Step 1: Understanding the Concept:
The Michaelis constant ($K_m$) is a fundamental parameter in enzyme kinetics defined as the substrate concentration at which the reaction velocity is half of its maximal value ($V_{\text{max}}/2$).
In many systems, $K_m$ is an indicator of the affinity or specificity of an enzyme for a particular substrate: a lower $K_m$ value indicates higher affinity/specificity, while a higher $K_m$ value indicates lower affinity/specificity.
Detailed Explanation:
Let us compare the given $K_m$ values for the three enzymes:
- $K_m$ of E1 = $5\times10^{-12}$
- $K_m$ of E2 = $5\times10^{-10}$
- $K_m$ of E3 = $5\times10^{-15}$
Arranging these $K_m$ values in increasing order:
\[ 5\times10^{-15}\text{ (E3)} < 5\times10^{-12}\text{ (E1)} < 5\times10^{-10}\text{ (E2)} \]
Since $K_m$ is inversely related to substrate affinity and specificity:
- E3 has the lowest $K_m$, so it has the highest specificity/affinity.
- E2 has the highest $K_m$, so it has the lowest specificity/affinity.
- The order of specificity is: $\text{E3} > \text{E1} > \text{E2}$.
Now let us evaluate the given statements:
- (A) E1 is more specific than E2: True, because $K_m$ of E1 ($5\times10^{-12}$) $<$ $K_m$ of E2 ($5\times10^{-10}$).
- (B) E2 is more specific than E3: False, because $K_m$ of E2 ($5\times10^{-10}$) $>$ $K_m$ of E3 ($5\times10^{-15}$).
- (C) E3 is more specific than E1: True, because $K_m$ of E3 ($5\times10^{-15}$) $<$ $K_m$ of E1 ($5\times10^{-12}$).
- (D) E3 is more specific than E2: True, because $K_m$ of E3 ($5\times10^{-15}$) $<$ $K_m$ of E2 ($5\times10^{-10}$).
Therefore, statements (A), (C), and (D) are correct.
Step 2: Final Answer:
The correct option is (A).