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
- 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)
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}$.
- 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 ________
