Unveiling the influence of salt concentration on the different stages of the catalytic cycle of a halophilic enzyme

Abstract

Enzymes from halophilic organisms function in near‐saturating salt concentrations. To explore enzyme adaptation to these conditions and the broader effects of salt on enzyme catalysis, we examined the salt effect on the kinetics of a glucose‐6‐phosphate dehydrogenase from the halophilic archaeon Haloferax volcanii (HvG6PDH). This enzyme has a negatively charged surface and catalyzes the oxidation of the negatively charged substrate glucose‐6‐phosphate (G6PDH activity) and glucose (glcDH activity). We found strikingly different salt effects on the two activities. Steady‐state kinetics experiments revealed a 50‐fold decrease in K _M ^G6P for G6PDH activity. Instead, for glcDH activity, the main effects were a 10‐fold increase in k _cat and a 10‐fold increase in k _cat ^glc/K _M ^glc. The effect of salt in each step of the catalytic cycle was assessed using pre‐steady‐state kinetic experiments. We found that KCl increases both the binding and release rates of NAD⁺ in G6PDH activity, whereas in glcDH it does not affect binding but decreases the release rate. In G6PDH, KCl does not affect the chemical step, while in glcDH this step is significantly accelerated. The results further indicate that the increase in G6P affinity is the main contributor to the increase in G6PDH activity, whereas the increase in glcDH activity is primarily driven by the increase in the chemical step rate. Together, these findings highlight charge screening as a key factor underlying the differential effects of salt, by reducing electrostatic repulsion between the enzyme surface and its substrates and modulating interactions between the positively charged active site and the substrates.

We examine how salt affects each step of the catalytic cycle of a halophilic glucose‐6‐phosphate dehydrogenase (G6PDH), which also catalyzes glucose oxidation (glcDH). We found that an increase in substrate binding rates is the main driving factor behind the increase in G6PDH activity, whereas the acceleration of the chemical step underlies the increase in glcDH activity. The role of charge screening as a key factor is discussed.

Abbreviations

6‐PGL

6‐phosphogluconolactone

G6P

dehydrogenase activity

G6P

glucose‐6‐phosphate

GL

gluconolactone

glcDH

glucose dehydrogenase activity

HvG6PDH

G6PDH enzyme from Haloferax volcanii

NAD⁺

Nicotinamide adenine dinucleotide oxidized form

NADH

Nicotinamide adenine dinucleotide reduced form

Introduction

Halophilic organisms live in salt concentrations close to saturation. During evolution, these organisms have developed different adaptive strategies, such as the active expulsion of salt from the cytoplasm, the accumulation of organic osmolytes, or the accumulation of ions like potassium to avoid osmotic pressure stress. Consequently, proteins belonging to the latter group of organisms have developed physical–chemical properties to adapt to this functional context. These enzymes have been proposed as suitable candidates for biotechnological applications [1, 2, 3] and constitute an interesting model for studying the effect of salt on enzyme function.

The effect of salt concentration has been well described in functional macromolecular properties like solubility, stability [4, 5, 6], and ligand binding, being the interaction with nucleic acids a subject with high theoretical and experimental development [7, 8, 9]. However, the effect of salt on enzyme catalysis has not been studied to the same extent. In 2001, Park and Raines [10, 11] developed a theoretical model to explain the decrease in enzyme activity caused by salt concentration in bovine pancreas ribonuclease. This protein has a positively charged surface and catalyzes the hydrolysis of a negatively charged linear substrate (RNA). By changing the enzyme surface charge in the vicinity of the active site and using RNAs with different lengths, hence with different amounts of negative charge, they concluded that the main effect of salt would be a decrease in electrostatic attraction between the enzyme and the substrate [10, 11]. However, the validity of this theoretical model is restricted to enzymes whose activity decreases with salt concentration and whose surface charge is the opposite of the charge of the substrate [10, 12]. It remains unclear whether this model can be applied to enzymes with other characteristics, like a different surface charge, different substrate charge, or interacting with nonlinear polymeric substrates.

Halophilic enzymes exhibit properties that are, in many respects, opposite to those of RNases. First, increasing salt concentration increases their activity, reaching optimum values at molar concentrations [13]. On the contrary, one common adaptive strategy in this kind of enzyme has been the development of a highly negatively charged surface [1, 14, 15, 16]. Studies have been reported for their stability, structure, and general kinetic properties [13, 15, 17, 18], but a detailed kinetic study assessing the effect of salt in the different stages of the catalytic cycle has not yet been carried out.

A suitable model for studying the effects of salt concentration on halophilic enzyme activity is the glucose‐6‐phosphate dehydrogenase from the halophilic archaea Haloferax volcanii (HvG6PDH). This enzyme has no homology with the canonical G6PDHs from other organisms [19] and catalyzes the NAD⁺‐dependent oxidation of G6P, producing 6‐Phosphogluconolactone (6PGL) and NADH as products (Scheme 1 [20]). It can also catalyze the NAD⁺‐dependent oxidation of glucose, producing gluconolactone (GL) (glcDH activity, Scheme 2) but with lower efficiency [19]. The surface of this enzyme is enriched with acidic residues, while the active site cavity is enriched with basic residues, so the former has a net negative charge and the latter a positive charge at pHs above neutral [19]. Since its substrate, G6P, has a negative charge, a repulsive interaction between the enzyme and this substrate is expected. Also, since glucose has no net charge, no repulsion is expected. On the contrary, NAD⁺ has both positive and negative moieties and, when transformed to NADH, it loses a positive charge.

$$\mathbf{G}\mathbf{6}\mathbf{P}+{\mathbf{NAD}}^{\mathbf{+}}\rightleftharpoons \mathbf{6}\mathbf{PGL}+\mathbf{\text{NADH}}$$ (1)

$$\mathbf{\text{Glucose}}+{\mathbf{NAD}}^{\mathbf{+}}\rightleftharpoons \mathbf{\text{Gluconolactone}}+\mathbf{\text{NADH}}$$ (2)

