Temperature independent kinetic isotope effects as evidence for a Marcus-like model of hydride tunneling in phosphite dehydrogenase

Abstract

Phosphite dehydrogenase catalyzes the transfer of a hydride from phosphite to NAD⁺, producing phosphate and NADH. We have evaluated the role of hydride tunneling in a thermostable variant of this enzyme (17X-PTDH) by measuring the temperature dependence of the primary ²H kinetic isotope effects (KIEs) between 5 °C and 45 °C. Pre-steady-state kinetic measurements were used to demonstrate that the hydride transfer is rate-determining across this temperature range, and that the observed KIEs are equal to the intrinsic isotope effect on the chemical step. The KIEs on the pre-exponential factor (A_H/A_D) and the activation energy (ΔE_a) were 1.6 ± 0.1 and 0.21 ± 0.05, respectively, suggesting that 17X-PTDH facilitates extensive tunneling of both isotopes via a Marcus-like model. Site-directed mutagenesis was used to evaluate the role of an active-site threonine (Thr104) found on the back face of the nicotinamide in promoting the close packing of the substrates. In mutants with reduced steric bulk at this position, values of A_H/A_D and ΔE_a fall within the range describing semi-classical “over the barrier” reactivity, suggesting that Thr104 acts as a steric backstop to promote tunneling in 17X-PTDH. Whereas hydrogen tunneling is now a widely appreciated feature of C-H activating enzymes, these observations with a P-H activating system are consistent with the proposal that that tunneling is likely to be a common feature on all enzymes that catalyze hydrogen transfers.

Graphical Abstract

Introduction

Phosphite dehydrogenase (PTDH; Uniprot accession code: O69054) catalyzes the oxidation of phosphite (PT) to orthophosphate with the concomitant reduction of NAD⁺ to NADH (Scheme 1).¹ This enzyme was first identified as a component of a phosphate salvage pathway in Pseudomonas stutzeri WM88 that oxidizes reduced, inorganic phosphorus compounds under conditions of phosphate starvation.² As PTDH endows microorganisms with the unique ability to grow on PT, the enzyme has found use as a component of biocontainment strategies.^3–7 The favorable thermodynamics of the reaction catalyzed by PTDH (ΔG° = −15 kcal/mol)¹ and the low cost of PT (~ $0.1 USD/g) have also attracted considerable attention to the enzyme as a cofactor regeneration system.^8–11 This potential utility spurned several engineering efforts that led to the production of PTDH variants with increased thermostability,¹² increased activity,¹³ and a decreased specificity for NAD⁺ over NADP⁺ that allows for efficient regeneration of both NADH and NADPH.¹⁴ These enzymes have been employed in various biocatalytic systems, both as stand-alone cofactor regenerators, and as fusions with flavin monooxygenases within self-sufficient biocatalysts.^15–19

Scheme 1.

Overall reaction catalyzed by PTDH

The reaction catalyzed by PTDH is a formal phosphoryl transfer reaction with a very unusual hydride leaving group. Significant effort has been directed towards understanding how this enzyme catalyzes the cleavage of the P-H bond using a water nucleophile.^{1, 20–27} Most of these studies have focused on a thermostable variant of PTDH termed 17X-PTDH.²⁴ All available evidence indicates that 17X-PTDH and the naturally occurring enzyme operate via identical mechanisms.^{23, 24} Based on considerable sequence identity (~25 – 40%) with the family of D-hydroxyacid dehydrogenases (DHDHs), a combination of site-directed mutagenesis,²⁰ crystallography,²⁵ and computation²⁷ have led to the identification of active-site residues that are important for 17X-PTDH catalysis. His292 is the putative base that activates the water nucleophile. Glu266 is hydrogen-bonded to His292 and likely plays a role in modulating the pK_a of the active site base and in substrate binding.⁹ Arg237 and Arg301 are believed to be involved in binding and orienting the substrate for catalysis,²⁴ and Met53 interacts with His292 through a ‘face-on’ interaction that likely stabilizes the developing positive charge on the catalytic base.²⁷ These roles, along with the proposed mechanism, are summarized in Figure 1.

Figure 1.

Proposed mechanism of 17X-PTDH including the residues known to be important for catalysis.

