Carbon dioxide is a major end product of aerobic metabolism. In mammals, this carbon dioxide is released into the blood and transported to the lungs for exhalation. While in the red blood cells, carbon dioxide reacts with water (Section 7.3). The product of this reaction is a moderately strong acid, carbonic acid (pK_a = 3.5), which is converted into bicarbonate ion on the loss of a proton.

Even in the absence of a catalyst, this hydration reaction proceeds at a moderately fast pace. At 37°C near neutral pH, the second-order rate constant k₁ is 0.0027 M⁻¹ s⁻¹. This value corresponds to an effective first-order rate constant of 0.15 s⁻¹ in water ([H₂O] = 55.5 M). The reverse reaction, the dehydration of , is even more rapid, with a rate constant of k₋₁ = 50 s⁻¹. These rate constants correspond to an equilibrium constant of K₁ = 5.4 × 10⁻⁵ and a ratio of [CO₂] to [H₂CO₃] of 340 : 1 at equilibrium.

Carbon dioxide hydration and dehydration are often coupled to rapid processes, particularly transport processes. Thus, almost all organisms contain enzymes, referred to as carbonic anhydrases, that increase the rate of reaction beyond the already reasonable spontaneous rate. For example, carbonic anhydrases dehydrate in the blood to form CO₂ for exhalation as the blood passes through the lungs. Conversely, they convert CO₂ into to generate the aqueous humor of the eye and other secretions. Furthermore, both CO₂ and are substrates and products for a variety of enzymes, and the rapid interconversion of these species may be necessary to ensure appropriate substrate levels. So important are these enzymes in human beings that mutations in some carbonic anhydrases have been found to be associated with osteopetrosis (excessive formation of dense bones accompanied by anemia) and mental retardation.

Carbonic anhydrases accelerate CO₂ hydration dramatically. The most-active enzymes hydrate CO₂ at rates as high as k_cat = 10⁶ s⁻¹, or a million times a second per enzyme molecule. Fundamental physical processes such as diffusion and proton transfer ordinarily limit the rate of hydration, and so the enzymes employ special strategies to attain such prodigious rates.

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Less than 10 years after the discovery of carbonic anhydrase in 1932, this enzyme was found to contain a bound zinc ion. Moreover, the zinc ion appeared to be necessary for catalytic activity. This discovery, remarkable at the time, made carbonic anhydrase the first known zinc-containing enzyme. At present, hundreds of enzymes are known to contain zinc. In fact, more than one-third of all enzymes either contain bound metal ions or require the addition of such ions for activity. Metal ions have several properties that increase chemical reactivity: their positive charges, their ability to form strong yet kinetically labile bonds, and, in some cases, their capacity to be stable in more than one oxidation state. The chemical reactivity of metal ions explains why catalytic strategies that employ metal ions have been adopted throughout evolution.

X-ray crystallographic studies have supplied the most-detailed and direct information about the zinc site in carbonic anhydrase. At least seven carbonic anhydrases, each with its own gene, are present in human beings. They are all clearly homologous, as revealed by substantial sequence identity. Carbonic anhydrase II, a major protein component of red blood cells, has been the most extensively studied (Figure 9.21). It is also one of the most active carbonic anhydrases.

Zinc is found only in the +2 state in biological systems. A zinc atom is essentially always bound to four or more ligands; in carbonic anhydrase, three coordination sites are occupied by the imidazole rings of three histidine residues and an additional coordination site is occupied by a water molecule (or hydroxide ion, depending on pH). Because the molecules occupying the coordination sites are neutral, the overall charge on the Zn(His)₃ unit remains +2.

How does this zinc complex facilitate carbon dioxide hydration? A major clue comes from the pH profile of enzymatically catalyzed carbon dioxide hydration (Figure 9.22).

At pH 8, the reaction proceeds near its maximal rate. As the pH decreases, the rate of the reaction drops. The midpoint of this transition is near pH 7, suggesting that a group that loses a proton at pH 7 (pK_a = 7) plays an important role in the activity of carbonic anhydrase. Moreover, the curve suggests that the deprotonated (high pH) form of this group participates more effectively in catalysis. Although some amino acids, notably histidine, have pK_a values near 7, a variety of evidence suggests that the group responsible for this transition is not an amino acid but is the zinc-bound water molecule.

