1 Introduction

The Diels-Alder (DA) reaction has been proposed as a key transformation in the biosynthesis of many cyclohexene-containing secondary metabolites. So far, only four purified enzymes have been implicated in these biotransformations: namely, solanapyrone synthase (Oikawa et al., 1995), LovB (Auclair et al., 2000; Ma et al., 2009), macrophomate synthase (Watanabe et al., 2000; Ose et al., 2003), and riboflavin synthase (Eberhardt et al., 2001; Kim et al., 2010). Although the stereochemical outcomes of these reactions indicate that the product formation could be enzyme-guided in each case, enzymes typically demonstrate more than one catalytic activity, leaving their specific influence on the cycloaddition step undefined.

Spinosyn A (1) has attracted much attention as it possesses potent insecticidal activity, with low toxicity to beneficial insects and rapid degradation in the environment (Kirst et al., 1991; Kirst, 2010). Very recently, Kim et al. (2011) published the first example of an in vivo enzyme-catalyzed [4 + 2] cycloaddition, and thus fully established the biosynthesis of spinosyn A (1) (see Scheme 9.1).

Four genes in the spinosyn A biosynthetic gene cluster of Saccharopolyspora spinosa—spnF, spnJ, spnL, and spnM—were proposed to convert the product (2) of the polyketide synthase (PKS) to the tetracyclic aglycone (6) (Waldron et al., 2001). Kim et al. (2011) carried out experiments with the separated genes in order to establish which one was responsible for the conversion of intermediate (3) into the formal [4 + 2] cycloadduct (5), an intermediate in the formation of the tetracyclic compound (6) (see Scheme 9.1). These authors established that SpnF is a cyclase catalyzing the conversion of (4) into (5) with an apparent k_cat of 14 ± 1.6 min^− 1, presenting an estimated rate enhancement (k_cat,spnF versus k_non) of approximately 500-fold (Kim et al., 2011). In addition, Kim et al. (2011) suggested that in order to confirm the hypothesis that SpnF could catalyze the DA reaction, it is required to demonstrate that the reaction progresses through a single pericyclic transition state (TS). Therefore, a stepwise [4 + 2] cycloaddition mechanism was not ruled out.

The complete characterization of the mechanism of a DA reaction, which is difficult to predict experimentally, can be addressed in silico due to the availability of computational resources. Thus, very recently, Hess and Smentek (2012) performed a density functional theory (DFT) computational investigation on the enzyme-catalyzed cyclization reaction in the biosynthesis of spinosyn A (1). For this study, two computational models were selected (see TS-M1 and TS-M2 in Figure 9.1).

In spite of the high asynchronicity found in the CC single bond formation in both TSs, these authors suggested that the reaction takes place via a concerted mechanism since no zwitterionic intermediate was located (Hess and Smentek, 2012). The B3LYP activation energy associated with TS-M2 was estimated to be 20 kcal/mol, while that obtained for this model at the MP2 level was 10 kcal/mol. They found an activation energy of 15 kcal/mol for the TS-M1-reduced model. Since some global electron density transfer (GEDT) (Domingo, 2014) was found at the B3LYP level, 0.10e, they also suggested that the possibility of additional stabilization of the polar TS by the enzyme might lower the activation energy to a value for which the reaction could easily be catalyzed enzymatically (Kim et al., 2011). However, it is interesting to note that the GEDT at TS-M2 is too low to cause an efficient stabilization by the enzyme. It should be highlighted that favorable polar Diels-Alder (P-DA) reactions present GEDT values in the range of 0.30e–0.40e (Domingo and Sáez, 2009).

Paraherquamide A (9) (Yamazaki et al., 1981; Blanchflower et al., 1991) and VM55599 (11) (Blanchflower et al., 1993) (see Scheme 9.2) are indolic secondary metabolites isolated from various fungi. These alkaloids share an unusual bicyclo[2.2.2]diazaoctane ring system that has been proposed to arise via an intramolecular Diels-Alder (IMDA) reaction of the isoprene double bond across the α-carbons of the amino acid subunits (see Scheme 9.2) (Williams et al., 1998; Stocking et al., 2000, 2001; Sanz-Cervera and Williams, 2002; Williams and Cox, 2003).