Recently, we reported the use of ¹⁸O kinetic isotope effects (KIEs) and computation to determine the transition state (TS) of the phosphoryl transfer catalyzed by 17X-PTDH.²⁸ This analysis revealed that the reaction occurs asynchronously, through an extremely tight TS in which P-O bond formation is significant and P-H bond cleavage is marginal. In that work, the role of quantum mechanical tunneling, in which the system passes through the potential energy barrier rather than passing over it, was evaluated indirectly using the Bell tunneling correction model.²⁹ However, many enzymatic hydride transfers are known to involve more extensive tunneling,^30–40 and while studies of enzyme-mediated tunneling have focused largely on C-H activation, this phenomenon is likely not restricted to this class of reaction. The possibility that 17X-PTDH facilitates tunneling in the cleavage of the P-H bond of PT represents an unexplored mechanistic feature of this enzyme and may serve to further illustrate how general the role of tunneling is within dehydrogenases.

Here, we have evaluated the possible role of tunneling in 17X-PTDH using the temperature dependence of the primary ²H KIE. The results suggest that 17X-PTDH facilitates tunneling of both ¹H- and ²H-PT, invoking a form of tunneling often described as a Marcus-like model.^{31, 41–47} From the crystal structure of 17X-PTDH,²⁵ an active site threonine was identified on the face of the nicotinamide ring opposite to PT and this residue was hypothesized to promote the close packing of the hydride donor and acceptor. The role of this threonine in promoting tunneling was evaluated using site-directed mutagenesis to reduce the steric bulk of the residue. Perturbation of this residue resulted in increasingly temperature dependent KIEs, consistent with a role in substrate packing in the tunneling-ready state (TRS).^{36, 40} Collectively, these results suggest that 17X-PTDH catalysis is appropriately described by a Marcus-like model of tunneling,^{36, 40} in which the enzyme facilitates the transient degeneracy of the reactant and product wells at the TRS and achieves sufficiently short hydride donor-acceptor distances (DADs) to facilitate efficient tunneling of both hydrogen and deuterium.

Methods

General Methods

All reagents were purchased from Sigma Aldrich and used without further purification. All ¹H and ³¹P NMR spectra were recorded with an Agilent 600 MHz NMR spectrometer. The concentrations of NAD⁺ stock solutions were determined using the absorbance at 260 nm (ε₂₆₀ = 28,000 M⁻¹ cm⁻¹). Concentrations of PT stock solutions were determined by mixing an aliquot with excess NAD⁺ and treating this mixture with 17X-PTDH. After allowing the reaction to run to completion, the concentration of produced NADH was determined from the absorbance at 340 nm (ε₃₄₀ = 6,200 M⁻¹cm⁻¹). This value is equivalent to the concentration of PT present in the initial mixture.

Preparation of ²H-PT

Deuterated PT (²H-PT) was prepared as described previously.²⁸ Briefly, PCl₃ was dissolved in dry chloroform and the mixture was stirred at 0 °C under N₂. D₂O was added slowly to the stirring mixture. The mixture was then removed from the ice bath, stirred at room temperature for 2 h, and then concentrated by rotary evaporation. The resulting material was neutralized by the addition of a sodium carbonate solution. The extent of deuterium incorporation, as evaluated by ¹H-coupled ³¹P NMR spectroscopy, was greater than 98%.

Preparation of 17X-PTDH mutant constructs

All mutants were generated in the 17X-PTDH gene encoded in the pET-15b plasmid. Mutants were prepared by PCR using the Q5 Site-Directed Mutagenesis Kit (New England Biolabs). The following primers were used to incorporate the desired mutation: T104S: 5’ – G ACG GTC CCG TCT GCC GAG CTG GCG ATC GG – 3’; 5’ – CAG CTC GGC AGA CGG GAC CGT CAA CAG ATC AG – 3’; T104A: 5’ – G ACG GTC CCG GCT GCC GAG CTG GCG ATC GG – 3’; 5’ – C CAG CTC GGC AGC CGG GAC CGG GAC CGT CAA CAG ATC AGG C – 3’; T104G: 5’ – G ACG GTC CCG GGT GCC GAG CTG GCG ATC GG – 3’; 5’ – CAG CTC GGC ACC CGG GAT CGT CAA CAG ATC AG – 3’. The mutant codons used to introduce the desired mutations are underlined. Following the incorporation into the pET-15b vector, mutant genes were sequenced in their entirety to ensure that only the desired mutation was introduced into the 17X-PTDH backbone.

