Exploring the challenges of computational enzyme design by rebuilding the active site of a dehalogenase

Significance

The goal of rational computer-aided enzyme design is hampered by the lack of knowledge of the maximum possible rate enhancement. We address this problem by considering the enzyme DhlA, which is naturally adapted for the degradation of dihalogenated ethanes. Using empirical valence bond calculations, we determine the effect of finding mutations that reduce the catalysis and then introducing mutations that restore catalysis. One of our predicted cycles is confirmed experimentally, while the other attempt remains inconclusive. We believe that the proposed strategy provides a very powerful way of validating and refining approaches for computational enzyme design.

Abstract

Rational enzyme design presents a major challenge that has not been overcome by computational approaches. One of the key challenges is the difficulty in assessing the magnitude of the maximum possible catalytic activity. In an attempt to overcome this challenge, we introduce a strategy that takes an active enzyme (assuming that its activity is close to the maximum possible activity), design mutations that reduce the catalytic activity, and then try to restore that catalysis by mutating other residues. Here we take as a test case the enzyme haloalkane dehalogenase (DhlA), with a 1,2-dichloroethane substrate. We start by demonstrating our ability to reproduce the results of single mutations. Next, we design mutations that reduce the enzyme activity and finally design double mutations that are aimed at restoring the activity. Using the computational predictions as a guide, we conduct an experimental study that confirms our prediction in one case and leads to inconclusive results in another case with 1,2-dichloroethane as substrate. Interestingly, one of our predicted double mutants catalyzes dehalogenation of 1,2-dibromoethane more efficiently than the wild-type enzyme.

The need to progress with enzyme design is a major practical and fundamental challenge (1, 2). Unfortunately, despite interesting progress (3–7), the main advances have been made by directed evolution and not by computational design (7, 8). This point can be concluded by examining the references mentioned in ref. 7 or, for example, in ref. 9. Furthermore, at present, there are major difficulties in using directed evolution to obtain the catalytic effects that approach those of naturally evolved enzymes.

Apparently, reasonable attempts to use charge−charge interactions with a high dielectric, to predict the effect of distanced ionized groups on the reactivity of the substrate (e.g., ref. 1), are not likely to lead to a large catalytic effect. Thus, it seems that one must focus on groups at a close and medium distance to the substrate (although directed evolution appears to also use distant groups). In the case of groups in proximity to the substrate, it seems that approximations such as the linear response approximation (LRA) are not likely to give sufficiently reliable results, and one should probably move to the more expensive empirical valence bond (EVB) calculations. However, even with the EVB method, it is not clear what it takes to make a reliable prediction. For example, we recently encountered (10) a major stumbling block in the study of the directed evolution of Kemp eliminases. We found that the ability to evaluate the catalytic power of each step in the evolution process is not sufficient for constructing a good catalyst. We have found that, apart from the knowledge of the key catalytic residues in the active site, we also need to figure out what are the other residues that will lead to the correct preorganization of the catalytic residues.

In view of the difficulties of obtaining reliable prediction of the sequence needed for optimal catalysis, we explore here a part of the problem. That is, we try here to computationally mutate residues that are known to contribute to catalysis and then attempt to find mutations that restore the activity. Such a strategy is useful since we know the maximum possible catalysis: probably close to that of the wild-type (WT) enzyme. Thus, we should be able to assess the effectiveness of some crucial steps in a given computational design approach. As a model system, we take the enzyme haloalkane dehalogenase DhlA, which catalyzes the conversion of toxic haloalkanes to alcohols (11). DhlA from bacterium Xanthobacter autotrophicus GJ10 converts 1,2-dichloroethane (DCE) to chloroethanol via a series of steps that involve an S_N2 reaction, hydrolysis, isomerization, and a Cl⁻ ion departure (12). The S_N2 step involves the attack of the nucleophilic D124 on DCE, and the formation of an ester intermediate, which subsequently undergoes hydrolysis and leads to the formation of an alcohol (Fig. 1). The final step involves the departure of Cl⁻ ion from the active site, which is believed to be preceded by an isomerization.

Fig. 1.

The S_N2 step and the hydrolysis steps in the haloalkane dehalogenase DhlA catalyzed conversion of DCE to chloroethanol and a Cl⁻ ion.

