Structural insights into the effect of active-site mutation on the catalytic mechanism of carbonic anhydrase

Enzymes are catalysts of biological processes. Significant insight into their catalytic mechanisms has been obtained by relating site-directed mutagenesis studies to kinetic activity assays. However, revealing the detailed relationship between structural modifications and functional changes remains challenging owing to the lack of information on reaction intermediates and of a systematic way of connecting them to the measured kinetic parameters. Here, a systematic approach to investigate the effect of an active-site-residue mutation on a model enzyme, human carbonic anhydrase II (CA II), is described. Firstly, structural analysis is performed on the crystallographic intermediate states of native CA II and its V143I variant. The structural comparison shows that the binding affinities and configurations of the substrate (CO₂) and product (HCO₃⁻) are altered in the V143I variant and the water network in the water-replenishment pathway is restructured, while the proton-transfer pathway remains mostly unaffected. This structural information is then used to estimate the modifications of the reaction rate constants and the corresponding free-energy profiles of CA II catalysis. Finally, the obtained results are used to reveal the effect of the V143I mutation on the measured kinetic parameters (k_cat and k_cat/K_m) at the atomic level. It is believed that the systematic approach outlined in this study may be used as a template to unravel the structure–function relationships of many other biologically important enzymes.

1. Introduction

Enzymes greatly enhance the catalytic rates of biochemical reactions compared with their uncatalyzed counterparts and are therefore essential to speed up biochemical processes (Jencks, 1987; Fersht, 1999; Frey & Hegeman, 2007). Enzyme active sites provide highly optimized microenvironments for their specific substrates by providing reactive groups such as nucleophiles or acids/bases that stabilize the transition state. Consequently, changes in the active-site residues can have large effects on enzyme activity. However, direct prediction of the impact of a single mutation on the activity of an enzyme remains challenging owing to the lack of precise correlations between the structure of the protein and its function at atomic resolution (Ishida, 2010). In this study, we describe the effect of a single amino-acid variation on a prototypical enzyme, human carbonic anhydrase II (CA II), by correlating its high-resolution reaction-intermediate structures with the measured kinetic parameters. Human carbonic anhydrases are well suited to serve as a model system for our study because their structures and active sites are well defined, and their overall enzymatic mechanism is fairly straightforward and has been studied extensively (Krishnamurthy et al., 2008).

Human carbonic anhydrases catalyze the reversible hydration/dehydration of CO₂/HCO₃⁻ (Davenport, 1984; Christianson & Fierke, 1996; Chegwidden et al., 2013; Frost & McKenna, 2013; Supuran & De Simone, 2015). In the CO₂-hydration direction, the first step of catalysis is the conversion of CO₂ into HCO₃⁻ via the nucleophilic attack of a zinc-bound hydroxide. This reaction is followed by the displacement of the zinc-bound HCO₃⁻ by a water molecule (equation 1, where E stands for the enzyme; Silverman & Lindskog, 1988). The second step involves the transfer of a proton from the zinc-bound water to bulk solvent, regenerating the zinc-bound hydroxide (equation 2, where B stands for a general base: either a water or a proton-shuttling residue).

In CA II, the active-site zinc is located at the base of a 15 Å deep cleft and is tetrahedrally coordinated by three histidines (His94, His96 and His119) and a zinc-bound water (W_Zn) [Fig. 1(a)] (Christianson & Fierke, 1996). The active-site cavity is further subdivided into two distinct faces consisting of hydrophilic and hydrophobic residues. The hydrophilic face (Tyr7, Asn62, His64, Asn67, Thr199 and Thr200) of the active site coordinates the hydrogen-bonded water network (W1, W2, W3a and W3b) that connects the zinc-bound water to His64, the proton-shuttling residue [Fig. 1(b)] (Steiner et al., 1975; Tu et al., 1989; Nair & Christianson, 1991; Fisher et al., 2005, 2010; Fisher, Maupin et al., 2007; Fisher, Tu et al., 2007; Maupin & Voth, 2007; Silverman & McKenna, 2007; Zheng et al., 2008). It is known that the proton-transfer process is the rate-limiting step in CA II catalysis (Silverman & McKenna, 2007).

