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1
Determining Bacterial Growth Rates
Introduction and Background
Bacteria are very small prokaryotes, that are everywhere in the world around us! Many
of us are prescribed antibiotics by a doctor, medicine used to stop a bacterial infection, when we
are sick. Antibacterial hand soap is a common product that can be found almost anywhere. This
product is designed to kill "bad" bacteria. However, not all bacteria are harmful. We, humans,
have "good" bacteria in our stomachs that help us digest the food that we eat. The majority of
bacteria is neither helpful nor harmful to humans and exists everywhere around us.
The type of bacteria that we will be looking at is known as Vibrio fischeri. This species
is bioluminescent, so it can glow at night. V. fischeri are able to form symbiotic relationships
with the bobtailed squid. The squid have a light organ packed with bioluminescent bacteria on
their ventral (bottom) side. These bacteria will illuminate from within the squid, projecting light
downward. This allows a night forager, like the squid, to avoid appearing as a dark silhouette and
is an effective camouflage in moonlight.
Figure 1A. Bioluminescent Vibrio fischeri under a microscope and B. a bobtailed squid, with a
mantle length of roughly 1.2 inches.
Other types of Vibrio, however, form parasitic relationships with humans. Vibrio
cholerae causes cholera, a disease that causes profuse, watery diarrhea in infected individuals.
Other species of Vibrio, ingested from eating raw seafood, can cause vomiting, diarrhea,
abdominal pain, and skin blisters. By working with a relatively safe species of Vibrio, V.
fischeri, scientists can learn more about this genus of bacteria without worrying about getting
themselves infected with a potentially harmful bacterium.
http://microbewiki.kenyon.edu/index.php/Vibrio_fische ri
A B
2
Microbiologists that study bacteria use a variety of ways to detect bacterial populations
and whether or not these populations are healthy and growing. One of the ways they study
bacteria is using a flow cytometer, a machine that pushes a stream of water past a laser and
detects light scattered from the laser beam by any organism or particle in the water. This
scattered light is roughly proportional to the size of the particle. A flow cytometer will also
detect several colors of fluorescence, which occur when photosynthetic pigments (such as
chlorophyll) or stains absorb the blue laser light and reemit it as green, yellow or red light.
Figure 2. Simplified flow cytometer illustration (left) and a flow cytometer on board a research
vessel (right). Light scattered by particles passing through the laser beam in either the forward or
side directions is roughly proportional to cell size, while the green fluorescence detector is used
to quantify fluorescence from the DNA stain Sybr Green.
Because Vibrio fischeri only produce bioluminescence under specific conditions, they are
difficult to detect using flow cytometry unless the cells are stained with a fluorescent stain. The
DNA within bacteria is commonly stained with a dye known as Sybr Green. Cells stained with
Sybr Green emit green light when put through a flow cytometer and the amount of green
fluorescence is proportional to the amount of DNA per bacteria (cells with high green
fluorescence also have a high DNA content).
Figure 3. Seawater sample stained with Sybr Green, a
fluorescent DNA stain. Bacteria are the larger green dots. If
the stain was not applied, the bacteria would be
undetectable. For more information, see
http://www.uib.no.rg/mm/artikler/2009/01/virusesand
bacteria.
Cells
Laser Forward light
scatter detector
Simplified Flow Cytometer Schematic
Side scatter light detector
Green fluorescence
detector
3

dimensional plot represents a cell or particle that has been detected by the instrument. The dot
plot presented below shows green fluorescence (FL1) or DNA content on the yaxis versus side
scatter (SSC) or a measure of cell size on the xaxis (Fig 4A). Another way that scientists can
events or counts corresponds to the number of cells or particles with a specific fluorescence
value that the flow cytometer was able to detect. This will give you a graph showing the
abundance of particles that have a low or high DNA content (low or high green fluorescence)
(Fig 4B). The number of events with a specific SSC and FL1 can also be shown in a three
dimensional plot (Fig 4C).
Figure 4A. Dot plot of FL1 (DNA fluorescence) versus SSC (relative to cell size) for a dense
culture of Vibrio fischeri. Standard beads, in this case 1 m in size, are added to each sample to
monitor instrument performance and determine the volume of sample run. B. FL1 histogram of
Vibrio fischeri, showing peaks of abundance for cells with both low and high DNA contents. C.
