E coli growth curve
Throughout the project, we have observed that colonies with larger construct correctly transform into the e coli results in a slower growth. To investigate whether the growth of e coli in neb5alpha will decrease due to the large plasmid contained, we hope to model the growth of different transformed e coli using different growth models and curve fitting methods. Unless specified, in all equations below, a is the upper limit of the growth curve, b and k sets the horizontal displacement and growth rate respectively.
Method
A single
clone is picked from a perti dish, then incubated in
2 mL of LB with ampicillin for 16 hours, then diluted such that OD_{600}
is 0.040.06. The cultures are then shaken at 250 r.m.p
in 37 C. OD_{600 } is taken at 15minutes to 1hour
intervals. E coli with inserts of pETBlue2 (size: 3600
bp) and our construct FP 1.2.2 16 (size: 14471bp) are compared. Experiments are
duplicated.
Assumptions
s
Assumptions 
Justification 
OD_{600}
= 0.1 corresponds to 2*10^7 cells/mL. 
It is taken for
convenience as calibration is very time consuming, and it is given by 
The OD_{600 }of
the overnight culture is the maximum OD_{600}. 
OD_{600 }remains
constant staring from the stationary phase 
Results
Time
(h) 
16.1
(OD_{600}) 
16.2
(OD_{600}) 
pETBlue2.1
(OD_{600}) 
pETBlue2.2
(OD_{600}) 
0.00 
0.059 
0.052 
0.045 
0.048 
0.52 
0.038 
0.035 
0.059 
0.066 
1.02 
0.064 
0.056 
0.115 
0.188 
2.00 
0.183 
0.136 
0.349 
0.355 
2.55 
0.293 
0.295 
0.599 
0.645 
3.20 
0.443 
0.438 
0.813 
0.883 
3.47 
0.574 
0.538 
1.113 
1.248 
3.75 
0.658 
0.626 
1.326 
1.352 
4.02 
0.768 
0.715 
1.439 
1.63 
4.67 
1.101 
1.02 
2.128 
2.273 
5.08 
1.352 
1.65 
2.355 
2.597 
16.00 
2.871 
3.045 
3.195 
3.279 
Modelling
Gompertz function
Gompertz model is the most frequently used sigmoid model to fit growth data
in biology
The form is given by
Logistic function
The
Logistic function is proposed Pierre François Verhulst, which takes a common
“S” shape.
The form
is given by
Plot of models
Curve Fitting
Curve
fitting is done by the curve fitting app in Matlab.
Coefficients
of the Gompertz function when f(x) represents OD_{600} are as follows:

a 
b 
k 
16.1 
2.877 
7.258 
0.4341 
16.2 
3.059 
10.43 
0.5145 
pETBlue2.1 
3.24 
9.755 
0.6461 
pETBlue2.2 
3.345 
10.89 
0.6933 
Coefficients
of the Logistic function when g(x)
represents OD_{600} are as follows:

a 
b 
k 
16.1 
2.871 
74.28 
0.8241 
16.2 
3.054 
153.8 
0.9832 
pETBlue2.1 
3.205 
73.74 
1.047 
pETBlue2.2 
3.307 
81 
1.099 
Coefficients of the Gompertz
function when f(x) represents log_{10}(cells/mL)
are as follows:

a 
b 
k 
16.1 
8.834 
0.262 
0.2928 
16.2 
8.874 
0.2766 
0.2886 
pETBlue2.1 
8.898 
0.2669 
0.4016 
pETBlue2.2 
8.901 
0.2566 
0.4121 
Coefficients of the Logistic function when f(x) represents log_{10}(cells/mL)
are as follows:

a 
b 
k 
16.1 
8.829 
0.2979 
0.3184 
16.2 
8.869 
0.3169 
0.3153 
pETBlue2.1 
8.89 
0.3031 
0.4341 
pETBlue2.2 
8.895 
0.2898 
0.4431 
Conclusion
By comparing the growth rate of each model, we can see that a e coli containing a larger plasmid grows slower. Therefore, when overexpressing modified nif genes, it will take longer time to reach the designated phase compared to smaller constructs like PETase.
References
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