BMEN E 3500, fall 1999

Problem Set 3.  Note added 9/26/99.   You are responsible for these problems.  Problem 2 will be discussed in the week of 9/27/99

  1. A typical cell utilizes about 5 10-17 g-mole of oxygen per second. If used exclusively for the oxidation of glucose, C6H12O6, this oxygen utilization will produce about 30 molecules of ATP. At steady-state the cell will utilize these molecules at the same rate at which they are being synthesized (none are imported or exported) to sustain the cellular functions that sustain energy. Assume (the reality is more complicated), that the enzyme Adenosine triphosphtase is required for each ATP utilization. A cell which is a 9 micrometer sphere contains about 109 ATP molecules at steady state. If the enzyme has a value of k2 of 104 sec-1 and a Km-1 of 79,000 M-1, calculate the following:
    1. The molarity (M) of ATP in the cell, assuming it to be a single compartment.
    2. From this calculation, the value of v/vmax assuming the reaction to be irreversible.
    3. The number of Adenosine triphosphtase molecules that must be in the cell. Compare this value with the number of ATP's that are present.
    4. If synthesis of ATP is interrupted, the time required for the ATP concentration to fall to 25% of its initial value.
    5. Comment on the appropriateness of this enzyme (under the assumptions suggested) for this cell. What would be the consequences of a higher or lower value of Km, or of k2?
  2. Show that the Michaelis-Menten equation can be rearranged to the form:

This expression suggests that one can obtain the parameters Km and vmax from a plot of 1/v versus 1/s. The following data for s (mol/L) and v mol/(L-min) x 106 are to be plotted and fitted by this method:

s v
4.1 10-3 177
9.5 10-4 173
5.2 10-4 125
1.03 10-4 106
4.9 10-5 80
1.06 10-5 67
5.1 10-6 43

The type of plot that you are asked to make is called a Lineweaver-Burke plot.

Derive the formula given without proof in the lecture notes for the rate of a reversible enzyme reaction. This formula is not so important for enzyme reactions but is for the transporter model of transmembrane transport, to be discussed.

Stryer (Stryer, L., "Biochemistry", Freeman, San Francisco [1975], p. 132 - 133) discusses two forms of enzyme inhibition. Each is illustrated below.

Competitive inhibition:

Noncompetitive inhibition:

Derive these equations and show that they produce two different Lineweaver-Burke plots.

The following data are obtained with two different inhibitors acting on the same enzyme. Identify the type of inhibition for each. The v's are given in micromole/min.

s, M v, no inhibitor v, inhibitor A v, inhibitor B
0.3 10-5 10.4 4.1 2.1
0.5 10-5 14.5 6.4 2.9
1.0 10-5 22.5 11.3 4.5
3.0 10-5 33.8 22.6 6.8
9.0 10-5 40.5 33.8 8.1

Return to course main page.