Modeling Example: Sunlight Responsor System

Here we raise an example of a specific device models, which includes the source of the device, its formulae with numerical solutions, and comparison with our experiment data as a test of model. We provide this example to better explain the modeling function of our software, and we make further error analysis to examine the accuracy of our models, as an effective proof.

Device Sources

We pick two devices from our database, sourcing from the former iGEM teams: Bologna, (https://2008.igem.org/Team:Bologna) and ETH-Zurich, (https://2012.igem.org/Team:ETH_Zurich) as they made study on toggle switch and sunlight sensor, which are representative and useful structures in circuit design. We made some modifications to the devices and put them together to build a system.

System Overview

Formulae

Assume that , which is a t-based function that represents the trend of UVB, to serve as the human-defined condition of the whole device. The whole equation group is shown as below, obeying the rule system we introduced in the former modeling page:

In which we introduce five Eigen functions, signaled as χ , to help make judge of certain terms in equations. Thus when the symbol substance appears, the χ function value will equals to 1, making sense of the term including it; otherwise χ function value equals to 0. By Eigen functions we create the switch of important conditions or changes of some chemicals or necessary structures in equations, to reach the flexibility for users to lead in or move out something in the circuits.

Parameter Table

Comparison between Numerical Simulation and Experiment Results

Based on the differential equations, we use the modeling function of CORE to make graphs of the dynamic performance of certain parts chosen by users. In the system we mainly observe the performance of YFP Protein and GFP Protein, as they are signaled by the light density they produced. The flexibility of toggle switch as regulators in circuits can be shown in its behavior pattern that the YFP or GFP protein dominates while the other one is close to 0, and they have the completely opposite varying trends. The boundary conditions and parameter values can be reset if different performance needed, with different slopes and initial values. In the example, we set the initial values of all variables as zero, which accords with the initial state of the experiment. (Users can also rewrite those values.)

In the graphing field of CORE we can easily get the graph of simulating dynamic performance of YFP, GFP and CI, as shown below:

So based on the model we can see in the graph that YFP is produced, while the production of GFP is inhibited. The result echoes the simulation result run from MATLAB, shown in the graph below:

We run our model (left curve) and experiment data (right curve) at the same time on MATLAB platform (the time interval is set as 10 hours according to the experiment time) and find the curves are close. Further, we make the fitted curve of the experiment data and find that it has the approaching trend with the simulation curve of the model, as shown below:

Error Explanation

But there is still some inevitable errors. We can see fluctuation in the data of the 2nd, 3rd and 4th hour. This may be caused by random error of the plate reader. The data curve went more steadily from 5th to 8th hour than the simulate one. That's because we only used one tube of culture for measurement. Every time we took out 200μ culture for measurement, some of the bacteria were lost, and the growth were also paused for a moment due to the low temperature. This influence is especially obvious in the first few hours, but the two curves would finally be closer to each other. From 8th to 10th hour, the data curve rose much more rapidly because in this period, the loss of bacteria caused by measurement can be neglected. As there were less bacteria in the earlier period, the resources and space made it possible for bacteria to grow more rapidly.