In this work, we performed a detailed analysis of the effect of salt concentration in the different stages of the catalytic cycle of HvG6PDH. Using steady‐state kinetics, we determined that the enzyme follows an ordered‐sequential kinetic mechanism, in which NAD⁺ is the first substrate to bind, and NADH is the last product to be released. We found that, for the oxidation of G6P, the main effect of salt is on the K _M for G6P, which decreased approximately 50‐fold. For glucose oxidation (glcDH activity), the main effects were a 10‐fold increase in k _cat and a roughly 10‐fold increase in k _cat/K _M for glucose. To analyze the effect of salt on the different stages of the catalytic cycle, we performed pre‐steady‐state kinetic experiments for both activities at two different KCl concentrations. We found that the effect of KCl on the two activities is strikingly different. Increasing the salt concentration enhances both the binding and the release rates of NAD⁺ in G6PDH activity, while in glcDH activity, neither its binding rate nor its release rate is affected. Additionally, in G6PDH, the chemical step is strongly shifted toward product formation and is not influenced by KCl, while in glcDH it is accelerated in both the forward and reverse directions, together with an increase in product release rate. Finally, a combined analysis of steady‐state and transient‐state kinetics suggests that the main factor underlying the increase in G6PDH activity is an enhanced binding affinity for G6P. In contrast, the affinity for glucose in glcDH activity appears to be very low. These results strongly support a role for charge screening in explaining the differential effects of salt on each enzymatic activity, by reducing the electrostatic repulsion between the negatively charged enzyme surface and the negatively charged substrate and differentially affecting the electrostatically driven binding of charged substrates. This study sheds light on the impact of salt on halophilic enzymes and enzyme catalysis more broadly, providing a detailed analysis of the effect of salt on each step of the catalytic cycle of a halophilic enzyme. It also discusses the role of charge screening and suggests additional mechanisms, such as differential ion penetration into the active site, that foster further investigation.

Results and discussion

Steady‐state kinetic analysis

Determining the kinetic mechanism of HvG6PDH

Steady‐steady kinetic experiments were performed to determine the order of substrate binding and product release. Initial velocity curves for G6P were obtained at various fixed concentrations of NAD⁺ (Fig. 1A) in the presence of 2 m NaCl. The Michaelis–Menten equation (Eqn 9) was fitted to each curve, and the resulting apparent kinetic parameters k _cat and K _M for G6P were plotted against NAD⁺ concentration (Fig. 1B,C, respectively). Similarly, k _cat and K _M for NAD⁺ were estimated from initial velocity curves of NAD⁺ obtained at different G6P concentrations (Fig. 1D–F).

Fig. 1.

Initial velocity experiments varying cosubstrate and nicotinamide adenine dinucleotide reduced form (NADH) concentrations to determine the kinetic mechanism of the G6PDH activity. Substrate curves were obtained at different cosubstrate and NADH concentrations. For each substrate curve, the Michaelis–Menten equation was fitted using nonlinear regression analysis, and the parameters k _cat and K _M were estimated. All experiments were performed at 25 °C in Tris pH 8.5 and NaCl 2 m, and the stability of the enzyme was controlled for each experimental condition. Solid lines represent the equation fitted for each curve. (A) Initial velocity curves for G6P at different NAD⁺ concentrations. (B) k _cat for G6P at different NAD⁺ concentrations; an equilateral hyperbola was fitted. (C) K _M for G6P at different NAD⁺ concentrations; the continuous line corresponds to the average value. (D) Initial velocity curves of NAD⁺ performed at different G6P concentrations. (E) k _cat for NAD⁺ at different G6P concentrations; an equilateral hyperbola was fitted. (F) K _M for NAD⁺ at different G6P concentrations; the continuous line corresponds to the average value. (G) Initial velocity curves for G6P obtained at different NADH concentrations. (H) k _cat for G6P at different NADH concentrations; a hyperbolic decay with zero asymptote was fitted. (I) K _M for G6P at different NADH concentrations; the continuous line corresponds to the average value. (J) Initial velocity curves for NAD⁺ obtained at different NADH concentrations. (K) k _cat for NAD⁺ at different NADH concentrations; the continuous line corresponds to the average value. (L) K _M for NAD⁺ at different NADH concentrations; a straight line was fitted. Error bars represent the standard error of the parameter values obtained by nonlinear regression analysis. The data are from a representative experiment. Assays under key conditions were performed independently, and the resulting kinetic parameters (K _M and k _cat) were reproducible across all experimental replicates.

For both substrates, G6P and NAD⁺, it was observed that k_cat follows an equilateral hyperbola (Fig. 1B,E) and K _M remains constant as a function of cosubstrate concentration (NAD⁺ and G6P, respectively) (Fig. 1C,F). These features indicate that the catalytic cycle occurs through the formation of a ternary E‐NAD⁺‐G6P complex. Otherwise, an equilateral hyperbola would be expected for K _M vs. cosubstrate, which would have indicated a substituted enzyme mechanism.

To determine the order of substrate binding and product release, product inhibition studies were conducted with NADH. Initial velocity curves for G6P were obtained at various fixed concentrations of NADH in 2 m KCl (Fig. 1G). Apparent k _cat and K _M values for G6P were obtained and plotted as a function of the NADH concentration (Fig. 1H,I, respectively). An analogous experiment was performed by varying NAD⁺ at different fixed concentrations of NADH (Fig. 1J–L).

For G6P, k _cat decreased hyperbolically with increasing [NADH], approaching a lower limit of zero (Fig. 1H), while K _M remained constant (Fig. 1I). This pattern is diagnostic of pure noncompetitive inhibition by NADH with respect to G6P. For NAD⁺, k _cat was unaffected by NADH (Fig. 1K), whereas K _M increased linearly with [NADH] (Fig. 1L), indicating competitive inhibition.

These results allow us to conclude that the catalytic cycle of HvG6PDH follows a Bi Bi ordered‐sequential mechanism, with NAD⁺ as the first substrate to bind and NADH as the last product to be released.

Analyzing the effect of ions on the G6PDH activity

To assess the effect of ions on the kinetics of HvG6PDH, we initially conducted steady‐state kinetic experiments. For both G6PDH and glcDH activities, initial velocity curves for each substrate were performed at different KCl and NaCl concentrations, and the values of the respective kinetic parameters were analyzed as a function of both salt concentrations (Figs 1 and 2).

Fig. 2.