Figure 1 Structure of V143I CA II. (a) Overall structure of V143I-0atm: V143I CA II with no CO2 pressurization. The active site (red box) is located at a depth of 15 Å from the surface. Note that Ile143 is located at the hydrophobic pocket in the active site. (b) Ordered water network in the hydrophilic region serving as a proton-transfer pathway. (c) Surface rendition of V143I-0atm. The entrance conduit (diameter of 7–10 Å, guided with a yellow dotted line) connects the active site to the bulk solvent outside, forming the replenishment pathway. The electron density of the entrance-conduit waters is contoured at 1.5σ. Hydrophobic amino acids are shaded in red, while hydrophilic amino acids are coloured white.

The hydrophobic face (Val121, Val143, Leu198, Val207 and Trp209) is located adjacent to the zinc-bound hydroxide and is responsible for substrate binding (Liang & Lipscomb, 1990; Domsic & McKenna, 2010). Leu198, Trp209 and Val121 constitute the mouth and sides of the hydrophobic pocket, while Val143 comprises the base of the hydrophobic pocket. A water molecule termed the `deep water' (W_DW) is located at the mouth of this pocket and forms van der Waals contacts with Leu198 and Trp209. W_DW occupies the pre-catalytic association site for substrate and is displaced by one of the O atoms of CO₂ during binding (Domsic et al., 2008). The hydrophobic pocket residues are highly conserved and are known to be critical for CO₂ sequestration, although they do not directly interact with the CO₂ molecule.

Between the hydrophilic and hydrophobic sides of the active site, a cluster of ordered waters has recently been identified located near the active-site entrance, termed the entrance-conduit (EC) waters [Fig. 1(c)] (Kim et al., 2018). This ordered water ensemble connects the active site to the external bulk solvent, creating a pathway where water, substrate and product can interchange and interact with bulk solvent. These EC waters are believed to be involved in water replenishment during catalysis, displacing the zinc-bound bicarbonate and restoring the proton-transfer water network.

In order to elucidate the catalytic details of the active site of CA II, several mutational studies have been performed. Most of these variants have been focused at the zinc ion-binding site (Alexander et al., 1993; Kiefer et al., 1993; Ippolito & Christianson, 1994; Lesburg & Christianson, 1995; Huang et al., 1996; Lesburg et al., 1997), the hydrophilic side (proton-transfer pathway; Behravan et al., 1990; Krebs, Ippolito et al., 1993; Xue et al., 1993; Ippolito et al., 1995; Huang et al., 2002; Tu et al., 2002; Fisher et al., 2005; Zheng et al., 2008; Turkoglu et al., 2012; Mikulski et al., 2013; Aggarwal et al., 2014) and the hydrophobic pocket (CO₂-binding site; Alexander et al., 1991; Fierke et al., 1991; Nair et al., 1991; Krebs, Rana et al., 1993; West et al., 2012; Nair & Christianson, 1993). In the hydrophobic pocket, a series of mutational studies have been performed targeting the Val121, Val143 and Leu198 residues. It was found that CA catalysis is severely compromised (an ∼10⁴–10⁵-fold decrease) when the deep water W_DW is displaced by replacement of the relevant amino acid by one with a larger side chain (for example, replacement of Val143 by Phe or Tyr), leading to a substantial blockage of CO₂ binding. On the other hand, some of the point mutations, such as Val121 to Ala, Val143 to Ile and Leu198 to Glu, do not directly displace W_DW and the CA catalysis is only moderately compromised (a fewfold to a 20-fold decrease). Understanding these moderate effects is most challenging as the overall structures and active sites show little deviation when compared with native CA II. It is expected that delicate perturbations are introduced at the level of intermediate structures during the moderately modified CA catalysis.

In this study, we investigate one of the most challenging cases and describe the subtle effects brought on by a Val143 to Ile (V143I) mutation. As shown in Table 1, the V143I variant shows an approximately tenfold decrease in k_cat/K_m, while k_cat remains almost the same as that for native CA II. Structural analysis was performed by comparing the catalytic intermediate states of native and V143I CA II, which were obtained by cryocooling protein crystals under four different CO₂ pressures [ranging from 0 (no CO₂ pressurization) to 15 atm]. The intermediate states are henceforth referred to as native-0atm (PDB entry 6km3), native-7atm (PDB entry 6km4), native-13atm (PDB entry 6km5) and native-15atm (PDB entry 6km6) and as V143I-0atm (PDB entry 6klz), V143I-7atm (PDB entry 6km0), V143I-13atm (PDB entry 6km1) and V143I-15atm (PDB entry 6km2), respectively. Based upon the structural modifications, we successfully estimated the alterations in the reaction rate constants and the corresponding free-energy profiles in the CA II enzymatic mechanism. This study systematically reveals how a single point mutation influences an enzyme's catalytic pathway at the atomic level, leading to an estimation of the kinetics governing its individual mechanistic steps.

