening of the Cα—F precedes
the positive electronic activity that reaches a maximum coinciding with the beginning of the transition state region. This spontaneous activity is mostly related to the overlapping between the electronic densities of the nucleophile with the substrate involving the formation of the O—Cα bond. This is followed by the non-spontaneous activity inside the transition state region, which indicates the Cα—F bond dissociation. In the product region, a positive peak of the REF is observed, it is related to intramolecular transfer of the fluoride to the vicinal carbon with formation of a new carbon fluoride bond. Finally, a negative peak shows up, it is ascribed to the cleavage of the carbon oxygen double bonds into a single bond. The REF associated to R2 is mostly concentrated within the transition state region. The positive and negative fluctuation around the zero flux regions observed within the reactant region should be associated to bond strengthening and weakening processes due to electronic redistribution on the Cα atom and the subsequent weakening of the Cα—F bond as described for R1. Once the transition state region is reached, R2 exposes the main changes on the electronic activity, indicating that the majority of the electronic reorganization is localized in this region. This points out that R1 has to adopt a conformation very close to the TS before it starts
FIG. 4. Reaction electronic flux profile for reactions R1-R3. The plots at the right show the individual behavior of the electronic flux profiles, which are divided into reactant (R), transition state (T S), and product (P) regions.
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TABLE II. Natural population analysis at three critical points of the reaction coordinate of R1-R3. Model
Onuc—H2C—F
—H2C—
—F
R1R R1ξ1 R1TS R2R R2ξ1 R2TS R3R R3ξ1 R3TS
−0.84 −0.89 −0.98 −0.97 −1.00 −1.13 −0.84 −0.88 −0.94
0.37 0.38 0.36 0.28 0.31 0.29 0.38 0.39 0.37
−0.40 −0.51 −0.66 −0.43 −0.55 −0.74 −0.41 −0.51 −0.61
with the electronic reorganization necessary to continue with the reaction, revealing a resistance towards adopting the electronic density distribution needed for this SN2 reaction. From a qualitative point of view, the REF of R2 presents three major peaks, revealing the three major events involved in this particular reaction. The first positive peak is the one associated to the O—Cα bond formation. The second is a negative peak that was related to the Cα—F bond breaking; the third is a positive peak associated to bonds strengthening in the equilibration process to reach the product conformation. It is important to note that after leaving the transition state region, a zero REF regime rules, indicating that the product region is unequivocally characterized by structural relaxation. The REF obtained for R3 did not show electronic activity until the reactants were very close to each other at the end of the reactant region. This is because R3 suffers a minor change in the F—C—C==O dihedral angle when compared to R1 and R2, accompanied by the change of Cα from a
tetrahedral sp3 to a planar sp2 conformation that takes place further in the reaction coordinate. Both seem to be caused by the intramolecular hydrogen bond between the carboxylic proton and the halogen, which adds conformational strain. At the end of the reactant region the electronic activity shows up developing a positive peak, indicative of a process similar to that described for R1, where the conformational change of the Cα involves bond strengthening processes, followed by the O—Cα bond formation at the transition state region. Then, a negative peak develops within the transition state region, this is the clear signature of the Cα—F bond dissociation. After the transition stage region, a new negative peak emerges, it is assigned to the O—H bond breaking step in the proton transfer from the carboxylate group to the fluoride. The low intensity and broad positive peak in the product region should be basically attributed to the formation of the H—F bond. E. Charge distribution and Fukui function
At this stage of the study, we have characterized different mechanistic scenarios for the nucleophilic attack of aspartate to FAc in different protonation states. Nevertheless, the remaining question about the decrease of the energy barrier by the protonation of the substrate still needs to be answered. According to the analysis of the reaction works, there is a structural component that contributes to the increase of the barrier for the negatively charged substrate, which is followed by an electronic process that is also less favored in R2. The decrease of the electrostatic repulsion between the reactants of R1 and R3 can be responsible for the structural part. Meanwhile, the large electronic work of R2 might be attributed to some source of electronic strain that difficult the proper progress along the TS region, also inferred from the REF
FIG. 5. Schematic representation of the LUMO for R1-R3 at ξ1, corresponding to the geometry at the transition from the reactant to the TS region (a) upper view (b) side view.
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TABLE III. Fukui function values associated to the local reactivity of Cα toward a nucleophilic attack. Model R1ξ1 R2ξ1 R3ξ1 a Condensed
b Condensed
f +(r )a
f +(r )b
0.18 0.00 0.16
0.13 0.01 0.10
Fukui function calculated by neglecting relaxation effects. Fukui function calculated by the Yang Mortier approach.