A B3LYP/6-31G* study on the reaction model established that when the folded conformation of azadiene 7 is taken as an energy reference for the IMDA reaction, the activation free energy is ca. 24 kcal/mol, an energy that furnishes a rationalization for a spontaneous (i.e., nonenzymatically catalyzed) cyclization process in the biosynthesis of paraherquamide A (9) and VM55599 (11) (Domingo et al., 2003). Consequently, both the folding of the precursor at the active site of the putative oxidase that forms the azadiene system from the diketopiperazine precursor and the low negative activation entropy associated with the intramolecular process can thus be invoked to account for the feasibility of these biosynthetic cyclizations.

Recently, Houk et al. reported a theoretical prediction of an enzyme-catalyzed transannular 1,3-dipolar cycloaddition (13DC) reaction in the biosynthesis of lycojaponicumins A and B (Krenske et al., 2013). DFT calculations using the M06-2X functional predict that the uncatalyzed 13DC reaction of the putative lycojaponicumin precursor in water is moderately facile (ΔG_act = 21.5 kcal/mol, k = 10^− 3 s^− 1) and that an enzyme could accelerate the cycloaddition by the formation of two hydrogen bonds (HBs) of two explicit water molecules to the enone oxygen while maintaining an otherwise nonpolar active site (see Scheme 9.3). The theoretical enzyme-catalyzed process presents ΔG_act ca. 17 kcal/mol, corresponding to a 2000-fold rate enhancement, and the predicted k_cat (2 s^− 1) was found to be similar to those of known enzymes involved in secondary metabolic pathways.

Considering that the preliminary computational work carried out by Hess and Smentek (2012) does not allow to definitively establish if SpnF is a cyclase catalyzing the conversion of macrocyclic lactone (4) into tricyclic compound (5), we decided to perform a further DFT study using the actual molecular system 4 proposed by Kim et al. (2011) as intermediate in the biosynthesis of spinosyn A (1; see Schemes 9.1 and 9.4).

In addition, Kim et al. (2011), Hess and Smentek (2012), and Townsend (2011) proposed that the cyclization step in SpnF takes place via a concerted mechanism. Hess and Smentek also proposed that “the hallmark of Diels-Alder [4 + 2] cycloadditions is that they are concerted.” Establishing whether the one-step mechanism of the SpnF-catalyzed cyclization has a concerted nature is important as pericyclic reactions, defined in 1965 (Woodward and Hoffmann, 1969), are commonly assumed to take place through a concerted mechanism. Although Hess and Smentek (2012) performed a complete geometrical analysis of the asynchronicity in the CC single bond formation, this analysis offers no information about the evolution of the CC double bonds. A rigorous study of the concerted nature of a reaction requires an exhaustive topological analysis of all changes in bonding along the reaction, which cannot be performed by experimental procedures.

The bonding evolution theory (BET) (Krokidis et al., 1997; Gilmore, 1981), consisting of the joint use of electron localization functions (ELF) (Savin et al., 1991, 1996, 1997; Silvi and Savin, 1994) and Thom’s catastrophe theory (Thom, 1976; Woodcock and Poston, 1974), has been proposed as a tool for the understanding of electronic changes in chemical processes (Polo et al., 2008). BET studies have shown that even the synchronous DA reactions between butadiene/ethylene (Berski et al., 2003), cyclopentadiene/ethylene (Domingo et al., 2010), and cyclopentadiene/tetracyoanoethylene (Domingo et al., 2012) are nonconcerted processes. Consequently, a topological ELF bonding analysis along the cyclization of macrocyclic lactone (4) is also performed in order to establish the nonconcerted nature of the reaction.

