Our model of the delayed auxotrophy system, which acted via thymineless death, first defined a mean number of plasmids in each bacterium and distributed plasmids across the initial population of bacteria according to a standard deviation from this mean value. With each division, a time step that was defined to be one day, some plasmids were lost, with a probability defined in the model. When a bacterium had zero remaining plasmids, it was considered “dead” and removed from the count of total bacteria. Because we did not have time to experimentally determine initial plasmid number and rate of plasmid loss, sensitivity analysis was performed for these values within ranges determined from literature values. The rate of plasmid loss was varied between 0.001% and 50% loss per division, giving the first plot seen above. As the rate of plasmid loss increased, the peak number of bacteria decreased and rate at which the bacterial population decreased rose, as shown by the steeper downward slope after the peak with higher rates of plasmid loss. The initial plasmid number was varied between 40 and 80 plasmids per bacterium, with a standard deviation of 10, giving the second plot shown above. As the initial plasmid number increased, the peak number of bacteria increased and the rate of decrease in the bacterial population decreased.

This model illustrates the relationship between the E.coli population and the zebra mussel population. It utilizes a system of differential equations to calculate zebra mussel population as a function of initial zebra mussel population, zebra mussel growth rate, and rate of zebra mussel death due to the bacteria, which is a function of the total number of bacteria, itself a function of our first model, the delayed auxotrophy system. The value of zebra mussel growth rate was determined from literature values, and the initial population of zebra mussels was taken to be 1000. In the first plot illustrates the general relationship between the changing population of E.coli and the changing population of zebra mussels, for a zebra mussel death rate due to bacteria of 0.00005. However, as we did not have time to experimentally determine the values of this death rate constant, we instead performed sensitivity analysis using a range death rate values. This sensitivity analysis is shown in the second plot, with the large orange peak representing the bacterial population, and the smaller peaks representing the changing zebra mussel population for death rate due to bacteria values ranging from 0.00001 to 0.0005. For smaller death rates, the zebra mussel population decreased more slowly and began to rebound at long times, while for larger death rates, the zebra mussel population decreased more quickly and reached lower values before the bacterial population began to decline, which in turn resulted in a smaller incidence of rebounding zebra mussel population.

Cost Analysis for Cultivating and Maintaining Zebra Mussel Regulating Pseudomonas in Minnesota Lakes

This report is a quick summary of the potential cost benefits of the. Up until now, the total consumable laboratory equipment that have been used round up to 600 USD, the total expenses is expected to be much higher upon the completion of this project.

Zebra mussel is an invasive species originated from Eastern Europe and Western Russia, adult mussels are in between a quarter inch to one and a half in long. Female zebra mussel produces on average 100,000 to 500,000 eggs annually. The fast proliferation and attaching of zebra mussel to other surfaces are the two major problems it causes. The major economic damages that zebra mussels cost is the clotting of water intake for cities’ water plants and power plants, the relative minor damages are the damages they made on boats and other water structure.

Indirectly, massive proliferation of zebra mussels disrupts the water body’s eco system by consuming resources that are available to other filter- feeder, which consequently can cause economic damages to fishing industry.

Based on estimation, 8.6 million dollar was spend in Minnesota in 2013 for controlling zebra mussel population in the infested lakes, this amount will be used as a threshold to determine whether our project will bring meaningful economic benefits.
In nature condition, the zebra mussel population can be estimated by the population growth model with carrying capacity, using theoretical values in the model, the population can be roughly represented by the following graph:

When zebra-mussel-killing Pseudomonas is introduced, the rate of population growth should decrease, the following graph is when the growth rate is decreased by 50%:

This plot is based on the assumption that the population of Pseudomonas in the model is in at its population steady state, therefore its effect on zebra mussel growth rate can be estimated to be a constant.

If cost benefits are considered through these two models, and the goal is to maintain zebra mussel population under 200/m3. Treatment only need to be applied every 60 days instead of every 28 days (numbers is estimated through graph). Therefore, potential cost benefits of zebra mussel treatment can be cut in half annually.

Furthermore, if based on this new 60 cycle for zebra mussel treatment, the Pseudomonas will need to be renewed every 60 days, giving 6 renewal cycles per year. In the state of Minnesota, among more than 10,000 lakes, 2% of which is confirmed to be infested by zebra mussel, meaning approximately 200 lakes need Pseudomonas renewal, this adds up to about 1200 deliveries of lab-grown Pseudomonas to different lakes annually.

As stated above, if meaningful economic benefits were to be achieved, each the cost of each batch of renewed Pseudomonas need to be controlled under 3580 USD. This result seems very positive based on current expenses.

Alternative treatment:

Microfiltration/UV

Not used for open water (power plants/pipes only)
Annual operating cost is between $3,150-$4,350
once per year chemical treatment would still be necessary to effectively remove any mussel settlement that occurred from mussels that manage to pass through the UV lights uninjured

Chlorine

100% fatality in adult mussels occurs at 2.0 mg chlorine/l which can come from
Sodium hypochlorite ($1.43/lb so $0.00000315/L treated water)
Potassium hypochlorite ($700 to $1600/ton so $0.00000077/L treated water to $0.00000176/L treated water)
Calcium hypochlorite ($1.76/lb so $0.00000388/L treated water)
Chlorine gas ($0.45/lb so $0.000000992/L treated water)

Disclaimer:

This analysis is merely based on theoretical values and ideal assumptions, actual values will be affected by the performance of Pseudomonas and other environmental factors, such as temperature and nutrient level.

Written by Zhipeng Ding and Kathryn Almquist

Team:Minnesota/Model

Minnesota