A three dimensional graph of the data shown in A, a white arrow points out the standard bead
peak.
In flow cytometry, the scientists will often run a standard consisting of fluorescent beads
specific, known size and a specific fluorescence. Therefore, the scientist knows exactly where
the beads should show up on the flow cytometry graph (Fig 4). If the beads are not showing up
as or where expected, the scientist knows that something is not working correctly and they can
try to fix the problem. In addition, the concentration of beads added to each sample is known, so
that the number of beads analyzed can be used to determine the volume of sample that was
actually run through the flow cytometer.
A B C
Vibrio
Beads
Low DNA content
High DNA content
Vibrio
SSC
FL1
FL1
Counts
4
Methods
In this activity, we will be graphing Vibrio cell concentrations with time and calculating
Vibrio growth rates in Control (High Iron Media) and Low Iron Media to determine if the
bacteria were iron limited. Flow cytometry dot plots similar to Fig 4A were collected throughout
a 19 hour period (attached). In each dot plot, the Vibrio population and the standard beads are
identified using their size (side scattered light or SSC) and DNA content (green fluorescence or
FL1). The beads are 1 micron in diameter, which gives you an idea of the size of marine bacteria
(nearly half a million beads, specifically 3.9 x 105, can fit into an inch). The number of Vibrio
and beads detected in each sample is noted on each dot plot.
In order to graph Vibrio cell numbers and calculate bacterial growth rates, we will need to
make a few calculations. The beads have a known concentration, which we will use to help us
calculate the concentration of Vibrio.
Part 1: Calculate Vibrio concentration:
1. Calculate the volume of sample that was run through the machine at time T = 0 using the
equation below and write your answers in Table 1 on your data sheet:
Equation 1:
NOTE: If you notice, we are doing a type of conversion, so you can use
dimensional analysis to solve this problem.
You will need to look at the attached flow cytometry graphs to get the numbers for the “# beads
in dot plot”. For this calculation, look on the “High Fe A” at T = 0 dot plot for the number of
beads in the sample. By counting the fluorescent beads under the microscope, we know that 1
mL of bead stock solution contains 4.56 x 104 beads.
2. Calculate the concentration of Vibrio at T = 0 using Equation 2 (below) and record your
answer in Table 1 on your data sheet. Round your answer to the nearest whole number.
Equation 2:
5
3. Calculate the natural logarithm of each Vibrio concentration, ln (Vibrio/mL) and record
your answer in the last column of Table 1 on your data sheet. The advantages of working
with ln (Vibrio/mL) will be explained in the next sections.
4. Using the procedures above and the attached flow cytometry graphs, continue filling out
Table 1 and fill out Tables 2, 3, and 4.
Part 2: Graphing Vibrio Concentration with Time
1. Graph Vibro concentration (Vibrio/mL) vs time on the first graph paper space in Part 2
of your data sheet. Note that the Vibrio concentrations in the High Iron Media were much
higher than those in the Low Iron Media by the end of the experiment. As a result, you
will graph the Low Iron and High Iron Media data on two different graph spaces. On the
Vibrio
graphs:
1) Table 1 Data (High Iron A)
2) Table 2 Data (High Iron B)
2. In the second graph space in Part 2 on your data sheet, graph the following two plots on
Vibrio Concentration vs. Time:
3) Table 3 Data (Low Iron A)
4) Table 4 Data (Low Iron B)
You may want to use a different color for each plot so you can tell them apart.
You may notice that none of the plots in the graph are straight lines (If they are, go back and
check your work). The High Iron Media data plots are typical examples of bacterial growth
curves. These plots
Figure 5. A typical growth curve with lag, exponential and stationary phases labeled.
Time
Cell Concentration
Exponential
phase
Lag phase
Stationary phase
6
This shape occurs because bacterial numbers are initially very low in a sample and often need
time to adapt before increasing exponentially over time. When you graph bacterial populations,
you will often notice 3 phases. The first phase is called the lag phase. During this phase,
bacteria are adapting to the new environment they have just been placed in and the population
size increases slowly, if at all.
