Tips for handling specific types of data:
Dilutions.
If you perform a viable count to determine the number of bacteria in a culture, plate aliquots of the dilutions onto agar with sterile pipettes, spread with glass hockey sticks, incubate at 37°C and count the number of colonies. It is imperative that you utilize your best aseptic technique. Not all bacterial cells produce colonies, as some bacteria tend to clump or aggregate, and some are nonviable. For this reason results are reported as colony forming units (CFU)/ml of bacterial culture. Ideally only plates with 25250 colonies are used. Counts above 250 are considered Too Numerous To Count (TNTC) because it is impossible to tell whether colonies are separated. Plates with less than 25 colonies do not have a statistically significant number of colonies. When the approximate number of bacteria is unknown, plate a wide range of dilutions. In this way you will have at least 12 plates within the countable range (25250) to use in your calculations. If more than one plate is countable, average the counts together.
In order to make the calculation of the number of cells/ml in the original samples less formidable, dilutions are designed to be easy to handle mathematically. The most common dilutions are 1/10 and 1/100, but any dilution can be made. Because dilutions are large when counting bacteria, exponents are used. Answers should be written with two significant figures in proper scientific notation, i.e. 1.5 x 10^{8} (Remember: 1 x 10^{a} = 10^{a}).
a. To Determine Dilution:
Dilution = _____Volume transferred_______ = Volume transferred
Vol. transferred + diluent volume Total Volume
Example #1: 1 ml of culture was transferred to 99 ml of diluent.
What is the dilution?
Answer: Dilution = 1 ml = 1 ml = 1 or 10^{2}
1 ml + 99 100 ml 100
Example #2: 1 ml of a bacterial culture is transferred to 9.0 ml of diluent. Then 4 serial 10fold dilutions are made. To arrive at a final dilution, multiply successive dilutions together.
#1 #2 #3 #4 #5
1 ml à 1 ml 1 ml 1 ml 1 ml
9 + 1 9 + 1 9 + 1 ml 9 + 1 ml 9 + 1 ml
1/10 1/10 X 1/10= 1/10 X 1/10 X 1/10 X 1/10 X 1/10 X 1/10 X
1/100 1/10 = 1/1000 1/10 X 1/10 = 1/10 X 1/10 X
1/10,000 1/10 =1/100,000
(10^{1}) (10^{2}) (10^{3}) (10^{4}) (10^{5})
b. General Formula:
CFU/ml = colonies formed
dilution x ml plated
Example 1: after plating 0.1 ml from a 10^{5} dilution, 30 colonies grew. How many CFUs were in the original sample?
CFU/ml = ___30___ = _30_ =
10^{5} x 0.1 10^{6}
30 colonies x 10^{6} = 3.0 x 10^{7} CFU/ml
Example 2: After plating 0.2 ml of a 10^{5} dilution, 183 colonies grew.
CFU/ml = ___183___ = _183___ =
10^{5} x 0.2 2 x 10^{6}
91.5 x 10^{6} = 9.2 x 10^{7} CFU/ml
Growth curve.
Table 2. The results of a growth curve of Escherichia coli grown at 37^{o}C on nutrient broth (one ml plated).
TIME (min.) 
DILUTION PLATED 
# OF COLONIES 
AVERAGE CFU/ML 