2 Computational methods

DFT computations were carried out using the MPWB1K functional (Zhao and Truhlar, 2004), together with the 6-31G* and 6-311G** basis sets (Hehre et al., 1986). Optimizations were carried out at the MPWB1K/6-31G* level using the Berny analytical gradient optimization method (Schlegel, 1982, 1994). Stationary points were characterized by frequency computations in order to verify that TSs have only one imaginary frequency. Intrinsic reaction coordinates (IRC) paths (Fukui, 1970) were traced in order to check the energy profiles connecting each TS to the two associated minima of the proposed mechanism using the second-order González-Schlegel integration method (González and Schlegel, 1990, 1991). Values of enthalpies, entropies, and free energies within a dielectric environment of an active site (Krenske et al., 2013), modeled in implicit diethyl ether (ɛ = 4.24), were calculated at the MPWB1K/6-311G** level with standard statistical thermodynamics at reaction conditions (Hehre et al., 1986). Thermodynamic calculations were corrected by a factor of 0.96 (Scott and Radom, 1996). Solvent effects of diethyl ether on the thermodynamic calculations were considered by using a self-consistent reaction field (SCRF) (Tomasi and Persico, 1994; Simkin and Sheikhet, 1995) based on the polarizable continuum model (PCM) of Tomasi’s group (Cances et al., 1997; Cossi et al., 1996; Barone et al., 1998). The electronic structures of stationary points were analyzed by the natural bond orbital (NBO) method (Reed et al., 1985, 1988) and by ELF topological analysis, η(r) (Savin et al., 1991, 1996, 1997; Silvi and Savin, 1994). The ELF study was performed with the TopMod program (Noury et al., 1999) using the corresponding monodeterminantal wavefunctions of the selected structures of the IRC. All computations were carried out with the Gaussian 09 suite of programs (Frisch et al., 2009).

A conformational analysis for the precursor macrocyclic lactone 4 was performed to search the minimum energy structure using the Merck molecular force field (MMFF) in the MacroModel (MacroModel, 2009); see the “Supplementary Material” section for further details on these calculations). However, the MMFF global minimum geometry, once reoptimized at the MPWB1K/6-31G* level, was 2.3 kcal/mol above the macrocyclic lactone (4) conformation used as a reference in this study.

3 Results and discussion

An exploration of the potential energy surface for the conversion of macrocyclic lactone (4) into the tricyclic compound (5) allows establishing that this cyclization reaction takes place through a one-step mechanism. Consequently, the precursor macrocyclic lactone (4), the only TS, and the tricyclic compound (5) were located and characterized. The energy results are summarized in Table 9.1.

The activation enthalpy associated with the cyclization of macrocyclic lactone (4) via TS is 20.1 kcal/mol. This value, which is close to the activation energy computed by Hess and Smentek (2012) for TS-M2 using the B3LYP functional (20 kcal/mol), indicates that the activation enthalpy for the conversion of macrocyclic lactone (4) into tricyclic compound (5) might be around 20 kcal/mol. Formation of tricyclic compound (5) is exothermic by −17.9 kcal/mol.

Interestingly, the activation free energy associated with TS is only 21.1 kcal/mol. Inclusion of the activation entropy increases the activation enthalpy by only 1.0 kcal/mol. This behavior is a consequence of the intramolecular nature of the cyclization process, which increases the entropy of TS by only −3.4 cal/mol K. Formation of tricyclic compound (5) is exergonic by −15.9 kcal/mol; thus, the cyclization can be considered irreversible. The computed activation free energy associated with TS, which is similar to that found by Houk et al. for the uncatalyzed 13DC reaction of the putative lycojaponicumin precursor in water (Krenske et al., 2013), predicts that the uncatalyzed cyclization of the putative spinosyn A precursor is moderately facile in a low-polar medium, in clear agreement with the fact that the cyclization takes place easily at room temperature (Kim et al., 2011).

The activation free energy associated with TS is less than that for the IMDA reaction of folded azadiene (7), ΔG_act = 24 kcal/mol. Considering that this IMDA reaction takes place spontaneously at room temperature (Sanz-Cervera et al., 2000), we can conclude that cyclization of lactone (4) via TS can be easily performed at room temperature (Kim et al., 2011) without the participation of any Diels-Alderase.

One possibility to accelerate cyclization is to raise the polar character of the reaction by increasing the electrophilicity of the unsaturated ketone framework present in macrocyclic lactone (4). This electrophilic activation can be reached via the formation of HBs between the carbonyl oxygen and hydrogen-bond donor molecules; however, it is to be noted that the carbonyl oxygen is already intramolecularly hydrogen-bonded to the hydroxyl group present at C17. In spite of this behavior, we considered a theozyme in which one water molecule was also hydrogen-bonded to the carbonyl oxygen. Thermodynamic calculations for the theozyme and the geometry of the corresponding TSw are given in the “Supplementary Material” section. Although formation of the second hydrogen-bond decreased the activation enthalpy by 0.4 kcal/mol, it increased the free activation energy by 0.8 kcal/mol as a consequence of the unfavorable entropy decrease; −4.0 cal/mol K. Consequently, thermodynamic calculations for the proposed theozyme suggest that HBs are not involved in the observed acceleration in the SpnF gene. These energy results allow one to rule out Hess and Smentek’s proposal that a stabilization of the highly polarized transition structure could also accelerate the reaction.