The catalytic triad, which is commonly found in α/β-hydrolases, is composed of D124, H289, and D260. Other residues, that have been proven important using mutation studies, include W125, W175, F172, and V226 as shown in Fig. 2A. It has been found, using both experimental and computational studies, that W125 and W175 help in stabilizing the departing Cl⁻ ion by forming H bonds, while F172 has been shown to interact with the DCE substrate. V226 does not interact with the substrate directly, although it forms van der Waals interactions with W125 and F172. The mutants V226A (13) and F172W (14) are interesting, as they lead to a decrease in the rate of the S_N2 step but to an increase in the rate of the Cl⁻ ion release. The hydrolysis step becomes the rate-limiting step in the V226A, F172W, and W175Y mutants. Apart from these, other residues that line the active site cavity include E56, F128, F164, F222, L262, and L263. The backbone NH group of W125 and E56 form H bonds with the oxygen of the carboxylate of D124. These two amide groups form an oxyanion hole, which is similar to that in other hydrolases.

Fig. 2.

(A) The active site of DhlA with the substrate DCE and the residues that have been proven to be important, using both experiments and computations. (B) Residues lining the active site that have been studied in the current study. The dashed lines show the important H-bonding interactions.

The current design study used the X-ray structure of DhlA [Protein Data Bank (PDB) ID code 2DHC (12)] as a starting point for the EVB simulations. We started by reproducing the observed effects of single mutations and then explored the effort needed for computer-aided restoration of the WT activity after computational mutations of key catalytic residues. This was followed by experimental determination of the effects of the predicted mutations on the individual catalytic steps, with focus on the rate of the S_N2 reaction step. Our computational catalytic restoration is confirmed in one test case, while another case remains inconclusive.

Results and Discussion

Computational Studies.

We started by using the EVB approach to calculate the activation free energy of the S_N2 step in the WT enzyme and several known mutants. The excellent agreement between the calculated and experimental values (Fig. 3 and Table 1) encouraged us to try to predict mutants that would reduce the catalytic activity and then to look for other mutants that would enhance the catalytic activity of the enzyme.

Fig. 3.

Comparison of observed and calculated activation free energies (kilocalories per mole). The error in estimating the experimental rate constants is around 10 to 20%, which would correspond to an error of ∼0.1 kcal/mol in the free energy. The assigned error for the reference water reaction is discussed in the caption of Table 1.

Table 1.

Calculated and observed activation free energies (in kilocalories per mole) for different mutants with DCE as substrate

System	ΔG‡2,obs	ΔG‡2,cal
Water (cage)	23.6	25.4*
WT	15.3†	14.5
W125F	17.6§	16.7
F172Y	17.3§	15.7
F172W	16.8†	17.3
W175F	18.3¶	17.9
W175Y	18.3§	18.2
V226A	16.0†	14.0

^*In contrast to the regular EVB procedure, we did not insist on calibrating the water reaction on the observed value, since we are more interested in the effects of mutations. The value for water (cage) is taken from ref. 28.

^†Based on k₂; values for WT, F172W, and V226A are taken from refs. 14 and 13.

^§Based on k_cat; values for W125F, F172Y, and W175Y are taken from refs. 29, 14, and 30, respectively.

^¶Based on specific activity of the W175Y mutant (30).

Before addressing the above challenge, we explored the role of the E56 residue and its ionization state. This residue forms a part of the oxyanion hole, and its backbone NH forms an H bond with the D124 nucleophile, as shown in Fig. 2B. Thus, one might assume that the presence of E56 is crucial for the dehalogenase activity. The pK_a of E56 was found to be 9.58, by using the Protein Dipole Langevin Dipole method within its semimacroscopic LRA (15). Even the increase of the consistent protein dielectric from 4 to 6 kept the pK_a above 7. This suggests that it should be protonated during the reaction. In fact, if E56 is assumed to be ionized, the activation free energy becomes ∼3 kcal/mol higher than when it is unionized. The E56Q mutation led to only a 0.5 kcal/mol increase in the activation free energy relative to that of the WT (where E56 is in the unionized form). Thus, it is very likely that E56 is not ionized and offers an attractive target for our mutational study, which is explored below. Calculated pK_a using the H++ web server was again found to be around 7.