The next phase is known as the exponential phase. Most cell division occurs during this phase,
which is characterized by an exponential increase in cell concentrations over time. During the
exponential phase the amount of time it takes for the bacteria population to double is constant.
As a result, data from the exponential phase is used to calculate the growth rate.
The last phase is known as the stationary phase. This phase occurs when the bacteria are
starting to use up the nutrient resources and waste products start to build up in the culture,
leading to slower population growth.
3. Label the lag, exponential and stationary phases (if present) on each graph.
4. Graph ln (Vibro concentration) vs time on the graph space Vibrio
in Part 2 of your data sheet. This graph will have 4 different
plots on it. Note that when using the natural logarithm of the cell concentration data, the
High Iron and Low Iron Media data can be graphed using the same yaxis. You should
graph:
1) Table 1 Data (High Iron A)
2) Table 2 Data (High Iron B)
3) Table 3 Data (Low Iron A)
4) Table 4 Data (Low Iron B)
You may want to use a different color for each graph so you can tell them apart.
Part 3: Determining the Growth Rate
Equation 3 below is used to calculate the rate of growth for our Vibrio samples. To completely
understand how this equation was derived calculus is required. Please see the Extension at the
end of this activity to see how scientists use calculus every day in their work. However, some
important points can be made without using calculus. For instance, it is important to realize that
the form of the equation is exponential, with variables (r and t) occurring in the exponent.
Equation 3:
N0 = number of cells per mL (cell concentration) at time zero
Nt = cell concentration at time, t
e = mathematical constant that is the base of the natural logarithm
t = time, for fast growing bacteria, such as Vibrio, usually expressed in hours
r = instantaneous growth rate (balance between cell division and cell death, units of t1).
7
You should also notice that the concentration of cells at a specific time depends on:
1) Initial concentration of cells N0, (the more Vibrio you start with, the more you will have a
day later)
2) Amount of time the bacteria have had to divide (if you allow Vibrio to grow for 10 days,
3) Instantaneous growth rate or the balance between cell division and death.
If r >0, the population size will increase, if r = 0, the population size will remain constant. In this
experiment, we know the initial concentration of Vibrio (N0) as well as the bacteria concentration
(Nt) at different time points (t), and will solve for the instantaneous growth rate, r.
For more details, see the Extension section.
To make it easier to calculate r, the equation is often transformed by taking the natural logarithm
of both sides such that:
Equation 4:
This is now a linear equation of the form y = mx + b, with:
y = ln (Nt)
m = r
x = t
b = ln (N0)
Therefore, if Vibrio concentrations are graphed on the yaxis as the natural logarithm of Nt, with
time on the xaxis, the slope of the linear portion of the growth curve will be the growth
rate, r.
The slope can be calculated using the LINEST function in Excel or the formula below:
Equation 5:
8
Extension: Calculus in the Real World
In order to calculate the growth rate of the bacteria in our samples, we must understand
the difference between exponential and linear growth and use calculus.
Two different characteristics of cell growth are important to keep track of when thinking
about linear and exponential growth: 1) the increase in cell numbers during a time interval
(marked with the symbol # in Tables 1 and 2) and 2) the time it takes a population to double in
size (the doubling time, marked with the symbol * in Tables 1 and 2).
In exponential growth, cell numbers increase in proportion to the amount of bacteria
present. What this means can be understood by looking at the data in Table 1, which shows the
number of bacteria in an exponentially growing population which starts from one cell, with a
doubling time of 1 hour. Every hour the number of cells in the population doubles, because each
cell divides into two daughter cells. In exponential growth, the time it takes the population to
double stays constant. This means that the number of bacteria must increase by a different
amount each hour. For example, the bacteria population increases by one cell between hours 0
and 1, but by 896 cells between hours 10 and 11. In both cases, the population size doubles. In
practical terms the size of an exponentially growing population increases quickly. The
exponentially growing bacteria population in Table 1 starts from only one cell, but includes 1792
cells in 11 hours. In roughly 20 hours, this bacteria population hits one million cells a scary
prospect if the bacteria are pathogenic.
Table 1. Exponential population growth with a starting population of 1 bacterium and a
doubling time of 1 hour.