The geometries of macrocyclic lactone (4), TS, and the formal [4 + 2] cycloadduct (5) are given in Figure 9.2. In macrocyclic lactone (4), the distance between the C4 and C12, and C7 and C11 carbons are 4.659 and 2.927 Å, respectively. The length of this HB in lactone (4) is 2.024 Å. At TS, the distance between the C4 and C12, and C7 and C11 carbons are 2.772 and 1.918 Å, respectively. These values, which are close to those found by Hess and Smentek (2012) at TS-M1 and TS-M2, clearly indicate that at this highly asynchronous TS, while the C7C11 is being formed, no bonding interactions between the C4 and C12 carbons take place (as discussed later in this chapter). It is worth to note that at TS, the HB length is 1.988 Å. The shortening of this HB length with respect to that of the macrocyclic lactone (4) clearly indicates a stronger HB interaction at the polar TS, which in turn can increase the electrophilic character of the unsaturated ketone residue. In the tricyclic compound (5), the lengths of the C4C12, and C7C11 single bonds are 1.577 and 1.528 Å, respectively. Compound (5) remains hydrogen-bonded with an HB length of 2.069 Å.

Natural population analysis (NPA) allows evaluating GEDT along the cyclization process. The natural atomic charges at TS were shared between the two fragments resulting from the disconnection of the C8C9 and C18C19 bonds of the macrocyclic lactone ring. As some GEDT can take place in macrocyclic lactone (4) following this disconnection scheme, the natural atomic charges in lactone (4) were also computed. The net charges in the conjugated ketone frameworks in (4) and TS are 0.04e and −0.06e, respectively. Consequently, upon going from macrocyclic lactone (4) to TS, the GEDT that takes place from the unsaturated ester framework to the unsaturated ketone one is 0.10e; a value identical with that computed at TS-M2 using the B3LYP functional (Hess and Smentek, 2012). This low GEDT, which points to a low-polar process, accounts for the high activation energy found at this cyclization reaction (Domingo and Sáez, 2009).

Macrocyclic lactone (4) has an ellipsoid structure that presents two main axes: (i) an x-axis along the two conjugated diene systems involved in the cyclization reaction, and (ii) a y-axis along the C—C single bond formation [see (4) in Figure 9.2]. While macrocyclic lactone (4) is relatively rigid along the x-axis, it may experience some flexibility along the y-axis. Therefore, when macrocyclic lactone (4) enters the active site of the enzyme, it may experience some strain, which may increase its internal energy. However, this energy penalty can be compensated by favorable HB interactions between the enzyme and the oxygenated functional groups, two alcohols and two carbonyl groups, that are present in macrocyclic lactone (4).

Thus, when macrocyclic lactone (4) is strained along the y-axis, reducing the C3C15 distance by 0.4 Å, the stressed lactone 4-S is found to be only 3.8 kcal/mol higher in free energy (3.2 kcal/mol in enthalpy) than the free lactone (4; see Table 9.1), a value that could easily be reached by lactone (4) as it enters the active site of the enzyme. Thus, when the strained lactone 4-S is considered as the complex precursor of the cyclization process, the corresponding activation free energy to reach TS is found to be ca. 17.0 kcal/mol. This decrease of the activation free energy, which is similar to that found by Houk in the hydrogen-bonding activation and represents a 2000-fold rate enhancement (Krenske et al., 2013), might account for the low acceleration of the cyclization reaction of (4) in the presence of the SpnF gene: 500-fold (Kim et al., 2011). Note that this very low rate enhancement indicates that the strain inside the SpnF gene should be lower than the computed 3.8 kcal/mol, a very accessible value.