profile of R2. To address the source of this strain, we analyzed the charge distribution at the critical points of the reaction coordinate, data listed in Table II. The charge on the reaction axis constituted by the O—CαH2—F group of atoms presents a huge amount of negative charge. This charge increases further in the reaction coordinate due to the negative nature of the nucleophile and the leaving group, leading to a TS with a high concentration of negative charge localized at the reaction axis. Interestingly, the model with the lowest negative charge on the reaction axis at the TS was R3, followed by R1, and then by R2 with the largest negative charge. These results correlate with the reaction barriers obtained for these models, thus revealing that the decrease of the negative charge on the reaction axis is the source of the lowering of the reaction barrier. The charge analysis of the CαH2— group denotes the electrophilic nature of this group along the whole process reflected by its positive charge. In addition to that, its slight decrease of charge (more positive) at the beginning of the TS region followed by an increase due to the donation from the nucleophile is indicative of the weakening of the Cα—F bond followed by the beginning of the O—Cα bond formation, in perfect agreement with the analysis of the REF profiles. As mentioned above, the charge at the region of the reaction axis of R1 and R3 is lower than in R2, which is reflected by a more positive charge on the CαH2— of the two former models. This holds along the reaction, revealing that the carboxylic moiety acts as a charge acceptor, able to stabilize this excess of negative charge. More important, it seems that the protonation of the substrate turns the carboxylic moiety into a better charge acceptor, thus performing an active role during the reaction. This finding allows to rationalize the earlier experimental evidence that pointed out the increased activity of FAc towards nucleophilic substitution in its undissociated form.13 The problem with this finding is that to achieve the charge transfer from the reaction axis to the carboxylic moiety, it is necessary that the pz orbital involved in the reaction to interact with the π∗ (charge acceptor) from the carboxylic group. However, this does not seem geometrically feasible in R3, even though it also shows a decrease on the charge and the energy barrier. To explore the independence of the charge transfer on the conformation, we analyzed the LUMO of the supermolecule, from which it is possible to analyze the shape of the acceptor orbital involved in the process at the early stages of the reaction. The results showed in Fig. 5 denote that independent of the conformation, the LUMOs of the three models present the pz-π∗ orbital interaction. Thus, according to our results this orbital interaction that enables the charge
transfer is a determinant feature of the electronic structure, able to provide the necessary stabilization of the LUMO in order to facilitate the course of the reaction. We would like to remark that our findings argue against the previous proposal,12 in which is stated that the reaction depends on the geometry of the TS, involving the π orbital instead of the π∗ as here proposed, orbital that is not a charge acceptor as required by the mechanism. To understand how for the particular cases of R1 and R3 their LUMO structure leads to lower energy barriers, we found that the contribution of the carboxylic carbon to the molecular orbital is larger for the protonated cases. This may point out that for these systems, the carboxylic acid is better as a charge acceptor and this orbital may allow to concentrate more charge on the carboxylic carbon decreasing the electronic repulsion at the TS. To corroborate this hypothesis and how the contributions to the LUMO affect the Cα, we obtained the Fukui function to measure the local reactivity of Cα toward a nucleophilic attack ( f +(r)) by the condensed Fukui function neglecting relaxation effects (for detailed description of the method see references)46–48 and the approach based on population analysis introduced by Yang and Mortier.49 To get a better representation of the variables under study, we used the geometries at ξ1 due to two reasons: first, at this point it starts to dominate the electronic activity involved in the reaction; and second, the conformation of the substrate is closer to the TS geometry, effect that is one of our main focuses of study. The results listed in Table III show that independent of the method of calculation, the Fukui function shows that the protonation of the substrate independent of the conformation increases the electrophilicy of Cα, which actually is close to 0 for R2 in accordance with its high energy barrier. V. CONCLUSIONS
In the present work, we explored the intrinsic chemical variables that determine the reactivity of FAc towards its defluorination through an SN2 reaction. To accomplish this goal, we focused on the study of the influence that the carboxylic acid has as the vicinal group of the reactive center. We found that the protonation of the carboxylic moiety of FAc catalyzes the nucleophilic substitution by decreasing the excess of electronic density at the reaction axis during the reaction, which was found to be the main reason of the electronic strain along the reaction coordinate. This was achieved by the augmented ability of the carboxylic group of receiving charge when it is protonated, property that we found was not restricted by the relative conformation between the carboxylic acid and the reaction axis. Under the right conditions, the proton from the carboxylic acid was transferred to the emerging fluoride during the reaction, process able to provide a marked exergonic behavior. We concluded that the relative thermodynamic behavior relies mainly on the mechanism involved in the stabilization of the fluoride anion formed as a product of the reaction. Thus, it is also expected that the residues of the halogen pocket from dehalogenases to be able to stabilize the anion, helping the enzymatic reaction to advance towards the next step of the catalytic process.
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Driven by our main findings, we raise the question if the use of different chemical groups of similar electronic properties to the carboxylic acid would be able to provide a similar catalytic effect. The answer to this question may be useful in the search of new strategies to catalyze complex SN2 reactions. As concluding remarks, the combination of several methods for the analysis of reaction mechanisms is presented as a framework to integrate key information regarding the structural and electronic processes that take place during the reaction. In particular, here we analyzed the reaction mechanisms by using the reaction force profiles, reaction electronic flux, charge distribution, and the Fukui function. Finally, this combined approach proved to be a powerful strategy to describe the actual mechanism by which a particular reaction is catalyzed. ACKNOWLEDGMENTS
The authors thank financial support from Grant ICM No. 120082 and FONDECYT through Projects Nos. 3130383 and 1130072. S.M.-R. also thanks the support of Basal Financing Program CONICYT-FB0807 (CEDENNA), to the invaluable help of Dr. Jorge Martinez-Araya for insightful discussions on conceptual DFT and to Dr. Diego Cortés-Arriagada for helpful revision on the manuscript. 1M.