Another interesting residue is F128, which is replaced by Ala in the LinB and DhaA enzymes (16, 17), and it has been postulated that the presence of this residue enables the catalysis of DCE, which is otherwise not a good substrate for the other two enzymes (18). It presumably does so by rendering compactness to the active site. Thus, it would be interesting to see the effect of mutating phenylalanine to alanine in the current system as well. In the mutant F128A, the active site cavity might enlarge and can help in the catalysis of larger and bulkier haloalkanes. Additionally, residues F164 and F222 were considered important in previous studies (19). We also found it interesting to explore the mutations of A149 and A227 to charged residues (based on calculating the electrostatic contribution to catalysis of mutants of these residues). The results of the computationally tested mutants that were inspired by the above consideration are given in Table 2. Some of the studied mutants led to a significant reduction in catalysis and thus could serve as candidates for the second step of our study, i.e., experimental verification.

Table 2.

Activation free energies (kilocalories per mole) calculated for different mutants with DCE as substrate

System	ΔG‡2,cal
WT (E56 ionized)	18.2
WT (E56 unionized)	14.5
E56Q	15.0
A149D	13.0
A227D	15.4
F128A	14.4
F164A	12.9
F222A	15.0
W125F/V226N	15.9/21.9*
W125F/V226Q	13.9
W175Y/V226N	21.8
W175Y/V226T	17.9
W175Y/E56N	15.8
W175Y/A149D	18.8
1BEE.pdb (W175Y mutant)	18.2 (18.3)†
1BEE.pdb+Y175W (conf1)§	18.3
1BEE.pdb+Y175W (conf2)	14.1

^*EVB calculations starting from different initial geometries gave different results. The lower activation energy is obtained for cases when the NH₂ group of 226Q mutant forms an H bond with the departing Cl⁻ ion.

^†The experimental activation free energy is given in parentheses.

^§A back-mutation of Y to W, where 1BEE.pdb serves as the starting point for the simulation of the W175Y mutant.

In looking for a way to restore the activity of the W125F and W175F/Y mutants (Table 1), we noted that the stabilization offered by the tryptophan residues to the departing Cl⁻ ion is lost in these mutants (resulting in an increase in the activation free energy). We therefore decided to mutate an additional residue that can stabilize the Cl⁻ ion. Reasonable candidates were V226 and E56 that were found to be at a suitable position to interact with the Cl⁻ ion (Fig. 4). Thus, these residues were replaced with N/Q, where the NH₂ side chain can form H bonds with the Cl⁻ ion.

Fig. 4.

Attempt to restore the catalytic activity of the W175Y and W125F mutants. The mutated residues are highlighted in blue. Distances are given in angstroms.

In deciding which mutations to explore, we propagate molecular dynamics (MD) trajectories with different mutational options. Our analysis of the trajectories of the W175Y/V226Q mutant reveals that, although the NH₂ group of the Q226 side chain interacts with the Cl⁻ ion, the existing H bond between W125 and the Cl⁻ ion is lost, thereby resulting in an increase in the activation free energy (Fig. 4). In the W175Y/E56N mutant, the NH₂ group of N56 forms H bonds with the OH group of Y175, and thus should be useful for lowering the activation free energy. It should also be noted that, in the enzymes LinB and DhaA, the role of W175 is played by asparagine residue. Thus, we explored the effect of the E56N mutation in DhlA, to see whether it can play the stabilizing role offered by W175. The EVB calculations of the double mutants, W125F/V226N and W125F/V226Q, were carried out using different starting structures. For the W125F/V226N mutant, a total of seven profiles starting from seven different trajectories were studied. Out of these seven simulations, four showed a decrease in the activation free energy with respect to the W175Y mutant, whereas the others showed an increase in the activation free energy. Further analysis revealed that, for the cases where the H bond between the mutated N226 and Cl⁻ ion is maintained, a decrease in activation free energy is obtained (15.9 kcal/mol). The W125F/V226Q mutant also showed a decrease in the activation free energy (13.9 kcal/mol) compared with the W125F mutant (16.7 kcal/mol) (Fig. 5).

Fig. 5.

Calculated activation free energies (kilocalories per mole) for different mutants in the restoration cycle. The observed values are provided in parentheses. Distances are given in angstroms.

Experimental Studies.

Based on the above computational design, we have constructed and characterized experimentally four mutants: E56Q, F164A, W175Y/E56N, and W125F/V226Q. The first step involved the construction of these variants followed by CD spectroscopy, specific activity measurements, and transient kinetic analysis. The specific activity was evaluated for both DCE and 1,2-dibromoethane (DBE).

