With or without light: comparing the reaction mechanism of dark-operative protochlorophyllide oxidoreductase with the energetic requirements of the light-dependent protochlorophyllide oxidoreductase

Proton-transfer events

The experimentally-obtained enzyme activity of dPChOR (Muraki et al., 2010) (50 nmol min⁻¹ mg⁻¹) sets an upper limit of 19.3 kcal mol⁻¹ for the rate-determining step of the overall process, using the well-known Eyring equation, $k_{cat}=\frac{k_{B}T}{h}{e}^{-\frac{\Delta G^{‡}}{RT}}$, where k_cat is the measured rate-constant, k_B is the Boltzmann constant, h is the Planck constant and ΔG^‡ is the activation free energy. The initial generation of a reaction intermediate from proton-transfer from Asp274 to C₁₇ can therefore be ruled out, as its energy lies 31.4 kcal mol⁻¹ above the reactant state (Fig. 3 and Table 1). In contrast, the computed barrier for the proton transfer from the propionic side chain to C₁₈ (24.7 kcal mol⁻¹) agrees reasonably well with the experimental value. The difference in computed stabilities between the C₁₇- and C₁₈-protonated isomers is more pronounced in the gas phase, which shows that the most important factor favoring the C₁₈- over the C₁₇- isomer is of an electrostatic nature. Indeed, although both systems contain a positive charge in the substrate aromatic ring and a negative charge on a carboxylate group, the distance between these charges is much larger in the C₁₇-isomer/Asp274 carboxylate system.

In the one-electron-reduced state, the excess spin is, as expected, strongly delocalized across the porphyrin π-system (≈0.1 spin each on rings B and D, ≈0.25 on ring A, ≈0.30 on the C/E rings, and the remaining spin on the methylene bridges). In this state, the proton uptake becomes much more favorable than before (by >15 kcal mol⁻¹, irrespective of the protonation site), due to the formation of a neutral protochlorophyllide/negative carboxylate intermediate, rather than the charge-separated pair observed in the non-reduced state. Proton-transfer to C₁₈ is predicted to occur with a very small barrier of 9.2 kcal mol⁻¹, whereas the proton-transfer from Asp274 to C₁₇ has a larger barrier of 13.6 kcal mol⁻¹. This difference in barriers seems to be correlated to the proton/protochlorophyllide distance observed in the transition state (1.46 Å for the Asp274-C₁₇ transfer vs. 1.31 Å for the carboxylate sidechain-C₁₈ transfer). The transfer of an additional proton to the one-electron-reduced/singly-protonated substrate may then occur with moderate barriers. The transfer from the propionic side chain to C₁₈ is again faster than that of Asp274 to C17 (10.8 kcal mol⁻¹, vs. 18.9 kcal mol⁻¹). The total barrier for the two consecutive proton-transfer events at the one-electron-reduced is fully consistent with the experimental value, regardless of the precise sequence of these events (13.6 kcal mol⁻¹ for Asp274-C₁₇ transfer followed by propionic sidechain-C₁₈ transfer; 18.9 kcal mol⁻¹ for the sequence initiated with transfer to C₁₈).

In the two-electron-reduced state, the barrier for the Asp₂₇₄-C₁₇ proton transfer (8.5 kcal mol⁻¹) is almost as low as the barrier for the proton transfer from the propionic sidechain to the C₁₈ atom (4.8 kcal mol⁻¹). Transfer of the second proton to the ring occurs without an enthalpic barrier in both cases, yielding the chlorophyllide product with the deprotonated Asp274 and propionate sidechain.

