Answer :
The catalytic efficiency of carbonic anhydrase can be calculated by using the ratio of the rate constant for the enzyme-catalyzed reaction (kb) to the rate constant for the uncatalyzed reaction (km).
In Example 17F.2, the rate constant for the uncatalyzed reaction (km) was found to be 2.2 × 10^−3 s^−1, and the rate constant for the carbonic anhydrase-catalyzed reaction (kb) was found to be 3.3 × 10^6 M^−1 s^−1.
Therefore, the catalytic efficiency can be calculated by dividing kb by km, resulting in a value of approximately 1.5 × 10^9 M^−1 s^−1.
This high value for the catalytic efficiency of carbonic anhydrase demonstrates its ability to greatly accelerate the rate of the reaction it catalyzes. This is due to the enzyme's active site, which is specifically designed to bind and orient the substrate molecules in a way that maximizes their reactivity and allows for efficient conversion to the product.
The high catalytic efficiency of carbonic anhydrase is particularly important in biological systems, where the enzyme plays a key role in regulating pH and carbon dioxide levels in the body.
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Final answer:
Catalytic efficiency, represented as k₁/Kₘ, combines an enzyme's catalytic turnover number with its binding affinity. Carbonic anhydrase, with a turnover number of 36,000,000, indicates high efficiency, but Kₘ is needed for precise calculation.
Explanation:
The catalytic efficiency of an enzyme is a measure of how effectively an enzyme converts substrate into product. It is represented by the ratio kcat/KM, where kcat is the turnover number that denotes the maximum number of substrate molecules converted to product per unit time by an enzyme when the enzyme is fully saturated with the substrate, and KM is the Michaelis constant representing the substrate concentration at which the reaction rate is at half its maximum value.
For the enzyme carbonic anhydrase, which has one of the highest known turnover numbers of 36,000,000, we need to know the specific KM value to calculate its catalytic efficiency. However, without the specific KM value provided, we can conclude that because carbonic anhydrase has such an exceptional turnover number, it is highly efficient in its catalytic role, enabling the conversion of CO2 to bicarbonate ions swiftly in human blood.
Note: The specific calculation of efficiency for carbonic anhydrase would require the exact value of KM which is not provided here and should be found in the referred example 17f.2 for an accurate calculation.
