Question

The following question focuses on how the parameters regulating enzyme function might change, and how these might appear graphically on a Michaelis-Menton plot and a Lineweaver-Burke plot.

Carbonic anhydrase is an enzyme that will convert CO2 and water into HCO3.

CO2 + H20 >   H+ + HCO3

There are many different isoforms of this enzyme. see for instance:

http://en.wikipedia.org/wiki/Carbonic_anhydrase

1 Assume that one variant has a Km of 1 µM and a different variant has a Km of 10 µM. Draw on the same graph a typical Michaelis-Menton plot showing the alteration in the rate of carbonic anhydrase as the CO2 level is varied for the two different variants of enzyme, assuming the concentration of the enzyme (10 mM) in the test tube is kept constant. Assume that you have equal amounts of the two different variants of carbonic anhydrase in a number of test tubes and that the Vmax for both enzymes are the same.   Label the axes

2. For the same conditions as above, draw a Lineweaver-Burke plot for both enzymes on one graph.

3. Morphine is a non-competitive inhibitor of carbonic anhydrase. Draw on the same Lineweaver-Burke plot as above a graph showing the effect of a concentration of morphine that inhibits the first enzyme such that it reduces the Vmax to ½ its maximal value. Make sure to put in sample data points.

4. Imidazol is a competitive inhibitor of carbonic anhydrase. It is effective at an alkaline (high) pH; in lower (more acidic) pH, it no longer inhibits the enzyme. Draw on a separate graph a Lineweaver-Burke plot for the effects of this compound at high pH and low pH.   Be sure to label the axes and put in sample data points

Answer 1

To answer this we have to know how each one of this values behave in the plots, where are they located, and what is the change in behavior in presence of different types of inhibitors. Let us analyze each question:

1.- Km is the concentration of substrate needed to reach half the Vmax. The Michaelis Menten curve plots substrate concentration against velocity, then the Km value will be located at the X axis where the value of the Y axis corresponds to half the V max. In our case, the Vmax values are the same, so the curve will tend to the same Y value, but the Km values greatly vary. The plot would look like this:

Vmax V [S] Km: 10 microM Km: 1 microM

2.- Now, the Lineweaber Burk graph will plot the inverse values of from Michaelis Menten. In this graph the Vmax intercepts the Y axis, and Km interceps the X axis, now the values don't draw a curve, but a line instead:

Km: 10 Km: 1 [S]

Note that they intercept the Y axis in the same point (Vmax), but they intercept the X axis at different points (Km)

3.- Noncompetitive inhibitors modify the line by only reducing the Vmax, Km is unaffected, it would look like this:

Km: 10 Km: 1 [S]

The gray line is the inhibited reaction for the enzyme with Km 10, and the pink line is the one for the Km 1. Note how the Km values don't vary (X axis intercept) but the Vmax is reduced

4.- Competitive inhibitors modify the line by only increasing the Km, Vmax is unaffected, it would look like this:

Km: 10 Km: 1 [S]

Again, the grey line corresponds to the enzyme with original Km 10, and the pink for the Km 1. Note how they have a same Vmax, but Km values were increased