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C. Price and W. G. Jackson, J. Am. Chem. Soc. 69, 1065 (1947). Kamachi et al., Chem.–Eur. J. 15, 7394 (2009). 15T. Nakayama et al., Chem.–Eur. J. 18, 8392 (2012). 16A. Toro-Labbé, J. Phys. Chem. A 103, 4398 (1999). 17A. Toro-Labbé et al., Mol. Phys. 105, 2619 (2007). 18P. Politzer et al., J. Phys. Chem. A 110, 756 (2005). 19A. Toro-Labbé et al., J. Mol. Model. 15, 707 (2009). 20B. Herrera and A. Toro-Labbé, J. Phys. Chem. A 111, 5921 (2007). 21S. Vogt-Geisse and A. Toro-Labbe, J. Chem. Phys. 130, 244308 (2009). 22K. Fukui, Acc. Chem. Res. 14, 363 (1981). 23C. Gonzalez and H. B. Schlegel, J. Phys. Chem. 94, 5523 (1990). 24P. Politzer et al., J. Chem. Sci. 117, 467 (2005). 25S. Gutiérrez-Oliva et al., J. Phys. Chem. A 109, 1748 (2005). 26E. Rincón, P. Jaque, and A. Toro-Labbé, J. Phys. Chem. A 110, 9478 (2006). 27V. Labet et al., J. Phys. Chem. A 112, 11487 (2008). 28F. Duarte and A. Toro-Labbé, J. Phys. Chem. A 115, 3050 (2011). 29P. Flores-Morales et al., J. Mol. Struct.: THEOCHEM 943, 121 (2010). 30M. Cerón et al., Sci. China Chem. 54, 1982 (2011). 31K. Sen and C. Jorgenson, Structure and Bonding: Electronegativity, Vol. 66 (Springer, Berlin, 1987). 32P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000). 33L. Pauling, in The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry (Cornell University Press, 1960), Vol. 18. 34R. G. Parr et al., J. Chem. Phys. 68, 3801 (1978). 35R. G. Pearson, J. Am. Chem. Soc. 107, 6801 (1985). 36R. G. Pearson, Coord. Chem. Rev. 100, 403 (1990). 37P. Geerlings, F. De Proft, and W. Langenaeker, Chem. Rev. 103, 1793 (2003). 38R. Pearson, Hard and Soft Acids and Bases (Dowden, Hutchinson, and Ross, Stroudsburg, 1973). 39T. Koopmans, Physica 1, 104 (1933). 40A. D. Becke, J. Chem. Phys. 98, 5648 (1993). 41C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). 42B. Miehlich et al., Chem. Phys. Lett. 157, 200 (1989). 43S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980). 44M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford, CT, 2009. 45A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev. 88, 899 (1988). 46R. R. Contreras et al., Chem. Phys. Lett. 304, 405 (1999). 47P. Fuentealba, P. Pérez, and R. Contreras, J. Chem. Phys. 113, 2544 (2000). 48E. Chamorro and P. Pérez, J. Chem. Phys. 123, 114107 (2005). 49W. Yang and W. J. Mortier, J. Am. Chem. Soc. 108, 5708 (1986). 14T.
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THE JOURNAL OF CHEMICAL PHYSICS 142, 194301 (2015)
Mechanistic insights into the dehalogenation reaction of fluoroacetate/fluoroacetic acid Sebastián Miranda-Rojas1,a) and Alejandro Toro-Labbé2 1
Chemical Processes and Catalysis (CPC), Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Avenida República 275, Santiago, Chile 2 Laboratorio de Química Teórica Computacional (QTC), Facultad de Química, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile
(Received 11 February 2015; accepted 29 April 2015; published online 15 May 2015) Fluoroacetate is a toxic compound whose environmental accumulation may represent an important contamination problem, its elimination is therefore a challenging issue. Fluoroacetate dehalogenase catalyzes its degradation through a two step process initiated by an SN2 reaction in which the aspartate residue performs a nucleophilic attack on the carbon bonded to the fluorine; the second step is hydrolysis that releases the product as glycolate. In this paper, we present a study based on density functional theory calculations of the SN2 initiation reaction modeled through the interaction between the substrate and the propionate anion as the nucleophile. Results are analyzed within the framework of the reaction force and using the reaction electronic flux to identify and characterize the electronic activity that drives the reaction. Our results reveal that the selective protonation of the substrate catalyzes the reaction by decreasing the resistance of the structural and electronic reorganization needed to reach the transition state. Finally, the reaction energy is modulated by the degree of stabilization of the fluoride anion formed after the SN2 reaction. In this way, a site-induced partial protonation acts as a chemical switch in a key process that determines the output of the reaction. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4920946]
I. INTRODUCTION
The environmental accumulation of organohalogen compounds represents a major pollution problem and dehalogenation reactions are the main way for degradation.1,2 Among these compounds, the fluorinated molecules are the hardest to eliminate due to thier strong C—F bond.3,4 Related to the latter, the fluoroacetate (FAc) is a compound commonly present in nature and has been found to be highly toxic for mammals because of its conversion into fluorocitrate, a precursor of a potent inhibitor of aconitase, enzyme involved in the citric acid cycle.5–7 Dehalogenases in general share the first step of the reaction mechanisms, which corresponds to a nucleophilic attack to the carbon Cα bonded to the halogen atom (see Fig. 1).8–10 In the particular case of the fluoroacetate dehalogenase (FAcD) enzyme, this key step represents a chemically interesting problem because the Cα under nucleophilic attack is adjacent to a carboxylate. The study of this SN2 step that initiates the catalytic reaction is the target of this paper. From the most recently available crystal structure of the FAcD enzyme,11 it is possible to identify key structural features that help to understand the way the FAcD enzyme acts. In this structure, the nucleophile (aspartate) was mutated into asparagine in order to capture the substrate before its conversion to product. Fig. 1(a) displays the available crystal structure,11 where the nitrogen from asparagine amide was replaced by a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2015/142(19)/194301/9/$30.00
oxygen to represent the aspartate, nucleophile of the SN2 reaction. From the reactant conformation displayed in Fig. 1(a), it can be noticed that the Cα—F bond is practically coplanar to the carboxylate. However, according to previous theoretical studies,12 the preferred transition state for this type of SN2 reaction in vacuum situate the Cα—F bond out of the plane of the carboxylic moiety. This was explained by the stabilizing interaction between the π-bond of the carboxylate group with the orbitals involved in the reaction axis.12 Fig. 1(b) shows the conformation of the product of the SN2 reaction and intermediate of the whole catalytic process, where the orientation of the carboxylate barely changed with respect to the reactant. Consistency between the crystal structure of the reactants, transition state, and intermediate described above would imply an internal rotation of the CH2—F group along the Cα—C bond that should involve important structural work. Then, two probable scenarios are possible, the first where the transition state actually changes its conformation from the reactant situating the Cα—F bond out of the plane of the carboxylate moiety; and the case where the transition state has a similar conformation with reactant and product. Therefore, these scenarios open the question about the relevance of the conformation of the transition state of the SN2 reaction. On the other hand, the close interaction of the carboxylate from the substrate with two arginines and a tyrosine, also depicted in Fig. 1, may allow a partial proton transfer that could modify the behavior of the reaction. Something that have not received much attention is that experimental evidence reported in the mid forties suggested that FAc is more reactive toward nucleophilic substitution when its carboxylic acid is in the protonated
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© 2015 AIP Publishing LLC
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FIG. 1. Crystal structure of the complex formed between the substrate (FAc) and the nucleophile (aspartic acid) in the reactant (a) and product (b) states.11 Here are depicted the main interactions between the carboxylate moiety of the substrate with the binding site. The red ellipse encloses the reduced reaction model that is used in this study and the black arrow connects the atoms involved in the nucleophilic attack.