All mutations were successfully introduced into the dhlA gene. The correct sequence was confirmed by sequencing of both strands. Variants E56Q, F164A, W175Y/E56N, and W125F/V226Q were expressed in Escherichia coli BL21(DE3) and purified to homogeneity using the metalloaffinity chromatography. Expression, purity, and size of purified proteins were checked by SDS/PAGE. Purification yields of E56Q, F164A, and W175Y/E56N mutants were ∼35 mg⋅L⁻¹ to 60 mg⋅L⁻¹ of culture. The W125/V226 double mutant was purified with a significantly lower yield, 5 mg⋅L⁻¹ of culture, and SDS/PAGE showed that most of the protein remained in the insoluble phase after the cell lysis (SI Appendix, Fig. S2). Proper folding and secondary structure of the newly constructed variants were verified by far-UV CD spectroscopy (SI Appendix). Similar to DhlA WT, the mutant enzymes exhibited CD spectra with one positive peak at about 195 nm and two negative maxima at about 208 nm to 210 nm and at 221 nm, characteristic for alpha-helical content. W175Y/E56N retains a very similar structure to the WT enzyme, while, for the remaining variants, small changes in intensity and shape of the spectra in comparison with the WT are visible. Observed variations reflect a partial loss of alpha-helical structure caused by introduced mutations, implying slight conformational changes of the enzymes. Information obtained using SDS/PAGE and far-UV CD spectroscopy for the W125/V226 variant suggests that the protein is not properly folded and has limited solubility. Therefore, this variant was not studied by the pre-steady-state kinetics.

The rapid mixing of DhlA WT and its variants with DCE was associated with kinetic quenching of fluorescence intensity of endogenous tryptophan (Fig. 6). The initial kinetic phase of fluorescence traces was fitted to a single exponential to provide k_obs and amplitudes for each substrate concentration (Fig. 7). Fitting the dependence of observed rate on DCE concentration by Eq. 1 provided estimates for rate constants (Table 3) of corresponding minimal reaction pathway for DhlA WT and W175Y/E56N (Scheme 1). The dependence of amplitude on the concentration of DCE was used to calculate an estimate of apparent binding constant K_s,app for E56Q (Eq. 2). By using K_s,app as a fixed parameter, the estimates for kinetic parameters were obtained for E56Q by fitting the dependence of observed rate on DCE concentration by using Eq. 1.

Fig. 6.

Fluorescent traces recorded by multiple-turnover stopped-flow analysis upon rapid mixing of (A) 6.8 μM DhlA WT, (B) 6.8 μM E56Q, (C) 6.2 μM F164A, and (D) 6.7 μM W175Y/E56N with different DCE concentrations. Each trace shown is the average of 5 to 10 individual experiments.

Fig. 7.

Dependence of the (A) observed rate and (B) amplitude on the concentration of DCE for reactions with DhlA WT (●), E56Q (○), and W175Y/E56N (☐).

Table 3.

Estimates of kinetic constants for the conversion of DCE by DhlA WT and its mutants

Constants	DhlA WT	E56Q	F164A	W175Y/E56N
Ks, mM	3.7 ± 0.5	5.4 ± 1.2*	n.d.	30 ± 12
k2, s−1	201 ± 9	16 ± 9	n.d.	25 ± 10
kx, s−1	23 ± 3	26 ± 4	n.d.	10 ± 2
Km, mM	0.5 ± 0.1	1.2 ± 0.1	5.2 ± 0.9	1.3 ± 0.1
kcat, s−1	2.2 ± 0.1	1.1 ± 0.1	0.05 ± 0.01	0.31 ± 0.01

^*K_s,app calculated based on Eq. 2; n.d., not detected.

Scheme 1.

Kinetic fluorescence quenching has not been detected for F164A. This result indicates that the S_N2 reaction became the rate-limiting step for the conversion of DCE by this variant, and the reaction does not provide any observable accumulation of alkyl-enzyme intermediate. Since the first chemical step determines the steady-state turnover, the steady-state equilibrium constant K_m closely indicates substrate binding equilibrium K_s. The 5.2 ± 0.9 mM value for the equilibrium binding of the DCE to F164A is similar to the values estimated for WT enzyme. This result suggests that the binding affinity of DCE has not been changed for the F164A variant.