Table 1
Steady-state kinetic parameters for CO₂ hydration by native and V143I CA II

	kcat/Km (µM^−1 s^−1)	kcat (µs^−1)	Km (mM)	k1† (M^−1 s^−1)	k−1† (s^−1)	k2† (s^−1)	k−2† (M^−1 s^−1)	k3† (s^−1)
Native	89 ± 7‡/120§	0.93 ± 0.05‡/1.0§	11 ± 1‡	1.3 × 10^8	1.8 × 10^6	1.7 × 10^7	2.0 × 10^8	1.2 × 10^6
V143I	11 ± 1‡/9.3 ± 0.3§	1.0 ± 0.2‡/0.7 ± 0.1§	100 ± 24‡	—	—	—	—	—

†From Behravan et al. (1990).
‡From Fierke et al. (1991).
§From West et al. (2012).

2. Results

Our X-ray studies (methods are reported in the supporting information) revealed that the overall protein backbones (tertiary structures) of the native and V143I CA II structures were very similar, with C^α–C^α r.m.s.d. values of less than 0.14 Å (Supplementary Tables S1 and S2). However, careful structural analysis successfully established subtle but clear changes in the active site (CO₂-binding site, proton-transfer pathway and water-replenishment pathway; EC waters). The key bound water molecules in native and V143I CA II are listed in Supplementary Tables S3 and S4.

2.1. CO₂-binding site around the zinc ion

Fig. 2 shows the CO₂-binding site and crucial water molecules (W_Zn/W_DW/W_I/W_I′/W1) in the vicinity of the zinc ion. In native CA II [Figs. 2(a)–2(d)], the water molecules (W_Zn/W_DW/W1) around the zinc ion are initially well ordered at 0 atm CO₂ pressure. At higher CO₂ pressures of 7–15 atm, electron density for the CO₂ molecule becomes apparent, displacing the deep water (W_DW). Concurrently, two intermediate waters W_I and W_I′ emerge near Thr200, while W1 disappears at higher CO₂ pressures. The distance between W_I and W2 is ∼4.7 Å, suggesting that the hydrogen-bonded water network that facilitates proton transfer is disrupted when the CO₂-binding site is fully occupied.

Figure 2 CO2/HCO3^−-binding site of native and V143I CA II. The intermediate waters (WI and WI′) are coloured steel blue for clarity. The electron density (2Fo − Fc) is contoured at 1.5σ where not indicated otherwise. (a)–(d) Native CA II structures. (e)–(h) V143I CA II structures. WI′ at 7, 13 and 15 atm is contoured at 1.25σ and WI at 0 atm is contoured at 1.0σ. Partial occupancies of HCO3^− and WDW were determined in V143I-0atm and V143I-7atm, and partial occupancies of HCO3^− and CO2 were determined at the higher CO2 pressures (see the supporting information). The inset (red box) in V143I-0atm shows the difference map (Fo − Fc contoured at 3.0σ; green) when the HCO3^− molecule is not included in the structure refinement.

On the other hand, the active site of V143I CA II shows noteworthy modifications. The most striking difference is that HCO₃⁻ is stabilized and is observable at 0 atm CO₂ pressure with an estimated occupancy of ∼20% [Fig. 2(e)]. In the absence of experimentally introduced CO₂, it is likely that the captured HCO₃⁻ is converted from CO₂ absorbed into the crystal from ambient air. As the CO₂ pressure increases, the HCO₃⁻ occupancy increases to 54% at 13 atm and subsequently decreases slightly to 48% at 15 atm, with increased CO₂ occupancy [Figs. 2(f)–2(h)]. It is likely that the observed decrease in the HCO₃⁻ occupancy at 15 atm is owing to steric hindrance from the bound CO₂ molecule. When superimposed with the previously reported coordinates of HCO₃⁻ bound to native CA II (PDB entry 2vvb; Sjöblom et al., 2009), the HCO₃⁻ position observed in V143I CA II shows noticeable deviations. The HCO₃⁻ molecule is tilted by 35° with respect to the plane containing W_Zn, CO₂ and HCO₃⁻ in native CA II (Supplementary Fig. S1). In addition, the central C atoms of the two superimposed HCO₃⁻ molecules in native and V143I CA II are separated by 0.5 Å.

