Consider an LB broth flask into which two E. coli strains are inoculated. Strain
ID: 195753 • Letter: C
Question
Consider an LB broth flask into which two E. coli strains are inoculated. Strain "A" is wild-type, with g = 22 min at 37oC, and 45 min at 27oC. Strain "B" has a temperature-sensitive mutation, such that g = 52 min at 37oC, but at 27oC g = 44 min.We inoculate equal amounts of cells (1 ml of each starter culture whose population is 1 x 106 cfu/ml) into each of two separate 1 liter volumes of LB broth at time = 0. One of the flasks is incubated at 37oC, one at 27oC.Assuming constant exponential growth (i.e. no lag phase, and no exhaustion of nutrients), answer each of these questions:
1) After 6 hours of growth, what is the final concentration of each strain in each flask?
2) What fraction of the total population is Strain A and Strain B in each flask?
Explanation / Answer
1) Final concentration of each strain in each flask:
Time = 6 hours = 6*60 = 360 minutes
Concentration of starter culture (Xo) = 1*106 CFU/ml
Final concentration = Xo * 2Time/g
i) 37oC:
Strain A : Generation time (g) = 22 minutes;
Final concentration = 1 * 106 * 2360/22 = 1 * 106 * 216.36 = 8.4111 * 1010
Final concentration of strain A = 8.4111 * 1010 CFU/ml
Strain B : Generation time (g) = 52 minutes;
Final concentration = 1 * 106 * 2360/52 = 1 * 106 * 26.92 = 1.2110 * 108
Final concentration of strain B = 1.2110 * 108 CFU/ml
ii) 27oC:
Strain A : Generation time (g) = 45 minutes;
Final concentration = 1 * 106 * 2360/45 = 1 * 106 * 28 = 2.56 * 108
Final concentration of strain A = 2.56 * 108 CFU/ml
Strain B : Generation time (g) = 44 minutes;
Final concentration = 1 * 106 * 2360/44 = 1 * 106 * 28.18 = 2.9002 * 108
Final concentration of strain B = 2.9002 * 108 CFU/ml
Final concentration of each strain in each flasks in CFU/ml
2) Total concentration = Final concentration of strain A + Final concentration of strain B
i) 37oC :
Total concentration = (8.4111 * 1010) + (1.211 * 108) = 8.4232 * 1010
Fraction of strain A = Final concentration of strain A / Total concentration = 8.4111 * 1010 / 8.4232 * 1010 = 0.9986
Fraction of strain B = Final concentration of strain B / Total concentration = 1.211 * 108 / 8.4232 * 1010 = 0.0014
ii) 27oC :
Total concentration in flask at 27oC = (2.56 * 108) + (2.9002 * 108) = 5.4602 * 108
Fraction of strain A = Final concentration of strain A / Total concentration = 2.56 * 108 / 5.4602 * 108 = 0.4688
Fraction of strain B = Final concentration of strain B / Total concentration = 2.9002 * 108 / 5.4602 * 108 = 0.5312
Fraction of each strain:
Strain A Strain B 37oC 8.4111 * 1010 1.211 * 108 27oC 2.56 * 108 2.9002 * 108