Stomach Butterflies or E-coli?

by Khanh

E.coli, short for Escherichia coli, is a common bacteria found in the lower intestine of warm-blooded animals (like humans!)

What is binary fission?

Like other bacteria, E.coli reproduces through binary fission where cells grow in volume and splits to yield two identical daughter cells. As the original cell grows, a pole forms at the point of division (in the middle of the cell) and will cinch inwards to split the cell in half. These daughter cells continue to grow at the same rate as their parent cell and will reproduce similarly.

There are four phases of bacterial growth. The lag phase occurs first. It is the adaptation period for bacteria, and therefore, the population will not be growing. The following phase is the exponential phase, where bacteria begin their separation. The population at this point will duplicate at a consistent rate, known as the generation time. The stationary phase follows, with the population growth slowing down (almost stunting). Finally, during the death phase, the bacteria population will rapidly decline due to limited nutrients to sustain growth.

The Exponential Phase

Since cells duplicate at a consistent rate during the exponential phase, there is a fixed relationship between the initial and final number of cells.

Knowing the initial and final concentration of cells in the exponential phase allows us to calculate the number of generations, or how many times the cells reproduce. This number will help us find the generation time, which is defined as the intervals in which cells duplicate.

So how does this apply for E.coli?

We need to first establish what we know about E.coli's nature.

E. coli bacteria are cylindrical, with lengths from 1-2 micrometers/µm and a radius of 0.5 µm (Riley).

E.coli's optimal environment for growth is 37.4 ℃ and can thrive with less nutrition and oxygen (“E.coli”). This means that it would be easier to cultivate E.coli in this environment. Upon incubating E.coli cells, the lag phase will end after 360 minutes of culturing (Madar et al.) In the exponential phase, E.coli's generation time is 24 minutes (“The Growth of Bacterial Population”) .

Changing the exponential relationship

The exponential relationship of the initial and final cell population is flawed because it fails to consider how the growth of bacteria is affected by time. Knowing the generation time, we can express n, or generations, in terms of time, t.

Determining the maximum number of E.coli that can be developed

Before solving for t, I needed to determine the maximum number of E.coli that could develop inside the petri dish. Calculating its volume will help determine when E.coli will run out of space to continue developing, establishing a range for the final number of cells.

From the calculations, I concluded that the true volume of E.coli lies within 1.18µm^3 ± 0.39.

The rule of thumb, or the standard measurements based on previous microscopic research, determines that a typical E.coli bacterium has a volume of around 1µm^3 (“How Big Is An E.Coli”). Since this is within the error bounds, I can guarantee that my measured volume is applicable to real-life scenarios.

Size of Petri Dish

The petri dish in this scenario has a diameter of 35 mm and a height of 10 mm. I decided to calculate the volume of the petri dish in micrometers because it is the measurement value for E.coli.

1 mm = 0.01µm

Final Number of Bacteria

The theoretical maximum of E.coli bacteria is 8153.5 billion cells. While the theoretical maximum seems high, a study conducted by Yap and Trau has found that for a container that could hold 200 ml of liquid, the cell count ranges from 500 million to 6 billion cells per milliliter after overnight incubation (Yap and Trau). It is realistic to assume that the calculated population is achievable due to a longer incubation time.

Solving For T

However, since 1029 minutes is not a multiple of 24, the number of E.coli cells won’t ever reach 8153.5 billion cells. It is important to note that bacteria cells grow at the same rate rather than duplicating at spontaneous times. Therefore, I must round the number of generations down as E.coli cells would not have enough time to create a new generation.

Therefore, the number of generations is:

Graph 1: Sample of plotted data without regression

I plotted the 24 minutes intervals t, or x values, and the cell count, or y values, on a graph to identify the percentage error.

Graph 2: Sample of plotted data with regression

I compared the measured points to an exponential regression model with parameters:

As a reminder, here is our established parameters below:

Comparing Established Parameters to Regression Model

Upon observing Graph 4 above, it is clear that the plotted points fit into the regression equation. While the % error is low, the calculated r^2 value on Desmos, which determines how well the regression model fits the data, is also 0.9948. Since this is close to 1, we can conclude that our measurements are precise and valid.

