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 nitrogencontaining 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 "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. \((\mathbf{d})\) 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 of \(\mathrm{Zn}(\mathrm{II})\) Center in Carbonic Anhydrase

Based on the information provided, we know that the \(\mathrm{Zn}(\mathrm{II})\) center is tetrahedrally coordinated, meaning it has a 4-coordinate geometry with a Zinc ion at the center. There are three neutral nitrogen-containing groups and a water molecule coordinated to the zinc ion. To draw this active site geometry, simply draw Zn in the center with 4 ligands surrounding it in a tetrahedral arrangement, marking the nitrogen ligands as "N" and the water molecule as "H2O".

02

(b) Comparison of \(\mathrm{p}K_{a}\) Values

The \(\mathrm{p}K_{a}\) value of the coordinated water molecule in the carbonic anhydrase active site is given as 7.5. The \(\mathrm{p}K_{a}\) of pure water is about 14. Since lower \(\mathrm{p}K_{a}\) values indicate higher acidity, we can conclude that the carbonic anhydrase's active site is more acidic than pure water.

03

(c) Ligands Bound to the \(\mathrm{Zn}(\mathrm{II})\) Center After Deprotonation

When the coordinated water molecule at the \(\mathrm{Zn}(\mathrm{II})\) center is deprotonated, it will lose a hydrogen ion, leaving behind a hydroxide ion (OH-). Since the three neutral nitrogen ligands are unaffected, the ligands bound to the \(\mathrm{Zn}(\mathrm{II})\) center after deprotonation would be the three nitrogen-containing groups and a hydroxide ion (OH-).

04

(d) Explanation for the \(\mathrm{p}K_{a}\) Difference

The difference in \(\mathrm{p}K_{a}\) values between \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (10) and carbonic anhydrase (7.5) is related to their structure and coordination environment. In carbonic anhydrase, the \(\mathrm{Zn}(\mathrm{II})\) center is coordinated to three nitrogen ligands and a water molecule, creating an active site that can participate in enzymatic reactions. This unique structure likely causes the active site to be more acidic (lower \(\mathrm{p}K_{a}\)) than the \(\mathrm{Zn}(\mathrm{II})\) complex with six coordinated water molecules.

05

(e) Carbonic Anhydrase Color Expectation

The color of a metal-ion-containing protein is primarily determined by the nature of the metal ion and the ligands involved in its coordination environment. Hemoglobin, for example, is colored due to the visible light absorption by its iron(II) center within heme groups. Since carbonic anhydrase contains a \(\mathrm{Zn}(\mathrm{II})\) center, which typically does not absorb light in the visible range, we would not expect it to have a deep color like other metal-ion-containing proteins such as hemoglobin.

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