Dilution Series and Calculations

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First, learn the language...

A solution has 2 components.

Solute – the solid component of the solution à In our example, our solid components our the cells!
Solvent (Diluent) – the liquid component of the solution à In our example, our solvent is nutrient broth.

The Value of Concentration is given as…

Concentration is a RATIO that expresses the amount of solids you have to the amount of liquid you have.

Scientific Notation

In microbiology, it is convenient to use scientific notation, because we are often dealing with huge numbers of cells.

Round the number so you only have 3 “non-zero” digits. This is a good rule of thumb, unless the directions or your instructor says otherwise.
Then, put a decimal point after the first digit!

Count the number spaces you have after the decimal point.
Now we get rid of all those zeros and add the notation “ (x 10) ”.
The exponent on the 10, will simply be the number of spaces we had after the decimal point, which in our example was 12.

This works for small numbers too!

We just count the number of zeros that come AFTER the decimal point, and use a negative sign for our exponent...

Concentration Practice Problem #1

Let’s say we have a Bacillus cell culture with a concentration of 6.2 x 10^4 cells/ml.
If I have 3 ml of the Bacillus cell culture and add 5 ml of TSB (nutrient broth) to the cell culture, what is my final concentration

Concentration Practice Problem #2

What would our concentration be if we took an 8 ml cell culture of bacillus and we added 10 ml of TSB broth? The cell culture has a concentration of 6.2 x 10^4 cells/ml.

Once we have the number of cells, we get the final concentration, by dividing the number of cells by the final volume.

How do we count cells in culture?

The cells are way too small to just simply count directly!

BUT... If the culture was dilute enough, we could just mix our entire sample with warm agar..

And Then Incubate Overnight at Optimal Temperature, to Get Visible Colonies
We know one cell will yield one colony.

Calculate How Many Cells There Were in the Original Sample?

Calculate the Concentration of Cells in Original Sample.?

BUT…. Here’s the problem! There can be millions of cells in a single drop! So, doing this is the without a serial dilution, will give you something more like…..

We could try again, but this time instead of using the entire contents of the original 5.0 ml cell culture, we only use 0.5 ml to create the pour plate!

We’ll take 0.5ml of our original cell culture, and mix with warm TSA (trypsin Soy Agar) to make sure there are enough nutrients… And make our plate with only 0.5ml of the original culture!

Then We Incubate Overnight at Optimal Temperature, to Get Visible Colonies
If we counted 300 colonies, then that means that we had 300 cells in the 0.5ml we used to make the plate.

Calculate the Concentration of Cells in Original Sample.?

Calculate How Many Cells There Were in the Original Sample?

BUT…. 99.9% of the time, even with using this smaller amount, you‘ll something more like…..

All of our previous ideas will work, once we get a sample of our cell culture that is dilute enough to yield between 30 and 300 colonies on a Petri plate/dish.

What if we did this same idea again, and just kept track of the volume?
We’ll Use Numbers that are Super Easy to Work With!

Setting up a serial dilution!
1:10

Start with 10 ml of your cell culture. This undiluted tube will be our tube #1.
Then set up a number of tubes containing 9 ml each of broth alone (for dilutions).
Take 1 ml from the first tube and add it to the 9 ml of plain broth you have in tube 2. Tube 2 now contains a 1:10 dilution.
Next, take 1 ml from tube #2 and place it into tube #3. Tube 3 has 1 / 10th of its volume that is composed of the 1 : 10 dilution from tube 2. So, tube #3 has 1 / (10 x 10) dilution which is 1 / 100 or 1 : 100.
Now, we can take 1 ml from tube #3 and place it into tube #4. Tube 4 has 1 / 10th of its volume that is composed of the 1 : 100 dilution from tube 3. So, tube #4 has 1 / (10 x 10 x 10) dilution which is 1 / 10^3 or 1 / 1000 or 1 : 1000.
You guessed it! We'll take 1 ml from tube #4 and place it into tube #5. Tube 5 has 1 / 10th of its volume that is composed of the 1 : 1000 dilution from tube 4. So, tube #5 has 1 / (10 x 10 x 10 x 10) dilution which is 1 / 10^4 or 1 / 10,000 or 1 : 10,000.
I think you are beginning to see the pattern here! Then we take 1 ml from tube #5 and place it into tube #6. Tube 6 has 1 / 10th of its volume that is composed of the 1 : 10,000 dilution from tube 5. So, tube #6 has 1 / (10 x 10 x 10 x 10 x 10) dilution which is 1 / 10^5 or 1 / 100,000 or 1 : 100,000.