However, the % error between established and regression model's parameter b is quite high.

The established model did not consider the element of generation time. Therefore, the growth factor of cell count, or the value of b, can not be exactly 2, rendering the established model incapable of representing the plotted data.

Conclusion

What happens to E.coli after the exponential phase?

E. coli will reach its decline or death phase after 4320 minutes of continuous incubation. Approximately 90-99% of E. Coli’s population dies (Llorens et al.). However, it is unlikely that all cells will be eradicated as bacteria can adapt to harsh environments and will feed off the nutrients from other dying cells. Therefore, the cycle will repeat when environmental conditions become optimal (Bruslind).

Changes to the model

Our model for cell count will hypothetically keep on expanding. To account for the start of the stationary phase, we could make the function for Cn asymptomatic where the value of Cn is close to but never reach the theoretical maximum. As I have addressed above, neither the generation time nor the limited space would allow the cell count to be equal or exceed 8153.5 billion.

Other flaws with the model

The calculations did not address changes in external factors such as moisture, temperature, environmental pH, and oxygen or nutrients. These factors could alter E.coli rate of growth, resulting in some uncertainty surrounding the real-life applicability of the calculations. However, this has been minimized by applying scientific microscopic measurements as the basis for finding missing variables.

Work Cited

Bruslind, Linda. "Microbial Growth." Biology LibreTexts, 4 Jan. 2021, bio.libretexts.org/Bookshelves/Microbiology/Book%3A_Microbiology_(Bruslind)/09%3A_Microbial_Growth. Accessed 3 Dec. 2021.

"E. Coli – the Biotech Bacterium." Science Learning Hub, www.sciencelearn.org.nz/resources/1899-e-coli-the-biotech-bacterium. Accessed 3 Dec. 2021.

"Exponential growth." Columbia. Lecture.

"Factors Affecting Microbial Growth." Airtek Environmental Corp, 15 June 2017, www.airtekenv.com/2017/06/15/factors-affecting-microbial-growth/#:~:text=Warmth%2C%20moisture%2C%20pH%20levels%20and,chemical%20factors%20affecting%20microbial%20growth. Accessed 3 Dec. 2021.

"HOW BIG IS AN E. COLI CELL AND WHAT IS ITS MASS?" Cell Biology by the Numbers, book.bionumbers.org/how-big-is-an-e-coli-cell-and-what-is-its-mass/. Accessed 3 Dec. 2021.

Llorens, Juan M., et al. "Stationary Phase in Gram-negative Bacteria." Oxford Academic, 1 July 2010, academic.oup.com/femsre/article/34/4/476/539852. Accessed 3 Dec. 2021.

Madar, Daniel, et al. "Promoter Activity Dynamics in the Lag Phase of Escherichia Coli." PubMed Central (PMC), 30 Dec. 2013, www.ncbi.nlm.nih.gov/pmc/articles/PMC3918108/#:~:text=Lag%20phase%20is%20a%20period,difficult%20to%20study%20this%20phase. Accessed 3 Dec. 2021.

Riley, Monica. "Correlates of Smallest Sizes for Microorganisms." National Center for Biotechnology Information, www.ncbi.nlm.nih.gov/books/NBK224751/. Accessed 3 Dec. 2021.

Rogers, Kara, and Robert J. Kadner. "Bacteria." Encyclopedia Britannica, 4 Dec. 2020, www.britannica.com/science/bacteria/Genetic-content#ref272358. Accessed 3 Dec. 2021.

Yap, Puay Y., and Dieter Trau. "DIRECT E.COLI CELL COUNT AT OD600." Tip Biosystems, Apr. 2019, tipbiosystems.com/wp-content/uploads/2020/05/AN102-E.coli-Cell-Count_2019_04_25.pdf. Accessed 3 Dec. 2021.

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