Use the Michaelis-Menten equation to complete the enzyme kinetic data set shown below (fill in the blanks), when Vmax is known to have a value of 100 nM/min. Answer with three significant digits.Substrate concentration (µM) Reaction rate (nM/min)4.00 50.05.00 10.0 20.0
Question
Use the Michaelis-Menten equation to complete the enzyme kinetic data set shown below (fill in the blanks), when Vmax is known to have a value of 100 nM/min. Answer with three significant digits.Substrate concentration (µM) Reaction rate (nM/min)4.00 50.05.00 10.0 20.0
Solution
The Michaelis-Menten equation is given by:
V = Vmax*[S]/(Km + [S])
where: V is the reaction rate, Vmax is the maximum reaction rate, [S] is the substrate concentration, and Km is the Michaelis constant.
From the given data, we can calculate the value of Km. We know that when the reaction rate (V) is half of Vmax, the substrate concentration ([S]) is equal to Km. So, from the first row of the table, we have:
50.0 nM/min = 100 nM/min * 4.00 µM / (Km + 4.00 µM)
Solving for Km, we get:
Km = 4.00 µM
Now, we can use the Michaelis-Menten equation to calculate the reaction rate (V) for the other substrate concentrations.
For [S] = 5.00 µM:
V = 100 nM/min * 5.00 µM / (4.00 µM + 5.00 µM) = 55.6 nM/min
For [S] = 10.0 µM:
V = 100 nM/min * 10.0 µM / (4.00 µM + 10.0 µM) = 71.4 nM/min
For [S] = 20.0 µM:
V = 100 nM/min * 20.0 µM / (4.00 µM + 20.0 µM) = 83.3 nM/min
So, the completed data set is:
Substrate concentration (µM) Reaction rate (nM/min) 4.00 50.0 5.00 55.6 10.0 71.4 20.0 83.3
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