Overexpression and purification of 17X-PTDH variants

All variants of 17X-PTDH were overexpressed and purified using the following procedure. BL21(DE3) cells were transformed with the pET-15b vector harboring the gene encoding the desired 17X-PTDH variant. Cells were plated on LB Agar plates supplemented with 100 μg/mL ampicillin and grown overnight at 37 °C. A single colony was picked and used to inoculate a 10 mL starter culture containing 100 μg/mL ampicillin. This culture was used to inoculate 1 L of LB (100 μg/mL ampicillin). The cells were grown at 37 °C (shaken at 200 RPM) until an OD₆₀₀ of 0.6 was reached. Expression was induced by the addition of IPTG (to a final concentration of 0.3 mM) and the culture was shaken at 18 °C for approximately 18 h. Cells were pelleted by centrifugation (4000 x g, 10 min) and resuspended in Buffer A (20 mM Tris, pH 7.6, 0.5M NaCl, 10% (v/v) glycerol). Resuspended cells were incubated with lysozyme and DNAse I at 4 °C for 45 min and were subsequently lysed using a French Press (Thermo Scientific; 10,000 psi, 4 passes). Insoluble material was removed by centrifugation (16,000 g, 1 h) and the supernatant was loaded onto a column of Ni²⁺-NTA resin that was pre-equilibrated with Buffer A. Non-specifically bound material was washed off of the column using approximately 10 column volumes (CV) of Buffer B (20 mM Tris, pH 7.6, 100 mM NaCl, 10 mM imidazole, 10% (v/v) glycerol). The bound protein was eluted using approximately 3 CV of Buffer C (20 mM Tris, pH 7.6, 100 mM NaCl, 500 mM imidazole, 10 % (v/v) glycerol). Aliquots of the collected fractions were added to solutions containing PT and NAD⁺ and the resulting absorbance at 340 nm was used to assay 17X-PTDH activity. The purity of the enzyme was assayed by SDS-PAGE. Fractions containing the desired 17X-PTDH variant were pooled and concentrated using a centrifugal filter unit (Amicon; 30 kDa MW cutoff). The concentrated enzyme was then desalted, and buffer exchanged into Buffer D (20 mM MOPS, pH 7.6, 100 mM KCl, 10% (v/v) glycerol) using a PD-10 Desalting Column (GE Healthcare). Aliquots of the enzyme stock were dispensed, flash frozen and stored at −80 °C. Protein concentrations were determined using the extinction coefficient at 280 nm calculated using the ExPASy ProtParam tool (ε₂₈₀ = 28,000 M⁻¹ cm⁻¹). This extinction coefficient was also used for all 17X-PTDH variants reported in this work. No significant differences were observed between protein concentrations determined by the absorbance at 280 nm and by the standard Bradford assay.

Steady-state kinetic analysis

Initial rates were measured using a Cary 4000 UV-Visible spectrophotometer (Agilent) equipped with a thermostatted cuvette holder (± 0.1 °C). All kinetics were performed with N-terminally His₆-tagged proteins. It has been demonstrated that this tag has no significant effect on the kinetic parameters of PTDH.¹⁴ Prior to all kinetic measurements, reaction mixtures were incubated in cuvettes within the cell holder for at least 5 min. The temperature of the solution within the cuvettes was evaluated by placing a digital thermometer into a cuvette containing buffer. Rates of NADH production were monitored at 340 nm (ε₃₄₀ = 6,200 M⁻¹cm⁻¹). Full kinetic assays were performed using varying concentrations of both ¹H-PT and NAD⁺. Initial rates were then fit to the equation describing an ordered binding mechanism (eqn 1).⁴⁸ In this equation, A represents the first substrate bound (NAD⁺) and B represents the second substrate bound (PT).⁴⁹ K_A, K_B, and K_iA represent K_m,NAD, K_m,PT, and the dissociation constant for NAD⁺, respectively.

$$v=\frac{V_{max}\left[A\right]\left[B\right]}{K_{iA}{K}_B+K_B\left[A\right]+K_A\left[B\right]+\left[A\right]\left[B\right]}$$ (eqn 1)