Analysis of alternative protonation events was also performed, to ascertain the reasons behind the observed stereochemical outcome. These computations showed that proton transfer from the propionic acid side chain to C₁₇ (yielding the wrong configuration in this carbon atom) is less favorable than any of the stereochemically correct proton transfers (Asp274 to C₁₇ and propionic acid to C₁₈), even in our simplified models which do not include the full steric constraints imposed by the hydrophobic amino acids lining the active site. The difference in total energies amounts to 11 kcal mol⁻¹ in the one-electron-reduced state, and to 8.5 kcal mol⁻¹ at the two-electron-reduced state. This intermediate contains (especially at the one-electron-reduced state) an unfavorable steric interaction, as the wrong configuration at C₁₇ pushes the propionate side chain towards Asp274 (Fig. 4). Protonation of C₁₈ by Asp274, which generates the wrong configuration on C₁₈, is also less favorable by 16 kcal mol⁻¹ at the one-electron-reduced state, and by 9.5 kcal mol⁻¹ at the two-electron-reduced-state. This destabilization occurs in spite of the lack of sterical clashes because no favorable stabilizing interactions of the carboxylate in Asp274 with the Mg²⁺-coordinating water are possible in this isomer, in contrast to the correct isomer that arises when the carboxylate forms on the propionic acid side chain.

Electron-transfer events

The ease of reduction of each intermediate may be easily computed by taking the difference of energies between any n-electron containing species and the corresponding n + 1-electron-containing analogues. It can readily be seen (Table 2, last column), that one-electron reduction of the reaction intermediates depends strongly on the charge present on the PChlide ring: species with negative or neutral protochlorophyllide rings have an absolute redox potential between 2.3 and 3.2 V, whereas intermediates bearing one or more positive charges have much more favorable absolute redox potentials between 4.0 V and 4.5 V. In dark-operating PChOR, the electron-donating species is an unusual (Cys)₃Asp-ligated [4Fe–4S] cluster, which has been assigned a redox potential of 3.1 V in previous computations (Takano et al., 2011). Since those computations were performed without geometrical constrains and with very truncated cysteine models (SCH₃) which do not allow the evaluation of the influence of the side chain geometry on the electronic properties of the clusters (Niu & Ichiye, 2009), we performed additional optimizations of the Fe–S cluster using ethanethiol as model for the cysteine side chains and appropriate constraining of their carbon atoms to their crystallographic positions. The absolute redox potential of the electron-donating (Cys)₃Asp-ligated [4Fe–4S] cluster in PChOR is thus computed to be 2.80 V, which implies that, in the absence of significant interactions between cluster and substrate, all electron-uptake events by protochlorophyllide (except those by the 1-electron-reduced substrate or by the 1-electron-reduced, C₁₈-protonated substrate) should be thermodynamically favorable, as electrons spontaneously move from the species with lower redox potentials to the ones with higher potentials. Additional single-point computations were then performed in models including the separately-optimized Fe–S clusters and reaction intermediates at their crystallographic positions to ascertain the mutual influence of the Fe–S electronic distribution on the redox potential of the reaction intermediates, and vice-versa (Table 2). Irrespective of the redox state of the Fe–S cluster, the reaction intermediates become harder to reduce by 0.1–0.15 V in the original, non-reduced, state, and by 0.25–0.4 V in the one-electron-reduced state. The electric dipoles of the reaction intermediates in turn lower the Fe–S cluster redox potential (i.e., facilitate its oxidation) by similar modest amounts (0.1–0.15 V), irrespective of the redox state of the substrate. These data also show that the oxidation state of the Fe–S cluster barely affects the energetics of the substrate protonation reactions and, consequently, should also barely affect their activation barriers.

