Modeling

Why did we model?

Our goal of this part was to develop the dynamic model of the expression of our outputs, to precisely describe, predict and control the expression of the proteins and the generation of our colors. What’s more, our modelling also provided instructions for our experiments.

What have we done?

Although various actuators were used in our project, we finally chose fluorescent proteins to build our models because fluorescence could be measured easily by ELIASA (microplate reader) and flow cytometry to get quantitative results, and the expression period of fluorescent proteins is much shorter than those of chromoproteins and enzymes. Besides the modelling of the expression of proteins, we also modelled the light intensity distribution in our hardware, to further optimize our hardware to get evener light on the plates and 96-well plates.

Our model consisted of six parts. In part 1, we established model about free growth of bacteria. In part 2, we discussed the influence of light on the growth of bacteria. In part 3, the expression of fluorescent proteins over time was described. In part 4, the effect of illuminance on the expression of fluorescence was shown. In part 5, we combined the models in part 3 and part 4, drawing a general view about how the expression of fluorescence changed with time and illuminance. In part 6, we introduced how we built models about our hardware and optimize the design of our hardware.

How did the models improve our project?

Our model was tightly combined with other parts of our project, especially our experiment and hardware. The part 2 of model provided methods for experiment to make the growth rate of bacterium on same plate even. The part 4 of model revealed how to get wanted R/G/B of color by changing the wavelength of projected light. The part 5 of model shew how to get wanted fluorescence intensity by adjusting the time and illuminance. The part 6 of model gave evidence on the feasibility of hardware improvement.

Part1 Dynamics of Free Growth

We created a model to simulate the process of bacteria’s free growth.

Questions to answer:

1. How fast the bacteria grow?

2. Is there growth difference between bacteria carrying different plasmids of outputs?

According to Logistic function [1]:

Where N refers to the number of bacteria, r refers to the growth rates, K refers to the carrying capacity.