Transcript Bacterial Growth and Decay

Bacterial Growth and
Decay
By: Karina Vanderbilt, Heidi Pang, & Yina Lor
Facts about Escherichia Coli
(E. Coli)
• E. Coli grows well between 21 degrees Celsius to 49 degrees
Celsius with an optimum at about 37 degrees Celsius
• The growth and decay rate are also affected by:
– Temperature
– Initial concentration of Bacteria
– Presence of antibacterial substances
– pH levels
– Oxidation reduction potential
• In our experiment, we demonstrate how K value is affected by
temperature
Objectives / Thesis
• Examine and construct a model that
represents bacteria’s behavior
• Compare K values from natural decay
to K values due to
– Temperature change
– Chemical Poisoning
• Compare logistic vs. exponential decay
from above the carrying capacity
Our Model: Description of
Bacteria
behavior
1.
2.
3.
4.
Bacteria gradually grow to a
certain point (lag phase)
They start to grow
exponentially (exponential
growth phase)
The population then
approaches the carrying
capacity (stationary phase)
Die off at a particular rate
(death or logistic decline
phase)
Model Conditions
• B(0) = 1000 bacteria in Petri dish with
glucose at 37 degree Celsius
• Carrying capacity= 100,000
• K- value found from research
– specific to 37 degrees Celcius conditions
Logistic Growth
• Used to model the first three phase of the
graph
• Equation:
Where K is 0.00029
PoC
P(t ) 
 kt
Po  (C  Po)e
Results of Logistic Growth
Population approaches carrying capacity at
t= 55, 544.95 seconds = 15 hours
Exponential Decay
• Equation:
B(t)=Bo*e
Exponential decay at carrying capacity
 kt
1200000
1000000
• B(t)=99999e^-0.00029t
B(t)
800000
600000
400000
200000
0
-10000
0
-200000
10000
20000
30000
time (s)
40000
50000
60000
Results of Exponential Decay
• Takes 71,459.5 seconds (19.8 hours) to
reach a population of 0.0001
• Rounded to the nearest bacterium
population = 0
• This is 4.58 hours longer than the bacteria
took to reach the carrying capacity in
Logistic growth
How does changing the K value
affect Bacteria Population?
•
•
•
We solved for time that would take the population to decay from 99999 to
0.0001 using K values both greater and smaller than our previous value of
0.00029.
Greater K value decays quicker
Ratio of K value to our initial K value proportionate to the decrease to the
time necessary for the population to decay
Table 1: K value versus time for Population to Decay to Zero
K
t(s)
K / 0.00029
t / 71459.5
0.00001
2072325.58
29
29
0.00009
230258.4
3.22
3.22
0.00029 (Initial K)
71459.5
1
1
0.001
20723.56
3.45
3.45
0.00137 (heat)
15126.46
4.72
4.72
0.01
2072.33
34.48
34.48
0.256 (Poison)
80.95
882.76
887.76
Adding Heat/Poison
• K value increased for bacteria population
under conditions where heat or poison
were added
• Heat: K= 0.00137, t= 15126.46
• Poison: K= 0.256, t = 80seconds
What happens if the initial
population is above the carrying
capacity?
• Modeled this decay with both exponential
and logistic model and compared the
population of bacteria at various times
Comparison of Logistic and
Exponential Decay
t (s)
B(t) of logistic growth
B(t) of exponential decay
0
150000
150000
100
147886.44
145712.47
1398.16
128,571.38
100000
27772.48
100010.595
47.64
41658
100000.1889
0.85
55544.95
100000.0034
0.015
Graph comparison of logistic and
exponential decay from above
capacity
Logistic growth model (starting above carrying capacity)
Exponential decay above carrying capacity
170000
160000
140000
120000
130000
100000
80000
B(t)
population of bacteria: B(t
150000
110000
60000
40000
90000
20000
70000
0
-10000
50000
-20000
0
10000
20000
30000
time (s)
0
10000
20000
30000
time, t (s)
40000
50000
60000
40000
50000
60000
Conclusion
• The bigger the K value, the quicker the
population is going to grow / decay
• Logically, death of bacteria cells speed up
under poisoning and heat conditions, thus,
our discovery that greater K values are
used for E. coli bacteria under these
conditions have appeared reasonable
• Logistic growth model best represents
bacteria growth if the population stabilizes