Time, Hours
Cell Number
*Doubling Time, Hours
# Increase in Cell Number
0
1
1
1
2
1
1
2
4
1
2
3
8
1
4
4
16
1
8
5
28
1
12
6
56
1
28
7
112
1
56
8
224
1
112
9
448
1
224
10
896
1
448
11
1792
1
896
*Doubling time is the time it takes the population to double. #The increase in cell numbers is the
difference in population size between two time points. For example, from t = 10 to t = 9, the
increase in cell number is 896 448 = 448.
9
If the increase in cell numbers with time is linear, then the bacteria population will
increase by the same number of cells in a given time interval. In Table 1 a bacteria population
starts out with 100 cells and increases by 100 cells each hour. The increase in population size
every hour is constant, rather than increasing proportionally with the number of bacteria present
(as in exponential growth). As a result, the amount of time it takes for the number of cells to
double actually increases as the population size gets larger. It would take 9999 hours for this
bacteria population to reach one million cells.
Table 2. Linear population growth with a starting population of 100 bacteria and 100 cells
added to the population every hour.
Time, Hours
Cell Number
*Doubling Time, Hours
# Increase in Cell Number
0
100
1
1
200
2
100
2
300
3
100
3
400
4
100
4
500
5
100
5
600
6
100
6
700
7
100
7
800
8
100
8
900
9
100
9
1000
10
100
10
1100
11
100
11
1200
12
100
*Doubling time is the time it takes the population to double. For example, at t = 5 there are 600
cells, this number doubles at 1200 at t = 11. So the doubling time is 11 5 = 6 hours. #The
increase in cell numbers is the difference in population size between two time points. For
example, from t = 10 to t = 9, the increase in cell number is 1100 1000 = 100.
The data from Tables 1 and 2 is plotted on the Fig E1 below. A quick look at the graph
might lead you to believe that the bacteria population represented by the exponential growth
curve went through a lag phase for the first four hours, in which little or no growth occurred.
between t = 0 and t=1 as it was later in the experiment. No lag phase actually occurred; it is just
the scale of the graph that makes it appear that nothing happened in the first four hours. To
identify a true lag phase, look for slower doubling times in the beginning of the experiment than
occur later in the exponential growth phase.
Fig E1 also shows the best fit line through the data points generated by the graphing
program Sigma Plot. In these equations, Nt = number of cells at time t and t = time.
The equation that best describes the exponential growth curve is:
Nt = 0.88 e0.69t
e
10
The equation that best describes the linear growth curve is:
Nt = 100 (t) + 100
This linear growth curve equation is in the familiar y = mx + b format, where m is the slope and
b is the yintercept. But where does e come
from?
Figure E1. Examples of linear and exponential growth from Tables 1 and 2. The best fit lines
through the data points are shown.
elculus.
The first step is to realize that in exponential growth, cell numbers increase in proportion to the
amount of bacteria present. In other words, the change in cell concentration with time (dN/dt) is
going to depend on the concentration of cells present (N). dN/dt also depends on the intrinsic or
instantaneous growth rate, r which represents the balance between cell division and cell death.
1) The differential equation below states that the change in cell concentration with time (dN/dt)
depends on the cell concentration (N) and the constant r.
2) The first step in solving this equation is to separate variables and then integrate:
Exponential vs Linear Growth
Time, hours
0 2 4 6 8 10 12
Cell Number
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Exponential Growth Curve
Linear Growth Curve
11
3) The solution is based on the definition of the natural logarithm and the recognition that r is a
constant:
where C1 and C2 are integration constants. By defining C = C1 + C2, the equation simplifies
to:
4) Raise each side of the equation to the power of e:
By defining eC as the positive constant, k the equation simplifies to:
5) Remove the absolute value sign by realizing:
it then follows that
Where k is any real number (positive, negative or zero). For bacteria growth curves k is set as
the population size (N0) at t = 0 and is for practical purposes is always a positive number.
6) The exponential growth rate equation with variables applicable for bacteria growth is:
N0 = # of cells at time 0
Nt = # of cells at time t
r = intrinsic growth rate = birth rate death rate
t = time
If r > 0, the population is increasing. If r < 0, the population is decreasing, and if r = 0, the
population is staying the same size.