Unlike the HCO₃⁻ molecule, the CO₂ molecule is less stable in V143I CA II. For example, CO₂ shows almost full occupancy at 7 atm in native CA II, while no CO₂ is visible at 7 atm in V143I CA II, which instead shows the appearance of W_DW [Figs. 2(b) and 2(f)]. The CO₂ molecule appears at higher pressures (13 and 15 atm) with a decreased occupancy of ∼50% [Figs. 2(g) and 2(h)]. The bound CO₂ is tilted by ∼6° and is situated closer to the zinc ion by 0.34 Å compared with that in native CA II (Supplementary Fig. S1). The distance between the end carbon (C^δ1) of Ile143 and the CO₂ molecule is only 3.0–3.2 Å, and this steric disruption seems to affect the critical interactions between the CO₂ molecule and the hydrophobic pocket, thereby destabilizing it in the active site. It is worth noting that in contrast to native CA II, the bound CO₂ molecule in V143I CA II is distorted from the plane defined by the bound HCO₃⁻ molecule, and this seems to be detrimental to the efficient conversion of CO₂ to HCO₃⁻.

Finally, the two intermediate waters W_I and W_I′ show different behaviour in V143I CA II. The intermediate water W_I is visible even in 0 atm V143I CA II but is not present in 0 atm native CA II [Figs. 2(a) and 2(e)]. However, it is observed that the electron densities of the two intermediate waters were less defined than in native CA II [Figs. 2(f)–2(h)]. These `weaker' intermediate waters were accompanied by the presence of W1 at all pressures (0–15 atm). It is likely that these weak intermediate waters are related to the perturbed structures and dynamical motions of the EC waters, as explained later.

2.2. Proton-transfer pathway

Fig. 3 shows the proton-transfer pathway including the water network (W1/W2/W3a/W3b) and His64. In native CA II, the water network is initially well ordered at 0 atm CO₂ pressure [Fig. 3(a)]. As the CO₂ pressure increases, W1 disappears and intermediate waters (W_I and W_I′) emerge instead [Figs. 3(b)–3(d)]. The W2 water, which transfers a proton from W1 to His64, shows an alternative position denoted W2′. Considering the steric hindrance between His64_in and W2′, it seems that the presence of W2′ pushes His64 towards the `out' conformation (away from the water network). Indeed, His64 shows a net movement from the `in' to the `out' conformation as W2′ becomes prominent at higher CO₂ pressures. W3a shows little change, but W3b shows an alternative water position, W3b′, and is found to interact with one of the entrance waters W_EC1 (and its alternative position W′_EC1).

Figure 3 Proton-transfer pathway including the water network and His64. The entrance-conduit waters (WEC) are coloured cyan and the intermediate waters (WI and WI′) are coloured steel blue for clarity. The electron density (2Fo − Fc) is contoured at 1.5σ where not indicated otherwise. The major hydrogen bonds between water molecules are represented by dashed lines, while alternative hydrogen bonds that are mutually exclusive are represented by dotted lines. (a)–(d) Native CA II structures. (e)–(h) V143I CA II structures. WI′ at 7, 13 and 15 atm and W′EC1 at 15 and 13 atm are contoured at 1.25σ, and WI at 0 atm is contoured at 1.0σ. The inset (red box) in V143I-0atm shows the difference map (Fo − Fc contoured at 3.0σ; green) when the HCO3^− molecule is not included in the structure refinement.

Similarly, in V143I CA II W2 shows the same alternative position W2′, and His64 shows the same `in' to `out' flip, with similar occupancies as observed in native CA II with increasing CO₂ pressure [Figs. 3(e)–3(h)]. W3b and W_EC1 also show the same alternative positions, although their electron densities are slightly weaker. As the distance between W2 and the N atom (N^δ1) of His64_in is relatively long (3.3 Å), efficient proton transfer seems to depend on the dynamical motions of W2/W2′ and His64_in/His64_out. These motions are quite similar in native and V143I CA II and therefore proton transfer is not significantly impacted in the variant.

