5-6 Generating a growth curve

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In this experiment, the classic bacterial growth curve will be demonstrated. A culture of Escherichia coli will be sampled at hourly or half-hourly intervals from the time of inoculation of the culture (0-time) through a 7 to 9-hour incubation period. The periodic samplings will be plated to determine viable counts (as colony-forming units per ml of culture) over the incubation period such that a growth curve may be plotted. From the graph, we may note the stages in the growth of the culture as it grows into the stationary phase. Additionally we will be able to determine the growth rate and generation time of E. coli under our experimental conditions from two points in the exponential phase of the graph.

Figure 5-16 Bacterial Growth

Graphing of bacterial growth on a linear scale

By definition, bacterial growth is cell replication - i.e., growth of the culture. Most species of bacteria replicate by binary fission, where one cell divides into 2 cells, the 2 cells into 4, the 4 into 8, etc. If this cell division occurs at a steady rate - such as when the cells have adequate nutrients and compatible growing conditions - we can plot numbers of cells vs. time such as on the graph at right. Before too long, we will need to extend the paper vertically as the population continues to double. For a culture where cells divide every 20 minutes, one cell can result in 16,777,216 (i.e., 224) cells after just 8 hours - barring nutrient depletion or other growth-altering conditions.

Figure 5-17 Bacterial Growth

Graphing of bacterial growth with cell number on a log scale.

If we were to convert our vertical axis to a logarithmic scale - as on the graph at right - we will not need as many sheets of graph paper, and we will find that a steady rate of growth is reflected as a straight line. (On the vertical axis, the same distance on the paper is covered with each doubling.) This type of graph paper is called semilogarithmic graph paper on which we will be plotting our class results. The numbers we plot will fall on the graph at the same place the logarithms of these numbers would fall when plotted on conventional graph paper.

The example below shows the type of graph we may obtain from our class data. We can plot both colony-forming units (CFUs) per ml and absorbance on the same graph, remembering that the absorbance units should also be on a logarithmic scale. Rather than "connecting the dots," we draw the best straight line among our CFU/ml plots to represent the phases of growth - lag, exponential, and the start of the maximum stationary phase.

Figure 5-18 Two measurements of growth

Example data showing a plot of cell number by VPC and by turbidity.

For the growth rate formula we are about to use, we need to choose two points on the straight line drawn through the exponential phase, also making note of the time interval between them. As we will be converting our numbers to logarithms for the formula, why not choose two points for which the logs are easy to obtain? (For example, the log of 1X1010 is simply 10.)

  • Higher CFU/ml = Xt = 1X1010 (at 5.75 hours)

  • Lower CFU/ml = X0 = 1X108 (at 2.75 hours)

  • Time interval (in hours) between the 2 points = t = 3



Using the first formula, we find the growth rate which is the number of generations (doublings) per hour:

Figure 5-19 Caluclating the growth rate

Use this formula to determine the growth rate k

With the second formula, we find the generation time which is the time it takes for the population to double:

Figure 5-20 Generation time

The generation time is the reciprocal of the growth rate.

When we graph the CFUs/ml and absorbance on the same graph, we would hope to see an upward trend for both. Sometimes the absorbance continues to rise after the CFUs/ml level off into the maximum stationary phase. What would be the cause of that?

With a clear graph, one should be able to determine the generation time without the use of formulas. Just look for a doubling of the population and the time it takes for that to happen. For example - in the above graph - the time it takes to go from 3 X 109 to 6 X 109 appears to be approximately 30 minutes, which is close to the generation time determined above.

In preparation for this exercise, be sure to read the relevant material in your textbook, and look over the procedure below.

Precautions regarding observance of aseptic technique:

  1. Remember the proper procedure for holding the tubes during inoculations. Do not allow the plugs or caps to contact the desk top or anything else.

  2. When using the pipettor, hold one tube at a time.

  3. Do not pipette from tube to tube with the tubes sitting open and vertical in the test tube rack!

  4. Also, one person should not be holding the tubes while another makes the transfers.

  5. Remember to use a new tip each time you begin to use a more dilute concentration of cells

Period 1

Materials

Samples (5-6 ml) which were taken at hourly or half-hourly intervals from a culture of E. coli growing in Nutrient Broth+0.2% yeast extract, incubated at 37°C on a shaker. These samples have been kept on ice for use in this experiment, and each pair will use one sample.

The following are provided for each pair of students:

7-9 nine ml dilution blanks

8 tubes of melted Plate Count Agar (PCA) in test tubes (15-20 ml/tube) - in 50°C water bath

8 empty, sterile petri dishes

Pipettors (P1000) and sterile tips

Spectrophotometer tube and spectrophotometer

  1. Each pair will pick up one culture from the ice-water bath on the front table. Record the number on the tube. It represents the age of the culture at which time the sample was taken.

  2. With the P1000 (blue) pipettor set at 1.0 ml, transfer 1 ml of the culture to the first nine ml dilution blank (for the first 1/10 dilution to work with in Step 5).

  3. Aseptically dump the remainder of the culture into the small spectrophotometer tube (to work with in step 4).

  4. With the culture in the spectrophotometer tube, one person in the pair will obtain and record the absorbance reading of the culture while the other begins the next step.

  5. With additional dilution blanks, make dilutions as specified below. Inoculate 1 ml from each of the four specified dilutions into each of two petri plates; plate inoculations can be made concurrently with preparation of the dilutions.



The dilutions to be plated are as follows:

For 0-hour through 2-hour sampling times:

10-4, 10-5, 10-6, 10-7

For 2.5-hour through 4.5-hour sampling times:

10-5, 10-6, 10-7, 10-8

For 5-hour through 9-hour sampling times:

10-6, 10-7, 10-8, 10-9



  1. For each plate, obtain a tube of melted PCA from the water bath and pour the contents into the plate. Mix the medium and inoculum by carefully swirling and allow the plates to solidify.

  2. Incubate the plates inverted at 30°C until the next period.



Period 2

  1. Each pair will determine the total plate count (no. of colony-forming units/ml of culture). Be sure you are counting colonies of all sizes. (E. coli typically produces small, lens-shaped colonies when growing below the surface.) Turn your result in to the instructor along with the absorbance reading. Be sure you have indicated the sampling time! Results will be compiled and presented next period.

For Your Assignment:

  1. Plot the plate count data on semi-logarithmic graph paper. Rather than generating a growth curve by connecting the dots, draw the best straight lines through the lag and exponential phases. (Transitions between the growth phases can be rounded out.)

  2. Determine the growth rate and generation time for the particular strain and cultural conditions in our experiment. Remember that the points you need to calculate these values are to be taken from the best straight line drawn through the exponential phase. Do not use individual data points from the class data. Also, be sure to indicate the proper units (gen/hr or hr/gen). Show your calculations!

  3. Plot the absorbance readings on semi-logarithmic graph paper. Note any similarities in the graph generated and that for the plate count data. Both the absorbance and plate count plots can be made on the same graph. Do not use the absorbance readings for any calculations of growth rate or generation time.

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