Analysis of salt concentration effect on G6PDH activity by steady‐state kinetics. Initial velocity curves for NAD⁺ were performed at different KCl (A) and NaCl (B) concentrations. The Michaelis–Menten equation was fitted by nonlinear regression analysis to each curve, and the parameters k _cat (C), K _M (D), and k _cat/K _M (E) for NAD⁺ were determined at different KCl ( violet) and NaCl ( orange) concentrations. Analogously, curves for G6P were performed at different KCl (F) and NaCl (G) concentrations, and the parameters k _cat (H), K _M (I), and k _cat/K _M (J) for G6P were determined. Solid lines correspond to phenomenological equations fitted to each parameter vs salt concentration curve; a hyperbola intersecting the Y‐axis for (B), (H), and (I), a straight line for (D) and (J), and a quotient between a hyperbola and a straight line for (E). The graphs in (E) and (I) are shown with a logarithmic scale on the X‐axis for data presentation purposes. All experiments were performed at 25 °C in Tris pH 8.5. Error bars correspond to the standard error in the estimation of the parameter value by nonlinear regression analysis. The data are from a representative experiment. Assays under key conditions were performed independently, and the resulting kinetic parameters (K _M and k _cat) were reproducible across all experimental replicates.

For G6PDH activity, initial velocity curves for NAD⁺ exhibited hyperbolic behavior at each salt concentration (Fig. 2A,B). Accordingly, the Michaelis–Menten equation (Eqn 9) was fitted to the experimental data, and the apparent kinetic parameters k _cat ^NAD and K _M ^NAD and k _cat ^NAD/K _M ^NAD (Figure 2C–E) were obtained as a function of salt concentration. The same procedure was performed for G6P (Fig. 2F–J). At this point, we use a phenomenological approach, so no theoretical model was presupposed to explain the salt dependence of the steady‐state kinetic parameters.

The observed k _cat for NAD⁺ increased hyperbolically, reaching 2.5‐fold its initial value with increasing NaCl concentration and 6‐fold with increasing KCl concentration (Fig. 2C). In contrast, K _M ^NAD showed a linear dependence on both NaCl and KCl concentrations (Fig. 2D), with a slightly steeper slope for KCl. Finally, the apparent second‐order rate constants (k _cat ^NAD/K _M ^NAD) showed a slight increase, followed by an apparently hyperbolic decrease as a function of NaCl and KCl concentrations (Fig. 2E). This behavior was consistent with the ratio of a hyperbola and a straight line.

For G6P, a slight 0.7‐fold hyperbolic decrease was observed for k _cat ^G6P in the range of assessed NaCl concentrations, while a hyperbolic increase of approximately twofold was observed in the range of assessed KCl concentrations (Fig. 2H). For K _M ^G6P, a pronounced hyperbolic decrease of more than one order of magnitude was observed as a function of both NaCl and KCl concentrations (Fig. 2I). The concentration of NaCl required to achieve half‐maximal saturation was higher than that required for KCl. For k _cat ^G6P/K _M ^G6P, an approximately linear increase was observed as a function of both salt concentrations (Fig. 2J), with an increase of approximately 40‐fold in the range of assessed concentrations of KCl and 10‐fold for NaCl.

Analyzing the effect of ions in glcDH activity

HvG6PDH also catalyzes the NAD⁺‐dependent oxidation of glucose (glucose dehydrogenase activity, glcDH). To assess the effects of ionic strength on this activity, initial velocity curves were obtained for both NAD⁺ (Fig. 3A,B) and glucose (Fig. 3C,D) at different NaCl and KCl concentrations. An equilateral hyperbola was obtained for NAD⁺ substrate curves, and k _cat ^NAD and K _M ^NAD were estimated by fitting the Michaelis–Menten equation to the data (Eqn 9).

Fig. 3.

Analysis of salt concentration effect on glucose dehydrogenase activity by steady‐state kinetics experiments. Initial velocity curves for NAD⁺ (A, B) and for glucose (C, D) were performed at different KCl and NaCl concentrations. The curves labeled 0 m salt are the same in panels A and B, and in panels C and D, respectively. The Michaelis–Menten equation (Eqn 9) was fitted to NAD+ curves by nonlinear regression analysis, and a straight line was fitted to glucose curves. From NAD⁺ curves, the kinetic parameters k _cat (E), K _M (F), and k _cat/K _M (G) were determined; and from glucose curves, the parameter k _cat/K _M (F) was obtained at different KCl ( violet) and NaCl ( orange) concentrations. Error bars correspond to the standard error in the estimation of the parameter value by nonlinear regression analysis. Solid lines correspond to the best fitted phenomenological equations; a straight line for (E, F, H), and a hyperbola intersecting the Y‐axis for (G). All experiments were performed at 25 °C in Tris pH 8.5. The data are from a representative experiment. Assays under key conditions were performed independently, and the resulting kinetic parameters (K _M and k _cat) were reproducible across all experimental replicates.

A linear increase was observed for both k _cat ^NAD (Fig. 3E) and K _M ^NAD (Fig. 3F) as a function of both NaCl and KCl concentrations. For k _cat ^NAD, the effect of KCl was greater than the effect of NaCl, producing a 10‐fold vs a 4‐fold increase, respectively, in the range of assessed concentrations (Figure 3E). This result contrasts with the observations for G6PDH activity, where k _cat ^NAD exhibits a hyperbolic dependence on salt concentration, with a less pronounced increase (Fig. 2C). For K _M ^NAD, both salts had a similar effect, increasing the value by approximately threefold in both cases, which is comparable to the effect observed on the equivalent parameter in G6PDH activity. Finally, a saturation‐like (hyperbolic) threefold increase in k _cat ^NAD/K _M ^NAD was observed between 0 and 2 m salt (Fig. 3G).

Due to the apparent low affinity of the enzyme for glucose, saturation concentrations were not achieved in the initial velocity curves (Fig. 3C,D). As a result, a linear fit was applied to the glc curves, and the parameter k _cat ^glc/K _M ^glc was estimated for each salt concentration (Fig. 3H). A fivefold linear increase in this parameter was observed between 0 and 2 m NaCl, whereas KCl induced a 10‐fold linear increase. This increment was notably lower compared with the 40‐fold increase in k _cat ^G6P/K _M ^G6P caused by salt concentration in G6PDH activity (Fig. 2J).

These findings indicate that salt concentration has differential effects on the two activities. In G6PDH the main effect is the dramatic decrease in K _M ^G6P (Fig. 2I), with lower effects in k _cat for both substrates (Fig. 2C,H). While in glcDH the main effect is the 10‐fold increase in k _cat ^NAD (Fig. 3E). To address what are the bases of this differential effect of salt in HvG6PDH, it becomes necessary to assess the effect of salt in the different stages of the catalytic cycle of the enzyme.