form,13 results that motivated this research. Experimentally, it is difficult to characterize the effect of a selective protonation of the substrate in solution without affecting the nucleophile since both have a carboxylic acid and a very low pH solution will protonate the two reactants, and not only the substrate as needed. However, the description of the behavior of this reaction in solution is possible by computational methods, thus helping to understand the features that the enzyme can exploit in order to reach its catalytic proficiency. The only insights about the activation of this catalytic step are associated to the interaction of the halogen with His155, Trp156, and Tyr219 (numbering according to PDB ID 3R3U from Rhodopseudomonas palustris11) which may facilitate the Cα—F bond dissociation.11,14,15 Nevertheless, there are intrinsic properties of the ligand that we will expose in this article that may be affected by the enzyme environment, which have not been explored and would help to explain how the enzyme decreases the energy barrier for this process. Moreover, we obtained new insights from the analysis of the electronic structure along the reaction coordinate that provides a deeper understanding of the behavior of FAc during the SN2 reaction. In this context, the effect of the conformational change of the transition states and the protonation of the substrate in the SN2 reaction without explicitly considering the enzyme environment are key issues that are going to be addressed in this study. We present a detailed study of the reaction using the model system enclosed within the ellipse displayed in Fig. 1. In Fig. 2 are displayed the key conformations of the three reactions under study. To characterize the effect that the protonation state of the carboxylic acid from the substrate has in the reaction mechanism, it was studied as a carboxylic acid (protonated form) and as a carboxylate (deprotonated form), reactions R1 and R2, respectively (Fig. 2). From this point, we will refer as protonated substrate when we need to discuss about the substrate with the protonated carboxylic acid, and deprotonated substrate when we need to refer to the substrate with the carboxylate anion. The possibility of the catalytic
site to change the conformation of the transition state was also studied, where comparison of reactions R1 and R3, both involving the protonated substrate, addresses this issue. All three reactions displayed in Fig. 2 were analyzed within the framework of the reaction force analysis16–21 and the reaction electronic flux,20,21 this to characterize the electronic activity taking place during the reaction.
II. THEORETICAL BACKGROUND A. Reaction force
The intrinsic reaction coordinate (IRC)22,23 procedure has become an extremely useful tool to follow the mechanistic events associated to a chemical reaction, it provides the minimum energy pathway that connects along a reaction coordinate (ξ = IRC), the transition state with reactants and products. Despite the relevance of the energy profile, which provides the kinetic and the thermodynamic information of the reaction, it is not able to provide information about the mechanism of a chemical reaction. The reaction force analysis provides a useful framework to characterize reaction mechanisms, it is defined as the negative derivative of the energy with respect to ξ,16–21 the reaction coordinate F(ξ) = −
dE . dξ
(1)
For any elementary step in which the products are separated from the reactants by an energy barrier, the reaction force profile presents two critical points, ξ1 and ξ2. The first critical point ξ1 is located somewhere between the reactants (ξR) and the transition state (ξTS); ξ2 is located between the ξTS and the products (ξP). This entails a natural division of the reaction coordinate into three reaction regions (RR); it has been observed in many different kinds of reactions that each RR is mostly associated to specific processes that drive the reaction until the final chemical product.18,24–27 First, the reactant region (ξR ≤ ξ ≤ ξ1), is generally dominated
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FIG. 2. Schematic representation of the reactant, transition state, and product of reactions R1-R3. In R1 the carboxylic acid is perpendicular to the axis of reaction (red dashed arrow); R2 represents the completely deprotonated reaction, and in R3 the carboxylic acid is parallel to the axis of reaction at the transition state.
by structural rearrangements that activate the reactant. Then follows the transition state region (ξ1 ≤ ξ ≤ ξ2), where most of the electronic reorganization occurs, in this region most of the bond formation and bond breaking processes take place. Finally, the product region (ξ2 ≤ ξ ≤ ξP) is mostly characterized by structural relaxation that accompanies the change from the transition state to the product. This partitioning scheme of ξ allows expressing both, the reaction and the activation energies (∆E ◦ and ∆E ,), in terms of reaction works (Wi ) linking specific amounts of energy with the different stages of the reaction. The reaction works are defined as the integrals of the reaction force within the specific regions ξ1 ξTS W1 = − F(ξ)dξ > 0, W2 = − F(ξ)dξ > 0, ξR
W3 = −
ξ2
ξ TS
ξ1
F(ξ)dξ < 0,
W4 = −
ξP
ξ TS
(2) F(ξ)dξ < 0.
Note that although W2 and W3 are reaction works belonging to the transition state region, they have been defined separately for a better characterization of the activation energy ∆E ,. The positive sign of W1 and W2 points out that there is a resistance to the activation process, whereas the negative sign of W3 and W4 indicates the spontaneity of the relaxation process. Since the reaction works are associated
to separated regions where the different effects, structural reordering or electronic activity, may prevail over the other, its physical nature can be characterized as being mostly structural {W1, W4} or electronic {W2, W3}. In this context, the reaction energy (∆E ◦) and the activation barrier (∆E ,) obey the following expressions:16,18–21 ∆E ◦ = [E(ξ P ) − E(ξ R )] = W1 + W2 + W3 + W4,
(3)
∆E , = [E(ξT S ) − E(ξ R )] = W1 + W2.