12
7) To transform the equation into a format that is easily graphed, you can take the natural log of
both sides:
8)
y = ln(Nt)
m = r
x = t
b = ln(N0)
As you can see, calculus is not something that math teachers created to make your life miserable.
Calculus was initially developed to help explain science by Isaac Newton in England (the apple
ontheheadguy) and Gottfried Leibniz in Germany. Leibniz was accused of plagiarism, but
modern scholars believe that the two men discovered calculus independently.
13
Name: ____________________________________ Date: _____________ Period: ________
Bacterial Growth Rates: Data Sheet
Answer the following questions. Show your work for all calculations and any calculations done
on another sheet of paper should be attached.
Part 1: Calculate Vibrio Concentration
Table 1. Control, High Iron Media A
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0
1.5
4.5
8.0
9.0
11.15
13.25
14.15
15.5
16.5
18.0
19.0
14
Table 2. Control, High Iron Media B
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0
1.5
4.5
8.0
9.0
11.15
13.25
14.15
15.5
16.5
18.0
19.0
15
Table 3. Control, Low Iron Media A
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0.50
2.0
3.75
5.5
9.25
12.15
13.5
17.0
18.0
Table 4. Control, Low Iron Media B
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0.50
2.0
3.75
5.5
9.25
12.15
13.5
17.0
18.0
16
Part 2: Graphing Vibrio Concentration with Time
1. Graph time on the xaxis and Vibrio concentration on the yaxis for the High Iron samples
(Table 1 and 2). Remember to label the x and yaxes. Also include a legend for your graph.
High Iron Vibrio Concentration vs. Time
17
2. Graph time on the xaxis and Vibrio concentration on the yaxis for the Low Iron samples
(Table 1 and 2). Remember to label the x and yaxes. Also include a legend for your graph.
Low Iron Vibrio Concentration vs. Time
18
3. Graph time on the xaxis and ln (Vibrio concentration) on the yaxis (Tables 1, 2, 3 and 4).
For this graph, start the yaxis with a value of 3.0. Remember to label the x and yaxes.
Also include a legend for your graph.
Ln (Vibrio Concentration) vs. Time
19
Part 3: Determining the Growth Rate
1.
Question 2.
Linear Equation: ___________________________________________
2. Calculate the slope (growth rate) of the exponential phase of the growth curves in Part 2,
Question 2 using either the LINEST function in Excel or Equation 5 in Part 3. The
exponential phase is shaded in Tables 1, 2, 3, 4 to help you see which points are located in
the exponential phase.
m (slope) for Control, High Iron A =__________________________________________
m (slope) for Control, High Iron B = __________________________________________
m (slope) for Control, Low Iron A = __________________________________________
m (slope) for Control, Low Iron B = __________________________________________
3. ls
at t=0?
20
Analysis
1. Were Vibrio grown in the Low Iron Media actually limited by iron? Why or why not?
2. What do you think would happen to the Vibrio cell numbers at the end of the experiment if
iron was added to the low iron experimental culture at 13.5 hours?
3.
cytometer could be responsible? Why or why not?
4. What do you think would happen if you forgot to add the Sybr Green DNA stain to the Vibrio
sample?
5. What do you think is the best way to handle outliers?
Going Further…
How long would it take for the Vibrio population in the Control, High Iron Media to double in
size? Show your work.