2.3. Water-replenishment pathway

Fig. 4 shows the water-replenishment pathway consisting of the ordered EC waters (W_EC1/W_EC2/W_EC3/W_EC4/W_EC5). In native CA II, the five W_EC waters are well ordered at 0 atm CO₂ pressure [Fig. 4(a)]. As the CO₂ pressure increases, W_EC1 shows an alternative position W′_EC1, and W_EC2 shifts to an alternative position W′_EC2 [Figs. 4(b)–4(d)]. These dynamical motions of W_EC1 and W_EC2 are accompanied by the emergence of the intermediate waters W_I and W_I′. The two intermediate waters are located deep within the entrance conduit near the active site and are transiently stabilized via hydrogen bonding to several W_EC waters (W_EC2, W_EC3 and W_EC5 and their alternative positions). The short distance (2.2 Å) between W_I and W_I′ suggests that W_I′ can rapidly shift to the W_I position as W_I refills the vacant water positions (W1/W_Zn/W_DW) during catalysis. Previous studies suggest that the intermediate waters (W_I and W_I′) play a critical role in the rapid replenishment of the active-site water network during catalysis and therefore could influence the overall catalytic rate (Kim et al., 2018).

Figure 4 The water-replenishment pathway including entrance-conduit waters (cyan) and intermediate waters (steel blue). The electron density (2Fo − Fc) is contoured at 1.5σ where not indicated otherwise. (a)–(d) Native CA II structures. WEC3 at 7 and 13 atm and WEC4 at 15 atm are contoured at 1.25σ, and WEC3 at 15 atm is contoured at 1.0σ. (e)–(h) V143I CA II structures. WI′ at 7, 13 and 15 atm and W′EC1 at 15 and 13 atm are contoured at 1.25σ and WI at 0 atm is contoured at 1.0σ. Compared with native CA II, V143I CA II shows significantly perturbed positions for WEC2.

Among the five W_EC waters in V143I CA II, W_EC2 is located close to the mutated residue Ile143. Indeed, the W_EC1 to W_EC4 waters show similar structures and dynamical motions as in native CA II, but W_EC2 shows a significantly distinct behaviour. Initially, at 0 atm CO₂ pressure, the W_EC2 water shows multiple alternative positions (W′′_EC2, W′′′_EC2 and W′′′′_EC2) [Fig. 4(e)]. As the CO₂ pressure increases, these alternative positions disappear and both the W_EC2 and W′_EC2 waters are observed instead [Figs. 4(f)–4(h)]. Compared with native CA II, W′′_EC2, W′′′_EC2 and W′′′′_EC2 are new alternative positions that are observed only at 0 atm CO₂ pressure in V143I CA II. Along with the perturbed dynamical motions of the W_EC2 water, much weakened electron densities of the intermediate waters W_I and W_I′ are observed. It should be noted that among the five EC waters, W_EC2 is unique in that it interacts with all three of the key waters, W1, W_I and W_I′. Therefore, the fact that the structures and dynamical motions of the W_EC2 waters are significantly perturbed in V143I CA II is likely to account for the stabilization of W1 but the destabilization of the two intermediate waters.

Another interesting aspect of W_EC2 is that its alternative position W′′′′_EC2 is situated close to the bound HCO₃⁻. The distances between W′′′′_EC2 and the closest O atom and the C atom of HCO₃⁻ are 1.4 and 2.5 Å, respectively (Supplementary Table S5). Since W′′′′_EC2 is too close to the bound HCO₃⁻, W′′′′_EC2 and HCO₃⁻ cannot coexist in tandem. Indeed, W′′′′_EC2 is only visible in V143I CA II at 0 atm, when the HCO₃⁻ occupancy is low, and disappears as the HCO₃⁻ occupancy increases at higher CO₂ pressures [Figs. 4(e)–4(h)]. It seems that the relationship between W′′′′_EC2 and HCO₃⁻ is analogous to the relationship between W_DW and CO₂. In native CA II, the hydrophobic cavity produces an electrostatic environment in which the deep water (W_DW) can be locally stabilized around the zinc ion and then replaced with one of the O atoms of CO₂ upon CO₂ binding. In V143I CA II, the altered hydrophobic cavity owing to the V143I mutation produces a slightly different electrostatic environment in which an additional water position (W′′′′_EC2) can be locally stabilized around the zinc ion and subsequently replaced with one of the O atoms in HCO₃⁻ during CA II catalysis. The release of the W′′′′_EC2 molecule upon HCO₃⁻ binding seems to reduce the entropic cost of the process, analogous to the release of W_DW upon CO₂ binding in native CA II. Thus, it is likely that the altered multiple conformations of W_EC2 allow HCO₃⁻ to bind more easily and firmly in a tilted configuration at the active site.