(4)
This is a very important result since the reaction and activation energies might be rationalized in terms of structural {W1, W4} and electronic {W2, W3} contributions, thus producing valuable information about their physical nature. Indeed, the physical nature of ∆E , will be determined by the relative weight of W1 and W2. B. Reaction electronic flux
In order to get a deeper insight about the mechanism of a chemical reaction, the reaction electronic flux (REF) is used to identify and characterize the electronic activity taking place during the reaction, it is defined as follows:20,21,28–30 ( ) dµ J(ξ) = − . (5) dξ
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Explicitly, the REF describes the rate of change of the electronic chemical potential (µ) along ξ. Its usefulness comes from the fact that the chemical potential defines the tendency of electrons to escape from an equilibrium state, thus producing electronic activity. The electronic chemical potential,31 was found to be the negative of the electronegativity ( χ)31–36 and it is defined as the energy derivative with respect to the total number of electrons (N) keeping the external potential (v(r)) constant31 ) ( dE = − χ. (6) µ= dN v(r ) Working formulae for µ can be obtained by using the finite difference approximation31,35,37,38 and the Koopmans theorem,39 thus obtaining ( ) dE 1 1 µ= ≈ − (I P + E A) ≈ (ε H + ε L ) , (7) dN 2 2 where I P and E A are the first ionization potential and electron affinity, respectively; ε H and ε L correspond to the energy of the frontier molecular orbitals HOMO and LUMO. Positive values of REF afford for spontaneous electronic reordering driven by bond strengthening and/or bond formation processes, whereas the negative values indicate non spontaneous electronic activity driven by bond weakening and/or bond breaking processes.20,28
III. COMPUTATIONAL DETAILS
To establish the starting geometry for the transition state optimization, the crystal structure of the complex between FAcD and the substrate was used as a Ref. 11, Fig. 1(a). The model system under study is confined within the elliptic frames in Fig. 1, it consists in the substrate FAc and the nucleophile propionate anion as a model for the aspartate residue. All transition states were optimized with density functional theory by using the Becke340 and the Lee-Yang-Parr41–43 (B3LYP) as the exchange and correlation functionals, and the 6-311g(d,p) basis set. Frequency calculations were carried out for the optimized structures of critical points across the reaction coordinate, namely, reactant, transition state, and product, to verify their nature as stable minima or transition states. Once the transition state was converged, an IRC calculation was performed at the same level of theory for each system in order to obtain the minimum energy path between reactant and products. The Polarizable Continuum Model (PCM) was included in all calculations, either optimization and IRC calculations, in order to consistently consider the solvent effect in every stage of the reaction mechanism when the substrate is outside the enzyme environment. All calculations were carried out by using the Gaussian 09 software.44 To explore the changes on the electronic distribution along the reaction coordinate, the NPA analysis was used.45 With the purpose of facilitating the comparative analysis of the reactions under study, the IRC calculations will be represented using a reduced reaction coordinate going from 0 at the reactants (ξ R ) to 1 at the product (ξ P ). Each point along the reduced reaction coordinate was obtained according to the
J. Chem. Phys. 142, 194301 (2015)
following expression: ξ∗ =
(ξ − ξ R ) . (ξ P − ξ R )
(8)
IV. RESULTS AND DISCUSSION
Two transition states (TS) were obtained for the protonated substrate and one for the deprotonated substrate. Each transition state led to its corresponding reactant and product after the IRC calculation, thus defining reactions R1, R2, and R3; the geometries of their reactants, TS and products are presented in Fig. 2. The reaction R1 exhibits a TS structure in which the plane of the carboxylic acid is perpendicular to the imaginary axis of the reaction coordinate (red arrows); R1 will be considered the reference reaction as the conformation of its protonated TS represents a base line for the theoretical and experimental data discussed above.12,13 The TS in reaction R2 is analogous to that of R1, but with the deprotonated substrate. It is relevant to mention that for R2, only the perpendicular conformation of the TS was obtained regardless of the starting geometry. The protonated substrate of reaction R3 presents a TS structure in which the carboxylic group is parallel to the reaction axis forming an intramolecular hydrogen bond between the fluoride and the proton from the carboxylic acid, required to obtain the TS in this conformation. The comparison between R1 and R3 will shed light into the relevance of the conformation of the transition state, while between R1 and R2 will allow to determine if the partial protonation of FAc may have a role in the reaction mechanism. A. Structural rearrangements during the reaction
The main conformational changes along each reaction, R1, R2, and R3 are displayed in Fig. 2. The chemical events taking place in R1 can be sequentially described from the reactant complex starting with an interaction distance of 3.21 Å defined between the attacking oxygen from aspartate and the Cα from the FAc moiety (Asp—O · · · Cα—FAc). This distance gets shortened by 1.33 Å reaching a value of 1.88 Å at the TS indicating the beginning of the Cα—O bond formation process that comes along with an elongation of the Cα—F bond from 1.40 Å at the reactant complex to 1.89 Å at the TS conformation. After the product is obtained, an O—Cα bond of 1.45 Å between Asp and FAc was finally formed. Because of the high reactivity of the fluoride anion, instead of leaving the substrate it attacks the vicinal carbon of the carboxylic acid, which is in the proper orientation, forming a bond 1.61 Å long with a tetrahedral carbon as a product. In this particular case, the electrophilicity of the carboxylic carbon is increased by the protonation of the substrate. The R2 reaction between the Asp and the negatively charged FAc starts with the two reactants at 3.44 Å (0.23 Å longer than R1) followed by the transition state with an O—Cα distance of 1.87 Å, indicative of the bond formation process. Meanwhile, the Cα—F bond is elongated from 1.42 to 2.01 Å, exposing the corresponding bond weakening process taking place mainly at the transition state region. Despite that the R1 and R2 transition states are quite similar, the Cα—F bond
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TABLE I. Reaction energies, energy barriers, and reaction works associated to reactions R1-R3.a Model
∆G◦
∆E◦
∆E,
W1
W2
W3
W4
R1 R2 R3
10.9 17.8 −19.1
6.5 15.1 −20.0
22.3 31.1 21.4
15.0 20.7 16.3
7.3 10.5 5.1
−5.7 −4.2 −18.3
−10.1 −11.8 −23.2
a All
values are in kcal/mol.