21
High Fe Media
High Fe A, T=0 High Fe B, T=0
High Fe A, T=1.5 High Fe B, T=1.5
High Fe A, T=4.5 High Fe B, T=4.5
574 Vibrio
2378 Beads
587 Vibrio
2214 Beads
791 Vibrio
2866 Beads
833 Vibrio
2990 Beads
950 Vibrio
2935 Beads
873 Vibrio
2568 Beads
22
High Fe Media
High Fe A, T=11.15 High Fe B, T=11.15
High Fe A, T=8.0 High Fe B, T=8.0
High Fe A, T=9.0 High Fe B, T=9.0
10864 Vibrio
2034 Beads
10717 Vibrio
2508 Beads
3710 Vibrio
2773 Beads
3155 Vibrio
2476 Beads
1900 Vibrio
2744 Beads
2750 Vibrio
2648 Beads
23
High Fe Media
High Fe A, T=15.5 High Fe B, T=15. 5
High Fe A, T=14.15 High Fe B, T=14.15
High Fe A, T=13.25 High Fe B, T=13.25
68579 Vibrio
2048 Beads
68152 Vibrio
2137 Beads
37399 Vibrio
2314 Beads
36261 Vibrio
2266 Beads
30323 Vibrio
2785 Beads
2 Vibrio
2299 Beads
24
High Fe Media
High Fe A, T=19.0 High Fe B, T=19.0
High Fe A, T=18.0 High Fe B, T=18.0
High Fe A, T=16.5 High Fe B, T=16.5
100767 Vibrio
2890 Beads
100419 Vibrio
3024 Beads
78748 Vibrio
1995 Beads
81352 Vibrio
2164 Beads
77020 Vibrio
2085 Beads
76518 Vibrio
2175 Beads
25
Low Fe Media
Low Fe A, T=2.0 Low Fe B, T=2.0
Low Fe A, T=0.5 Low Fe B, T=0.5
687 Vibrio
2114 Beads
780 Vibrio
2278 Beads
712 Vibrio
2066 Beads
762 Vibrio
2190 Beads
26
Low Fe Media
Low Fe A, T=5.5 Low Fe B, T=5.5
Low Fe A, T=3.75 Low Fe B, T=3.75
Low Fe A, T=9.25 Low Fe B, T=9.25
1394 Vibrio
2648 Beads
1376 Vibrio
2744 Beads
1030 Vibrio
2935 Beads
811 Vibrio
2568 Beads
1430 Vibrio
2476 Beads
1922 Vibrio
2773 Beads
27
Low Fe Media
Low Fe A, T=17.0 Low Fe B, T=17.0
Low Fe A, T=13.5 Low Fe B, T=13.5
Low Fe A, T=12.15 Low Fe B, T=12.15
3046 Vibrio
2314 Beads
3140 Vibrio
2266 Beads
2352 Vibrio
2299 Beads
3276 Vibrio
2785 Beads
2127 Vibrio
2034 Beads
2384 Vibrio
2508 Beads
28
Low Fe Media
Low Fe A, T=18.0 Low Fe B, T=18.0
3692 Vibrio
2048 Beads
3210 Vibrio
2137 Beads
29
TEACHER KEY
Bacterial Growth Rates: Data Sheet
Answer the following questions. Show your work for all calculations and any calculations done
on another sheet of paper should be attached.
Part 1: Calculate Vibrio Concentration
Table 1. Control, High Iron Media A
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0
2378
574
0.052
1.10E+04
9.31
1.5
2866
791
0.063
1.26E+04
9.44
4.5
2935
950
0.064
1.48E+04
9.60
8.0
2744
1900
0.060
3.16E+04
10.36
9.0
2476
3155
0.054
5.81E+04
10.97
11.15
2508
10717
0.055
1.95E+05
12.18
13.25
2299
2
0.050
40
3.69
14.15
2266
36261
0.050
7.30E+05
13.50
15.5
2137
68152
0.047
1.45E+06
14.19
16.5
2175
76518
0.048
1.60E+06
14.29
18.0
2164
81352
0.047
1.71E+06
14.35
19.0
3024
100419
0.066
1.51E+06
14.23
30
Table 2. Control, High Iron Media B
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0
2214
587
0.049
1.21E+04
9.40
1.5
2990
833
0.066
1.27E+04
9.45
4.5
2568
873
0.056
1.55E+04
9.65
8.0
2648
2750
0.058
4.74E+04
10.77
9.0
2773
3710
0.061
6.10E+04
11.02
11.15
2034
10864
0.045
2.44E+05
12.40
13.25
2785
30323
0.061
