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To determine the Michaelis constant (Km) and maximum velocity (Vmax) of an enzyme-catalyzed reaction, you can use the Michaelis-Menten equation and the provided data. Here's how:
1. Plot the data: Plot the initial velocity (v) against the substrate concentration ([S]). This should give you a hyperbolic curve, characteristic of Michaelis-Menten kinetics.
2. Linearize the data: To make the analysis easier, you can linearize the data using a Lineweaver-Burk plot. This involves plotting the reciprocal of the initial velocity (1/v) against the reciprocal of the substrate concentration (1/[S]). This will give you a straight line.
3. Determine the slope and intercept: From the Lineweaver-Burk plot, you can obtain the slope and intercept of the line. The slope of the line is Km/Vmax, and the intercept on the y-axis is 1/Vmax.
4. Calculate Km and Vmax: Using the values of the slope and intercept, you can calculate Km and Vmax. For instance, Vmax = 1/intercept, and Km = (slope
Vmax).
Note: While you provided only three data points, the accuracy of the calculated values would be improved with more data points. Remember that the Michaelis-Menten equation describes the relationship between substrate concentration, initial velocity, and the kinetic parameters Km and Vmax. This relationship is a fundamental concept in enzyme kinetics and plays a vital role in understanding how enzymes function.