Transient‐state kinetic experiments

To better understand the effect of salt concentration on both activities of HvG6PDH, and to have access to its effect on the different steps of the catalytic cycle, we performed pre‐steady‐state time‐course experiments using a stopped‐flow device attached to a fluorimeter and measuring NADH fluorescence (excitation at 340 nm and measuring emission intensity at 459 nm). A solution containing 2 μm NAD⁺ was mixed with equal volumes of solutions containing increasing enzyme concentrations to achieve a final reaction medium of 1 μm NAD⁺ and enzyme concentrations ranging from 1 to 10 μm. Both activities were assayed at high sugar concentrations of 20 mm G6P and 0.2 m glucose, respectively. The experiments were performed at 0.5 and 2 m KCl (Fig. 4).

Fig. 4.

Time‐course experiments. Time‐course experiments for G6PDH activity were performed at 0.5 m (A) and 2 m KCl (B) in 20 mm G6P, and for glcDH activity, they were performed at 0.5 m (C) and 2 m KCl (D) in 0.2 m glucose. The experiments were carried out at different enzyme concentrations: 1 μm (black), 2 μm (red), 3 μm (blue), 5 μm (green) and 10 μm (violet). The curves shown are representative of three independent replicates. Solid lines are the simulations of the model from Scheme 3 using parameters estimated by nonlinear regression analysis shown in Table 1.

For all time‐course curves, regardless of the enzymatic activity or salt concentration, no appreciable lag or burst phases were observed (Fig. 4). Therefore, a minimal kinetic model (Scheme 3), which includes the substrate binding, chemical transformation, and product release steps, was used to fit and analyze the experimental data.

$$\mathbf{S}+\mathbf{E}\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}\mathbf{ES}\underset{k_{-2}}{\overset{k_2}{\rightleftharpoons }}\mathbf{EP}\underset{k_{-3}}{\overset{k_3}{\rightleftharpoons }}\mathbf{E}+\mathbf{P}$$ (3)

This scheme includes only the second‐order step for NAD⁺ binding to the enzyme, excluding the sugar binding steps. This simplification is justified by the fact that the substrate concentration ratios used, [NAD⁺]/[sugar], were 1/20 000 for G6PDH activity and 1/200 000 for glcDH activity, which implies that: (a) sugar substrate concentrations remain effectively constant throughout the reaction. Consequently, its availability does not limit or impede the progress of the bi‐substrate reaction, and (b) the pseudo‐first‐order rate constants for sugar binding to the enzyme are very large, making these steps too fast to be experimentally resolved. Therefore, regardless of the order of substrate addition in the Bi‐Bi reaction, the binding of either sugar substrate will not be observed as a distinct kinetic step. Instead, it will proceed at the rate of the preceding, slower step.

In summary, these considerations indicate that under these experimental conditions, NAD⁺ can be regarded as the rate‐limiting substrate, thereby controlling or regulating the rate of the corresponding steps of the catalytic cycle of the enzyme.

The expressions for the steady‐state kinetic parameters in terms of the intrinsic rate constants of the kinetic Scheme 3 are:

$$k_{\mathrm{cat}}=\frac{k_2{k}_3}{k_2+k_3+k_{-2}}$$ (1)

$$K_{\mathrm{M}}=\frac{k_2{k}_3+k_{-1}\left(k_3+k_{-2}\right)}{k_1\left(k_2+k_3+k_{-2}\right)}$$ (2)

$$\frac{k_{\mathrm{cat}}}{K_{\mathrm{M}}}=\frac{k_1{k}_2{k}_3}{k_2{k}_3+k_{-1}\left(k_3+k_{-2}\right)}$$ (3)

Kinetic rate constants for Scheme 3 were estimated for each salt condition by globally fitting to all experimental data simultaneously by nonlinear regression analysis. K _M and k _cat values obtained from steady‐state kinetic experiments were imposed as constraints during the fitting procedure, in accordance with Eqns 1 and 2. The tolerance intervals for these constraints were set as follows: for each assessed condition: k _cat value ± 15% and K _M value ± 60%. Fig. 4 displays the experimental data and the model simulation with parameter values listed in Table 1.

Table 1.

Kinetic parameters characterizing the catalytic cycles of G6PDH and GlcDH obtained under steady‐state and pre‐steady‐state conditions at different KCl concentrations. Data were obtained under excess concentrations of sugar substrate, varying the total enzyme concentration at an initial concentration of 1 μm NAD⁺.

Parameters for NAD+	G6PDH		glcDH
	0.5 m KCl	2 m KCl	0.5 m KCl	2 m KCl
k 1, μm −1 s−1 *	0.9 ± 0.1	2.0 ± 0.8	0.111 ± 0.007	0.20476 ± 0.00005
k −1, s−1 *	6 ± 6	125 ± 63	2.5 ± 0.4	1.25 ± 0.09
k 2, s−1 *	50 ± 6	55 ± 6	91 ± 77	365 ± 3
k −2, s−1 *	< 0.007	< 0.020	84 ± 77	276 ± 25
k 3, s−1 *	62 ± 73	—	4.4 ± 0.7	16.7 ± 0.6
k −3, μm −1 s−1 *	68 ± 79	< 0.008	0.0035 ± 0.0004	0.043 ± 0.003
k cat (s.s.), s−1 **	24.4 ± 0.2	42.5 ± 0.1	2.87 ± 0.07	9.0 ± 0.2
K M (s.s.), μm **	78 ± 6	198 ± 6	25 ± 5	71 ± 10
k cat/K M (s.s.), μm −1 s−1 **	0.31 ± 0.07	0.22 ± 0.03	0.12 ± 0.02	0.13 ± 0.02

^*Intrinsic rate constants were obtained by fitting the model represented in Scheme 3 by nonlinear regression analysis to each dataset corresponding to the time course (Fig. 4) for G6PDH and glcDH activities at 0.5 m and 2 m KCl.

^**‘s.s.’ denotes values for the kinetic parameters for NAD⁺ obtained by steady‐state kinetic experiments at 0.5 m and 2 m KCl for each activity.

NAD ⁺ binding kinetics analysis

For both G6PDH and glcDH activities, KCl produces approximately a twofold increase in k ₁, On the contrary, in G6PDH it produces approximately a 20‐fold increase in k ₋₁, while in glcDH, it is reduced by half (Table 1). These variations point to an effect of KCl on NAD⁺ binding; however, for both activities, the values of k ₁ (Table 1) are between one and three orders of magnitude below what is expected for a diffusional second‐order rate constant (≥ 10 μm ⁻¹·s⁻¹). Consequently, it is likely that this step is not diffusion‐controlled. On the other hand, the values for k ₁ for NAD⁺ in glcDH activity are one order of magnitude below k ₁ for G6PDH, indicating that important differences may exist between both activities regarding NAD⁺ binding.