3. Discussion

In this study, we have successfully identified the `fine' structural changes in the CA II intermediates induced by a single-residue mutation at the active site. The V143I mutation in CA II produces steric hindrance and induces subtle changes in the electrostatic environment of the active site. The resulting effects on the CA II intermediates can be summarized as follows: (i) the dynamical motions and the allowed configurations of CO₂ are slightly restricted and the binding affinity of HCO₃⁻ is increased with a distorted configuration and (ii) the EC water network in the water-replenishment pathway is restructured, while (iii) the proton-transfer dynamics are mostly unaffected. These detailed structural insights can now be used to assess the modifications in the reaction rate constants (k₁, k₋₁, k₂ and k₃) and the corresponding free-energy profiles during the CO₂-hydration reaction of CA II.

Firstly, the V143I mutation restricts the configurational freedom of the CO₂ molecule within the hydrophobic pocket of CA II. Previous mutational studies on hydrophobic pocket residues (Val121 and Val143) suggest that the hydrophobic pocket of native CA II is involved in `ushering' the CO₂ molecule to the zinc hydroxide in the active site, but does not directly interact with the CO₂ molecule to hold it in a specific orientation. Therefore, it is most likely that the CO₂ molecule in aqueous solution is guided to the hydrophobic pocket of CA II but retains some degrees of freedom with regard to the acceptable configurations (positions and orientations) around the zinc hydroxide that eventually facilitate its rapid conversion into HCO₃⁻. In the V143I variant, although the hydrophobicity of the active-site pocket is increased, the added methyl group appears to sterically restrict the number of favourable configurations and the dynamical motions accessible to the CO₂ molecule within the cavity. This estimation is supported by the crystallographic observation that the CO₂ molecule is distorted towards the zinc ion, tilted by ∼6° and is destabilized with lower occupancies in the V143I variant. Consequently, interconversion from CO₂ to HCO₃⁻ becomes less efficient, leading to a reduced k₁ (k₁^V143I < k₁^native). The lower k₁ value also implies an enhanced activation-energy barrier for the step [Arrhenius relationship: k₁(T) = Aexp(−E₁/RT), where A is a pre-exponential constant, R is the molar gas constant, T is the absolute temperature and E₁ is the activation energy] (Fig. 5).

Figure 5 Estimated free-energy profiles for the CO2-hydration reaction catalyzed by CA II. The energy states of native CA II (black) are from a previous study (Behravan et al., 1990). The energy states of V143I CA II (red) are qualitatively estimated with respect to the native form by considering the structural information and the variations in the reaction rate constants. Note that the energy level of [EZnH2O + HCO3^−] in the V143I variant is assumed to be the same as that in native CA II. The depicted energy gaps are not to scale.

Secondly, the V143I mutation induces a slightly different electrostatic environment in the hydrophobic cavity, thereby altering the location and dynamics of the W_EC2 water. It seems that one of these altered W_EC2 waters (W′′′′_EC2) increases the binding affinity of the HCO₃⁻ molecule in the active site. This stronger binding of HCO₃⁻ suggests that the free energy of the enzyme–product (EZnHCO₃⁻) complex is lowered in the V143I variant (Fig. 5). In conjunction with the larger activation energy for the k₁ reaction, it can be deduced that the activation energy for the reverse reaction k₋₁ is increased even further, leading to a reduced k₋₁ value (k₋₁^V143I < k₋₁^native). On the other hand, the alterations of the W_EC2 water in the V143I variant make the intermediate waters (W_I and W_I′) slightly less stable, therefore possibly slowing down the replenishment of the active-site water network and HCO₃⁻ dissociation. This results in a reduced k₂ value (k₂^V143I < k₂^native).