The comparison between the computationally predicted and experimental activation free energies is shown in Table 4. While, for E56Q and W175Y/E56N, the results agree with the computations, F164A shows a variation. E56Q mutation shows that the E56 residue is not very important, and its role can be played by other residues as well. For W175Y/E56N, which includes two mutations, we were able to restore the catalytic activity. That is, although, the activity is lower than that of the WT (15.6 kcal/mol for W175Y/E56N and 14.4 kcal/mol for the WT), it shows an improvement over the W175Y mutant (18.3 kcal/mol). These results are encouraging and may provide a guide for the design of dehalogenases. The probable reason behind the low activity of F164A might be a change in other steps of the reaction. In this respect, we note that our EVB calculations only reflect the energetics of the S_N2 step and that there are no available values for the separate rate constants. F164A mutation might be affecting the hydrolysis or Cl⁻ release step, resulting in a low k_cat. For the W125F/V226Q mutant, the mutations might cause destabilization of the enzyme. In fact, Rossetta (20) estimated an 8 kcal/mol destabilization in this double mutant in comparison with the WT enzyme (SI Appendix). Although this result might be a significant overestimate, the fact that no activity is detected suggests that the active site region changes significantly. Interestingly, mutants E56Q and W175Y/E56Q show stabilization compared with the WT, whereas F164A and W125F/V226Q show destabilization (SI Appendix). Of course, we can try to use more reliable and time-consuming ways to assess the change in stability upon mutations (e.g., free energy perturbation methods), but such studies are outside of the scope of the present work.

Table 4.

Calculated and observed activation free energies (kilocalories per mole)

System	ΔG‡2,cal	ΔG‡2,obs, ΔG‡obs
DhlA WT	14.5	14.4*
E56Q	15.0	15.9*
F164A	12.9	19.4†
W175Y/E56N	15.8	15.6*
W175Y	18.2	18.3†
W125F/V226Q	13.9	n.a.§

^*The observed value is taken from k₂. Experiments are done at 37 °C in 100 mM glycine buffer at pH 8.6. Please note that the EVB calculations are done at the standard temperature of 300 K.

^†The observed value is calculated from k_cat of the whole reaction. For W175Y mutant, the observed value is taken from ref. 30.

^§No activity.

The specific activities of DhlA WT and its variants toward DCE and DBE were assayed at 37 °C (Table 5). For both substrates, W125F/V226Q does not show any activity, while E56Q shows an improved activity with DCE. Interestingly, all mutants show enhanced activity with DBE as the substrate. The difference in the effect of mutations on two closely related substrates is remarkable. For DBE, the k_cat of the S_N2 step, calculated using EVB simulations, remains largely unaffected in comparison with the WT. Thus, the enhanced activity of the mutants might be due to change in the hydrolysis or Cl⁻ ion release. The activities of E56Q and W175Y/E56N toward DBE are significantly improved over the WT.

Table 5.

Specific activities of studied mutants toward DCE and DBE

Enzyme	Specific activity, μmol⋅min−1⋅mg−1
	DCE	DBE
DhlA WT	2.0 ± 0.2*	2.9 ± 0.1
E56Q	2.5 ± 0.1	5.1 ± 0.3
F164A	0.022 ± 0.002	3.1 ± 0.1
W175Y/E56N	0.6 ± 0.2	4.2 ± 0.2
W125F/V226Q	n.a.	n.a.

Experiments were done at 37 °C in 100 mM glycine buffer at pH 8.6. Concentrations of substrates were 12.4 mM and 11.3 mM for DCE and DBE, respectively. Enzyme concentrations varied from 52 nM to 282 nM, depending on the catalytic activity; n.a., no activity detected.

^*Values are given with SDs calculated from three independent runs.

Conclusions

This work explored the issue of enzyme design, focusing on one of the key difficulties in validating the successes of the design process. That is, in trying to design an effective enzyme, it is not clear what the limit of maximum possible improvement is. Thus, we “modified” the challenge and address the problem of taking a known enzyme, reducing the catalytic residues, and trying to restore catalysis. In this way, we know what the likely maximum possible catalytic effect is, and have a relatively well-defined problem. In fact, even if there is a possible better enzyme than the WT enzyme, reaching the WT activation free energy is a well-defined challenge that can provide a powerful guide for the successes of enzyme design strategies.

In the present case, we chose DhlA, noting several specific challenges. The reaction catalyzed by DhlA is multistep, and therefore a single mutation can change the identity of the rate-limiting step. Thus, while a new mutant might lower the free energy for the S_N2 step, it might have a negative effect on other steps. For instance, the V226A mutation (13) decreases the activation free energy for the Cl⁻ release while simultaneously increasing the free energy for the S_N2 step, thereby resulting in a very small increase in the overall k_cat (3.3 s⁻¹ for WT versus 3.8 s⁻¹ for V226A mutant).

