The Green in Water - explosive growth of green algae

by Andy

Introduction

Ever wonder why masses of green plants exist within your local lake, rivers, and ponds? These strips of green microorganisms, also known as algae, grow when inoculated into any body of water. Cyanobacteria is an algae you can identify prospering in these natural water mediums, and in this blog, we will investigate how big in numbers can one single cell of cyanobacteria duplicate itself?

Figure 1: Algal bloom on a lake

Get to know it

As the name suggests, exponential growth is connected to exponents or rather the concept of growth that gets greater with passing time. An example could be the rising yearly population of mice where for every year, they double in numbers:

Table 1: Population of mice of the years.

We observe that in year 4, the rat population has risen 16 times their original population. We can use a function to represent this relationship, using exponential growth’s function:

Where P is the starting population of the mice, r is its growth rate, t is the years that have passed, and n is the number of compounds within a year. Regarding our scenario:

Through this function, we can predict that in 7 years, there will be 256 mice, assuming no deaths have occurred. This is how we’ll model and theoretically predict the growth of our cyanobacterium.

Cyanobacteria is a heterogeneous group of prokaryotic cells that duplicates asexually through binary fission. Their population grows geometrically and will continue to grow if provided with enough necessities (blue-green algae). We will look at a strand within the cyanobacteria, Synechococcus 2973 or Synechococcus elongatus. This cyanobacterium is characterized as the fastest-growing photosynthetic bacteria on Earth (“Max Schubert”), helping us optimize our investigation of nature’s wonders and the p (ower of rapid growth.

Microorganism growth has its own phases. Its growth is summarized into 4 phases; containing include lag, log, stationary, and declination phases.

Figure 2: Bacterial growth exemplar graph (“Algae Growth”)

The lag phase is when algae get accustomed to their new environment, and therefore, it won’t help us find out the microorganism’s growth (“Algal Growth”). We need to narrow our model, focusing on the exponential and linear phases to observe the duplication of these fast-growing microorganisms over a certain period.

Growth factors

The growth of Synechococcus 2973 depends on natural circumstances and conditions, they are organisms after all. The following list is indicators that have an effect on the growth of algae:

Temperature
Eutrophication - The nutrients mixed within their body of water.
Light density/exposure.
Oxygen supply
The pH of the body of water (“what causes algal blooms”)

Bacterial growth

Synechococcus 2973 doubles itself 16 times a day. Twenty-four hours (1440 minutes) duplicates at around every 1.5 hours, making the generation time 90 minutes. We’ll use minutes as our time frame because it can provide a more detailed account of the subject matter and make it easier for calculations; if necessary, we can always convert it. Achieving this growth requires the microorganism to be cultivated in an optimal environment. This includes having a constant temperature of 420C, 5% of CO2 concentration in the atmosphere, and exposure to light levels of 1,500 m-2 s-1 (Ungerer et al.). Starting with one cell, the variable duplicates over time:

Table 2: Data portrayed of exponential growth of Synechococcus 2973

Applying function 1, we create a general function:

Cn is the number of cells according to the number of generations.

n is the generations.

Both functions should give off the same solution when we sub in the same amount of time of cultivation. For example, if the cells were nurtured for 720 minutes, and according to our table, the population should be 256 cells.

This stayed true, verifying that our original function works. But, if we can find the number of cells cultivated and produced after a certain amount of time, can we use the same function to find the time when given the cell population. If I wanted to know how long it takes for the cell to duplicate to a million cells (1,000,000), I’d sub in the value 1 million for C8

Using logarithm, we altered the function to be expressed in t and, therefore, found out that it only needs 1794 minutes to procure up the number of 1,000,000 Synechoccus 2973 cells. All of which accomplished in a little over a day (29.9 hours), showing the immense growth of the species overall. However, we can find the relationship between both independent and dependent variables easier through a plotted line graph:

Figure 3: Correlation between the number of cells (Synechococcus Elongatus) and total time passed (minutes).

Through the graph, we effortlessly identify that the cell’s population is well over 200 million in less than two days, and prospecting reaches 300 million around the next 500 minutes.

Figure 3: Correlation between the number of cells (Synechococcus Elongatus) and total time passed (minutes).

Through the graph, we effortlessly identify that the cell’s population is well over 200 million in less than two days, and prospecting reaches 300 million around the next 500 minutes.

Validity

According to Max Schubert, a graduated student from the WYSS Institute of Harvard, the Synechococcus Elongatus doubles its population by 6,500,000% daily (“Max Schubert”). We can figure out whether this is true or not by calculating the growth percentage with our data. Acknowledging that the amount of time given is 1440 minutes (daily), we can rely on our function again.

After finding the population in a day, we find the increase of the population from the original and find the percentage of that increase:

So, according to my data, the percentage growth was significantly higher than what Max Schubert said. There are a few hypotheses that we can devise from such a difference.

The function doesn’t take into account all the growth factors. It’s missing the eutrophication of the water and the pH level of the water.
Max Schubert grows his cyanobacterium inside a cylindrical-like container, limiting their growth. This limits space for duplication and limits the number of nutrients provided.

Figure 3: The cylindrical container that was used for Max Schuberts’ experiment (“Max Schubert”)

We can see the caliber of difference between our growth percentage calculations through percentage error:

The percentage error wasn’t large despite the half a million difference. The 0.823% being less than one proves that there’s some quality of accuracy between our data and function. We can check whether our function works by inputting the data values and allowing Desmos to set up the correlating parameters through the expression:

Figure 4: The correlation between time/min and the population of the Synechococcus 2973.

The parameters are given from the calculator line up perfectly with the numbers written within the function. The r2value indicates the correlation and “fit rate” of the data along the exponential line, and it was 1, meaning that there was no error involved.

Conclusion

We found that the Synechococcus 2973 could rise to more than 200 million in less than two days with an optimal cultivation environment. That growth is substantial and could result in algal blooms in just a few hours. Additionally, the function formulated had proven to be quite successful in terms of accuracy. However, factors such as the eutrophication, the pH of the water inoculated, and the growth medium were unaccounted for. This gives uncertainty to the model and doesn’t accurately replicate real-life behavior. The function can still improve with more controlling factors.

After the growth, the algal cells should start declining and enter the stationary and death phases. At this time, the Synechococcus 2973 cells metabolism can no longer maintain and keep up with the requirements (“Algal growth”), resulting in an exponential decay, which is another topic for another blog.

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