1. There remains a controversy in the growth of individual Escherichia coli cells. Kubischek and Pai [1] claim that the cells grow linearly as their protein production is limited by the amount of DNA. Thus, the volume of the cell satisfies the differential equation;

VL' = a, VL(0) = V0.

Cooper[2] claims that the cells grow exponentially as their protein is dependent on the availability of ribosomes which increase with the volume. Thus, the volume of the cell satisfies the differential equation;

VE' = kVE, VE(0) = V0.

a. Let V0 = 1.6 mm3, then solve each of these differential equations. Determine a and k, if the cell divides in 30 min, i.e., the cell has doubled its volume in this amount of time.

b. On a single graph show the volume of a cell using each of these growth laws, 0 < t < 30.

c. Let the percent error between the two growth models be given by the formula:

Graph the percent error between the two growth curves, E(t), for 0 < t < 30. Find the greatest error between these growth curves and when this occurs.

d. Discuss at least two reasons why this controversy cannot be resolved at this time.


[1]H. E. Kubischek and S. R. Pai, "Variation in precursor pool size during the division of Escherichia coli : Further evidence for linear cell growth," J. Bacteriol . (1988) 170, pp. 431-437.

[2]S. Cooper, "What is the bacterial growth law during the division cycle?" J. Bacteriol . (1988) 170, pp. 5001-5005.