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?

Answer 1

1) Final concentration of each strain in each flask:

Time = 6 hours = 6*60 = 360 minutes

Concentration of starter culture (X_o) = 1*10⁶ CFU/ml

Final concentration = X_o * 2^Time/g

i) 37^oC:

Strain A : Generation time (g) = 22 minutes;

Final concentration = 1 * 10⁶ * 2^360/22 =  1 * 10⁶ * 2^16.36 = 8.4111 * 10¹⁰

Final concentration of strain A = 8.4111 * 10¹⁰ CFU/ml

Strain B : Generation time (g) = 52 minutes;

Final concentration = 1 * 10⁶ * 2^360/52 =  1 * 10⁶ * 2^6.92 = 1.2110 * 10⁸

   Final concentration of strain B = 1.2110 * 10⁸ CFU/ml

ii) 27^oC:

Strain A : Generation time (g) = 45 minutes;

Final concentration = 1 * 10⁶ * 2^360/45 =  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 * 2^360/44 =  1 * 10⁶ * 2^8.18 = 2.9002 * 10⁸

   Final concentration of strain B = 2.9002 * 10⁸ CFU/ml

Final concentration of each strain in each flasks in CFU/ml

	Strain A	Strain B
37oC	8.4111 * 1010	1.211 * 108
27oC	2.56 * 108	2.9002 * 108

2) Total concentration = Final concentration of strain A + Final concentration of strain B

i) 37^oC :

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) 27^oC :

Total concentration in flask at 27^oC = (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	0.9986	0.0014
27oC	0.4688	0.5312