Subsequent kinetic measurements were performed using saturating amounts of NAD⁺ ([NAD⁺] > 10 K_m,NAD) and varying concentrations of ¹H and ²H-PT. Values of k_cat and K_m,PT for each isotopologue were obtained by fitting the resulting data to the Michaelis-Menten equation. KIEs on k_cat and k_cat/K_m,PT (^Dk_cat and ^D(k_cat/K_m,PT), respectively) were obtained by direct comparison of the relevant kinetic parameters observed with each isotopologue. Some replicate Arrhenius plots were constructed using saturating amounts of both ¹H- or ²H-PT and NAD⁺. Values of ^Dk_cat derived from initial rates measured under these saturating conditions were in excellent agreement with ^Dk_cat values derived from complete Michaelis-Menten curves. Isotope effects on the Arrhenius pre-exponential factor (A_H/A_D) and the activation energy (ΔE_a) were obtained from the intercept and the slope, respectively, of plots of ln(^Dk_cat) against 1/T according to eqn 2.

$${ln}^D{k}_{cat}=\text{ln}(\frac{A_H}{A_D})-\frac{\text{Δ}{E}_a}{RT}$$ (eqn 2)

Pre-steady-state kinetic analysis

All pre-steady-state kinetic experiments were performed using an Applied Photophysics SX20 stopped-flow spectrophotometer equipped with a circulating water bath. At the lowest relevant temperature (5 °C), the dead time of the instrument was determined to be approximately 2 ms using the reaction of ascorbate with 2,6-dichloroindophenol.⁵⁰ Prior to each experiment, the enzyme was exchanged into 100 mM MOPS, pH 7.25 by repeated cycles of dilution and concentration through a centrifugal filter unit (Amicon; 30 kDa MW cutoff). Initial experiments involved one syringe containing the 17X-PTDH variant in 100 mM MOPS, pH 7.25, and the other syringe containing 10 mM NAD⁺ and 10 mM ¹H or ²H-PT, also in 100 mM MOPS, pH 7.25. In some experiments, the enzyme was buffer exchanged into 10 mM NAD⁺ in 100 mM MOPS, pH 7.25. This NAD⁺-enzyme mixture was loaded into one syringe and 10 mM ¹H- or ²H-PT (also in 100 mM MOPS, pH 7.25) was loaded into the other syringe. Prior to firing, both syringes were incubated in the circulating water bath of the SX20 for 5 min to allow the contained reagent mixtures to reach the desired temperature. In all experiments, the absorbance increase at 340 nm was followed for 1 s, with 2000 data points collected.

Results and discussion

Steady-state kinetics with 17X-PTDH at various temperatures

At 25 °C, the primary ²H KIE observed with 17X-PTDH (^Dk_cat = 2.27 ± 0.05) is well below the semi-classical maximum (KIE < 5 for cleavage of a P-H bond).¹ While tunneling is most commonly invoked to explain apparent violations of this limit, there are several enzymatic systems that have been shown to facilitate extensive tunneling while simultaneously displaying modest KIEs that are below the semi-classical limit.^{36, 51–58} To evaluate this possibility for 17X-PTDH catalysis, we opted to evaluate the temperature dependence of the primary ²H KIE. Importantly, to interpret this temperature dependence meaningfully, it must be demonstrated that the chemical step is rate limiting under all conditions used, such that the observed KIE (^Dk_cat) is the intrinsic KIE of the hydride transfer. While rate-limiting chemistry has been demonstrated for 17X-PTDH catalysis at 25 °C,²³ another process may become partially or completely rate-limiting at lower and/or higher temperatures. While the observation that ^Dk_cat and ^D(k_cat/K_m,PT) are equal at 5 °C, 25 °C, and 45 °C (Table 1) provide some indication that the hydride transfer remains rate-limiting across this temperature range,⁴⁸ this evidence is not concrete proof that the observed ^Dk_cat values reflect the intrinsic KIEs.

Table 1.

KIEs with 17X-PTDH at different temperatures^a

Temperature (°C)	Dkcatb	D(kcat/Km,PT)b	Dkobsc
5	2.30 (0.05)	2.3 (0.2)	2.4 (0.1)
25	2.27 (0.05)	2.3 (0.1)	2.35 (0.04)
45	2.23 (0.09)	2.1 (0.2)	2.3 (0.1)

^aAll data was collected at pH 7.25 in 100 mM MOPS.

^bValues derived from Michaelis-Menten curves constructed from steady-state measurements obtained using saturating concentrations of NAD⁺ and varied concentrations of ¹H- or ²H-PT.

^cValues derived from fits of pre-steady-state traces to the zeroth-order rate law.

