The coordination geometry of the metal center in the active site of the metalloenzyme carbonic anhydrase is a distorted tetrahedral geometry. The metal center is typically a zinc ion Zn that is coordinated to three histidine residues from the protein and a water molecule or hydroxide ion.This coordination geometry facilitates the enzyme's catalytic activity in the following ways:1. The tetrahedral geometry allows for optimal interaction between the metal center and the substrate carbon dioxide, CO . The arrangement of the histidine residues and the water molecule/hydroxide ion around the zinc ion creates a suitable environment for the binding and activation of CO.2. The zinc ion acts as a Lewis acid, polarizing the bound water molecule and making it more nucleophilic. This enables the water molecule to attack the CO molecule more effectively, leading to the formation of bicarbonate ion HCO .3. The tetrahedral geometry also allows for the stabilization of the transition state during the reaction. The negatively charged oxygen atom in the transition state is stabilized by the positively charged zinc ion, lowering the activation energy and increasing the reaction rate.4. The coordination geometry helps in the proton transfer step, which is essential for the regeneration of the active site. The zinc-bound hydroxide ion acts as a base, accepting a proton from a nearby residue usually a histidine and converting back to a water molecule. This proton transfer is facilitated by the hydrogen-bonding network present in the active site, which is supported by the tetrahedral coordination geometry.In summary, the distorted tetrahedral coordination geometry of the metal center in carbonic anhydrase plays a crucial role in the enzyme's catalytic activity by facilitating substrate binding, activation, transition state stabilization, and proton transfer steps.