4.96E+05
13.12
14.15
2314
37399
0.051
7.37E+05
13.51
15.5
2048
68579
0.045
1.53E+06
14.24
16.5
2085
77020
0.046
1.68E+06
14.34
18.0
1995
78748
0.044
1.80E+06
14.40
19.0
2890
100767
0.063
1.59E+06
14.28
31
Table 3. Control, Low Iron Media A
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0.50
2278
780
0.050
1.56E+04
9.66
2.0
2066
712
0.045
1.57E+04
9.66
3.75
2935
1030
0.064
1.60E+04
9.68
5.5
2744
1376
0.060
2.29E+04
10.04
9.25
2476
1430
0.054
2.63E+04
10.18
12.15
2508
2384
0.055
4.33E+04
10.68
13.5
2299
2352
0.050
4.66E+04
10.75
17.0
2266
3140
0.050
6.32E+04
11.05
18.0
2137
3210
0.047
6.85E+04
11.13
Table 4. Control, Low Iron Media B
Bead Concentration/mL: 4.56 x 104
Time
(hours)
# Beads
# Vibrio
Volume Run
(mL)
Vibrio/mL
ln (Vibrio/mL)
0.50
2114
687
0.046
1.48E+04
9.60
2.0
2190
762
0.048
1.59E+04
9.67
3.75
2568
811
0.056
1.44E+04
9.57
5.5
2648
1394
0.058
2.40E+04
10.09
9.25
2773
1922
0.061
3.16E+04
10.36
12.15
2034
2127
0.045
4.77E+04
10.77
13.5
2785
3276
0.061
5.36E+04
10.89
17.0
2314
3046
0.051
6.00E+04
11.00
18.0
2048
3692
0.045
8.22E+04
11.32
32
Part 2: Graphing Vibrio Concentration with Time
1. Graph time on the xaxis and Vibrio concentration on the yaxis for the High Iron samples
(Table 1 and 2). Remember to label the x and yaxes. Also include a legend for your graph.
High Iron Vibrio Concentration versus Time
Time, hours
012345678910111213141516171819202122
High Iron Vibrio per mL
0.0
9.0e+4
1.8e+5
2.7e+5
3.6e+5
4.5e+5
5.4e+5
6.3e+5
7.2e+5
8.1e+5
9.0e+5
9.9e+5
1.1e+6
1.2e+6
1.3e+6
1.4e+6
1.4e+6
1.5e+6
1.6e+6
1.7e+6
1.8e+6
1.9e+6
2.0e+6
Control A, High Iron
Control B, High Iron
33
2. Graph time on the xaxis and Vibrio concentration on the yaxis for the Low Iron samples
(Table 1 and 2). Remember to label the x and yaxes. Also include a legend for your graph.
Low Iron Vibrio Concentration versus Time
Time, hours
012345678910111213141516171819202122
Low Iron Vibrio per mL
1.2e+4
1.6e+4
2.0e+4
2.4e+4
2.8e+4
3.2e+4
3.6e+4
4.0e+4
4.4e+4
4.8e+4
5.2e+4
5.6e+4
6.0e+4
6.4e+4
6.8e+4
7.2e+4
7.6e+4
8.0e+4
8.4e+4
8.8e+4
9.2e+4
9.6e+4
Low Iron A
Low Iron B
34
3. Graph time on the xaxis and ln (Vibrio concentration) on the yaxis (Tables 1, 2, 3 and 4).
Remember to label the x and yaxes. Also include a legend for your graph.
Ln Vibrio Concentration versus Time
Time, hours
012345678910111213141516171819202122
Ln (Vibrio Cells per mL)
3.0
3.6
4.2
4.8
5.4
6.0
6.6
7.2
7.8
8.4
9.0
9.6
10.2
10.8
11.4
12.0
12.6
13.2
13.8
14.4
15.0
15.6
16.2
Control A, High Iron
Control B, High Iron
Low Iron A
Low Iron B
35
like this.
Ln Vibrio Concentration versus Time
Time, hours
012345678910111213141516171819202122
Ln (Vibrio Cells per mL)
9.0
9.3
9.6
9.9
10.2
10.5
10.8
11.1
11.4
11.7
12.0
12.3
12.6
12.9
13.2
13.5
13.8
14.1
14.4
14.7
15.0
15.3
15.6
Control A, High Iron
Control B, High Iron
Low Iron A
Low Iron B
36
Part 3: Determining the Growth Rate
1.
Question 2.