Pre-steady-state kinetics with 17X-PTDH at various temperatures

Stopped-flow experiments were used to evaluate the pre-steady-state behavior of 17X-PTDH at 5 °C, 25 °C, and 45 °C. No burst in activity was observed at any temperature, demonstrating that no step following hydride transfer has a significant impact on the steady-state kinetics (Figure 2). Additionally, the KIEs derived from the pre-steady-state traces (^Dk_obs) are in excellent agreement with the corresponding values derived from steady-state kinetic measurements (Table 1). In combination with the results of earlier studies on 17X-PTDH conducted at 25 °C,²³ these results demonstrate that hydride transfer remains entirely rate-limiting between 5 °C and 45 °C.

Figure 2.

Averages of five pre-steady-state traces for 17X-PTDH at 45 °C (A) and 5 °C (B). Traces were obtained by mixing a solution of 17X-PTDH (10 μM in Panel A; 150 μM in Panel B) with a solution of 10 mM ¹H- or ²H-PT, 10 mM NAD⁺ in 100 mM MOPS, pH 7.25. Data is fit (dashed line) to the zeroth-order rate law. Absorbance values corresponding to a single turnover are 0.062 in Panel A and 0.93 in Panel B.

Arrhenius plots for 17X-PTDH with ¹H- and ²H-PT

Having shown that the ^Dk_cat reflects the intrinsic KIE for 17X-PTDH catalysis at 5 °C and 45 °C, we measured values of k_cat with ¹H-PT and ²H-PT at temperatures between these two extremes. The resulting Arrhenius plots and ^Dk_cat values are shown in Figure 3. Across this temperature range, the ²H KIEs are identical within error (see Table S1). The corresponding isotope effects on the pre-exponential factor (A_H/A_D) and the activation energy (ΔE_a) were derived to be 1.60 ± 0.09 and 0.21 ± 0.05 kcal/mol, respectively.

Figure 3.

Arrhenius plots for 17X-PTDH catalyzed oxidation of ¹H- and ²H-PT (circles and squares, respectively; left ordinate), and the corresponding KIEs (triangles; right ordinate).

The observed value of A_H/A_D falls outside of the semi-classical limits describing a reaction that proceeds without tunneling (0.5 < A_H/A_D < 1.4).⁵⁹ While the semi-classical limits on ΔE_a(D-H) are not well defined, values near zero have been observed frequently in enzymatic systems that involve extensive hydrogen tunneling.⁴⁰ More specifically, values of A_H/A_D > 1.4 and ΔE_a ~ 0 kcal/mol have been suggested to be hallmarks of enzymes that operate via a Marcus-like model of tunneling.^{36, 40} In this model, reorganization of the enzyme brings about the transient degeneracy of the potential energy surfaces that define the reactant and product states. This degeneracy is achieved at an ensemble of states called the TRS, and it is in the TRS that the probability density of the hydrogen (or deuterium) can tunnel from the reactant well into the product well. The rate of tunneling is dependent on the mass of the particle and the DAD, with shorter DADs facilitating more extensive tunneling.³⁶ The values of A_H/A_D and ΔE_a derived from the data in Figure 3 suggest that 17X-PTDH operates by this Marcus-like model.

The A_H/A_D values are derived from extrapolation and carry considerable error, but an alternative line of reasoning⁶⁰ also arrives at the same conclusion. The observed temperature independence of the kinetic isotope effect can be rationalized in two ways: either the rate constants with H and D are also temperature independent or tunneling is occurring from the ground state. Since the observed values of k_cat are clearly temperature dependent with both isotopologues of PT, the conclusion must be that tunneling is operational. While there are several C-H activating enzymes that have been proposed to operate by the Marcus-like model (also referred to as “environmentally coupled tunneling”),^{31, 36, 40, 43, 47, 55} 17X-PTDH represents the first example of a P-H activating system that operates by such a mechanism.

Identification of a potential steric backstop

It has been suggested that all dehydrogenases have a bulky hydrophobic residue on the back side of the nicotinamide ring, opposite the substrate.³¹ This residue is proposed to play a role in enforcing short DADs by physically forcing the H donor and the C4 position of the nicotinamide together in the TRS. As this steric backstop is involved in close substrate packing, decreases in the bulk of this residue often lead to reduced tunneling efficiency. A threonine (Thr104) was identified in the crystal structure of 17X-PTDH that seemed likely to act as this steric backstop in this enzyme. As shown in Figure 4, in a co-crystal structure, Thr104 is found on the opposite face of the nicotinamide ring to sulfite, a competitive inhibitor of PT in 17X-PTDH (Figure 4).^{22, 25} Additionally, Thr104 is highly conserved amongst known variants of PTDH (see Figure S1), consistent with its potential role in promoting short DADs. Other residues that line the PT binding pocket may also promote short DADs by “pushing” the PT towards the nicotinamide ring. As mutations of these residues result in very poor catalysts,^{24, 25} we opted to focus on the temperature dependence of the T104X mutants.