The results may uncover an intermediary step between NAD ⁺ binding and the chemical step

One possible interpretation is that such low values of k ₁ in both activities reflect the existence of a first‐order rearrangement process that remains kinetically unresolved. In such a case, k ₁ and k ₋₁ can be regarded as the rate constants for the simple observable pathway in Scheme 4, which would be the effective equivalent rate constants resulting from the kinetic collapse of Step 1 in Scheme 5. The first step in Scheme 5 represents the formation of the collisional complex, governed by the diffusional rate constants k _d and k _−d, while the second step describes a first‐order rearrangement process characterized by the rate constants k _f and k _−f.

$$\mathbf{S}+\mathbf{E}\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}\mathbf{ES}$$ (4)

$$\mathbf{S}+\mathbf{E}\underset{k_{-\mathrm{d}}}{\overset{k_{\mathrm{d}}}{\rightleftharpoons }}{\mathbf{E}}^{\prime }\mathbf{S}\underset{k_{-\mathrm{f}}}{\overset{k_{\mathrm{f}}}{\rightleftharpoons }}\mathbf{ES}$$ (5)

Equivalent rate constants k ₁ and k ₋₁ from Scheme 4 expressed in terms of the rate constants corresponding to Scheme 5 are:

$$k_{-1}=k_{-\mathrm{f}}\left(\frac{k_{-\mathrm{d}}}{k_{-\mathrm{d}}+k_{\mathrm{f}}}\right)$$ (4)

$$k_1=k_{\mathrm{d}}\left(\frac{k_{\mathrm{f}}}{k_{-\mathrm{d}}+k_{\mathrm{f}}}\right)$$ (5)

Since k _d is the diffusion‐limited second‐order rate constant for the formation of the collisional complex, its minimum value (at the lowest salt concentration) must be at least 10 μm ⁻¹·s⁻¹. Substituting into Eqn 5 the value of k ₁ at 0.5 m KCl (0.9 μm ⁻¹·s⁻¹, Table 1) and assuming k _d = 10 μm ⁻¹·s⁻¹, it follows that k _−d/k _f ≥ 10. This indicates that k _−d is at least one order of magnitude greater than k _f. This quantitative relationship supports the conclusion that the second‐order step in Scheme 5 is under the condition usually called rapid equilibrium. This explains why this step remains kinetically unresolved in the pre‐steady‐state kinetic experiments. A similar analysis applied to the kinetic data for glcDH at low and high KCl concentrations yields qualitatively comparable results: k _−d/k _f ≥ 90 and k _−d/k _f ≥ 50, respectively. Thus, the same conclusion applies in these cases as well. The results and assumptions of this analysis are summarized in Table 2.

Table 2.

Salt effects on the kinetic parameters assuming Scheme 5 for the NAD⁺ binding step. In each case, the starting assumptions are indicated in the respective box.

Parameters for NAD+	G6PDH	glcDH
k d, μm −1·s−1	≥ 10 (assumed diffusional)	≥ 10 (assumed diffusional)
	Increase	No effect
k −d, s−1	Increase	Decrease
k f, s−1	k −d/k f ≥ 10	k −d/k f ≥ 50
	Assumed as nonaffected	Assumed as nonaffected
k −f, s−1	≥ 125	≥ 2.5
	Assumed as nonaffected	Assumed as nonaffected

It is well established that conformational changes often involve local rearrangements of atoms in contact across extensive interdomain interfaces and are primarily governed by the protein's internal viscosity rather than the surrounding solvent viscosity. These first‐order processes are minimally influenced by translational and rotational diffusion, which play a crucial role in the second‐order association rate constants for binding that are also highly sensitive to electrostatic interactions and solution conditions, particularly salt concentration [7, 21, 22, 23]. Thus, we will consider in the following analysis that the rate constants of the first‐order process (k _f and k _−f) are little or not at all affected by changes in KCl concentration and thus by ionic strength.

NAD ⁺ binding is differentially affected by KCl in each activity

As shown in Eqn 4, k ₋₁ exhibits a hyperbolic dependence on k _−d. So, the observed increase in k ₋₁ for G6PDH with rising KCl concentration (Table 1) must be attributed to the corresponding increase in k _−d. Similarly, the decrease in k ₋₁ for glcDH upon increasing salt concentration must be associated with a corresponding decrease in k _−d. A second conclusion that can be drawn from the hyperbolic relationship between k ₋₁ and k _−d is that k _−f is the upper bound of possible values for k ₋₁, so, considering the experimental values of k ₋₁ for both activities and both KCl concentrations (Table I), the lower bound value for k _−f must be at least 125 s⁻¹ for G6PDH and at least 2.5 s⁻¹ for GlcDH (Table 2).

Regarding k ₁, since in G6PDH activity k _−d increases as a function of KCl concentration, the observed increase in k ₁ necessarily implies a concurrent increase in k _d. Meanwhile, in the case of glcDH, the analysis of k ₋₁ indicates that k _−d must decrease with increasing KCl concentration. Since k ₁ increases concomitantly as k _−d decreases, calculations show that merely halving k _−d value would be sufficient to account for the salt's effect on k ₁. Interestingly, this implies that, under these experimental conditions, the value of k _d varies minimally, or practically not at all.

Charge shielding may explain the salt effects in NAD ⁺ binding kinetics in G6PDH activity

For G6PDH activity, the diffusional association rate constant (k _d) increases with rising KCl concentration. This contrasts with typical electrostatically driven enzyme–substrate binding, where elevated ionic strength generally reduces the value of microscopic association constants [7, 10, 11, 22, 23, 24]. However, these conclusions come from nonhalophilic enzymes that are strongly inhibited or inactivated at high salt concentrations. Also, in commonly studied cases, like ribonucleases [10, 11, 12], there is a charge complementarity between the enzyme and the substrate, so it is expected that charge shielding produces a negative effect in enzyme–substrate association. In the case of HvG6PDH, the enzyme exhibits a highly negatively charged surface under the assessed conditions [19], which is a common adaptive feature among many halophilic enzymes [1, 14, 15, 16]. In contrast, its active site, although rich in positive residues, resides in a pocket with limited solvent accessibility [19]. On the contrary, due to its pyrophosphate moiety, NAD⁺ is expected to have a net negative charge in solution; therefore, a net repulsive interaction between the substrate and the enzyme is expected. Thus, charge shielding may be reducing the repulsion between the enzyme and NAD⁺, explaining the increment in k _d, and therefore the observed twofold increase in k ₁, in the G6PDH activity (Table 1).