The electronic energies of the combined Fe–S cluster/active site systems show that electron-transfer from the reduced Fe–S cluster to the protochlorophyllide intermediates is thermodynamically favored in almost all cases (Table 2), except for the reduction of the one-electron-reduced/C₁₈-protonated species , which is unfavorable by a few kcal mol⁻¹. For this thermodynamically disfavored reduction step no activation energy could be computed through the Marcus formalism as the parabolas do not touch (Supplemental Information), but comparisons with the reorganization energies at lower dielectric constants (at which this transfer becomes spontaneous) suggest that the barrier should not be too different from the others. For the spontaneous steps the electronic reorganization energies of the combined Fe–S cluster/active site systems are quite low, yielding activation energies below 4 kcal mol⁻¹, which entails that) reduction will generally be much faster than the protonation events, which were shown above to have activation energies in excess of 10 kcal mol⁻¹. Electron transfer from the reduced Fe–S cluster should therefore precede each protonation event, though only if the rate of re-reduction of the Fe–S cluster by the ATP-dependent L-protein (Kondo et al., 2011) does not become limiting. Two possible pathways emerge from this analysis, both arising from an initial one-electron transfer to the protochlorophyllide. In one of them (Fig. 5A), re-reduction of the Fe–S cluster is slower than any of the proton-transfer events at the one-electron reduced state, which leads to the generation of a doubly protonated intermediated, preferably through the initial protonation at C₁₇, which has a lower overall barrier (13.6 kcal mol⁻¹) than the double-protonation starting with the C₁₈ atom (18.9 kcal mol⁻¹, as discussed earlier). After both protonations and cluster re-reduction occurs, electron transfer is both spontaneous and quite fast. In the second alternative (Fig. 5B) re-reduction of the Fe–S cluster is not rate-limiting and the second electron transfer to the substrate may occur immediately after the first protonation: in this instance, the reaction will likely proceed through protonation of C₁₈ by the propionic acid substituent of the protochlorophyllide D-ring, followed by electron transfer and barrier-less transfer of the second proton from Asp274 to C₁₇. This pathway affords a barrier below 10 kcal mol⁻¹ and reaction rates far in excess of those observed experimentally, suggesting that Fe–S cluster re-reduction should indeed be the rate-limiting stage of the process.

Estimating the influence of the protein environment on the reaction energetics

In the research mentioned in the previous sections, the inclusion of the full substrate binding-pocket was prevented by the unfavorable scaling of the computational cost of the high-levels of quantum theory used. Additionally, the extensive conjugation of the substrate π-system prevented the “sacrifice” of any portion of the substrate in the model for the sake of including more surrounding amino acids. Such exclusion should not affect the chemical steps since the omitted amino acids are relatively inert chemically due to their hydrophobic side chains and their influence is therefore only felt on the relative solvation of the reaction intermediates. The data computed at different dielectric constants (which is affected by the number and distribution of polar/apolar amino acids surrounding the substrate) show that the dependence of the reaction pathway with this factor is quite small. These observations agree with the large body of research (reviewed in Himo & Siegbahn, 2003; Shaik et al., 2005; Ramos & Fernandes, 2008; Siegbahn & Blomberg, 2010) which has established that the application of quantum chemical techniques to small-to-medium-size models of enzyme active sites can be extremely powerful in the thorough analysis of reaction pathways, provided that the charge distribution in the model accurately mimics that of the active site.

Several important characteristics of the reaction mechanism cannot be derived from truncated active site models due to the lack of the protein-induced electrostatic field, which depends on the overall charge distribution in the protein (Stephens, Jollie & Warshel, 1996; Kamerlin & Warshel, 2010; Ribeiro, 2013). In the enzyme studied in this report, such characteristics include the likelihood of occurrence of the active protonated states of Asp274 and propionic side chain at physiological pH and the susceptibility of the Fe–S cluster redox potential to the solution pH. Continuum electrostatics computations on the protochlorophyllide oxidoreductase structure bearing each of the quantum-chemically-optimized intermediate allowed us to quantify these effects (see Computational Methods for details). The inclusion of the protein barely affects the way the redox potentials of the Fe–S cluster vary as the intermediate gains electrons/protons (Table 3), but has an important effect on the sensitivity of the Fe–S cluster redox state towards changes in pH: in all instances the predicted change in redox potential per pH unit corresponds to the uptake of 0.8 protons by the Fe–S surroundings upon the one-electron reduction of the cluster. Analysis of the correlations matrixes clearly shows that the reduction of the Fe–S clusters increases the probability of finding the neighboring His53A and His13B in their protonated states. At lower pH, Asp147A also tends to become protonated as the cluster is reduced (Fig. 6).