The success reported in Fig. 3 indicates that our approach allows one to determine the catalytic power of a given mutant whose structure is approximately known. However, as we found recently (10), the challenge is to design an optimal enzyme, where the active site groups are preorganized in the correct way by other residues. The agreement between the computationally predicted activation energies and experiments for mutants E56Q and W175Y/E56N seems remarkable. Additionally, the higher specific activities with DBE as the substrate are noteworthy. Thus, it is encouraging to see that we obtained some success in active site restoration in the current study. Of course, this idea should be extended in the future to more than two mutations.

Methods

Computational Methods.

The starting structure for the EVB calculations (21–23) was taken from the X-ray crystal structure of DhlA [PDB ID 2DHC (12)]. In this structure, the substrate is bound to the protein, which circumvents the docking approach. Additionally, previous computational studies involving dehalogenase have also considered this PDB structure for the simulations. The EVB calculations were carried out using the MOLARIS package with the ENZYMIX force field. The ESP (electrostatic potential) charges for the two diabatic states that represent the reactant and product were calculated using the B3LYP level of theory at the 6-311+G** basis set using Gaussian software (24). The EVB region consists of the acetate group of Asp124 and DCE. The FEP/US (free energy perturbation/umbrella sampling) approach was used to calculate the activation free energies. The center of the reactive species was taken as the center of the system which was immersed in a water sphere of 18 Å and solvated using the surface constrained all-atom solvent model (25). The long-range effects were treated using the local reaction field method (26). The system was first relaxed for at least 100 ps using a step size of 1 fs, and then three different starting structures were generated. For the FEP mapping, the simulation was divided into 51 frames, and each frame was simulated for 30 ps with a step size of 1 fs, resulting in a total simulation time of over 1.5 ns. The specific EVB parameters used in the current calculations are given in SI Appendix.

Experimental Methods.

Stopped-flow analysis.

Multiple-turnover stopped-flow fluorescence technique was used to study the DCE conversion catalyzed by DhlA WT, E56Q, F164A, and W175Y/E56N. The experiments were performed by using an SFM-300 stopped-flow instrument combined with an MOS-200 spectrometer (BioLogic). Fluorescence emission from W residues was observed through a 320-nm cutoff filter upon excitation at 295 nm. All reactions were performed at 37 °C in 100 mM glycine buffer and pH 8.6. The relaxations of active site Trp fluorescence upon starting the reaction were recorded stepwise at different substrate concentrations.

Data analysis.

The fluorescence traces were fitted to a single or double exponential using KinTek Explorer (KinTek Corporation). The dependence of observed rate and amplitude on DCE concentration was fitted by Eqs. 1 and 2, respectively, by nonlinear regression using Origin 8.0 (OriginLab corporation).

$$k_{obs}=\frac{k_2.\left[S\right]}{\left[S\right]+K_S}+k_x$$ [1]

$$A=\frac{\left[S\right].A_{lim}}{K_{S,app}+\left[S\right]}\hspace{0.17em}.$$ [2]

The kinetic Eq. 1 was derived for fast initial phase of the reaction from kinetic pathway (Scheme 1) (27).

where S and P are a substrate and a product, respectively, ES is an enzyme−substrate complex, EI is a covalent alkyl-enzyme intermediate, EP is an enzyme-product complex, K_S is an equilibrium dissociation constant for enzyme−substrate complex, and k_i is an individual rate constant of ith step. Further details of the methods are provided in SI Appendix. Analytical procedure has been used for data analysis: (i) The initial part of fluorescence traces was fitted to a single exponential to provide observed rates and amplitudes, (ii) Eq. 1 describing the dependence of observed rate on substrate concentration was derived from minimal reaction pathway (Scheme 1) in simplified form, where k_x represents a net rate constant including contribution of k₃ and k₄, and (iii) fitting the kinetic data (the dependence of observed rate on DCE concentration derived from exponential fitting of fluorescence traces in step i) by Eq. 1 provided estimates for the rate parameters. The fitting of the dependence of amplitude (A) on the concentration of DCE by hyperbolic model Eq. 2, where A_lim is the upper limit for the observed amplitude, was used to calculate an estimate of the apparent equilibrium constant for dissociation of enzyme−substrate complex Ks_,app.