Figure 4.

A view of a co-crystal structure of 17X-PTDH. The position of Thr104 relative to the nicotinamide ring of NAD⁺ and to sulfite (a competitive inhibitor to PT) suggests this residue may enforce close substrate packing and short DADs in the TRS.

Kinetic analysis of T104X mutants of 17X-PTDH

To assess the role of Thr104 in promoting the close packing of PT and the nicotinamide ring, a series of mutants were generated in which the steric bulk of this residue was reduced. Initial rates measured with the T104S, T104A, and T104G mutants of 17X-PTDH showed only a modest impact of these mutations on the derived kinetic parameters (Table 2). As with the parent 17X-PTDH, values of ^Dk_cat and ^D(k_cat/K_m,PT) were found to be identical within error at 25 °C (Table 2), suggesting that the chemical step is rate-limiting with these mutants.⁴⁸ To further verify this possibility, stopped-flow experiments were performed with each mutant at 5 °C and 45 °C. At 45 °C, traces obtained with all mutants were linear with no suggestion of a burst phase (Figure S2). Additionally, the pre-steady-state KIEs (^Dk_obs) observed at 45 °C were identical to those obtained from steady-state measurements for all mutants (Table S2).

Table 2.

Kinetic parameters of T104X mutants of 17X-PTDH^a

Variant	kcatb (s−1)	Km,NADb (mM)	Km,PTb (mM)	KiA,NADb (mM)	kcat/Km,PTb (x 104 M−1s−1)	Dkcatc	D(kcat/Km,PT)c
17X	2.53 (0.07)	0.036 (0.005)	0.061 (0.006)	0.47 (0.06)	4.1 (0.4)	2.27 (0.05)	2.3 (0.1)
T104S	1.31 (0.02)	0.042 (0.007)	0.13 (0.01)	2.1 (0.3)	1.0 (0.1)	2.27 (0.01)	2.2 (0.1)
T104A	1.02 (0.03)	0.023 (0.002)	0.27 (0.02)	0.31 (0.03)	0.38 (0.03)	2.27 (0.07)	2.1 (0.2)
T104G	0.31 (0.01)	0.035 (0.003)	0.31 (0.02)	0.85 (0.07)	0.10 (0.01)	2.19 (0.02)	2.1 (0.1)

^aAll parameters were obtained at 25 °C and pH 7.25 in 100 mM MOPS.

^bValues determined using variable concentrations of ¹H-PT and NAD⁺.

^cValues determined using saturating concentrations of NAD⁺ and varied concentrations of ¹H- and ²H-PT.

At 5 °C, pre-steady-state traces observed with T104S were linear from t = 0 s and gave KIEs in excellent agreement with those derived from steady-state measurements (Figure S3). The pre-steady-state behavior observed with the T104A and T104G mutants at 5 °C was more complex, displaying an apparent slow onset of activity that typically lasted ~200 ms (Figure 5A; Figure S4A). Altering the enzyme concentration did not significantly influence the length of this lag. When the enzymes were pre-incubated with NAD⁺, a significantly reduced lag period was observed upon mixing with ¹H- or ²H-PT (Fig. 5B; Figure S4B), suggesting that NAD⁺ binding might facilitate the transition of T104A and T104G to more active states. Similar substrate activation, as well as the associated slow onset of activity, has been reported with several enzymes.^61–65 A generalized kinetic scheme to describe this hysteretic behavior, as formulated by Frieden,⁶¹ is shown below (Scheme 2). The data reported here do not demonstrate whether the unactivated enzyme (E) can catalyze slow product formation or if the reaction proceeds entirely through the activated species (E’). Future experiments to characterize this substrate activation more thoroughly are warranted, especially since it may also occur with 17X-PTDH within the dead time of the stopped-flow spectrophotometer. This scenario would be consistent with the conformational change previously observed upon incubating a variant of 17X-PTDH with NAD⁺.²⁵

Figure 5.