Charge shielding effect may also explain the increase in k _−d, hence in the observed k ₋₁ for G6PDH activity. Increasing the ionic strength of the medium will weaken the attractive ionic interactions between the substrate and the active site residues, thus increasing dissociation frequency.

For glcDH activity, in contrast to G6PDH, our analysis suggests that the second‐order constant (k _d) for NAD⁺ in glcDH activity is minimally affected by KCl, if at all. Meanwhile, k _−d is decreased instead of increased (Table 2). These findings underscore that, regarding the sugar substrate, unlike glucose‐6‐phosphate, which at physiological pH carries approximately two negative charges, the glucose molecule is electrically neutral. Consequently, the slight or negligible change in k _d, along with the decrease in k _−d for NAD⁺ as ionic strength increases, indicate that electrostatic forces are no longer the predominant factors driving and stabilizing the formation of the collision complex. Also, differential ion penetration and changes in active site dynamics between both activities produced by the absence of the phosphate moiety in the sugar substrate could have an influence on this effect, but further studies will be needed to address this interpretation.

Analysis of salt effect in chemical and product release steps

In the case of G6PDH activity, the k ₂ value remains practically constant despite variation in salt concentration and exhibits a difference of at least three orders of magnitude compared with the value of k ₋₂ at both KCl concentrations (Table 1). These observations indicate that (1) salt does not seem to affect the chemical step of the catalytic cycle of the enzyme, (2) this step markedly promotes the conversion of intermediate complexes toward product formation. The value for k ₃ at 2 m KCl could not be determined. However, in the steady‐state kinetic experiments, k _cat ^NAD was determined to increase as a function of KCl concentration (Fig. 2C). Since k ₂ is unaffected by KCl and k ₋₂ can be considered negligible (Table 1); considering Eqn 1, the observed increase in k _cat ^NAD must be due to an increase in k ₃. Therefore, KCl is increasing the rate of product release in G6PDH activity.

In contrast to G6PDH activity, the chemical step in glcDH is being affected by KCl, as demonstrated by an approximately fourfold increase in k ₂ and a threefold increase in k ₋₂ (Table 1). Additionally, in this activity, this step is not shifted toward product formation, as indicated by a k ₂/k ₋₂ ratio close to 1. Interestingly, this ratio is almost nonaffected by increasing KCl concentration. This difference in salt effect between the two activities can also be explained by a differential penetration of salt into the active site cavity. In glcDH activity, ions may be entering close to the site of catalysis, but not in G6PDH activity. In this process, the influence of the presence or absence of the phosphate moiety in the sugar substrate may also have a central role.

Considering the values of k ₃ and k ₋₃ obtained for glcDH activity (Table 1), k ₃ was determined to be about 20‐fold smaller than k ₂ in both KCl concentrations, and k ₃ was at least two orders of magnitude higher than k ₋₃ in both KCl concentrations. This indicates that some first‐order step after the chemical step is rate‐limiting, and that the process is shifted toward product release. However, the values for k ₋₃ are at least 2 orders of magnitude below what is expected for a diffusional second‐order rate constant. This may indicate the presence of a first‐order nonobservable process between the chemical step and NADH release, analogous to the observed association step for NAD⁺. Indeed, using the same rationale, and considering Eqn 5, but for k ₋₃ instead of k ₁, it is obtained that k _f ≪ k _−d for both KCl concentrations, which is consistent with the binding step being under rapid equilibrium conditions. Also, assuming again that this step is not affected (or mildly affected) by salt, the conclusion would be that both NADH reassociation and release rates are being increased by KCl.

NADH release is increased by KCl in both G6PDH and glcDH activities. Charge screening may also explain the effect of KCl in this step. NADH also has a net negative charge under the assessed conditions, so it is expected that charge screening by high KCl concentration produces a decrease in the attraction between this product and the positively charged active site, thus increasing its release rate. Additionally, a decrease in the repulsion between NADH and the enzyme surface by charge screening explains the increment in the rate of product association in glcDH activity. The effect cannot be evaluated in the case of G6PDH activity because it was not possible to model the product release/reassociation step in 2 m KCl.

Analysis of sugar substrate binding kinetics

Given that sugar substrates were present in excess as a background condition during pre‐steady‐state kinetic experiments, the influence of salt on sugar binding was assessed indirectly through a combined analysis of pre‐steady‐state and steady‐state kinetic results. First, regarding the chemical step, in G6PDH activity k ₂ is not affected by salt, and k ₋₂ is negligible (Table 1). Meanwhile, in glcDH activity, both the forward (k ₂) and reverse (k ₂) rate constants are increased to the same extent. Based on these assumptions, Scheme 3 will serve as a minimal kinetic framework for interpreting the steady‐state results for sugar substrates. The results and assumptions for this analysis are summarized in Table 3.

Table 3.

Salt dependence of the kinetic parameters for sugar substrates. Conclusions were drawn from a combined analysis of steady‐state and pre‐steady‐state kinetics. Where applicable, instances of assumed behavior are explicitly indicated.

Parameters for sugar substrate	G6P (G6PDH)	Glucose (glcDH)*
k1, μm −1·s−1	Probably increase	Probably no effect
k −1, s−1	Probably decrease	Assumed as higher than k 2 and k 3 *
K D = k −1/k 1	Decrease	≫ 500 mm
k 2, s−1	Considered unaffected	Assumed to increase
k −2, s−2	Assumed as negligible	**
K C = k −2/k 2	**	Considered unaffected
k 3, s−1	Increase	k 3 ≫ k 2 *
k −3, μm −1·s−1	**	**

^*In the case of the parameters for glucose, the assumptions were made adding structural evidence [19].

^**Denotes that no conclusion could be drawn regarding the dependence of these parameters on salt concentration based on the available data.

Analysis of G6P binding kinetics

Given that for G6PDH activity the chemical step is strongly favored toward product formation (i.e., k ₋₂ is negligible), the expression for k _cat ^G6P in Eqn 1 can be approximated as:

$$k_{\mathrm{cat}}^{\mathrm{G}6\mathrm{P}}\approx \frac{k_2{k}_3}{k_2+k_3}$$ (6)

With k ₂ being the same as that shown in Table 1. k _cat ^G6P was observed to increase in a hyperbolic manner, although it appeared approximately linear within the range of salt concentrations tested. Assuming that k ₂ is practically unaffected by KCl concentration (Table 1), the observed increase in k _cat ^G6P (Fig. 2H) must necessarily result from an increase in k ₃ (Table 3), that is, the rate of product release, within this KCl concentration range. The near‐linear increase in k _cat ^G6P further suggests that k ₂ is significantly greater than k ₃, making product release the rate‐limiting step under these conditions.

