Dilution Theory – Page 1:

Dilution Plating
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Selected General Topics  >  Dilution Theory:
Dilution Theory per se:
" Page 1 – Dilution Plating
" Page 2 – More Dilution Plating
" Page 3 – The MPN Method		 Supplementary Pages:
" Five-Tube MPN Table
" Practice Set 1 (Plating)
" Practice Set 2 (Plating&MPN)

In quantitative microbiology, we are concerned with determining the concentration of colony-forming units (CFUs) in our sample – i.e., the number of CFUs per ml or per gram of the sample. For example, if we were to plate out one ml of a lake water sample and then – after incubation of the plates – find that 100 colonies have arisen, we would then conclude that there were 100 CFUs per ml of the lake water.

More realistically (as with most of our area lakes), the concentration of CFUs in the water could have been considerably greater. Counting the colonies on a plate inoculated with one ml of water may be impossible. We would like to have "countable" plates – containing between 30 and 300 colonies. If fewer than 30, we run into greater statistical inaccuracy. If greater than 300, the colonies would be tedious to count and also would tend to run together.

We may try to plate out smaller and smaller amounts, as in the example shown at right. With this new lake water sample, a countable plate (Plate C: 100 colonies) is achieved with the inoculation of 0.01 ml of sample. Figuring out the number of CFUs per ml of the sample would go like this: Whatever the number of CFUs in the inoculum of Plate C (one-hundreth of a ml of the sample), there would be one hundred times as many CFUs in one ml of the sample. So, if 100 CFUs are determined to be in the 0.01 ml inoculum, then 100 X 100 CFUs would be present in one ml; the final answer is 10,000 CFUs/ml of the sample.

Two drawbacks to this procedure: It is difficult with our equipment to dispense amounts smaller than 0.1 ml. Also, the smaller the amount tested, the less representative it is of the sample.

So we now get into "dilution theory" to accomplish the equivalent of plating out succeedingly smaller amounts of sample. Making serial decimal dilutions (i.e., successive 1/10 dilutions, each made by adding one part of inoculum to 9 parts of diluent) and inoculating one ml into each of the plates, we can construct a plating procedure (shown at right) that is equivalent to the above. Note that for each 1/10 dilution, we are taking one part of inoculum and spreading it out over a total of 10 parts; the concentration of organisms thereby becomes one-tenth as dense.

Illustrating further how the concentration of CFUs decreases according to how these cell suspensions are diluted: We determined above that the sample contains 10,000 CFUs per ml. Taking out one ml and inoculating it into a 9 ml dilution blank (the second tube) would put the 10,000 CFUs into a total of 10 ml which is equivalent to 1000 CFUs per ml of the 1/10 dilution of the sample. The density of CFUs continues to decrease ten-fold with each subsequent dilution.

Counting 100 colonies in Plate C, note how we can work back to a concentration of 10,000 CFUs per ml of the sample. So, by inoculating 1 ml of a 10–2 dilution into the plate which is subsequently counted, we are theoretically doing the equivalent of plating 10–2 ml (i.e., 0.01 ml) of the lake water sample. (Scientific notation is reviewed here.)

IF 100 colonies arise from having plated one ml of a 1/100 dilution of the lake water,
THEN there would have been 10,000 CFUs (from 100 X 100) per one ml of the undiluted water sample.

Compare the solution just obtained with the previous solution where Plate C was inoculated with 0.01 ml of sample:

IF 100 colonies arise from having plated 0.01 ml of the water sample,
THEN there would have been 10,000 CFUs per one ml of the water sample.

SOME MORE EXAMPLES:

  1. For Bacteriology 102 students, the above setup is applicable to Experiment 1, Period 2 where we plated one ml of a 10–2 (i.e., 1/100) dilution of lake water. In Period 3 – after incubation of the plates – if we were to find 75 colonies on our plate, we could determine the CFUs per ml of the sample (at the time of Period 2) as follows:

    IF 75 colonies arise from having plated one ml of a 1/100 dilution of the lake water,
    THEN there would have been 7,500 CFUs (from 75 X 100) per one ml of the undiluted water sample.


  2. As we used a 10–4 (i.e., 1/10,000) dilution of soil in the same experiment, we could figure out the CFUs per gram of the soil the same way, remembering that we consider milliliters and grams to be equivalent:

    IF 75 colonies arise from having plated one ml of a 1/10,000 dilution of the soil,
    THEN there would have been 750,000 CFUs (from 75 X 10,000) per one gram of the undiluted soil sample.


  3. Consider this problem, the likes of which we often give in quizzes and on problem sets:  Five ml (not one!) of an undiluted spring water sample were added to a petri dish to which 15 ml of melted Plate Count Agar were then added. After mixing, the plate was allowed to solidify and then was incubated appropriately. After incubation, 50 colonies were counted. How many CFUs were present per one ml of the original, undiluted spring water sample?

Here's the solution (and note the continued careful use of correct terminology):  If 50 colonies arise from having plated 5 ml of the sample, then there would have been 10 CFUs per one ml of the sample.

In working through this problem, consider the special bit of extraneous information thrown in – i.e., the amount of medium in the plate. Wouldn't you expect the same answer if you used a different amount of melted Plate Count Agar, say 20 or 25 ml? So, you should still wind up with the answer being 10 CFUs per ml of the water sample.

On occasion, we unfortunately see an answer of more CFUs in one ml then there would have been in 5 ml! This can happen if one does not think through the setup of the problem and then treats the addition of sample to medium as a dilution. On the next page is the same problem worked out with our formulas.

Continued on Page 2.

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John Lindquist, Department of Bacteriology,
University of Wisconsin – Madison