Linear Equation: ln(Nt) = rt + ln(N0)
where ln(Nt) = y, r = m, time = x, and ln(N0) = b
2. Calculate the slope (growth rate) of the exponential phase of the growth curves in Part 2,
Question 2 using either the LINEST function in Excel or Equation 5 in Part 3. The
exponential phase is shaded in Tables 1, 2, 3, 4 to help you see which points are located in the
exponential phase.
m (slope) for Control, High Iron A =__________________________________________
Using the data from t = 8.0 and 15.5, with Equation 5
For both High Iron, Control cultures the growth rate should be ~ 0.48 cells/hr.
m (slope) for Control, High Iron B = __________________________________________
Using the data from t = 8.0 and 15.5, with Equation 5
m (slope) for Control, Low Iron A = __________________________________________
Using the data from t = 3.75 and 18.0, with Equation 5
For both Low Iron cultures the growth rate should be ~ 0.10 cells/hr.
m (slope) for Control, Low Iron B = __________________________________________
Using the data from t = 3.75 and 18.0, with Equation 5
37
3.
at t=0?
b represents the yintercept. Solving equation 4 using the growth rates calculated above
as (r), any Nt value from the same experiment within the exponential growth period and
t=0 would give you the N0 value if there was no lag phase.
Analysis
1. Were Vibrio grown in the Low Iron media actually limited by iron? Why or why not?
The Vibrio fischeri grown in the Low Iron media were iron limited because the growth
rate, r of these cultures was significantly lower than that of the Vibrio in the control,
High Iron media.
2. What do you think would happen to the Vibrio cell numbers at the end of the experiment if iron was
added to the Low Iron experimental culture at 13.5 hours?
If iron was added to the Low Iron experimental cultures at 13.5 hours, you would expect
the growth rates of the previously ironlimited Vibrio to increase, leading to higher cell
numbers in the “Low Iron” treatments at the end of the experiment.
3.
be responsible? Why or why not?
At time 13.25, the Vibrio concentration in the High Iron Bottle A was unusually low,
much lower than observed at the time points either before or after. This is definitely
“odd”.
A problem with the flow cytometer itself is an unlikely explanation for the low Vibrio
concentration because 1) the standard beads had the expected SSC and FL1 values
(appeared in the dot plot in the usual place) and 2) about the same number of beads were
counted as in the other samples, so the volume of sample run through the instrument was
also within the expected range.
4. What do you think would happen if you forgot to add the Sybr Green DNA stain to the Vibrio
sample?
If Sybr Green was not added to the sample, the Vibrio would not fluoresce green and
would be difficult to detect with the flow cytometer.
5. What do you think is the best way to handle outliers?
Answers may vary. The best way to handle outliers is to be as transparent as possible.
Ideally, the scientist would have realized this while the sample was being run on the flow
cytometer, made a note in his or her lab notebook of what might be wrong and then re
analyzed the sample. When this is not possible, outliers can be dropped from the data
analysis but only if there are probable technical explanations for the problem, the
exclusion will not affect the conclusions of the study and the “odd” value is reported in
the text.
38
Going Further…
How long would it take for the Vibrio population in the control, high iron media to double in
size?
Using Equation 4
When a population doubles, then Nt should be twice the value of N0. If N0 is set at 1.0 and
Nt at 2, then Equation 4 reduces to
since the ln(1) = 0. Assuming that the average growth rate of the Control, High Iron
cultures was 0.49 hr1, then
and solving for t, it would take t = 1.41 hours for the control, Vibrio culture to double in
size. Note that the selection of any Vibrio concentration where Nt = 2 x N0 would work,
setting N0 at 1.0 is just convenient.
39
Georgia and National Standards met by this activity
Georgia Standards:
Characteristics of Science: SCSh4, SCSh5
Microbiology: SMI2, SMI3, SMI5, SMI7
Math Process Standards: MM1P1, MM1P3, MM1P4, MM1P5
Math I: MMIA1
Math II: MM2D1, MM2D2
National Standards:
Unifying Concepts and Processes: HU2, HU3c
Science as Inquiry: HA1c, HA2
Physical Science: HB3b
Life Science: HC1a, HC1e, HC4c, HC3e, HC5e, HF1b
Acknowledgements
This activity was created by:
Emily Kroutil
Science Teacher
Savannah Arts Academy
Funding for this project was provided by:
The National Science Foundation Project OCE0550365
and
Dr. E. Mann
Assistant Professor
Skidaway Institute of Oceanography