The probability p of finding the postulated proton-donating moieties (Asp274 and the propionic acid substituent) in their protonated states can also be computed using these techniques, and converted into energetic barrier increases through the expression ΔΔG = −RTlnp (Table 4). The predicted 6.9 kcal mol⁻¹ increase in the barrier of the initial step further prevents the reaction from proceeding through an initial protonation step, but does not prevent the one-electron reduction of the substrate due to its high energetic driving force and low (<4 kcal mol⁻¹) barrier. The barriers for subsequent steps increase by smaller values, so that both mechanisms depicted in Fig. 5 remain possible even after taking account the variable probabilities of finding Asp274 and propionic acid sidechain in the appropriate protonation states.

Additional effects of the assymetric protein-induced electrostatic field on the reaction energetics were analyzed using the ONIOM-inspired methodology described in the Methods section. The inclusion of all possible protonation states of the titrating amino acids on the computation of the “average” electrostatic field proved to be crucial, as several of the amino acids whose protonation state showed the higher electrostatic effects on the reaction energetics would otherwise be assumed to be present in their non-protonated states: for example, histidines 404B and 404D (present in the interface between subunits B and D, ca. 21 Å from the substrate) favor electron-transfer from the cluster to the substrate by 5–7 kcal mol⁻¹, but their effect would have been neglected by a computation that only took account of the most likely protonation state of each amino acid, as each remains (on average) 1/3 protonated in the pH/potential windows studied. Other amino acids whose protonation strongly favors electron-transfer are His 35, His 288, and His 378B. Protonation of His 86, His 13B, His 31B, His 64B and Asp 147, in turn, tend to disfavor this electron transfer. The presence of a protonated His378B favors the proton-transfer from the propionic acid side chain in the substrate to C₁₈, whereas protonation of His35 and His53 disfavors the proton-transfer from Asp274 to C₁₇ (Fig. 7 and Supplemental Information).

The energetic profiles of the proton-transfer-steps computed with the isotropic PCM model (Table 2) broadly agrees with the profile computed with the ONIOM-based correction to the gas-phase energies of infinitely-separated Fe–S cluster and substrate intermediates (Table 5), as proton-transfer from the propionic acid side chain to C₁₈ is consistently found to be thermodynamically more favorable than the transfer of Asp274 to C₁₇. Large differences are, however, observed in the electron-transfer steps, which are predicted by the ONIOM-based approach to be much more favorable (by ca. 115 kcal mol⁻¹ for the first electron moving to the substrate and by 25–30 kcal mol⁻¹ for the second electron), though their relative magnitudes closely follow the trends predicted by PCM. The exaggerated exergonicity afforded by the ONIOM-based computations are surely artifactual, as they would imply extremely high redox potentials for the substrate/intermediates: for example, a value of 3.15 V above the standard hydrogen electrode is predicted for PChlide, which is higher than the experimental values of the very strong oxidants fluorine (2.87 V) and ozone (2.07 V). This artifact most likely arises from the neglect of the relaxation of the protein upon protonation of its amino acids and of the surrounding water shell, which has been shown (Schutz & Warshel, 2001) to require the use of a higher “effective dielectric constant” to obtain accurate electrostatic stabilization energies. “True” electrostatic stabilization energies should be obtainable by dividing the value computed with ε = 1 (as in this work) by this “effective” dielectric constant, whose magnitude is site-dependent (Schutz & Warshel, 2001) and not immediately accessible from first-principles considerations. Interestingly, the Fe–S cluster (which lies buried inside the protein and far from the high-dielectric environment of the water solution) is predicted by the ONIOM-based methodology to have a much more reasonable redox potential (0.10 V vs. the standard hydrogen electrode) than PChlide, which lies much closer to the protein surface and whose redox potential should therefore be much more sensitive to the neglect of water in the computations. Indeed, screening the electrostatic stabilization of the Fe–S cluster with ε = 1.06 is enough to yield a computed redox potential of −0.32 V, in agreement with −0.4 V to −0.3 V range deduced from the redox potential of the Mg-ATP-activated Fe-cluster present in the nitrogenase Fe protein (Ryle, Lanzilotta & Seefeldt, 1996) which is known to be related to the L-protein that acts as electron-donor to PChOR.

