Using Scientific Notation to Study Bacteria

When you examine a liquid culture of bacteria that has grown long enough you will notice the culture is turbid. A culture that is just barely turbid contains nearly 100 million bacteria per mL. Some bacteria are bigger than other species. Cultures of big bacteria are visibly turbid at fewer cells per mL (at lower titer).

100000000 bacteria per mL is a difficult number to write or comprehend. 100,000,000 is not much better. 108 means the same thing. 108 = 100,000,000 = 100 million. Notice that the 8 is the number of zeros. 103 = 10 x 10 x 10 = 1000 = one thousand.

1 x 108 is the scientific notation for 100 million. 2 x 108 is the scientific notation for 200 million.

If you do not understand Scientific Notation very well, please study the webpages and exercises at the bottom of this page.

I have grown and counted the bacteria in hundreds of cultures of Escherichia coli B. One of the most widely used strains of E. coli is strain B. We write E. coli B and everyone understands that B is the designation of the strain. If you isolate an E. coli colony from New York sewage you might call it E. coli NY and a strain isolated from the feces of your dog might be called E. coli D or E coli 1 if you prefer. You can use any alphanumeric sequence you wish to designate the strains you isolate. I do not know where E. coli B was isolated (found). Other bacteria would not grow at the same speed as E. coli B which I used for the following examples. These examples are intended as a guidelines for you in your study of your favorite bacterium--provided your bacterium grows well on tryptone or nutrient broth. Some genera which should grow similarly are Proteus, Pseudomonas, Serratia, etc. CAUTION: many species of these genera are somewhat or highly pathogenic. At lower temperature, bacteria grow slower. However, 37o C is too hot for many bacteria found in soil and other cool places.

If you have a 20 ml tube of tryptone broth and add a drop or loop of E. coli B from a slant and incubate it overnight (12 to 24 hours) at 37o C with aeration (via gentle shaking or bubbling by an aquarium pump) you have what we call an overnight culture. You could save it in a refrigerator for future use. If you take the titer, you will find there are about 1 x 109 to 4 x 109 cells per mL.

If you dilute 1 mL of a fresh overnight culture of E. coli B into 20 ml of TB (tryptone broth) and aerate at 37o C for about 105 minutes you will find the titer is 2 x 108 cells per mL and the cells will be in log phase with a doubling time of about 20 minutes. If the doubling time is 20 minutes, then the titer at 125 minutes will be 4 x 108 cells per mL. At 145 minutes you would expect the titer to be 8 x 108, but due to crowding, waste products, and lack of food, the titer is likely to be about 6.5 x 108 (I have never measured the titer at 145 minutes).

The above numbers will be very useful to you if try to plate the bacteria to determine the titer. As you have seen when cells are growing in log-phase (doubling at a definite interval) the numbers are increasing rapidly and you better have all your plates, pipets, and other tools ready.

Plotting a Bacterial Growth Curve

In this experiment, we will grow E. coli B with aeration, plate samples at intervals, incubate the plates overnight, count the colonies, list the results in a table, and plot the data on semi-log paper. This will be a lot of work for a beginning student, I suggest several students or the entire class participate with each student doing one plate.

I have never done this complete experiment. I am giving a table below to help guide. Since your conditions may differ from mine you may want to bracket my suggested dilutions or volume plated. Read the subpages about plating (spread vs pouring) for details of plating.

At 105 minutes the titer was usually 2 x 108 cells per mL. As a beginner, you might want to just work at that time for practice. I would strongly recommend that preliminary experiment.

Suppose you dilute 105 and plate 1 ml and get 200 colonies. That indicates a titer of 200 x 105 which reduces to 2 x 107 , but we expect a titer of 2 x 108 and that would give 2000 colonies per plate. Therefore, we could plate 0.1 ml. If we get 200 colonies that calculates as 105 x 10 x 200 = 2 x 108 cells per mL.

time --- dilution ---- vol plated --- expected count --- calc'd titer

Source Typical Titer of bacteria per mL or gram

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Put this hard stuff in a separate section and subpages. It is also true that all killing and growth in bacteria cultures follows a logarithmic function, not a linear function. If those words are new to you, you have not completed a good algebra course. Do not fear this page and its subpages will teach you all you need to know. This page is a remarkable opportunity for you to learn some very interesting mathematics and biology. This biomath is very interesting to me. I use it to count bacteria in cultures, molecules in cells, the number of particles involved in a reaction, etc. From these numbers I can make guesses about how something happens inside a test tube or inside a cell (I can propose possible mechanisms for a reaction).

Please do not give up. I have some easy and hard stuff in this page. Work on the easy stuff and someday you will understand the hard stuff. You can be very proud of yourself if read some of these pages.

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If you know there are 2 x 108 bacteria per mL of your culture, we say the titer of the culture is "2 times 10 to the 8th". That is 200 million cells per mL. Recall one mL is about 20 drops of water. If all this is new to you try reading about Scientific Notation(LINK). Scientific notation is easy. "2 times ten to the eighth" means 2 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10. Notice there are eight 10s. 10 to the eighth is very familiar to any bacteriologist as a bacterial culture having that titer is just barely turbid.

Links on scientific notation = b038a - to be started. Have a page on sci notation under math.

http://www.altavista.com/cgi-bin/query?pg=q&kl=XX&q=scientific+notation&search=Search

http://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html - good summary

This page is barely started. To be continued.


First draft = 98 Nov 25     Revision #2 = 98 March 11
If you have questions please write me    indbio@disknet.com
Written by Harold Eddleman, Ph. D., President, Indiana Biolab, 14045 Huff St., Palmyra IN 47164

The material below will be used in writing this page

H2SO4     1022m