Difference between revisions of "Team:Georgia State/Model"

Revision as of 15:45, 21 October 2019

GSU iGEM

Predator-Prey Model

Predator-prey models can deal with the general loss-win interactions. Our group use predator-prey model to construct the relationship between two algaes, Oxyrrhis marina and Dunaliella tertiolecta.

The Lotka-Volterra Equations

explain Lotka-Volterra

Why a model?

The reason why a predator/prey model for Oxyrrhis marina and Dunaliella tertiolecta is being viewed in ASP-8A rather than F2 media (the media GSU iGEM decided to grow O. marina in) is because the team noticed than D. tertiolecta will begin to overgrow in ASP-8A media alongside the O. marina and eventually outcompete O. marina in the culture. This observation was made from June through August when the different types of media were being tested. The goal is to examine how much to feed the predator (O. marina) until the prey (D. tertiolecta) begins to overgrow.

Defining Our System

Figure.1 The basic model construction.

Parameters

D.T: Concentration of Dunaliella tertiolecta
O.M: Concentration of Oxyrrhis marina
a: Rate D.T is added to the system
b: D.T growth rate
c: Predation rate
d: O.M growth rate
f: O.M death rate

The model satisfies the identity:

Determining Our Rate Constants

To determine the constants we needed, we conducted an experiment

We start 5 different Dunaliella tertiolecta amount to feed in each 75ml flask. The start points are 0.25 ml, 0.5ml, 1.0ml, 1.5ml, 2.0ml of add-in D.T on concentration of 792,000/ml, and set all the O.M at the concentration of 1.2 x 10^4 cells/ml.

The two conditions start of 0.25ml and 0.5ml D.T are seem as the ideal condition that D.T will not overgrow and O.M concentration continues to increase.

Based on the net growth rate in 0.25ml and 0.5ml condition:

0.25 (net growth rate for DT)

9/10-9/13(3 days): 0

9/13-9/18(5 days): 4000/ml / 5days = 800/(day.ml)

9/18-9/20(2 days): (150000/ml - 4000/ml) / 2 days = 73000/(day.ml)

9/20-9/25(5 days): (1420000/ml - 150000/ml) / 5 days = 254000/(day.ml)

9/25-9/26(1 day): (890000/ml-1420000/ml) / 1 day = -530000/(day.ml) (delete)

9/26-10/4(8 days): (1180000/ml - 890000/ml) / 8 days = 36250/(day.ml)

Average growth rate = 91012.5 /(day.ml)

0.5 (net growth rate for DT)

9/10-9/13(3 days): (86000/ml - 42000/ml) / 3 days = 14667/(day.ml)

9/13-9/18(5 days): (332000/ml - 86000/ml) / 5days = 49200/(day.ml)

9/18-9/20(2 days): (150000/ml - 332000/ml) / 2 days =-91000/(day.ml) (delete)

9/20-9/25(5 days): (394000/ml - 332000/ml) / 5 days = 12400/(day.ml)

9/25-9/26(1 day): (658000/ml-394000/ml) / 1 day = 264000/(day.ml)

9/26-10/4(8 days): (3060000/ml - 658000/ml) / 8 days = 300250/(day.ml)

Average growth rate = 128103.4/(day.ml)

Final growth rate = (91012.5 /(day.ml) + 128103.4/(day.ml))/2 = 109557.95/(day.ml)

Thus, we get the D.T growth rate b is 109557.95/(day.ml).

We can rearrange the formulas as such:

Where g = d - f

From this we get the following:

For 1.0ml:

For 1.5ml:

For 2.0ml:

Thus, the predation rate c is 9.3/(day.ml), and the mix O.M growth and death rate is -20890424/(day.ml).

Results

From the data we get above, we can simplify the model as the following:

An application of our model is to get the suitable initial concentration and feed in data for the D.T and O.M. Here is an example of the ideal initial and feed-in to reach a stable condition:

With an initial O.M concentration of 1.2 x 10^9 cells/ml and an initial D.T concentration of 19787 cells/ml and feeding with 2000 D.T cells/day, the environment can reach a stable condition.

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