The catalytic efficiency of an enzyme is a measure of how efficiently an enzyme converts a substrate into a product. It is defined by the ratio of two key kinetic parameters: the catalytic constant (\( k_{cat} \)) and the Michaelis constant (\( K_m \)). Mathematically, it is expressed as:
\(\frac{k_{cat}}{K_m}\)
Let's understand why this particular ratio is used to define the catalytic efficiency:
- Catalytic Constant (\( k_{cat} \)): This represents the turnover number of an enzyme, indicating the number of substrate molecules converted to product per enzyme molecule per unit time when the enzyme is fully saturated with substrate. A higher \( k_{cat} \) signifies a faster turnover.
- Michaelis Constant (\( K_m \)): This constant reflects the affinity of the enzyme for its substrate. A lower \( K_m \) indicates a higher affinity, as the enzyme can achieve its half-maximal velocity at a lower substrate concentration.
The ratio \(\frac{k_{cat}}{K_m}\) effectively combines these two properties to determine how well an enzyme functions under conditions of low substrate concentration, thereby providing a measure of catalytic efficiency.
Now, let's examine the options to justify the correct answer:
- \( k_{cat} \): This only describes the turnover rate and not the efficiency considering substrate affinity.
- \( \frac{V_{max}}{k_{cat}} \): This expression does not relate to catalytic efficiency but could imply the amount of enzyme active sites contributing to \( V_{max} \).
- \( \frac{k_{cat}}{K_m} \): This is the correct definition of catalytic efficiency as it considers both the turnover rate and substrate affinity.
- \( \frac{k_{cat}}{V_{max}} \): This ratio does not meaningfully describe catalytic efficiency. \( V_{max} \) is impacted by enzyme concentration, not by inherent enzyme properties.
Thus, the expression that defines catalytic efficiency is \(\frac{k_{cat}}{K_m}\), which is why the correct answer is this option.
Important Questions from Enzyme Kinetics and Michaelis Menten Equation
- The catalytic efficiency of an enzyme following Michaelis-Menten kinetics is defined by
You are characterizing a new enzyme isolated and purified in the laboratory. If the maximum velocity of the enzyme is $1800 \text{ } \mu moles \text{ L}^{-1} \text{min}^{-1}$ and the total concentration of the enzyme in the reaction mixture is $1.5 \mu \text{M}$, then the turnover number of the enzyme is _______ $\text{s}^{-1}$. (answer in integer)
You have purified an enzyme using a series of chromatographic methods. It was observed that a $10 \mu \text{ g mL}^{-1}$ of this purified enzyme converted $10 \text{ mM}$ substrate per hour at 25$^{\circ}$C and pH 7. Its specific activity is _______ $\text{IU } \mu\text{g}^{-1}$. (rounded off to three decimal places)
Within the Michaelis-Menten framework, the ratio of $v_0/V_{max}$
when $[S] = 20 \times K_m$ is _________.
(Round off to two decimal places)
The activity of lactate dehydrogenase can be measured by monitoring the following reaction:
Pyruvate + NADH $ \longrightarrow $ Lactate + $NAD^+$
The molar extinction coefficient of NADH at 340 nm is $6220 \ M^{-1}.cm^{-1}$. $NAD^+$ does not absorb at this wavelength. In an assay, $25 \ \mu L$ of a sample of enzyme (containing $5 \ \mu g$ protein per mL) was added to a mixture of pyruvate and NADH to give a total volume of 3 mL in a cuvette of 1 cm pathlength. The rate of decrease in absorbance at 340 nm was $0.14 \ min^{-1}$. The specific activity of the enzyme will be ____________________ $ \mu mol.min^{-1}.mg^{-1}$.
