Metallic elements are essential components of many important enzymes operating within our bodies. Carbonic anhydrase, which contains \(\mathrm{Zn}^{2+}\) in its active site, is responsible for rapidly interconverting dissolved \(\mathrm{CO}_{2}\) and bicarbonate ion, \(\mathrm{HCO}_{3}^{-}\). The zinc in carbonic anhydrase is tetrahedrally coordinated by three neutral nitrogen- containing groups and a water molecule. The coordinated water molecule has a \(\mathrm{p} K_{a}\) of \(7.5,\) which is crucial for the enzyme's activity. (a) Draw the active site geometry for the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase, just writing \({ }^{4} \mathrm{~N}^{n}\) for the three neutral nitrogen ligands from the protein. (b) Compare the \(\mathrm{p} K_{a}\) of carbonic anhydrase's active site with that of pure water; which species is more acidic? (c) When the coordinated water to the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase is deprotonated, what ligands are bound to the \(\mathrm{Zn}(\mathrm{II})\) center? Assume the three nitrogen ligands are unaffected. (d) The \(\mathrm{p} K_{a}\) of \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is \(10 .\) Suggest an explanation for the difference between this \(\mathrm{p} K_{a}\) and that of carbonic anhydrase. (e) Would you expect carbonic anhydrase to have a deep color, like hemoglobin and other metal-ion containing proteins do? Explain.

Step by step solution

01

(a) Active site geometry drawing

To draw the active site geometry, imagine the Zn(II) at the center surrounded by three neutral nitrogen ligands and a water molecule in a tetrahedral arrangement. Label the nitrogen ligands as \(^{4}$$N^n\), and the water molecule as H2O.

02

(b) Comparing pKa of carbonic anhydrase's active site with that of pure water

The pKa of the coordinated water molecule in the carbonic anhydrase active site is 7.5, while the pKa of pure water is 14. A lower pKa indicates a higher acidity. Thus, the coordinated water molecule in carbonic anhydrase's active site is more acidic compared to pure water.

03

(c) Ligands bound to Zn(II) center after deprotonation

Upon deprotonation, the coordinated water molecule will lose a proton (H+) and become a hydroxide ion (OH-). So, the ligands that remain bound to the Zn(II) center are the three neutral nitrogen ligands (\(^{4}$$N^n\)) and the hydroxide ion (OH-).

04

(d) Explanation for the difference between the pKa values

The pKa of [Zn(H2O)6]\(^{2+}\) complex is 10, and that of carbonic anhydrase is 7.5. The difference in pKa values suggests a difference in acidity between the two complexes. The lower pKa of carbonic anhydrase's active site, almost a 2.5 unit difference, contributes to its higher acidity compared to the [Zn(H2O)6]\(^{2+}\) complex. This difference can be attributed to the unique coordination environment (three nitrogen ligands and one water molecule) in the carbonic anhydrase active site, which enhances its acidity and catalytic activity.

05

(e) Expectation of carbonic anhydrase having a deep color like hemoglobin

The deep color of metal-ion containing proteins like hemoglobin results from the electronic transitions involving the d orbitals in their metal ions. Zinc(II) has a filled 3d10 electronic configuration and lacks the available d orbital states for transitions. As a result, the carbonic anhydrase enzyme does not display any deep colors like some other metal-ion containing proteins, such as hemoglobin.

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