The IRC from TS connects it directly with macrocyclic lactone (4) and tricyclic compound (5), indicating the one-step nature of this cyclization reaction (see Figure 9.3). A geometrical analysis of the evolution of the C4C12 and C7C11 single bond formation along the IRC, which is similar to that for TS-?M2 (Hess and Smentek, 2012), suggests that this one-step cyclization reaction takes place through a two-stage mechanism (Domingo et al., 2008). While at the first stage of the reaction only the C7C11 single bond is formed, the C4C12 single bond is formed at the second stage of the reaction (as discussed later). Point P2 of the IRC, which presents a minimum value in the energy gradient, shares the IRC in the two stages (see Figure 9.3). Interestingly, at this point, while the C7C11 single bond is practically formed [d(C7—C11) = 1.624 Å], the formation of the C4C12 single bond has not started yet [d(C4—C12) = 2.603 Å]. In addition, the high asynchronicity found at the TS in the CC single bond formation, Δl = d(C4C12)-d(C7—C11) = 0.95, slightly increases at point P2, where Δl = 0.98. Considering that ELF bonding analysis shows that the C—C single bond formation takes place in the short range of 1.9 − 2.0 Å (Domingo, 2014), this geometrical analysis clearly shows that the formation of the two new C—C single bonds is nonconcerted.

Finally, in order to establish the concerted or nonconcerted nature of this cyclization process, an ELF bonding analysis was performed. Details of the ELF bonding analysis are given in the “Supplementary Material” section. The topological ELF bonding analysis along the cyclization clearly supports the nonconcerted nature of the bond-breaking/bond-formation processes, which take place in the following order (see Table 9.2): (i) breaking of the C4—C5, C6—C7 and C11—C12 double bonds before reaching the TS geometry; (ii) creation of the pseudoradical centers at the C7 and C11 carbons present at TS; (iii) formation of the first C7C11 single bond at P1 by coupling of the aforementioned pseudoradical centers at a distance of 1.895 Å; (iv) formation of the C5—C6 double bond at P3; (v) creation of the pseudoradical centers at the C4 and C12 carbons; and finally, (vi) formation of the second C4C12 single bond at P5 by coupling of the aforementioned pseudoradical centers at a distance of 2.052 Å.

Table 9.2

Sequential Bonding Changes Along the Nonconcerted One-Step Conversion of Macrocyclic Lactone (4) into Tricyclic Compound (5).

	IRC	d1	d2	Chemical Process	Topological Characterization [a]
a		< 1.918	< 2.772	Breaking of the CxCy double bonds present in (5)	Formation of one single disynaptic basin V(Cx,Cy) in the CxCy region
b	TS	1.918	2.772	Formation of the C7 and C11 pseudoradical centers	Formation of the two monosynaptic basins V(C7) and V(C11)
c	P1	1.895	2.766	Formation of the first C7C11 single bond	Formation of the disynaptic basin V(C7,C11)
d	P3	1.590	2.406	Formation of the C5C6 double bond	Formation of the two disynaptic basins V(C5,C6) and V('C5,C6)
e	P4	1.556	2.075	Formation of the C4 and C12 pseudoradical centers	Formation of the two monosynaptic basins V(C4) and V(C12)
f	P5	1.555	2.052	Formation of the second C4C12 single bond	Formation of the disynaptic basin V(C4,C12)

Note: The positions of TS and selected points P1-P5 in the IRC are given in Figure 9.3.

^[a] The full topological ELF bonding analysis is given in the “Supplementary Material” section.

While the analysis of the geometrical parameters along the IRC accounts for the asynchronicity in the formation of the two new CC single bonds (see Figure 9.3), the concerted or nonconcerted nature of the reaction demands an exhaustive topological ELF analysis of the changes of electron density along the cyclization path in order to establish when the bonding changes take place. Consequently, with a single geometrical analysis, Hess and Smentek were not able to establish the concerted or nonconcerted nature of the cyclization, although the high asynchronicity found in the formation of the two C—C single bonds along the IRC anticipates the nonconcerted nature of the cyclization.

4 Conclusions

The conversion of macrocyclic lactone (4) into tricyclic compound (5), as a key step in the biosynthesis of spinosyn A 1, experimentally studied by Kim et al. (2011), has been theoretically investigated using DFT methods at the MPWB1K/6-31G* and the MPWB1K/6-311G** computational levels. The cyclization process takes place along a one-step mechanism characterized by a nonconcerted breaking/forming bond process. In spite of the high activation enthalpy computed for this cyclization process, 20.1 kcal/mol, the very low activation entropy associated with the cyclization of lactone (4), − 3.4 cal/mol K, makes it feasible for the reaction to take place at room temperature due to the computed activation free energy of 21.1 kcal/mol. The large exergonic character of the cyclization, −15.9 kcal/mol, makes the cyclization process irreversible. The relatively low activation free energy found for this cyclization furnishes a rationalization of the spontaneous (i.e. nonenzymatically catalyzed) cyclization process in the biosynthesis of spinosyn A (1).

