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 neb5-alpha 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 OD₆₀₀ is 0.04-0.06. The cultures are then shaken at 250 r.m.p in 37 C. OD₆₀₀ is taken at 15-minutes to 1-hour intervals. E coli with inserts of pET-Blue-2 (size: 3600 bp) and our construct FP 1.2.2 16 (size: 14471bp) are compared. Experiments are duplicated.

Assumptions

s

Assumptions	Justification
OD₆₀₀ = 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 [1].
The OD₆₀₀of the overnight culture is the maximum OD₆₀₀.	OD₆₀₀remains constant staring from the stationary phase [2] and 16 hours of incubation takes the e coli to stationary phase [3].

Results

Time (h)	16.1 (OD₆₀₀)	16.2 (OD₆₀₀)	pET-Blue-2.1 (OD₆₀₀)	pET-Blue-2.2 (OD₆₀₀)
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 [4].

The form is given by [5]:

Logistic function

The Logistic function is proposed Pierre François Verhulst, which takes a common “S” shape.

The form is given by [5]:

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 OD₆₀₀ are as follows:

	a	b	k
16.1	2.877	7.258	0.4341
16.2	3.059	10.43	0.5145
pET-Blue-2.1	3.24	9.755	0.6461
pET-Blue-2.2	3.345	10.89	0.6933

Coefficients of the Logistic function when g(x) represents OD₆₀₀ are as follows:

	a	b	k
16.1	2.871	74.28	0.8241
16.2	3.054	153.8	0.9832
pET-Blue-2.1	3.205	73.74	1.047
pET-Blue-2.2	3.307	81	1.099

Coefficients of the Gompertz function when f(x) represents log₁₀(cells/mL) are as follows:

	a	b	k
16.1	8.834	0.262	0.2928
16.2	8.874	0.2766	0.2886
pET-Blue-2.1	8.898	0.2669	0.4016
pET-Blue-2.2	8.901	0.2566	0.4121

Coefficients of the Logistic function when f(x) represents log₁₀(cells/mL) are as follows:

	a	b	k
16.1	8.829	0.2979	0.3184
16.2	8.869	0.3169	0.3153
pET-Blue-2.1	8.89	0.3031	0.4341
pET-Blue-2.2	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

[1]	R. Milo, P. Jorgensen, U. Moran, G. Weber and M. Springer, "BioNumbers—the database of key numbers in molecular and cell biology," Nucleic Acids Research, vol. 38, no. Database , p. D750–D753, 2009.
[2]	R. M. Maier, "Bacterial Growth," in Environmental Microbiology, Elsevier Inc, 2009, pp. 37-54.
[3]	B. G. Hall, H. Acar, A. Nandipat and M. Barlow, "Growth Rates Made Easy," Molecular Biology and Evolution, vol. 31, no. 1, p. 232–238, 2014.
[4]	K. M. C. Tjørve and E. Tjørve, "The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family," PLoS ONE, vol. 12, no. 6, p. e0178691, 2017.
[5]	P. R. Koya and A. T. Goshu, "Solutions of Rate-state Equation Describing Biological Growths," American Journal of Mathematics and Statistics, vol. 3, no. 6, pp. 305-311, 2013.

Team:HKJS S/Model

E coli growth curve