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)
Michaelis-Menten Kinetics: Calculating $v_0/V_{max}$ Ratio
The Michaelis-Menten equation describes the initial reaction velocity ($v_0$) in enzyme kinetics:
$ v_0 = \frac{V_{max}[S]}{K_m + [S]} $
Where:
- $v_0$ = Initial reaction velocity
- $V_{max}$ = Maximum reaction velocity
- $[S]$ = Substrate concentration
- $K_m$ = Michaelis constant (substrate concentration at which $v_0 = V_{max}/2$)
Determining the $v_0/V_{max}$ Ratio
To find the ratio $v_0/V_{max}$, we can rearrange the Michaelis-Menten equation:
$ \frac{v_0}{V_{max}} = \frac{[S]}{K_m + [S]} $
Substituting Substrate Concentration
The question states that the substrate concentration $[S]$ is 20 times the Michaelis constant $K_m$. Therefore:
$ [S] = 20 \times K_m $
Substitute this value into the ratio equation:
$ \frac{v_0}{V_{max}} = \frac{20 \times K_m}{K_m + (20 \times K_m)} $
Calculating the Final Ratio
Simplify the expression:
$ \frac{v_0}{V_{max}} = \frac{20 K_m}{21 K_m} $
$ \frac{v_0}{V_{max}} = \frac{20}{21} $
Now, calculate the numerical value and round to two decimal places:
$ \frac{20}{21} \approx 0.95238... $
Rounding to two decimal places, the ratio $v_0/V_{max}$ is approximately 0.95.
This value falls within the specified correct answer range of 0.94 to 0.96.
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 ________
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____.
An enzymatic reaction exhibits Michaelis-Menten kinetics. For this reaction, on doubling the concentration of enzyme while maintaining [S] >> [$E_o$],
- 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.