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The binding of a water molecule to the positively charged zinc center reduces the pK_a of the water molecule from 15.7 to 7 (Figure 9.23). With the pK_a lowered, the water molecule can more easily lose a proton at neutral pH, generating a substantial concentration of hydroxide ion (bound to the zinc atom). A zinc-bound hydroxide ion (OH⁻) is a potent nucleophile able to attack carbon dioxide much more readily than water does. Adjacent to the zinc site, carbonic anhydrase also possesses a hydrophobic patch that serves as a binding site for carbon dioxide (Figure 9.24). Based on these observations, a simple mechanism for carbon dioxide hydration can be proposed (Figure 9.25):

Thus, the binding of a water molecule to the zinc ion favors the formation of the transition state by facilitating proton release and by positioning the water molecule to be in close proximity to the other reactant.

Studies of a synthetic analog model system provide evidence for the mechanism’s plausibility. A simple synthetic ligand binds zinc through four nitrogen atoms (compared with three histidine nitrogen atoms in the enzyme), as shown in Figure 9.26. One water molecule remains bound to the zinc ion in the complex. Direct measurements reveal that this water molecule has a pK_a value of 8.7, not as low as the value for the water molecule in carbonic anhydrase but substantially lower than the value for free water. At pH 9.2, this complex accelerates the hydration of carbon dioxide more than 100-fold. Although its rate of catalysis is much less efficient than catalysis by carbonic anhydrase, the model system strongly suggests that the zinc-bound hydroxide mechanism is likely to be correct. Carbonic anhydrases have evolved to employ the reactivity intrinsic to a zinc-bound hydroxide ion as a potent catalyst.

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As noted earlier, some carbonic anhydrases can hydrate carbon dioxide at rates as high as a million times a second (10⁶ s⁻¹). The magnitude of this rate can be understood from the following observations. In the first step of a carbon dioxide hydration reaction, the zinc-bound water molecule must lose a proton to regenerate the active form of the enzyme (Figure 9.27). The rate of the reverse reaction, the protonation of the zinc-bound hydroxide ion, is limited by the rate of proton diffusion. Protons diffuse very rapidly with second-order rate constants near 10¹¹ M⁻¹ s⁻¹. Thus, the backward rate constant k₋₁ must be less than 10¹¹ M⁻¹ s⁻¹. Because the equilibrium constant K is equal to k₁/k₋₁, the forward rate constant is given by k₁ = K · k₋₁. Thus, if k₋₁ ≤ 10¹¹ M⁻¹ s⁻¹ and K = 10⁻⁷ M (because pK_a = 7), then k₁ must be less than or equal to 10⁴ s⁻¹. In other words, the rate of proton diffusion limits the rate of proton release to less than 10⁴ s⁻¹ for a group with pK_a = 7. However, if carbon dioxide is hydrated at a rate of 10⁶ s⁻¹, then every step in the mechanism (Figure 9.25) must take place at least this fast. How is this apparent paradox resolved?

The answer became clear with the realization that the highest rates of carbon dioxide hydration require the presence of buffer, suggesting that the buffer components participate in the reaction. The buffer can bind or release protons. The advantage is that, whereas the concentrations of protons and hydroxide ions are limited to 10⁻⁷ M at neutral pH, the concentration of buffer components can be much higher, of the order of several millimolar. If the buffer component BH⁺ has a pK_a of 7 (matching that for the zinc-bound water molecule), then the equilibrium constant for the reaction in Figure 9.28 is 1. The rate of proton abstraction is given by . The second-order rate constants and will be limited by buffer diffusion to values less than approximately 10⁹ M⁻¹ s⁻¹. Thus, buffer concentrations greater than [B] = 10⁻³ M (or 1 mM) may be high enough to support carbon dioxide hydration rates of 10⁶ M⁻¹ s⁻¹ because · [B] = (10⁹ M⁻¹s⁻¹) · (10⁻³M) = 10⁶ s⁻¹. The prediction that the rate increases with increasing buffer concentration has been confirmed experimentally (Figure 9.29).

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The molecular components of many buffers are too large to reach the active site of carbonic anhydrase. Carbonic anhydrase II has evolved a proton shuttle to allow buffer components to participate in the reaction from solution. The primary component of this shuttle is histidine 64. This residue transfers protons from the zinc-bound water molecule to the protein surface and then to the buffer (Figure 9.30). Thus, catalytic function has been enhanced through the evolution of an apparatus for controlling proton transfer from and to the active site. Because protons participate in many biochemical reactions, the manipulation of the proton inventory within active sites is crucial to the function of many enzymes and explains the prominence of acid–base catalysis.

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