0 
10^{6} 
32, 35, 41^{a} 
3.6 X 10^{7} 

10^{7} 
3, 11, 1 

30 
10^{6} 
42, 59, 39 
4.7 X 10^{7} 

10^{7} 
5, 5, 3 

60 
10^{6} 
48, 71, 62 
6.0 X 10^{7} 

10^{7} 
10, 4, 5 

90 
10^{6} 
68, 77, 72 
7.2 X 10^{7} 

10^{7} 
12, 8, 4 

120 
10^{6} 
92, 96, 78 
8.9 X 10^{7} 

10^{7} 
9, 8, 6 

^{a}Amounts that are significant are in bold type.
These numbers would then be entered into an Microsoft Excel spreadsheet and the log of the average cell count (CFU/ml) graphed vs. time, using the following instructions:
a. To graph these data, start the spreadsheet software package Microsoft Excel. Directions are for Microsoft Office 2000.
b. Enter the time points in descending order in column A and corresponding colony counts (or average CFU/ml) in column B. When entering average CFUs/ml that include exponents, they are entered as X EY. For example, enter the exponent 5.1 x 10^{7 }by typing 5.1 E7; the display will show 5.1E +07.
c. At this point you would have data in cells A1 to A5 and B1 to B5 (if using the data from Figure 2). With the mouse, start in cell A1 and drag the mouse to B5. Your data cells (and only your data cells) should be highlighted.
d. With the mouse choose (click) the icon at the top of your screen called “Chart Wizard.”
e. Step 1: Pick XY (Scatter); 1^{st} chart.
f. Step 2: Data range should include your selected data cells ($A$1:$B$5). If data graphed are not correct, click series and enter the correct X and Y values. Time is in X and CFU/ml are in Y.
g. Step 3: Add appropriate title, X and Y units. Change axes, gridlines, legend, etc. Click “Finish.”
h. Step 4: Indicate if you want the chart as a new sheet or as an object in present chart.
i. Once you have your graph, click on the y axis and change scale to logarithmic. You can also add more hatch marks to make it easier to read the graph.
j. If all the points appear to indicate exponential growth, you could click on data points, go to Chart and click on “Add trendline.” Choose linear.
k. At this point you can click on “Series 1” box to change to appropriate name or delete. If you click on the graph and choose print, it will size graph to full page.
Figure 1. Cell concentration (CFU/ml) over time of Escherichia coli grown in nutrient broth at 37^{o}C. Linear trendline added.
You can use the graph to determine the generation time. Choose two points on the graph between which the population doubled and determine the time it took for this to happen. For example at 0 time the cell number was 4 X 10^{7} CFU/ml and at 90 minutes it was 8 X 10^{7 }CFU/ml, so the generation time was 90 minutes.
Electrophoresis data.
When separating DNA, RNA, or proteins by electrophoresis, markers are always included in a separate lane. For DNA, the sample is loaded onto an agarose gel and subjected to an electrical current. All DNA has a net negative charge so the DNA is separated by size and topological form. Numerous markers are commercially available, so DNA size may be determined. Here we will describe a fX174 RF DNA/HaeIII marker set. The replicating form of the fX174 virus has been digested with the restriction enzyme HaeIII. The 11 bands produced by this digest are shown in Figure 2. These fragments are suitable for sizing linear doublestranded DNA from 721353 bp. When the gel is finished and a photograph of all bands made, the distance each band has traveled on the gel is graphed vs. the base pair size of each band and a standard curve made (Figure 3). The size of the DNA you have isolated can then be determined by comparing the distance it traveled to the standard curve.
Figure 2. fX174 RF DNA/HaeIII Fragments
Figure 3. Standard curve of fX174 RF DNA/HaeIII fragments
Statistics.
One of the most common types of statistical analysis done on laboratory data is determination of standard deviation. It is a useful measure of what is called the “scatter of observations,” giving an idea of how much importance to place upon variations in repeated observations or replicate experiments. Standard deviation is defined as the positive square root of the variance. The formula is:
s = square root of s^{2}, where s^{2} is the sample variance
The formula for the sample variance is:
s^{2} = 1 Sy_{i}^{2} _ (Sy_{i})^{2}
n – 1 n
where n = number of measurements
y_{i} = each individual measurement
The sample deviation can be determined for an individual sample or for a population. In order to determine standard deviation, one must first calculate the sample mean and the deviation between each sample and the sample mean.
Let’s say that you grew 5 different batches of E. coli, under identical conditions. The data for the experiment are listed in the first 2 columns of Table 3.
Table 3. The results of Escherichia coli grown at 37^{o}C on nutrient broth (one ml plated).
SAMPLE NUMBER 
AVERAGE
CFU/ML 
DEVIATION 
STANDARD DEVIATION 

1 
3.6 X 10^{7} 
2.5 
6.25 
2 
4.7 X 10^{7} 
1.4 
1.96 
3 
6.0 X 10^{7} 
0.1 
0.01 
4 
7.2 X 10^{7} 
1.1 
1.21 
5 
8.9 X 10^{7} 
2.8 
7.84 
The sample mean for these data is achieved by adding all the average CFU/ml (column 2) and dividing by the number E. coli cultures grown (column 1):
3.6 x 10^{7} + 4.7 x 10^{7} + 6.0 x 10^{7} + 7.2 x 10^{7} + 8.9 x 10^{7} = 6.1 x 10^{7}
5
The deviation for each sampling point (column 3) is obtained by subtracting the sample mean. The standard deviation for each sampling point (column 4) is obtained by taking the positive square root of the deviation. This information can then be added to a graph, to illustrate the difference among the five batches of culture.
Follow the growth curve instructions described above to graph the data (using Microsoft Excel program) listed in columns 1 and 2 (use batch number on the x axis instead of time). Once you have your graph, instead of adding a trendline (step j), add standard deviations to each data point by doing the following:
Doubleclick on an individual data point. Select “y error bars.” Under display, select “both.” Click next to standard deviation and then type in the appropriate value. Repeat for each data point.
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