Based on the same assumptions, k _cat ^G6P/K _M ^G6P can be approximated to

$$\frac{k_{\mathrm{cat}}^{\mathrm{G}6\mathrm{P}}}{K_{\mathrm{M}}^{\mathrm{G}6\mathrm{P}}}\approx \frac{k_1{k}_2}{k_2+k_{-1}}$$ (7)

This parameter (k _cat ^G6P/K _M ^G6P), which represents the apparent second‐order rate constant for substrate binding to the enzyme, increases linearly with KCl concentration over the tested range (Fig. 2J). Assuming that k ₂ is independent of KCl concentration, this increase may result from any of the following scenarios:

1. A linear increase in k ₁ with salt concentration while k ₋₁ remains constant.

2. a decrease in k ₋₁ with salt concentration (e.g., hyperbolic) while k ₁ remains constant, provided that k ₋₁ ≫ k ₂, or

3. a simultaneous increase in k ₁ (e.g., linear) and decrease in k ₋₁ (e.g., hyperbolic), again assuming that k ₋₁ ≫ k ₂.

The same three options can also explain the hyperbolic decrease of K _M ^G6P as a function of KCl concentration (Fig. 2I). Also, the three scenarios will produce a net increase in G6P affinity, with the concomitant decrease on K _D = k ₋₁/k₁.

These results allow us to conclude that an increase in G6P binding affinity is a key effect of KCl on G6PDH activity. This effect may be explained by a decrease in the electrostatic repulsion between this negatively charged substrate and the negatively charged enzyme due to charge screening. This would be reflected in both an increase in k ₁ and a decrease in k ₋₁ (Table 3).

The scenario in which k ₋₁ decreases (Table 3) contrasts with what has been observed for NAD⁺ binding, in which KCl causes an increase in k ₋₁ (Table 1). It is expected that increasing the ionic strength of the medium weakens the attractive ionic interactions between the negatively charged G6P and the positively charged active site. A possible explanation for the net increase in G6P affinity is that this substrate may form local contacts that are not as strongly affected by ionic strength. Therefore, this weakening effect is outweighed by the increase in the binding rate. Additional factors may also contribute to the net increase in G6P affinity—contrasting with the observed increase in NAD⁺ dissociation rate upon KCl addition—such as the entry of ions into the active site and their interaction with specific residues and with the substrates, as well as potential effects on active site dynamics. Further work is required to corroborate these hypotheses.

Analysis of glucose binding kinetics

Interpreting the effect of salt on the glucose binding rate is particularly challenging, as in steady‐state kinetic experiments, glucose saturation was not achieved even at concentrations as high as 500 mm (Fig. 3C), suggesting very high values for K _M ^glc. Consequently, only k _cat ^glc/K _M ^glc could be determined as a function of salt concentration (Fig. 3D). In this case, the only assumption that can be made based on the pre‐steady‐state kinetics results is that k ₂ and k ₋₂ are increased by salt to a very similar extent (Table 3), implying that K _C = k ₂/k ₋₂ remains practically unchanged and close to 1. The following discussion will rely on integrating kinetic data with the available structural evidence for this enzyme [19].

The high value of K _M ^glc can be due to very low values in k ₁ or to very high values in k ₋₁ (Scheme 3, Eqn 2). Glucose has no net charge and hence no repulsion with the enzyme is expected; so it is very unlikely that k₁ would have values significantly different from those corresponding to a diffusional rate constant. On the other hand, regarding structural evidence [19], G6P binding is mainly stabilized by interactions with the phosphate moiety. Due to the absence of this moiety in glucose, a very low affinity for glucose is expected. This suggests that the high value of K _M ^glc may be due to the high value of k ₋₁ (Table 3).

Considering the model represented in Scheme 3, if k ₋₁ is very high and K _C = k ₂/k ₋₂ is constant and close to 1, then k _cat ^glc/K _M ^glc (Eqn 3) can be approximated to

$$\frac{k_{\mathrm{cat}}^{\mathrm{glc}}}{K_{\mathrm{M}}^{\mathrm{glc}}}\approx \frac{k_1{k}_2{k}_3}{k_{-1}\left(k_3+k_2{K}_{\mathrm{C}}\right)}$$ (8)

In transient‐state kinetic experiment results, an approximately fourfold increase for k ₂ was observed (Table 1). Similarly, in steady‐state kinetic experiments an approximately fourfold increment was also observed for k _cat ^glc/K _M ^glc (Fig. 3H). Considering Eqn 8, the increase in k _cat ^glc/K _M ^glc can be attributed to an increase in k ₂ only if k ₃ ≫ k ₂. Considering the structural information, it is reasonable to expect high values for k ₃, since the product gluconolactone is neutral and, similar to the case of glucose release, the enzyme is expected to have a very low affinity for it.

Given the wide variety of possible mechanisms through which salt can exert effects on enzyme catalysis, this work does not aim to develop a comprehensive theory on the effect of salt on enzyme catalysis. Using a detailed approach integrating steady‐state and transient‐state kinetics, we were able to differentiate the effect of salt in different stages of the catalytic cycle of the enzyme of both G6PDH and glcDH enzymatic activities. It remains to be seen how this effect may be occurring at the structural level. One probable explanation has to do with the fact that some interactions formed with the phosphate moiety of G6P will not be present when glucose is the substrate, leaving free space for the entrance of ions to the active site, thus affecting the steps occurring after the enzyme–substrate complex formation.

The effect of salt concentration on enzyme properties is a complex phenomenon. Each enzyme has unique features that can be affected by salt concentration. The cases previously studied regarding the effects of salt in catalysis were enzymes with positive surface charge and negatively charged linear substrates (RNAases) [10, 11]. In this work, we have studied an enzyme with a negatively charged surface, a positively charged active site cavity acting on substrates with different charge distributions. Other cases may exist in which the effect of salt could not be straightforwardly attributable. In the case, we have analyzed, having a negatively charged surface corresponds to an adaptive property that halophilic proteins of this group of organisms have developed through evolution to function in high salt concentrations. But alternatives may exist. For example, Gonzalez‐Ordenes et al. [25] describe a noncanonical adaptation to high salt concentration in proteins from halophilic archaea from the Methanosarcinales group. In addition, there are other systems in which salt effects are particularly relevant, where electrostatic interactions are expected to play a central role. For instance, in membrane‐associated proteins, electrostatic interactions with the negatively charged membrane surface are thought to be crucial for their function.