Modeling of a feasible theozyme, in which the carbonyl oxygen present at C17 is hydrogen bonded to an additional water molecule, suggests that although the hydrogen bonding slightly favors the cyclization enthalpically, the corresponding activation free energy is slightly disfavored due to the decrease of activation entropy associated with the HB formation.

A geometrical analysis of macrocyclic lactone (4) suggests that it has some flexibility along the Y-axis parallel to the C—C single bond formation. Consequently, a slight strain suffered by macrocyclic lactone (4) inside the active site of the SpnF gene may slightly increase its energy, thus decreasing the corresponding free activation energy. This behavior, which is similar to that found in the biosynthesis of paraherquamide A 9 and VM55599 11 (Domingo et al., 2003; Williams, 2011) accounts for the relatively low 500-fold acceleration found by Kim et al. (2011) in the SpnF gene.

A geometrical analysis for the C—C single bond formation along the IRC of the one-step mechanism indicates that formation of the two C—C single bonds takes place along a two-stage mechanism. While at the first stage only the C7—C11 single bond is formed at the terminal carbons of the two conjugated carbonyl frameworks of macrocyclic lactone (4), the second C4—C12 single bond is formed at the second stage.

Finally, an ELF bonding analysis of the breaking/forming bond processes along the one-step cyclization unambiguously allows the establishment of the nonconcerted nature of this process and thus clears up the hypothetical doubt for DA. While the three double bonds of unsaturated lactone (4) participating in the DA reaction are topologically broken before reaching the TS geometry, formation of the new bonds takes place after passing the TS in the sequence: (i) formation of the first C7C11 single bond; (ii) formation of the C5C6 double bond; and finally (iii) formation of the second C4C12 single bond. These significant chemical changes, which take place in differentiated regions of the IRC, account for the nonconcerted nature of the bond-breaking and bond-formation processes as demanded in pericyclic reactions.

Supplementary Material: Conformational analysis of macrocyclic lactone (4). Modeling of a theozyme for the conversion of macrocyclic lactone (4) into tricyclic compound (5). ELF bonding analysis of the conversion of macrocyclic lactone (4) into tricyclic compound (5). Cartesian coordinates of the stationary points involved in the cyclization reaction of lactone (4).

1 Conformational analysis of macrocyclic lactone (4)

Macrocyclic lactone (4), obtained from the retro-cyclization of compound (5), was first submitted to a preliminary minimization in the Macromodel [1] using the Merck molecular force field (MMFF)[2] and water as solvent. Taking the MMFF optimized structure, a conformational analysis was performed using a mixed torsional/large-scale low-mode sampling (LLMOD) analysis [3], with False Non-Match Rate (FNMR) as a minimizer with the recommended 1.0 gradient convergence threshold and 100,000 steps. The energy window to select structures was of 50 kJ/mol. The chirality of all the carbon atoms was the only variable fixed in this analysis. From the 12,777 structures found in this conformational analysis, only 7483 of them converged with the imposed criteria. Taking the structure with the lowest energy of this conformational analysis (see Figure S1), we can see that the C4 = 5-C6 = C7 s-cis conformation of the unsaturated ester framework, and the s-trans conformation of the unsaturated ketone framework present in macrocyclic lactone (4) is preserved.

However, when the MMFF minimum conformation was reoptimized at the MPWB1K/6-31G* computational level, this MMFF minimum was found to be 2.3 kcal/mol more energetic than macrocyclic lactone (4).

2 Modelling of a theozyme for the conversion of macrocyclic lactone (4) into tricyclic compound (5)

In principle, an enzyme may accelerate the cyclization of macrocyclic lactone (4) through selective hydrogen bonding to the oxygen of the unsaturated ketone framework. This HB would increase the electrophilicity of the unsaturated ketone framework, thus accelerating the cyclization through a more polar process [4]. Lactone (4) already presents an intramolecular HB between the carbonyl oxygen atom at C-15 and the hydroxyl group present at C—17. Apart from this HB, an additional rate enhancement coming from the hydrogen bonding of a water molecule to the unsaturated ketone oxygen at C—15 within a typical dielectric environment of an enzyme active site was studied by optimizing 4w, TSw, and 5w at the MPWB1K/6-311G** computational level in implicit diethyl ether [5] (see Scheme S1). Thermodynamic data associated with the proposed theozyme are given in Table S1.

