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Bio481: OrientationLabExampleMathProblems

Example Math Problems

1. You diluted a bacterial culture through 6 rounds (6 wells) of dilution. After plating 100µL, you count 43 colonies. What was the concentration of bacteria in the culture? (The common unit of concentration/density of bacteria is CFU (colony forming units) / mL).
   
   
   Working backwards from the Petri dish to the sample works best:
   
   43 colonies on the dish = 43 bacterial cells
   
   [43 bacterial cells / 100µL (amount plated)] × (1000µL/mL) = 430 CFU/mL
   
   So that makes 4.3 × 10² CFU/mL in the well that was plated
   
   Or, 4.3 × 10² CFU/mL / (1/10 dilution) = 4.3 × 10³ CFU/mL in the fifth well
   
   Or, 4.3 × 10³ CFU/mL / (1/10 dilution) = 4.3 × 10⁴ CFU/mL in the fourth well
   ...
   Or, 4.3 × 10⁶ CFU/mL / (1/10 dilution) = 4.3 × 10⁷ CFU/mL in the first well
   
   Finally, 4.3 × 10⁷ CFU/mL / (1/10 dilution) = 4.3 × 10⁸ CFU/mL in the culture

2. You have been informed that a tube of bacteria has a density of 6.7 × 10⁴ CFU/mL. What well should you sample and how many colonies should you expect?

First off, you want Petri dishs with easily countable numbers of colonies (30-300). Too few and you can get an imprecise measurement; too many and you won't be able to count them all.

If you plated 100µL (.1 mL) of the sample directly:

6.7 × 10⁴ CFU/mL * .1 mL = 6700 CFU (or 6700 colonies); quite uncountable.

Plating of the first titer well:

6.7 × 10⁴ CFU/mL × (1/10 dilution) = 6.7 × 10³ CFU/mL in the first well

6.7 × 10³ CFU/mL × .1 mL = 670 CFU; still outside of the acceptable range

Plating of the second well:

6.7 × 10⁴ CFU/mL × (1/10 dilution) × (1/10 dilution) × .1 mL = 67 CFU;

So, you would want to dilute to the second well and expect 67 colonies on the Petri dish.

In-class problems

3. You diluted a bacterial culture through 4 rounds (4 wells) of dilution. After plating 100µL and incubating, you count 72 colonies. What was the concentration of the bacteria in the culture?

4. A sample of bacteria should have a concentration of 4.4 × 10⁷ CFU/mL; how many colonies at what dilution (what well) would you use to confirm this?

At home (for self-gratification)

5. You discover that the microtiter plate (used in Problem 3) actually was filled with only 170µL of saline (instead of 270µL). What is the corrected concentration of bacteria?