distance is longer in R2 due to the fact that in R2 the fluoride is completely eliminated, as shown in the product of the reaction. Reaction R3 presents structures along the reaction pathway that are notably different from the other two reaction models. The interaction distance of the reactant complex was 3.41 Å, 0.20 Å longer than R1 and very similar to R2 exposing that the difference observed between R1 and R2 is not completely due to electrostatic repulsion. Then, the O · · · Cα interaction distance decreased to 2.03 Å at the transition state, 0.15 Å longer than in R1. In R3, where the carboxylate is parallel to the axis of reaction, the fluoride leaves the substrate after the formation of the Cα—O bond, and then it captures the proton from the carboxylic acid making a hydrogen bond (F—H · · · O) with the carboxylate moiety. B. Minimun energy pathway
Reaction and activation energies, as well as their related reaction works are listed in Table I. The calculated energy barriers for R1, R2, and R3 were of 22.3, 31.1, and 21.4 kcal/mol, respectively. The activation energy of R1 is in good agreement with the value obtained using a model similar to R1 previously reported (18.7 kcal/mol).14 The comparison of R1 and R3, both protonated forms of FAc, with R2 showed that the protonation of the carboxylic moiety causes a reduction of the energy barrier of 8.8 and 9.7 kcal/mol for R1 and R3, respectively. These results indicate that R1 and R3 are kinetically similar and that the protonated form of the carboxylic acid from the substrate provides an important catalytic effect for the nucleophilic attack to the Cα, completely independent of the conformation of the TS. The reaction energies were very different among the studied models. To correctly assess the thermodynamic behavior of the three reaction models, we performed thermal correction to the energies in order to provide the Gibbs free energies (data listed in Table I). The Gibbs free energies of R1 and R2 exposed that both reactions have endergonic behavior. For the case of R1, it is able to partially stabilize the negative charge of the fluoride formed during the reaction, by intramolecularly reacting with the anion as described above (Sec. IV A). This allows to decrease the energy difference between reactants and products in R1. Meanwhile, the inability of R2 to somehow stabilize the fluoride anion formed as a product led to a highly endergonic reaction. On the other hand, R3 was exergonic by 19.1 kcal/mol, inferring that the protonation of the fluoride has also an important role in the stabilization of the anion. Then, the thermodynamic behavior depends on the mechanism in charge of the stabilization of the fluoride formed as a product. According to our findings, this anion is highly unstable in absence of proton donors in the vicinity, which are necessary to stabilize its charge.
It is important to mention that a partial or complete selective protonation of the substrate can be easily achieved in the enzymatic catalytic site, but not in solution, in which case it is only possible to get either both reactants protonated or both deprotonated. To support our proposal about the need of a selective protonation we calculated the energy profile for the doubly protonated system, meaning that the carboxylic acid from the substrate and the nucleophile in their protonated forms. The resulting energy barrier was of 36.3 kcal/mol, 5.2 kcal/mol higher than the model completely ionized, being this the less favored mechanism. C. Reaction force analysis
The reaction force profiles of R1, R2, and R3 are displayed in Fig. 3. It can be observed that R1 showed no activity until approaching the transition state region. Meanwhile, R2 presented a small amount of work in the reactant region indicating early structural rearrangements to adopt the necessary conformation to reach the TS. As a consequence, R2 has the highest value of W1, which is 5.7 and 4.4 kcal/mol higher than the corresponding values of R1 and R3, respectively. The activity showed by R3 in the reactant region, which is gradually increasing until entering the TS region, is mainly associated to the difficulty to elongate the Cα—F bond due to the intramolecular hydrogen bond between the halogen and the proton from the carboxylic acid that reinforces and restricts the spatial position of the F atom. This explains the slightly higher value of W1 of R3 with respect to R1. Once in the transition state region, R2 showed the highest value of W2, work mostly associated to the electronic activity necessary to reach the transition state, which seems to be more difficult when the carboxylic group is deprotonated than protonated. This highlights that the energy barrier of R2 involves larger structural and electronic works when compared to R1 and R3. The fact that R3 presented the lowest value of W2 can be explained by the polarization of the fluoride atom at the reactant region caused by the interaction with the proton that acts as a charge acceptor. This induces a polarization of the electronic density in the Cα—F bond when compared to R1, similar to what can be expected from the interactions with the residues of the halogen binding site, but in a smaller scale. Despite the fact that in R3 the bond Cα—F should be weaker, as inferred from the lower electronic work involved in reaching the TS, the longer O—Cα and shorter Cα—F interaction distances at the TS structure (Fig. 2) reveal that the hydrogen bond with the fluoride also demands structural work at this point, due to conformational strain. The latter work can be decreased by the enzyme machinery aiding to lower the energy barrier by this means. Interestingly, the W1/W2 ratio in R1 and R2 is about 2, whereas it goes up to 3.2 in R3. First, this exposes that the work associated to the electronic reorganization is always smaller than that associated to the structural changes, which predominates in all three reactions. Second, the intramolecular hydrogen bond in R3 demands a major structural work and a low electronic work in order to reach the transition state
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FIG. 3. Reaction force profiles for reactions R1-R3. The plots at the right show the individual behavior of the force profiles, which are divided into reactant (R), transition state (T S), and product (P) regions.