Averaged pre-steady-state traces for T104G-17X-PTDH at 5 °C with and without NAD⁺ preincubation. (A) Traces were obtained by mixing a solution of T104G-17X-PTDH (0.25 mM) with a solution of 10 mM ¹H- or ²H-PT and 10 mM NAD⁺. Data recorded at t > 0.2 s is fit to the zeroth-order rate law. (B) Traces were obtained by mixing a solution of T104G-17X-PTDH (0.4 mM) and 10 mM NAD⁺ with a solution of 10 mM ¹H- or ²H-PT. All data is fit to the zeroth-order rate law. Insets in both panels contain the first 200 ms of data. Absorbance values corresponding to a single turnover are 1.55 in Panel A and 2.48 in Panel B.

Scheme 2.

Simplified kinetic scheme to describe substrate activation

The pre-steady-state lag observed with T104A- and T104G-17X-PTDH at 5 °C does not necessarily imply that chemistry is not rate-limiting in the steady-state. During conventional steady-state measurements, the NAD⁺-mediated activation phase will be completed in the few seconds required to initiate the reaction and begin data collection. Thus, the chemical step likely remains rate-limiting with these mutants at 5 °C. The observation that the KIEs derived from the post-200-millisecond pre-steady-state are equal to those observed in the steady-state supports this argument (Table S3). Values of k_cat were not significantly altered in any Thr104 mutant, as might have been expected if these mutations resulted in a change of the rate-limiting step. Finally, values of ^Dk_cat and ^D(k_cat/K_m,PT) were not significantly different for these enzymes at 5 °C and 45 °C (Tables S2 and S3). Collectively, these results strongly suggest that the ^Dk_cat values derived from steady-state measurements reflect the intrinsic KIE for the hydride transfer catalyzed by 17X-PTDH and the Thr104 mutants between 5 °C and 45 °C.

KIE temperature dependence with T104S-, T104A-, and T104G-17X-PTDH

The temperature dependence of ^Dk_cat was evaluated for each of the Thr104 mutants in the same manner as with 17X-PTDH. The Arrhenius plots for each mutant, as well as the corresponding KIEs (Table S4), are given in Figure 6. The isotope effects on the Arrhenius parameters for each enzyme are listed in Table 3.

Figure 6.

Arrhenius plots for the oxidation of ¹H- and ²H-PT (circles and squares, respectively; left ordinate) catalyzed by T104S- (A), T104A- (B), and T104G-17X-PTDH (C). The corresponding KIEs are also shown for each mutant (triangles; right ordinate). All values were obtained in 100 mM MOPS at pH 7.25.

Table 3.

Isotope effects on tunneling-related parameters derived from Arrhenius plots with Thr104 mutants^a

Variant	AH/AD	ΔEa (kcal/mol)
17X-PTDH	1.6 (0.1)	0.21 (0.05)
T104S	0.66 (0.07)	0.75 (0.06)
T104A	0.45 (0.05)	0.96 (0.06)
T104G	0.60 (0.05)	0.77 (0.05)

^aAll values were derived from fits of ln^Dk_cat against 1/T according to equation 2.

While the effect of the Thr104 mutations may not be immediately apparent by comparing the data in Figure 3 and Figure 5, the derived values of A_H/A_D and ΔE_a suggest that the Thr104 mutants do not facilitate tunneling as efficiently as the 17X-PTDH. The isotope effect on the pre-exponential factor falls to within the semi-classical limit upon mutation of Thr104, while values of ΔE_a become significantly larger. The values of A_H/A_D might be taken to indicate that the reactions catalyzed by the Thr104 mutants proceed in a semi-classical “over the barrier” manner. However, Klinman has proposed an alternative view of this apparent semi-classical behavior, in which the mutations introduce substrate packing defects that result in longer DADs and subsequently give rise to more temperature dependent KIEs.⁴⁰ In this model, the apparent semi-classical behavior simply represents a transitionary state of packing perturbation (a “modestly impaired enzyme”),⁴⁰ which falls between that of the native enzyme (A_H/A_D > 1.4; ΔE_a ≈ 0 kcal/mol) and “greatly impaired enzymes” (A_H/A_D < 0.4; ΔE_a >> 0 kcal/mol) that require much more significant DAD sampling in the TRS to facilitate tunneling. In this view, all Thr104 mutants are “modestly impaired” and reduction of the steric bulk of this residue results in moderate increases in the DADs (see below).