Although formation of the second HB decreases the activation enthalpy of TSw by 0.4 kcal/mol relative to that of TS, it increases the activation free energy of TSw by 0.8 kcal/mol relative to that of TS as a consequence of the unfavourable entropy decrease associated with the cyclization; ΔΔS^≠ −4.0 cal/mol K. Consequently, thermodynamic data suggest that hydrogen bonds are not involved in the acceleration observed in the SpnF gene. Note that formation of an additional HB at the lactone oxygen would disfavor the cyclization since it may decrease the nucleophilic character of the unsaturated ester framework.

The geometry of TSw is given in Figure S2. At TSw, the distance between the C4 and C12, and C7 and C11 carbons are 2.814 and 1.909 Å, respectively. Consequently, formation of the second HB with a water molecule makes the process slightly more advanced and more asynchronous. At this TS, while the intramolecular HB length is 1.917 Å, the intermolecular HB length involving the water molecule is 1.988 Å.

3 ELF bonding analysis of the conversion of macrocyclic lactone (4) into the tricyclic compound (5)

Several theoretical studies have shown that topological ELF analysis along an organic reaction path can be used as a valuable tool to understand the bonding changes along a reaction [6,7]. After an analysis of the electron density, the ELF provides basins, which are the domains in which the probability of finding an electron pair is maximal. The basins are classified as core basins and valence basins. The latter are characterized by the synaptic order; i.e., the number of atomic valence shells in which they participate. Thus, there are monosynaptic, disynaptic, and trisynaptic basins, and so on [8]. Monosynaptic basins, labeled V(A), correspond to the lone pairs or nonbonding regions, while disynaptic basins connect the core of two nuclei A and B and, thus, correspond to a bonding region between A and B and are labeled V(A,B). This description recovers the Lewis bonding model, providing a very suggestive graphical representation of the molecular system.

Recently, Domingo has shown that the C—C single-bond formation in organic reactions begins in the short C—C distance range of 1.9–2.0 Å by merging two monosynaptic basins, V(Cx) and V(Cy), into a new disynaptic basin V(Cx,Cy) associated with the formation of the new Cx—Cy single bond [9,10]. The Cx and Cy carbons characterized by the presence of the monosynaptic basins, V(Cx) and V(Cy), have been called pseudoradical centers [10,11].

In order to establish the nonconcerted nature of the one-step cyclization involved in conversion of the macrocyclic latone (4) into the tricyclic compound (5), an ELF bonding analysis along the IRC associated with the reaction path was performed. After an exhaustive ELF analysis of 150 points of the IRC from (4) to (5), the most relevant points involved in the C4—C12 and C7—C11 single-bond formation, TS, P1, P4, and P5, were selected. Point P2, which shares the two-stage mechanism, and point P3, associated with the formation of the C5—C6 double bond present in the formal [4 + 2] cycloadduct (5), were also analyzed. The most relevant ELF valence basins and their corresponding N populations of the selected points along the reaction paths are displayed in Table S2, while the attractor positions and atom numbering for TS, P1, P4, and P5 are shown in Figure S3. For simplicity, only the monosynaptic V(A) and the disynaptic V(A,B) basins involved in the forming and breaking bonds along the cyclization will be discussed here.

At the highly asynchronous TS, d1(C7—C11) = 1.918 Å and d2 (C4—C12) = 2.772 Å, the most relevant feature is the presence of two monosynaptic basins V(C7) and V(C11), integrating 0.37e and 0.45e, respectively. These monosynaptic basins, which are located at the end of the two conjugated carbonyl frameworks, are responsible for the subsequent C7—C11 single-bond formation. At TS, the two conjugated systems involved in the cyclization are characterized by the disynaptic basins V(C4,C5), 2.98e, V(C5,C6), 2.78e, V(C6,C7), 2.70e, and V(C11,C12), 2.74e, V(C12,C13), 2.53e, and V(C13,C14) 3.26e. No monosynaptic basin at the C4 or C12 carbons is found, indicating that the C4—C12 single-bond formation has not started yet.

