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Population Growth
The nineteenth century mathematician Rev. Thomas Malthus proposed what has
come to be known as the "Utterly Dismal Theorem." This idea stated that all populations
grow to the point that all individuals are on the brink of starvation. In other words,
populations can grow faster than resources to support them. As a consequence,
population size will rapidly outstrip the capacity of their environment to support them.
This idea generated great controversy at the time in the areas of science and political
philosophy. Charles Darwin realized that this meant that all offspring in a population
could not survive to reproduce and hypothesized that only the most fit in a population
would successfully reproduce. You may recognize this as one of the central concepts in
his theory of evolution by natural selection. The political philosopher Karl Marks was
deeply disturbed by this idea as it seemed to imply that all are not equal.
The study of natural populations to see how they grow is a complex task, but if the
right laboratory organism is chosen, it is possible to see population growth in a reasonable
time frame under controlled laboratory conditions. In this laboratory you will be
examining the growth of E. coli under conditions of limited resources.
Exercise 1: Making a standard curve
Counting individual E. coli bacteria can be done in at least three ways: 1) Placing
bacteria on a slide and directly counting using a microscope, 2) Placing a small sample of
the bacteria onto a plate and watching how many colonies develop from individual
bacteria, and 3) measuring the absorbance of the broth in which the bacteria are growing.
Because it is the simplest and fastest method, measurement of the number of bacteria in a
culture will be done using absorbance. which can be calculated from transmittance using
a Bausch and Lomb spectrophotometer (Spec 20). The principle is that as the number of
bacteria in a broth culture increases, the turbidity (cloudiness) of the solution increases.
As turbidity increases, less light can be transmitted through the solution as more of the
light is absorbed by the bacteria. The relationship between transmittance and absorbance.
is given in the equation:
Abs.= log 10 (100 - Trans.)
In this exercise you will construct a standard curve giving the relationship
between number of bacteria and O.D. From this information you will be able to figure
out the number of bacteria in solutions with unknown numbers of bacteria in them.
Before you get started you may want to review how to use the Spec. 20 in the
Photosynthesis laboratory from the fall Laboratory Manual. It is also important that you
use sterile technique which you will want to review from the Bacteriology laboratory in
this Laboratory Manual.
1
Obtain the following materials from the front desk of the laboratory room:
Bacterial culture of known concentration, Flask of sterile broth, and 7 sterile
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culture tubes.
2
Number six of the empty culture tubes 1 - 6 as the seventh tube will be used as a
blank write "B" on it. Using sterile technique, transfer 9 ml of broth to all seven
tubes.
3
Transfer 1 ml of the bacterial culture of known concentration to tube 1 vortex the
solution then transfer 1 ml from tube 1 to tube 2. Repeat this procedure for all six
numbered tubes so that you wind up with a serial dilution going from 10-1 10-6.
4
Use the Spec. 20 to measure the Transmittance at 660 nm of each solution, then
make a graph plotting O.D. on the Y axis and bacteria/ml on the X axis. This is
your standard curve. Now if you measure the O.D. of a bacterial culture you can
use the standard curve to figure out the number of bacteria/ml by going to the
O.D. on the Y axis then going over to the point at which the standard curve
intersects that particular O.D. By going straight down from this point you can
read off the bacteria/ml in a solution of that O.D.
Exercise 2 Population Growth Under Different Conditions
In this exercise you will be comparing the rates of growth of E. coli cultures in
different growth media and the rates of growth of another bacteria in the same media as
E. coli. All cultures will be started by transferring 5 ul of each bacterial culture to the
tubes.
1
Using sterile technique, prepare 8 tubes as follows:
Tube
1
2
3
4
5
6
7
8
2
Broth
10 ml Complete
10 ml Complete
10 ml Complete
10 ml Complete
10 ml Apple Juice
10 ml Apple Juice
10 ml Lactose
10 ml Lactose
Bacterial Culture
None
E. coli
E. coli
B. subtilus
None
E. coli
None
E. coli
Some of you who are interested may want to prepare an ninth tube in which you
place both E. coli and B. subtilus. This will give an idea of how populations
interact when competing for the same resources.
Using the tubes with no bacteria as blanks, measure the transmittance of each
culture then place all tubes except number 2 into the 37 oC water bath. Tube 2
should be placed in the refrigerator at 4 oC to test the effect of temperature on
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population growth in E. coli.
3
Record your measurements as time 0. For the next 5 hours, you will want to
measure the transmittance of your cultures every hour. Make sure that your
cultures are well mixed before measuring the transmittance. After 5 hours, you
can switch to 2 hour increments, and after 11 hours you can switch to 4 hour
increments. You will want to measure the transmittance for at least a 24 hour
period, but you may see some interesting things if you let your culture go even
longer.
4
Convert your transmittance readings into O.D. then use your standard curve to
figure out the bacteria/ml for each reading. Plot the bacteria/ml on the Y axis of a
graph and the time on the X axis. What observations can you make about E. coli
population growth in different media and under different temperature conditions?
How does the population growth of E. coli compare with that of B. subtilus under
the conditions used?
Materials
Equipment
Spec 20s
Small tubes that can fit in Spec 20s
Supplies
Liquid cultures of:
E. coli
B. subtilus
Complete broth 10 ml/tube in small tubes, 5 tubes/group.
Lactose broth 10 ml/tube in small tubes, 3 tubes/group.
Apple juice 10 ml/tube in small tubes, 3 tubes/group.