In some cases, mutations of the steric backstop can give a clear trend between the bulk of the residue and the tunneling efficiency of the mutant.⁶⁶ No such trend is apparent with the Thr104 mutants (Table 3). Instead, the data suggest that the methyl group of Thr104 promotes short DADs, and that this group is only moderately important to facilitate tunneling. From the crystal structure of 17X-PTDH, it is this -CH₃ unit that is most appropriately positioned to act as a backstop for the nicotinamide ring (Figure 4). Additionally, the hydroxyl group of Thr104 and the backbone amide of Gly294 are separated by 3.2 Å, such that a hydrogen bond between these residues may be involved in optimal positioning of the methyl group of Thr104 on the back face of the nicotinamide ring.

Despite the absence of a correlation between the KIE temperature dependence and the steric bulk of this backstop, the observation that perturbing Thr104 increases the temperature dependence adds additional support to the suggestion that 17X-PTDH catalysis can be described by a Marcus-like model of hydride tunneling. In the context of this model, KIEs become increasingly temperature dependent when thermally coupled DAD sampling at the TRS contributes more significantly to the reaction coordinate.³⁶ This model suggests that the parent 17X-PTDH achieves optimal substrate packing in the TRS, such that very little DAD sampling is required to facilitate tunneling. The expanded active sites of the Thr104 mutants result in longer DADs in the TRS. The resulting suboptimal substrate packing requires more significant DAD sampling to facilitate tunneling on the Thr104 mutants, giving rise to more temperature dependent KIEs.

Tunneling and the TS for 17X-PTDH catalysis

The reported TS structure for 17X-PTDH catalysis considered the possibility of a Bell tunneling model,²⁸ ultimately finding it unnecessary to correct the observed KIEs for tunneling near the top of the energy barrier. However, if 17X-PTDH catalysis involves a Marcus-like model of tunneling, the observed ²H KIEs cannot easily be interpreted in terms of a semi-classical TS structure. Instead, these KIEs report on discrepancies in the tunneling efficiency of hydrogen and deuterium in the TRS and in the DAD necessary to facilitate tunneling of each isotope.^{36, 40} While the magnitude of the ¹⁸O KIEs remain good evidence that the 17X-PTDH reaction proceeds asynchronously,^{67, 68} with P-O bond formation largely preceding P-H bond cleavage, the precise structure of the activated complex is unclear. We propose that the previously reported TS structure remains a reasonable facsimile of the saddle point on the reaction coordinate for hydride transfer and that this structure is likely to resemble the TRS from which tunneling occurs.

Conclusions

Phosphite dehydrogenase has attracted significant attention both as a cofactor regeneration system and as a catalyst of an unusual phosphoryl transfer reaction. Despite this attention, the role of hydride tunneling on this enzyme had gone unaddressed. While the limited thermostability of the wild type enzyme precludes an investigation of the temperature dependence of the KIEs with the natural enzyme, the thermostable 17X-PTDH variant generated by directed evolution is amenable to this type of study. Using the temperature dependence of the primary ²H-KIE as a probe of hydride tunneling, we have demonstrated that 17X-PTDH likely facilitates extensive tunneling of both hydrogen and deuterium through a Marcus-like model. Mutation of an active site threonine results in 17X-PTDH variants that exhibit KIEs with increased temperature dependence. This observation indicates that 17X-PTDH achieves optimal substrate packing to facilitate tunneling in the TRS, and that mutation of this threonine perturbs this substrate packing and the tunneling efficiency. We postulate that mutations introduced into 17X-PTDH by directed evolution would likely be either neutral or detrimental to the dynamic processes that facilitate hydride tunneling. As such, we propose that the tunneling efficiency observed with 17X-PTDH represents a lower limit for tunneling on naturally occurring PTDHs. While this tunneling represents a previously unappreciated feature of catalysis by phosphite dehydrogenase, this work also demonstrates that 17X-PTDH can be added to the large family of enzymes that catalyze hydrogen transfer and facilitate extensive quantum mechanical tunneling.^{31, 36, 39, 40, 43, 47, 51, 55–57, 60, 69–80} Additionally, the proposed Marcus-like model on this P-H activating enzyme is consistent with the proposal that tunneling is not restricted to C-H activating enzymes but is instead a general feature of enzymes that facilitate hydrogen transfer.