structure. The latter is exposed by the magnitude of W1 which triplicates the value of W2. The final balance between the bond formation and breaking together with the stabilization of the fluoride resulted in larger negative values of W3 and W4 for R3. This can be rationalized as a lower resistance towards electronic and structural modifications to arrive the product configuration as reflected by its exergonic behavior. D. Reaction electronic flux
The REF profile was calculated to characterize the main chemical events taking place along the reaction coordinate, and it is shown in Fig. 4. This allows to identify the regions of the reaction coordinate where electronic activity associated to bond formation and/or bond strengthening and bond breaking and/or bond weakening is occurring. The REF of R1 slightly increases at the reactant region at the very beginning of the reaction. This can be attributed to the strengthening of the Cα—H bonds and the polarization induced by conformational changes, Cα changes from a tetrahedral sp3 to a planar sp2. Then, a small peak of negative activity associated to a slight weakening of the Cα—F precedes
the positive electronic activity that reaches a maximum coinciding with the beginning of the transition state region. This spontaneous activity is mostly related to the overlapping between the electronic densities of the nucleophile with the substrate involving the formation of the O—Cα bond. This is followed by the non-spontaneous activity inside the transition state region, which indicates the Cα—F bond dissociation. In the product region, a positive peak of the REF is observed, it is related to intramolecular transfer of the fluoride to the vicinal carbon with formation of a new carbon fluoride bond. Finally, a negative peak shows up, it is ascribed to the cleavage of the carbon oxygen double bonds into a single bond. The REF associated to R2 is mostly concentrated within the transition state region. The positive and negative fluctuation around the zero flux regions observed within the reactant region should be associated to bond strengthening and weakening processes due to electronic redistribution on the Cα atom and the subsequent weakening of the Cα—F bond as described for R1. Once the transition state region is reached, R2 exposes the main changes on the electronic activity, indicating that the majority of the electronic reorganization is localized in this region. This points out that R1 has to adopt a conformation very close to the TS before it starts
FIG. 4. Reaction electronic flux profile for reactions R1-R3. The plots at the right show the individual behavior of the electronic flux profiles, which are divided into reactant (R), transition state (T S), and product (P) regions.
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TABLE II. Natural population analysis at three critical points of the reaction coordinate of R1-R3. Model
Onuc—H2C—F
—H2C—
—F
R1R R1ξ1 R1TS R2R R2ξ1 R2TS R3R R3ξ1 R3TS
−0.84 −0.89 −0.98 −0.97 −1.00 −1.13 −0.84 −0.88 −0.94
0.37 0.38 0.36 0.28 0.31 0.29 0.38 0.39 0.37
−0.40 −0.51 −0.66 −0.43 −0.55 −0.74 −0.41 −0.51 −0.61
with the electronic reorganization necessary to continue with the reaction, revealing a resistance towards adopting the electronic density distribution needed for this SN2 reaction. From a qualitative point of view, the REF of R2 presents three major peaks, revealing the three major events involved in this particular reaction. The first positive peak is the one associated to the O—Cα bond formation. The second is a negative peak that was related to the Cα—F bond breaking; the third is a positive peak associated to bonds strengthening in the equilibration process to reach the product conformation. It is important to note that after leaving the transition state region, a zero REF regime rules, indicating that the product region is unequivocally characterized by structural relaxation. The REF obtained for R3 did not show electronic activity until the reactants were very close to each other at the end of the reactant region. This is because R3 suffers a minor change in the F—C—C==O dihedral angle when compared to R1 and R2, accompanied by the change of Cα from a
tetrahedral sp3 to a planar sp2 conformation that takes place further in the reaction coordinate. Both seem to be caused by the intramolecular hydrogen bond between the carboxylic proton and the halogen, which adds conformational strain. At the end of the reactant region the electronic activity shows up developing a positive peak, indicative of a process similar to that described for R1, where the conformational change of the Cα involves bond strengthening processes, followed by the O—Cα bond formation at the transition state region. Then, a negative peak develops within the transition state region, this is the clear signature of the Cα—F bond dissociation. After the transition stage region, a new negative peak emerges, it is assigned to the O—H bond breaking step in the proton transfer from the carboxylate group to the fluoride. The low intensity and broad positive peak in the product region should be basically attributed to the formation of the H—F bond. E. Charge distribution and Fukui function
At this stage of the study, we have characterized different mechanistic scenarios for the nucleophilic attack of aspartate to FAc in different protonation states. Nevertheless, the remaining question about the decrease of the energy barrier by the protonation of the substrate still needs to be answered. According to the analysis of the reaction works, there is a structural component that contributes to the increase of the barrier for the negatively charged substrate, which is followed by an electronic process that is also less favored in R2. The decrease of the electrostatic repulsion between the reactants of R1 and R3 can be responsible for the structural part. Meanwhile, the large electronic work of R2 might be attributed to some source of electronic strain that difficult the proper progress along the TS region, also inferred from the REF
FIG. 5. Schematic representation of the LUMO for R1-R3 at ξ1, corresponding to the geometry at the transition from the reactant to the TS region (a) upper view (b) side view.