Overall, our findings provide new insights into the ways in which salt concentration can modulate enzyme catalysis and open the way for further research into how electrostatic mechanisms and ionic strength affect the behavior and function not only of enzymes but also in broader macromolecular systems.

Materials and methods

Expression and purification of HvG6PDH

Expression and purification of HvG6PDH were performed as described by [19]. Briefly, the cDNA for HvG6PDH was cloned into the vector pET‐TEV‐28a with an N‐terminal His‐tag, and the plasmid was inserted into E. coli BL21(DE3). Cells were cultured in L‐B medium in 30 μg·mL⁻¹ Kanamycin at 37 °C until an OD⁶⁰⁰ of 0.8–1. Protein expression was induced using 1 mm IPTG, incubating overnight at 37 °C with continuous agitation. The cells were sedimented by centrifugation at 6000  g for 20 min and resuspended in lysis buffer (2 m KCl, 50 mm Tris–HCl, pH 7.8, 1 mm EDTA, 5 mm 2‐mercaptoethanol, and 0.1% v/v Triton x‐114). Cell lysis was performed by sonication with 15 pulses of 20 s at 40% amplitude separated with pauses of 1 min, maintained at cold temperature. The lysate was centrifuged at 38 000  g for 20 min, and the insoluble fraction was recovered and resuspended in solubilization buffer (8 m urea, 50 mm Tris–HCl, pH 7.8, 1 mm EDTA, and 50 mm dithiothreitol) in a volume corresponding to 2.5% of the original culture volume. Then, the solution was incubated for 1 h at 37 °C with permanent mild agitation, centrifuged at 38000  g for 30 min, and the supernatant was recovered. Proteins were refolded by a 20‐fold dilution in renaturation buffer (2 m KCl, 50 mm Tris–HCl, pH 7.8, and 5 mm 2‐mercaptoethanol), incubating at 4 °C overnight with permanent agitation. The refolded proteins were centrifuged at 38 000  g for 20 min, and the supernatant was concentrated using a vivaflow filtration device (Sartorius, Göttingen, Germany) and loaded on a 5‐mL HisTrap‐HP column (GE Healthcare, Chicago, IL, USA) previously equilibrated with renaturation buffer. The column was washed with 10 volumes of renaturation buffer supplemented with 50 mm Imidazole. Elution was performed with a 50 mL linear gradient from 50 to 250 mm imidazole. Fractions with G6PDH activity were pooled. Protein purity was evaluated by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS/PAGE), for which the samples have to be previously precipitated with 20% trichloroacetic acid to remove the excess of KCl.

Steady‐state kinetics experiments

All experiments were performed in 100 mM Tris–HCl pH 8.5, and with different NAD⁺, G6P, NaCl, and KCl concentrations. To control protein stability during the assay, Selwyn tests [26] and incubation experiments were performed. The reaction was started by adding G6P or NAD⁺ after a preincubation of the enzyme for 5 min in the reaction medium. Before the assays were performed, the protein was dialyzed for 2 h against a buffer containing 100 mM Tris–HCl pH 8.5, 5 mm 2‐mercaptoethanol, and the desired KCl concentration.

G6PDH and glcDH enzymatic activities were measured following NADH production by recording Abs³⁴⁰, considering an extinction coefficient of 6.22 mm ⁻¹·cm⁻¹. The experiments were performed in 96‐well plates (Model 269620; Nunc, Rochester, NY, USA) using a Synergy 2 spectrophotometer (BioTek, Winooski, VT, USA). Initial velocities were obtained by linear regression analysis using the excel or graphpad prism software (Dotmatics, Boston, MA, USA). Initial velocity measurements were expressed in U·mg⁻¹, where U corresponds to μmol·min⁻¹.

Initial velocity curves for each substrate were obtained at different cosubstrate, NADH, KCl, or NaCl concentrations, and the Michaelis–Menten equation (Eqn 9) was fitted to the data of initial velocity vs substrate by nonlinear regression analysis using the Excel or graphpad prism software, and kinetic parameters k _cat and K _M were obtained as a function of cosubstrate or salt concentration. For k _cat calculations, a molecular mass of the protein was estimated to be 30 KDa [19].

$$v_0=\frac{V_m\left[S\right]}{K_M+\left[S\right]}$$ (9)

Transient‐state kinetics experiments

All experiments were performed at 25 °C in 100 mM Tris–HCl pH 8.5, 2 mM dithiothreitol, and 0.5 or 2 m KCl. For G6PDH a constant concentration of 20 mm G6P was used, while for glcDH a concentration of 0.2 m glucose was used.

The experiments were performed using a rapid mixing stopped‐flow accessory (RX2000 Applied Photophysics, Leatherhead, Surrey, UK) coupled with a spectrofluorometer Jasco FP‐8300. Reactions were initiated by mixing equal volumes of a solution containing NAD⁺ 2 μm with a solution containing the enzyme at various concentrations from 2 to 20 μm. NADH fluorescence was measured by exciting at 340 nm and recording emission intensity at 459 nm. NADH concentrations were determined using a NADH calibration curve and correcting the measures by subtracting the fluorescence emission of both the protein and NAD⁺ in these conditions.

A minimal model (Scheme 3) was used. The model was numerically solved and fitted to the time‐course data using the COPASI software [27]. The search for values of the intrinsic kinetic constants (k ₁, k ₋₁, k ₂, k ₋₂, k ₃, and k ₋₃) was restricted by limiting the possible values of these constants to a defined interval of k _cat and K _M deduced from the model as a function of the intrinsic kinetic constants (Eqns 1 and 2). These intervals were defined by values obtained from steady‐state kinetic experiments for the parameters k _cat and K _M.

Conflict of interest

The authors declare no conflict of interest.

Author contributions

GV‐B led the research, designed and performed all the experiments, performed the data analysis, developed the kinetic models, and wrote the manuscript. SBK performed the data analysis, developed the kinetic models, performed the numerical solution and nonlinear regression analysis, and wrote the manuscript.

Data availability statement

The data supporting the findings of this study are contained within the article. Raw data are available from the corresponding author upon reasonable request.