Question

Here's a precise problem for a chemistry student to solve related to enzyme kinetics and inhibition:A researcher wants to determine the Km and Vmax values of an enzyme that catalyzes the conversion of substrate A to product B. They measure the initial reaction rates at varying substrate concentrations and obtain the following data:| [A] (mM) | Initial Reaction Rate (μmol/min) ||----------|---------------------------------|| 1.0 | 0.10 || 2.5 | 0.20 || 5.0 | 0.28 || 10.0 | 0.32 || 20.0 | 0.35

Answer 1

a  To calculate the Km and Vmax using the Lineweaver-Burk plot, we first need to create a double reciprocal plot of the data. This means plotting 1/[A] on the x-axis and 1/Initial Reaction Rate on the y-axis.| 1/[A]  1/mM  | 1/Initial Reaction Rate  min/mol  ||--------------|-----------------------------------|| 1.0          | 10.0                              || 0.4          | 5.0                               || 0.2          | 3.57                              || 0.1          | 3.13                              || 0.05         | 2.86                              |Now, we can plot these points and find the best-fit line. The equation of the line will be in the form of y = mx + b, where y = 1/Initial Reaction Rate, x = 1/[A], m is the slope, and b is the y-intercept.The slope of the line  m  is equal to Km/Vmax, and the y-intercept  b  is equal to 1/Vmax. From the plot, we can estimate the slope and y-intercept. Let's say the slope  m  is approximately 5 and the y-intercept  b  is approximately 2.Now we can solve for Km and Vmax:Km/Vmax = 51/Vmax = 2From the second equation, we can find Vmax:Vmax = 1/2 = 0.5 mol/minNow, we can use the first equation to find Km:Km = 5 * VmaxKm = 5 * 0.5Km = 2.5 mMSo, the Km is 2.5 mM, and the Vmax is 0.5 mol/min.b  To determine the type of inhibition and calculate the new Km and Vmax values in the presence of the inhibitor, we need to know the effect of the inhibitor on the enzyme kinetics. Since we are given the Ki value  0.5 mM , we can use the following relationships for different types of inhibition:1. Competitive inhibition: Km apparent  = Km 1 + [I]/Ki , Vmax remains the same2. Non-competitive inhibition: Vmax apparent  = Vmax/ 1 + [I]/Ki , Km remains the same3. Uncompetitive inhibition: Km apparent  = Km/ 1 + [I]/Ki , Vmax apparent  = Vmax/ 1 + [I]/Ki Since the problem states that the researcher observes a decrease in reaction rate, we can assume that the Vmax value is affected. This suggests that the inhibition is either non-competitive or uncompetitive. However, without more information about the effect of the inhibitor on the Km value, we cannot definitively determine the type of inhibition or calculate the new Km and Vmax values. The researcher would need to provide additional data on the effect of the inhibitor on the enzyme kinetics to make this determination.