Energetic comparison to the light-dependent reaction

The moderate barriers computed for the reaction mechanism raise an intriguing question: why does the light-dependent enzyme require an external driving force, as a quantum of light, to catalyze the reduction of the C₁₇=C₁₈ bond in PChlide by NADPH? We have therefore compared the energies and redox potentials of several reaction intermediates to those of other biochemical redox models (Table 6). Direct comparison of the redox potential of NADPH (Table 6, line f) to that of the two-proton, two-electron conversion of PChlide to Chlide (Table 6, line d) shows that the PChlide reduction to Chlide by NADPH should be thermodynamically favored in the ground state. Further analysis of the computed redox data shows that hydride transfer from NADPH (Table 6, line f) to PChlide to yield a singly-protonated, two-electron reduced PChlide (Table 6, line g) is thermodynamically disfavored, which entails that the spontaneity of the overall process arises from the addition of the second proton. Furthermore, the energetic barrier for the direct hydride transfer in the ground state has previously been shown to be very high (>30 kcal mol (Heyes et al., 2009; Silva & Ramos, 2011)), even after accounting for quantum tunneling effects (Silva & Ramos, 2011). Ground-state hydride transfer from NADPH to the substrate therefore may only occur if it precedes the protonation event. Indeed, hydride transfer from NADPH to C₁₈-protonated PChlide (Fig. 8) should proceed efficiently with a negligible barrier (1.0 kcal mol⁻¹) and very high exergonicity (−33 kcal mol⁻¹), but the actual feasibility of this step depends on the relative abundance of the C₁₈-protonated PChlide. Our computations on the dark-dependent PChOR, above, showed that the initial protonation of the C₁₇=C₁₈ bond by carboxylic acids (the most acidic amino acid side chains present in proteins) is thermodynamically expensive by 20 kcal mol⁻¹, which means that the natural abundance of C₁₈-protonated PChlide is very small (e^{−20 kcal/mol/RT}). The overall barrier for the reduction of PChlide to Chlide by NADPH would therefore amount to at least those 20 kcal mol⁻¹+ the 1.0 kcal mol⁻¹ barrier for the hydride transfer when the initial PChlide protonation is performed by a carboxylic acid (like Asp or Glu) and would be even larger when weaker acids are used (like the Tyr or Lys residues actually present in the light-dependent PChOR active site (Wilks & Timko, 1995). Reduction of PChlide by NADPH therefore has too large an activation barrier to proceed at reasonable rates in the electronic ground state. The experimentally-observed initiation of the reaction upon uptake of a 590 nm photon (Griffiths, McHugh & Blankenship, 1996) can be easily computed to correspond to an increase of 1.05 V in the reduction potential of PChlide, which places it above the redox potential of NADPH and therefore makes the electron-transfer thermodynamically favorable.

More exotic pathways for ground-state reduction of PChlide by NADPH may also be excluded from consideration: for example, a two-electron transfer from NADPH to PChlide followed by energetically favorable H⁺ transfer is also unfeasible, as the E°of the NADPH/NADPH²⁺ pair (Table 6, line a) lies even farther above the PChlide substrate. On the other hand, two-electron transfer from a hypothetical (deprotonated) NADP⁻ species (Table 6, line h), to PChlide (Table 6, line d), might be very favorable but is ruled out by the extreme difficulty of deprotonating NADPH: indeed, the difference of energies between NADPH and NADP⁻ in water (337.2 kcal mol⁻¹) is far higher than computed for even moderately weak acids (e.g., the difference between phenol and phenoxide (Silva, 2009) is only 299.2 kcal mol⁻¹), which implies an extremely high pKa for the NADPH proton.

The preceding analysis explains the need for an external energetic event for the reduction of protochlorophyllide by NADPH. Incidentally, our comparative analysis also showed that the two-electron/two-proton reduction of the double bond in PChlide, (Table 6, line d) is approximately as favorable as the comparable reduction of the typical C–C double bond found in fumaric acid (Table 6, line c), whereas the absence of Mg²⁺ ion from PChlide disfavors this reduction process (Table 6, line e), which may explain why Mg²⁺ becomes inserted into the porphyrin ring before the reduction of the C₁₇=C₁₈ bond.