Question

Which of the following quantities is used to express Michaelis-Menten constant ($K_m$) of an enzyme?

• A. Velocity
• B. Length
• C. Time
• D. Concentration

Hint:

The units of $K_m$ are always the same as the units of your Substrate ($[S]$).
If the substrate is in moles per liter, $K_m$ is in moles per liter.
Low $K_m = $ "Strong Hug" (High Affinity).
High $K_m = $ "Weak Hug" (Low Affinity).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question focuses on enzyme kinetics and specifically seeks the physical unit or quantity used to define the Michaelis-Menten constant ($K_m$).
$K_m$ is a fundamental parameter used to describe the affinity of an enzyme for its substrate.
Key Formula or Approach:
The Michaelis-Menten equation is given by:
\[ v = \frac{V_{max} [S]}{K_m + [S]} \]
Where $v$ is the reaction rate, $V_{max}$ is the maximum rate, and $[S]$ is the substrate concentration.

Step 2: Detailed Explanation:

• Definition of $K_m$: By definition, $K_m$ is the substrate concentration at which the reaction velocity is exactly half of the maximum velocity ($v = V_{max}/2$).

• Derivation of Units: If we set $v = V_{max}/2$ in the Michaelis-Menten equation:
\[ \frac{V_{max}}{2} = \frac{V_{max} [S]}{K_m + [S]} \]
\[ 1/2 = \frac{[S]}{K_m + [S]} \]
\[ K_m + [S] = 2[S] \implies K_m = [S] \]

• Physical Meaning: Since $K_m$ is equal to $[S]$ under specific conditions, it must share the same units as $[S]$. Substrate concentration is typically expressed in Molar (M), millimolar (mM), or micromolar ($\mu$M).

• Affinity Interpretation: A small $K_m$ value indicates high affinity, meaning the enzyme reaches half-maximal velocity at a very low substrate concentration. Conversely, a large $K_m$ indicates low affinity.

• Comparison with other options: Velocity (A) describes the rate of product formation (e.g., mol/sec). Length (B) and Time (C) are unrelated to the physical definition of the Michaelis-Menten constant.

Step 3: Final Answer:
The Michaelis-Menten constant ($K_m$) is expressed as a Concentration, as it represents the amount of substrate required for half-maximal enzyme activity.