Thirdly, the V143I mutation seems to have little effect on the kinetics of the proton-transfer reaction. It is observed that W1 is more stabilized in the V143I variant intermediates. It should be noted that the intermolecular proton transfer can occur via the fully established water network W_Zn→W1→W2→His64. This implies that if a mutation induces the destabilization of W1, proton transfer could be significantly perturbed. However, stabilization of W1 as in the V143I variant does not necessarily suggest a faster proton-transfer process. Rather, it is the dynamical motions of W2 and His64 that have a more critical influence on the proton-transfer rate. Our results suggest that both W2 and His64 show very similar dynamical motions. Taken together, it seems that the overall proton-transfer rate k₃ is not significantly altered in the V143I mutant (k₃^V143I ≃ k₃^native).

The interplay between the modified reaction rate constants, as discussed above, now allows us to determine the effect of the V143I mutation on the measured kinetic parameters (k_cat and k_cat/K_m; Nair et al., 1991; Krebs, Ippolito et al., 1993). The steady-state kinetic parameters for the CO₂-hydration reaction are listed in Table 1. The k_cat value shows little change, but the second-order rate constant k_cat/K_m shows an approximately tenfold decrease in the V143I variant. The parameter k_cat contains rate constants from the initial enzyme–substrate complex through the remaining steps, including proton transfer. Therefore, for the proposed mechanistic scheme (equations 1 and 2), k_cat can effectively be represented as k_cat = k₂k₃/(k₂ + k₃). On the other hand, the ratio k_cat/K_m contains rate constants for the initial association of the substrate CO₂ through the dissociation of the product HCO₃⁻. Hence, k_cat/K_m only contains rate constants from equation 1 (and not equation 2) and is represented as k_cat/K_m = k₁k₂/(k₋₁ + k₂).

It is known that in native CA II the HCO₃⁻-dissociation process (k₂) is much faster than the reverse interconversion from HCO₃⁻ to CO₂ (k₋₁) and the proton-transfer rate (k₃), i.e. k₂^native ≫ k₋₁^native, k₂^native ≫ k₃^native, with k₂^native ≃ 10k₋₁^native, k₂^native ≃ 15k₃^native and k₋₁^native ≃ 1.5k₃^native (Table 1). Combining this information with the insights gleaned from our study (k₁^V143I < k₁^native, k₋₁^V143I < k₋₁^native, k₂^V143I < k₂^native and k₃^V143I ≃ k₃^native), we can estimate the effect of the V143I point mutation on the observed kinetic parameter k_cat in the following way. In the native state [k_cat]^native = k₂^nativek₃^native/(k₂^native + k₃^native) ≃ k₃^native (using k₂^native ≫ k₃^native), indicating that the turnover rate in the native is almost the same as the proton-transfer rate and that the proton-transfer process is the rate-limiting step. In the V143I variant [k_cat]^V143I = k₂^V143Ik₃^V143I/(k₂^V143I + k₃^V143I) ≃ k₃^native[k₂^V143I/(k₂^V143I + k₃^V143I)] (using k₃^V143I ≃ k₃^native), and the experimental measurement (Table 1) suggests that [k_cat]^V143I ≃ [k_cat]^native ≃ k₃^native, implying that [k₂^V143I/(k₂^V143I + k₃^V143I)] ≃ 1, or k₂^V143I ≫ k₃^V143I. This result indicates that HCO₃⁻ dissociation (k₂) remains faster than proton transfer (k₃) in the V143I variant and that the proton-transfer process is still the rate-limiting step in the V143I variant. The negligible reduction in k₂^V143I suggests that its activation energy is not significantly increased (Fig. 5).