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TABLE III. Fukui function values associated to the local reactivity of Cα toward a nucleophilic attack. Model R1ξ1 R2ξ1 R3ξ1 a Condensed
b Condensed
f +(r )a
f +(r )b
0.18 0.00 0.16
0.13 0.01 0.10
Fukui function calculated by neglecting relaxation effects. Fukui function calculated by the Yang Mortier approach.
profile of R2. To address the source of this strain, we analyzed the charge distribution at the critical points of the reaction coordinate, data listed in Table II. The charge on the reaction axis constituted by the O—CαH2—F group of atoms presents a huge amount of negative charge. This charge increases further in the reaction coordinate due to the negative nature of the nucleophile and the leaving group, leading to a TS with a high concentration of negative charge localized at the reaction axis. Interestingly, the model with the lowest negative charge on the reaction axis at the TS was R3, followed by R1, and then by R2 with the largest negative charge. These results correlate with the reaction barriers obtained for these models, thus revealing that the decrease of the negative charge on the reaction axis is the source of the lowering of the reaction barrier. The charge analysis of the CαH2— group denotes the electrophilic nature of this group along the whole process reflected by its positive charge. In addition to that, its slight decrease of charge (more positive) at the beginning of the TS region followed by an increase due to the donation from the nucleophile is indicative of the weakening of the Cα—F bond followed by the beginning of the O—Cα bond formation, in perfect agreement with the analysis of the REF profiles. As mentioned above, the charge at the region of the reaction axis of R1 and R3 is lower than in R2, which is reflected by a more positive charge on the CαH2— of the two former models. This holds along the reaction, revealing that the carboxylic moiety acts as a charge acceptor, able to stabilize this excess of negative charge. More important, it seems that the protonation of the substrate turns the carboxylic moiety into a better charge acceptor, thus performing an active role during the reaction. This finding allows to rationalize the earlier experimental evidence that pointed out the increased activity of FAc towards nucleophilic substitution in its undissociated form.13 The problem with this finding is that to achieve the charge transfer from the reaction axis to the carboxylic moiety, it is necessary that the pz orbital involved in the reaction to interact with the π∗ (charge acceptor) from the carboxylic group. However, this does not seem geometrically feasible in R3, even though it also shows a decrease on the charge and the energy barrier. To explore the independence of the charge transfer on the conformation, we analyzed the LUMO of the supermolecule, from which it is possible to analyze the shape of the acceptor orbital involved in the process at the early stages of the reaction. The results showed in Fig. 5 denote that independent of the conformation, the LUMOs of the three models present the pz-π∗ orbital interaction. Thus, according to our results this orbital interaction that enables the charge
transfer is a determinant feature of the electronic structure, able to provide the necessary stabilization of the LUMO in order to facilitate the course of the reaction. We would like to remark that our findings argue against the previous proposal,12 in which is stated that the reaction depends on the geometry of the TS, involving the π orbital instead of the π∗ as here proposed, orbital that is not a charge acceptor as required by the mechanism. To understand how for the particular cases of R1 and R3 their LUMO structure leads to lower energy barriers, we found that the contribution of the carboxylic carbon to the molecular orbital is larger for the protonated cases. This may point out that for these systems, the carboxylic acid is better as a charge acceptor and this orbital may allow to concentrate more charge on the carboxylic carbon decreasing the electronic repulsion at the TS. To corroborate this hypothesis and how the contributions to the LUMO affect the Cα, we obtained the Fukui function to measure the local reactivity of Cα toward a nucleophilic attack ( f +(r)) by the condensed Fukui function neglecting relaxation effects (for detailed description of the method see references)46–48 and the approach based on population analysis introduced by Yang and Mortier.49 To get a better representation of the variables under study, we used the geometries at ξ1 due to two reasons: first, at this point it starts to dominate the electronic activity involved in the reaction; and second, the conformation of the substrate is closer to the TS geometry, effect that is one of our main focuses of study. The results listed in Table III show that independent of the method of calculation, the Fukui function shows that the protonation of the substrate independent of the conformation increases the electrophilicy of Cα, which actually is close to 0 for R2 in accordance with its high energy barrier. V. CONCLUSIONS
In the present work, we explored the intrinsic chemical variables that determine the reactivity of FAc towards its defluorination through an SN2 reaction. To accomplish this goal, we focused on the study of the influence that the carboxylic acid has as the vicinal group of the reactive center. We found that the protonation of the carboxylic moiety of FAc catalyzes the nucleophilic substitution by decreasing the excess of electronic density at the reaction axis during the reaction, which was found to be the main reason of the electronic strain along the reaction coordinate. This was achieved by the augmented ability of the carboxylic group of receiving charge when it is protonated, property that we found was not restricted by the relative conformation between the carboxylic acid and the reaction axis. Under the right conditions, the proton from the carboxylic acid was transferred to the emerging fluoride during the reaction, process able to provide a marked exergonic behavior. We concluded that the relative thermodynamic behavior relies mainly on the mechanism involved in the stabilization of the fluoride anion formed as a product of the reaction. Thus, it is also expected that the residues of the halogen pocket from dehalogenases to be able to stabilize the anion, helping the enzymatic reaction to advance towards the next step of the catalytic process.
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Driven by our main findings, we raise the question if the use of different chemical groups of similar electronic properties to the carboxylic acid would be able to provide a similar catalytic effect. The answer to this question may be useful in the search of new strategies to catalyze complex SN2 reactions. As concluding remarks, the combination of several methods for the analysis of reaction mechanisms is presented as a framework to integrate key information regarding the structural and electronic processes that take place during the reaction. In particular, here we analyzed the reaction mechanisms by using the reaction force profiles, reaction electronic flux, charge distribution, and the Fukui function. Finally, this combined approach proved to be a powerful strategy to describe the actual mechanism by which a particular reaction is catalyzed. ACKNOWLEDGMENTS
The authors thank financial support from Grant ICM No. 120082 and FONDECYT through Projects Nos. 3130383 and 1130072. S.M.-R. also thanks the support of Basal Financing Program CONICYT-FB0807 (CEDENNA), to the invaluable help of Dr. Jorge Martinez-Araya for insightful discussions on conceptual DFT and to Dr. Diego Cortés-Arriagada for helpful revision on the manuscript. 1M.
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