The catalytic efficiency of an enzyme following Michaelis-Menten kinetics is defined by

Question

Which of the following bonds is responsible for maintaining the secondary structure of proteins?

Answer 1

Catalytic efficiency is a single number that tells you how good an enzyme is at converting substrate into product when there is not much substrate around, and the question wants the exact combination of Michaelis-Menten constants that gives this number.

$k_{Cat}$: this is only the maximum turnover number, the number of reactions one enzyme molecule can carry out per second once it is fully saturated with substrate. It says nothing about how well the enzyme finds and binds substrate when substrate is scarce, so on its own it cannot represent overall efficiency.
$V_{max} / k_{Cat}$: since $V_{max} = k_{Cat}[E]_0$, dividing $V_{max}$ by $k_{Cat}$ just cancels the turnover number and leaves total enzyme concentration $[E]_0$. That is a measure of how much enzyme you have, not how efficient it is.
$k_{Cat} / K_M$: at low substrate concentration, the Michaelis-Menten equation $v = \dfrac{k_{Cat}[E]_0[S]}{K_M + [S]}$ simplifies to $v \approx \left(\dfrac{k_{Cat}}{K_M}\right)[E]_0[S]$, which looks exactly like a simple bimolecular rate law between free enzyme and substrate. The constant $k_{Cat}/K_M$ therefore has units of a second order rate constant ($M^{-1}s^{-1}$) and directly measures how efficiently the enzyme converts substrate to product under real, non-saturating conditions. This is the accepted definition of catalytic, or specificity, efficiency.
$k_{Cat} / V_{max}$: this reduces to $1/[E]_0$, the reciprocal of enzyme concentration, which again carries no information about how well the enzyme binds or converts substrate.

Only $k_{Cat}/K_M$ combines both how fast the enzyme turns substrate over and how tightly it binds that substrate at low concentration, which is exactly what catalytic efficiency means, so option (C) is correct.

Let's summarize:

Catalytic efficiency is defined as $k_{Cat}/K_M$, sometimes called the specificity constant.
$V_{max}/k_{Cat}$ and $k_{Cat}/V_{max}$ both simplify to expressions involving only enzyme concentration, not true efficiency.

So the correct definition of catalytic efficiency is $k_{Cat}/K_M$, option (C).

Answer 2

Catalytic efficiency is a single number that tells you how good an enzyme is at converting substrate into product when there is not much substrate around, and the question wants the exact combination of Michaelis-Menten constants that gives this number.

$k_{Cat}$: this is only the maximum turnover number, the number of reactions one enzyme molecule can carry out per second once it is fully saturated with substrate. It says nothing about how well the enzyme finds and binds substrate when substrate is scarce, so on its own it cannot represent overall efficiency.
$V_{max} / k_{Cat}$: since $V_{max} = k_{Cat}[E]_0$, dividing $V_{max}$ by $k_{Cat}$ just cancels the turnover number and leaves total enzyme concentration $[E]_0$. That is a measure of how much enzyme you have, not how efficient it is.
$k_{Cat} / K_M$: at low substrate concentration, the Michaelis-Menten equation $v = \dfrac{k_{Cat}[E]_0[S]}{K_M + [S]}$ simplifies to $v \approx \left(\dfrac{k_{Cat}}{K_M}\right)[E]_0[S]$, which looks exactly like a simple bimolecular rate law between free enzyme and substrate. The constant $k_{Cat}/K_M$ therefore has units of a second order rate constant ($M^{-1}s^{-1}$) and directly measures how efficiently the enzyme converts substrate to product under real, non-saturating conditions. This is the accepted definition of catalytic, or specificity, efficiency.
$k_{Cat} / V_{max}$: this reduces to $1/[E]_0$, the reciprocal of enzyme concentration, which again carries no information about how well the enzyme binds or converts substrate.

Only $k_{Cat}/K_M$ combines both how fast the enzyme turns substrate over and how tightly it binds that substrate at low concentration, which is exactly what catalytic efficiency means, so option (C) is correct.

Let's summarize:

Catalytic efficiency is defined as $k_{Cat}/K_M$, sometimes called the specificity constant.
$V_{max}/k_{Cat}$ and $k_{Cat}/V_{max}$ both simplify to expressions involving only enzyme concentration, not true efficiency.

So the correct definition of catalytic efficiency is $k_{Cat}/K_M$, option (C).

The catalytic efficiency of an enzyme following Michaelis-Menten kinetics is defined by

Show Hint

The Correct Option is C

Solution and Explanation

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