Team:PKU Beijing/Modeling/Stochastic



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Stochastic Model

Modeling > Stochastic Model

We have successfully conduct ODE model for both T3 design and P2 design. However, there's a inborn defect. The ODE models regard memory as a switch, only two state - 0 and 1. Actually, the memory is continous. Besides that, since the number of molecules in cell is not large enough, which means the circuit itself has a stochastic property. For these reasons, we conduct a stochastic model. Since ODE model for P2 is not as good as the one for T3, we will only conduct stochastic model for the T3 design.

Goal of Simulation

This time, the goals are different. Here're our goals:

  • Learning Step by Step

No one can learn everything all at a time. No matter from scientific research or from our daily experience, learning is a slow process. We gain knowledge through practice, so does a dog.

  • Forget Gradually

All of us forget things. No matter whether you forget to shut down the computer before sleep or you lock the door without bringing the key, forgetting is a natural process. Why not a dog? In our stochastic model, we aimed at simulating the process of forget.

  • Truth Table

The first priority is to accord to the truth table. But hey, let's think about it. If we can simulating the learning and forgetting process, which means the bistable turn guadually from CI to CI434 and then back, there's no doubt that the dog will follow the truth table. So, we'll skip this part, you can check it by yourself!


Based on our ODE model, constructing stochastic model is a relatively simple process. We use the equations from ODE model, only splitting them into more elementary ones. We also use the parameters from the old model, with slightly changes.

Since there're not much new information involved, we'll leave out detailed construction process here. You can download source file here. You can even figure out a better set of parameters! If so, don't forget to tell us!


Here we'll demonstrate the simulating result. The green lines represent signals of bell, while if we give the dog food, a red line will appear. The blue line indicate dynamics of specific substance marked on the head of the figure. We train the dog(both food and bell signals present) at 200min, 600min, 1000min, 1400min, 1800min and 2200min. Every 400min from the beginning, we give the dog bell signals ONLY to check how it has learned. We'll show the dynamics of three key substance of our system, CI, CI434 and GFP. For other substances, you can plot it by yourself with the source file provided.

PKU sto CI.png During the six training sessions, the concentration of CI increases which indicates the dog's memory is being strenghened. After the whole training sessions, the concentration of CI decreases as the dog forgets the relationship between food and bell.

You may notice that during the six training sessions, the increase of GFP becomes lower and lower, which accord to psychological study about memory as we all know.

PKU sto CI434.png Contrarily, the trend of CI434 is exactly opposite to that of CI.
PKU Sto frac.png We calculate the fraction of cells in each state and plot the result in the left figure. In this picture, you can clearly tell that the dog learns step by step when getting trained, and forget the relationship after that.
PKU sto GFP.png The change of memory reflects on the GFP output. During the first several checking process(only bell), the GFP output increases while in other checking sessions, GFP output decreases.

How we achieve the goal?

  • Learning Step by Step YES!
  • Forget Gradually YES!
  • Truth Table Of Course..

This means...our stochastic model is successful!