The Michaelis-Menten equation states Vo= Vmax [S]/Km+[S]. An enzyme has a Km of 0.07mM. Calculate the % maximum activity observed at a substrate concentration of 3.3mM?
The Correct Answer and Explanation is :
To calculate the percentage of maximum activity (% Vmax) observed at a substrate concentration (([S])) of 3.3 mM for an enzyme with a Michaelis constant ((K_m)) of 0.07 mM, we can use the Michaelis-Menten equation:
[
V_0 = \frac{V_{max} \cdot [S]}{K_m + [S]}
]
Steps to Calculate % Vmax:
- Insert the values into the equation:
- (K_m = 0.07 \, \text{mM})
- ([S] = 3.3 \, \text{mM})
- Calculate (V_0):
[
V_0 = \frac{V_{max} \cdot 3.3}{0.07 + 3.3}
] First, compute the denominator:
[
0.07 + 3.3 = 3.37
] Now substitute into the equation:
[
V_0 = \frac{V_{max} \cdot 3.3}{3.37}
] - Calculate % Vmax:
The percentage of maximum activity can be calculated as:
[
\% V_{max} = \left( \frac{V_0}{V_{max}} \right) \times 100
]
Substituting (V_0):
[
\% V_{max} = \left( \frac{3.3}{3.37} \right) \times 100 \approx 97.9\%
]
Conclusion:
Thus, at a substrate concentration of 3.3 mM, the enzyme exhibits approximately 97.9% of its maximum activity.
Explanation:
The Michaelis-Menten model describes how the reaction velocity ((V_0)) of an enzyme-catalyzed reaction depends on the substrate concentration. The (K_m) value represents the substrate concentration at which the reaction velocity is half of (V_{max}). A low (K_m) indicates high affinity of the enzyme for its substrate.
In this case, with a substrate concentration of 3.3 mM significantly higher than the (K_m) of 0.07 mM, we can expect the enzyme to be almost saturated with the substrate. Consequently, the reaction rate approaches (V_{max}), reflecting that the enzyme is operating efficiently and rapidly converting substrate to product. This saturation implies that even small increases in substrate concentration beyond 3.3 mM will result in minimal increases in reaction velocity, illustrating the characteristic behavior of enzyme kinetics as described by the Michaelis-Menten equation.