At point P1, d1 = 1.895 Å and d2 = 2.766 Å, the two monosynaptic basins V(C7) and V(C11) present at TS have merged into the new disynaptic basin V(C7,C11), integrating 0.89e. This behavior indicates that the formation of the C7—C11 single bond has already started by coupling of the pseudoradical centers located at the C7 and C11 carbons with a high electron density. As in the case of TS, no monosynaptic basins at the C4 and C12 carbons were found at P1, indicating that the C4—C12 single-bond formation has not started yet.

At point P2, d1 = 1.628 Å and d2 = 2.613 Å, which divides the two stages of the one-step mechanism (see Figure 9.2 in the main chapter), no relevant topological change is observed with respect to P1. From P1 to P2, the electron density of the new C7—C11 single bond has increased to reach 1.54e. The C7—C11 length at P2, 1.628 Å, indicates that the first C—C single bond is already formed. Note that in a stepwise DA reaction, the length of the first C—C single bond formed at the corresponding intermediates is in the range of 1.60–1.65 Å. No topological changes at the C4 or C12 carbons is observed at this point.

At point P3, d1 = 1.590 Å and d2 = 2.406 Å, the disynaptic basin V(C7,C11) has reached an electron density of 1.63e. At this point, a new monosynaptic basin V(C4) appears at C4, integrating 0.23e. No monosynaptic basin appears at C12. The disynaptic basin V(C5,C6) present at P2 has been split into two disynaptic basins V(C5,C6) and V'(C5,C6), integrating 1.82, and 1.52e, indicating the formation of the C5—C6 double bond present in the tricyclic compound (5). In this cyclization reaction, the C5—C6 double bond is formed before the second C4—C12 single bond. Note that in most DA reactions, the creation of the C—C double bond present in the [4 + 2] cycloadduct takes place after formation of the second C—C single bond at the end of the IRC [6,9].

At point P4, d1 = 1.556 Å and d2 = 2.075 Å, while the monosynaptic basin V(C4) increases its electron density to reach 0.54e, and a new monosynaptic basin V(C12) appears at C12, integrating 0.23e. The monosynaptic basins V(C4) and C(12) are responsible for the subsequent C4—C12 single-bond formation.

Finally, at point P5, d1 = 1.555 Å and d2 = 2.052 Å, the two monosynaptic basins V(C4) and V(C12) present at P4 have merged into the new disynaptic basin V(C4,C12), integrating 1.16e. This behavior indicates that the formation of second C4—C12 single bond has already started. At this point of the IRC, the disynaptic basin V(C13,C14) present at P5 has been split into the two disynaptic basins, V(C13,C14) and V'(C13,C14), integrating 1.68e, and 1.67e, respectively, indicating the formation of the C13—C14 double bond present in the tricyclic compound (5).

Some interesting conclusions can be drawn from this ELF bonding analysis: (i) at TS, d1 = 1.918 Å, the presence of two monosynaptic basins, V(C7) and V(C11), indicates that the C7—C11 single-bond formation has not started. On the other hand, the two disynaptic basins, V(Cx,Cy) and V'(Cx,Cy), which topologically characterize the Cx—Cy double bonds present in macrocyclic lactone (4), have merged into one disynaptic basin, V(Cx,Cy), at TS. (ii) formation of the monosynaptic basins, V(C7) and V(C11), takes place at the end of the two conjugated carbonyl frameworks. (iii) formation of the first C7—C11 single bond takes place at the C7—C11 distance of 1.895 Å by coupling of the two pseudoradical centers located at the C7 and C11 carbons. (iv) from d1 = 1.90 to 1.63 Å, while the electron density of the V(C7,C11) disynaptic basin reaches 1.54e, the formation of the second C4—C12 single bond has not started. (v) at point P2, which divides the IRC into two stages, the C7—C11 length, 1.628 Å, indicates that this bond is practically formed. (vi) at point P3, the C5—C6 double bond present in the tricyclic compound (5) has been topologically formed with the creation of the two disynaptic basins, V(C5,C6) and V'(C5,C6). Interestingly, in this cyclization process, the C5—C6 double bond is created before the C4—C12 single bond. (vii) the C4—C12 single bond is created at the end of the IRC at the C4—C12 distance of 2.08 Å.