The second-order rate constant k_cat/K_m shows the following relationship in the native state: [k_cat/K_m]^native = k₁^nativek₂^native/(k₋₁^native + k₂^native) ≃ k₁^native (using k₂^native ≫ k₋₁^native). This indicates that [k_cat/K_m]^native mostly reflects the CO₂-binding step and its interconversion to HCO₃⁻. On the other hand, in the V143I variant both the dissociation of HCO₃⁻ (k₂) and the reverse interconversion (k₋₁) from HCO₃⁻ to CO₂ are retarded (k₂^V143I < k₂^native and k₋₁^V143I < k₋₁^native), leaving the relation k₂^V143I ≫ k₋₁^V143I unresolved. However, the relation k₂^V143I ≫ k₃^V143I ≃ k₃^native obtained from the k_cat analysis above suggests that k₂^V143I is still an order of magnitude larger than k₃^native, while k₋₁^V143I < k₋₁^native ≃ 1.5k₃^native suggests that k₋₁^V143I is comparable to or less than k₃^native, thereby ensuring that the relation k₂^V143I ≫ k₋₁^V143I remains valid. Thus, we can estimate the k_cat/K_m in the V143I variant in the following manner: [k_cat/K_m]^V143I = k₁^V143Ik₂^V143I/(k₋₁^V143I + k₂^V143I) ≃ k₁^V143I (using k₂^V143I ≫ k₋₁^V143I). This estimation indicates that the reduced [k_cat/K_m]^V143I is mostly owing to the decrease in k₁, reflecting the slower CO₂ binding and interconversion to HCO₃⁻ in the V143I variant. It should be noted that the reduction in the k₋₁ value has little effect on [k_cat/K_m]^V143I in the direction of CO₂ hydration, as long as the reduction in k₂ is small enough to keep the relation k₂^V143I ≫ k₋₁^V143I valid. However, it is expected that the reduction in the k₋₁ value would have significant consequences for the HCO₃⁻-dehydration direction.

Finally, considering that k_cat ≃ k₃ and [k_cat/K_m] ≃ k₁ in both native and V143I CA II, the Michaelis constant K_m is expressed in the following way: K_m^native = k₃^native/k₁^native and K_m^V143I = k₃^V143I/k₁^V143I. Consequently, K_m^V143I > K_m^native can be obtained using the estimated relationships k₁^V143I < k₁^native and k₃^V143I ≃ k₃^native. The relationship shows that the substrate concentration needed to reach half of the maximum reaction velocity is larger in V143I CA II mainly owing to the slower CO₂ binding and interconversion to HCO₃⁻.

Although our study was performed for a single point mutation within the hydrophobic pocket (V143I), our approach and interpretations can be extended to arbitrary mutations in CA II. Considering the forward CO₂-hydration direction, the mutation can first perturb substrate funnelling into the hydrophobic pocket via steric hindrance, thereby limiting the configurations that allow its efficient conversion into product. This influence is directly reflected in k_cat/K_m, but not in k_cat. Secondly, the mutation can structurally distort the proton-transfer pathway by perturbing the water network or its associated stabilizing residues, and this effect is directly reflected in k_cat but not in k_cat/K_m. Thirdly, the mutation can alter the product-dissociation process via direct steric hindrance or perturbations in the water-replenishment pathway. This influence can be intricate and is reflected both in k_cat and k_cat/K_m. On the other hand, the mutation can affect the reverse reaction, the interconversion from product to substrate and substrate dissociation, but this has little influence on either k_cat or k_cat/K_m in the hydration direction, as long as the reverse interconversion process is much slower than the product-dissociation process.

4. Conclusion

We systematically studied the effect of a single-residue mutation on the CA II catalytic pathway at atomic resolution. We have successfully captured the high-resolution intermediate states of the V143I variant and shown clearly that the single point mutation induces noticeable changes in substrate and product binding at the active site and in the water-replenishment pathway, but has little effect on the proton-transfer pathway. The structural information was then utilized to estimate the reaction rate constants and the free-energy profiles during the catalytic cycle, unravelling the effect of the point mutation on the altered kinetic parameters. We believe that the detailed and systematic approach in our CA II study can be extended to identify the specific roles of target amino-acid residues in many other biologically important enzymes. We also anticipate that our detailed descriptions could serve as a reference point for future theoretical and computational studies that may lead to an advanced understanding of enzyme mechanisms at the quantum-chemistry level.

5. Related literature

The following references are cited in the supporting information for this article: Emsley et al. (2010), Forsman et al. (1988), Henderson (1990), Khalifah et al. (1977), Kim et al. (2005, 2006, 2013, 2016), McPherson (1982), Murshudov et al. (2011), Otwinowski & Minor (1997) and Winn et al. (2011).