An enzymatic reaction exhibits Michaelis-Menten kinetics. For this reaction, on doubling the concentration of enzyme while maintaining [S] >> [$E_o$],
$K_m$ will remain the same but $V_{max}$ will increase.
Enzyme Kinetics Explanation
Michaelis-Menten kinetics describes the rate of enzymatic reactions. Key parameters are $K_m$ and $V_{max}$. The reaction follows the equation:
$v = \frac{V_{max}[S]}{K_m + [S]}$
where $v$ is the reaction velocity, $[S]$ is the substrate concentration, $K_m$ is the Michaelis constant, and $V_{max}$ is the maximum reaction velocity.
Enzyme Concentration Effects
The question asks about the effect of doubling the enzyme concentration ($[E_o]$) while keeping $[S] \gg [E_o]$.
- Effect on $K_m$: The Michaelis constant ($K_m$) reflects the enzyme's affinity for its substrate. It is generally independent of enzyme concentration. Doubling $[E_o]$ does not alter the intrinsic binding properties of the enzyme. Therefore, $K_m$ remains unchanged.
- Effect on $V_{max}$: The maximum velocity ($V_{max}$) is directly proportional to the total enzyme concentration ($[E_o]$) and the turnover number ($k_{cat}$), according to the relation $V_{max} = k_{cat}[E_o]$. When the enzyme concentration is doubled, $V_{max}$ also doubles, assuming $k_{cat}$ remains constant.
Thus, doubling the enzyme concentration leaves $K_m$ unchanged but increases $V_{max}$.
Important Questions from Enzyme Kinetics and Michaelis Menten Equation
- An enzyme (E) catalyzes the biochemical reaction $A \rightarrow B$ with $k_{cat}$ equal to $500 s^{-1}$. If the initial reaction velocity ($V_0$) is $10 \mu M.s^{-1}$ at the total enzyme concentration $[E_t]$ of 30 nM and substrate concentration $[A]$ of $40 \mu M$, the value of $K_m$ (in $\mu M$) is ________
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 enzyme $\alpha$-amylase used in starch hydrolysis has an affinity constant ($K_m$) value of $0.005$ M. To achieve one-fourth of the maximum rate of hydrolysis, the required starch concentration in mM (rounded off to two decimal places) is____.
- In an assay of the type II dehydroquinase of molecular mass 18 kDa, it is found that the $V_{max}$ of the enzyme is $0.0134 \ \mu mol.min^{-1}$ when $1.8 \ \mu g$ enzyme is added to the assay mixture. If the $K_m$ for the substrate is $25 \ \mu M$, the $k_{cat}/K_m$ ratio will be ____________________ $\times 10^4 \ M^{-1}.s^{-1}$.
- A single subunit enzyme converts 420 µmoles of substrate to product in one minute. The activity of the enzyme is __________ $ \times 10^{-6} $ Katal.
