# Kasey E. O'Connor Week 2 Journal

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## Assignment 2

#### Nutrient/Cell Population Model

In the chemostat model, the dependent variables are the nutrient concentration and the population of cells. These are both functions of time. The parameters of the model are inflow rate, concentration inflow, growth rate, saturation, and consumption. I initially ran the chemostat model with the all of the parameters set to 1, with an initial concentration of 5 and an initial population of 20.

I began to look at what would happen to the population and nutrient concentration when changing the values of the parameters. To best see this, I ran the model looking at a change in the rate of consumption, w. By increasing the rate to 10, there was an obvious "bump" in the graph where the amount of cells in the chemostat actually increased. However, shortly after this rise in cell population, the amount of nutrients available diminished and the cell population began to decrease as well. Keeping the consumption rate at 10, I then altered the initial concentration of nutrients. With every increase, the "bump" moved to the right, and the population hit its maximum at a much higher number. For example, an initial concentration of 50 allows for the population to grow to over 350 cells.

Next, I wanted to change the net growth rate, r. By increasing it to 10, there was a small increase in the cell population, but with a very quick decline in nutrients, the cells began to die shortly after starting the model. Decreasing the growth rate to 0.1, there is little obvious change between the original plot and the new one. Just as when r=1, the cell population decreases in a similar fashion as the nutrient concentration decreases.

#### Logistic Growth Model

The new logistical growth model introduced a carrying capacity to the chemostat model. With this set to 1 initially, the cell population (N0=10) quickly decreased. Through running different values for the carrying capacity and keeping everything else the same, it was clear that something else like nutrient level had to be changed as well. If there were more nutrients available, the cell population increased towards the capacity until they ran out of nutrients. It is clear that even with a carrying capacity, there has to be sufficient nutrient levels to maintain the population, and as soon as those are diminished, the cells began to die.

#### Other Suggestions

After looking at the waste products of yeast, I saw that they produce ethyl alcohol, and that can be toxic to the cells. This could affect the death rate of the cells in the chemostat. If the waste is not being removed quickly enough, many more cells can die than accounted for in the model due to the consumption of the ethyl alcohol. This could very well alter the way the model looks, and should be something accounted for when running the chemostat.