AND SO ON!

It doesn't really matter how many dilutions you do, but you want to make sure you do enough dilutions and make enough culture plates so that you won't waste time having to repeat the experiment, in case your plates end up having too many colonies!

After you've made your serial dilutions, you will want to make some pour plates using a few of the most dilute concentrations from the series.

Make sure to label your Petri dish with the dilution you used!
Create Each Pour Plate Separately by Adding the Entire Contents of the Diluted Cell Culture to Warm TSA (Nutrient Agar) in a Petri Dish.
Incubate Overnight at Optimal Temperature (You should check what the optimal temperature for growth is for your organism).
Following the incubation, inspect the pour plates and discern which of the plates contains between 30 and 300 colonies. This is the plate we will want to use!
Carefully count the colonies on the plate having between 30 and 300 colonies.
Record the number of colonies on the plate
Record the dilution factor that was used for that plate that was counted.
Now, calculate the number of cells in the original 1 : 1 undiluted cell culture, by multiplying (the # of colonies you counted) by (the reciprocal dilution factor).

Here's what's going on. One progenitor cell or parent cell or culture-forming unit (CFU) will yield one single colony. So counting the colonies that grew on our plate, gives us our cell count for our diluted cell culture.
We know what our dilution factor was that we used to make the plate.

To get the reciprocal of dilution factor, simply flip the fraction upside-down!

Calculate the Number of Cells in Original Sample.

What is the concentration of a cell culture that grew 79 colonies on a Petri dish at a dilution of 1 : 100?

What is the concentration of a cell culture that was able to grow 28 colonies using only 0.1 ml of a 1:10,000 dilution sample?

HOW TO SET UP A 3-FOLD DILUTION!
Setting up a serial dilution!
1:3

Start with 3 ml of your cell culture. This undiluted tube will be our tube #1.
Then set up a number of tubes containing ( 3 - 1 ) = 2 ml each of broth alone (for dilutions).
Take 1 ml from the first tube and add it to the 2 ml of plain broth you have in tube 2. Tube 2 now contains a 1 : 3 dilution.
Next, take 1 ml from tube # 2 and place it into tube # 3. Tube 3 has 1 / 3rd of its volume that is composed of the 1 : 3 dilution from tube 2. So, tube # 3 has 1 / (3 x 3) dilution which is 1 / 9 or 1 : 9.
Now, we can take 1 ml from tube # 3 and place it into tube # 4. Tube 4 has 1 / 3rd of its volume that is composed of the 1 : 9 dilution from tube 3. So, tube #4 has 1 / ( 3 x 3 x 3) dilution which is 1 / 3^3 or 1 / 27 or 1 : 27.
You guessed it! We'll take 1 ml from tube #4 and place it into tube #5. Tube 5 has 1 / 3rd of its volume that is composed of the 1 : 27 dilution from tube 4. So, tube #5 has 1 / (3 x 3 x 3 x 3) dilution which is 1 / 3^4 or 1 / 81 or 1 : 81.
I think you are beginning to see the pattern here! Then we take 1 ml from tube #5 and place it into tube #6. Tube 6 has 1 / 3rd of its volume that is composed of the 1 : 81 dilution from tube 5. So, tube #6 has 1 / (3 x 3 x 3 x 3 x 3) dilution which is 1 / 3^5 or 1 / 243 or 1 : 243.

AND SO ON!

QUESTION: Prepare a serial dilution to 1,000,000.
SHORT CUT :There are 6 zeros in 1,000,000, so you’ll dilute it 6 times!

MATH CHEAT SHEET!

10^0 = 1
10^1 = 10
10^2 = 100
10^3 = 1000
10^4 = 10,000
10^5 = 100,000
10^6 = 1,000,000
10^7 = 10,000,000
10^8 = 100,000,000
10^9 = 1,000,000,000
10^10= 10,000,000,000

MATH CHEAT SHEET!
10^-1 = 0.1 = 1/10
10^-2 = 0.01 = 1/100
10^-3 = 0.001 = 1/1000
10^-4 = 0.0001 = 1/10000
10^-5 = 0.00001 = 1/100000
10^-6 = 0.000001 = 1/1000000
10^-7 = 0.0000001 = 1/10000000
10^-8 = 0.00000001 = 1/100000000
10^-9 = 0.000000001 = 1/1000000000