The system we designed involves many kinds of relationships between populations and individuals. To help us understand these relationships better, we designed models to describe how the amount of E.coli and substance change with time.
    Concretely, to consider population interactions in a fluid environment, we designed a fluid model based on ODE. The system we considered here have no substance exchange except for some gas, which is, however, not considered in our model.
    What is more, we can use this model to help us design our experiment. (See more details at Improved gene circuit and Regulation of killing ability)
    Furthermore, we found that it will be much easier to consider effects of some factors (Like initial number of each populations) on population interactions if we can visualize it. Therefore, we designed our game---Fluid E.coli War (Game Overview & Discovery) based on our fluid model to satisfy our needs. What is more, the game can also help us realize educational purpose of our project and make public know more about synthetic biology! (Exhibition at National Museum)
    Our game is made on the structure of html5. The small video below is Fluid E.coli War.

    See more details on Fluid E.coli War.

Note:
1. Subscript 1 indicate warrior I, subscript 2 indicate farmer I, subscript 3 indicate beggar I, subscript 4 indicate warrior I, subscript 5 indicate farmer II, subscript 6 indicate beggar II.
2. Volume of medium (Vsys) here is 0.005L. Volume of E.coli(Vcell) is 1μm³

Detailed ODEs are shown below:
1. Amount of population (cell/medium):

    We extract part of this complete model and adapt it to our experiment results so that we can know how to design our experiment.
Concretely, we use our model to help us do things below:
(1)Design warriors that can be killed only by the warrior from the other group. See more at Improved gene circuit.
(2)Design an easy way to regulate killing ability of warriors. See more at Regulation of killing abilities.
    What is more, we use this model to design a game---Fluid E.coli War to help us consider effects of some factors (Like initial number of each populations) on population interactions and make the public more interested in synthetic biology. (See more at Fluid E.coli War)

(1)Why we detect RFP intensity but not OD600 directly in simplified model used in experiment
    When we look at the model, we will find many parts of model use hypothesis that is commonly used, like Volterra-Lotka equation or Michaelis-Menten equation, and they can be confirmed experimentally. However, parts of it are not, like hypothesis that the decreasing effect of chloramphenicol on population growth rate is proportional to amount of chloramphenicol inside that character. This is not confirmed by our experiment yet. Therefore, it is still not reasonable now to detect OD600 directly in simplified model used in experiment design. What is more, using RFP intensity to detect LacI and thus killing effect is confirmed by our experiment---Killing Test and so we detect RFP intensity to indicate killing effect.
(2)Delayed ODE may be a better choice
    Besides hypothesis mentioned above, the hypothesis that carrying capacity change in real time as the change of glucose concentration. This will cause that if there is just a little glucose inside medium, the carrying capacity will be very small and thus all characters will be dead in a very fast speed, shown as below:

    However, this may be not consistent with real situation, so it may be better to use carrying capacity before some time in equations that describe how amounts of each character change as time. Similar consideration may be also useful when we consider chloramphenicol’s effects on growth rate.
    In conclusion, fluid model is a powerful tool to help us design our experiment and design our game, though it can be improved in future to make it better in forecasting the behavior of the system.