Team:PKU Beijing/Modeling/Stochastic

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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.
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.
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==='''Construction'''===
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==='''Goal of Simulation'''===
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New model needs new equations. In stochastic model, the equations should represent more elementary reactions. So we split the 13 equations in our deterministic model into 29 more elementary ones. Here we'll demonstrate these equations, without much explaination. If you're confused by some equations, please visit [[Team:PKU_Beijing/Modeling/ODE|ODE]] page, on which there're detailed explainations for each equation we used.
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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.
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*'''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!
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{|cellpadding=5
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==='''Construction'''===
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|Equations||Remark
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|-
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|d[tRNA]/dt=||Synthesis of tRNA
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|-
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| ||Degradation of tRNA
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|-
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| ||Transformation from tRNA to Aa-tRNA
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|-
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| ||Degradation of Aa-tRNA (Aa-tRNA->tRNA)
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|-
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| ||Dilution of Aa-tRNA
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|-
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| ||Transcription of T7RNAP
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|-
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| ||Degradation of T7RNAP
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|-
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| ||AND Gate 1
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|-
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| ||Degradation of T7RNAP protein
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|-
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| ||Transcription of trigger CI
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|-
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| ||Transcription of Bistable CI
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|-
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| ||Degradation of trigger CI mRNA
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|-
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| ||Degradation of bistable CI mRNA
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|-
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| ||Translation of trigger CI mRNA
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|-
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| ||Translation of bistable CI mRNA
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|-
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| ||Degradation of CI protein
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|-
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| ||Transcription of CI434
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|-
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| ||Degradation of CI434 mRNA
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|-
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| ||Translation of CI434 mRNA
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|-
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| ||Degradation of CI434 mRNA
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|-
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| ||Transcription of T3
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|-
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| ||Degradation of T3 mRNA
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|-
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| ||AND Gate 2
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|-
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| ||Degradation of T3
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|-
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| ||Transcription of GFP - OR Gate
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|-
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| ||Transcription of GFP - AND Gate - OR Gate
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|-
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| ||Degradation of GFP mRNA
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|-
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| ||Translation of GFP mRNA
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|-
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| ||Degradation of GFP
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|}
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==='''Parameters'''===
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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.
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Generally, we just use the parameters from our ODE model, just to keep consistent. However, we did change a few, mainly translation rate of CI and CI434, aiming at simulating learning process and forgetting process. Here's the parameters we used. You can also visit [[Team:PKU_Beijing/Modeling/Parameters|parameters]] page for more detailed information.
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Since there're not much new information involved, we'll leave out detailed construction process here. You can download [[Media:PKU_Stochastic.rar|source file here]]. You can even figure out a better set of parameters! If so, don't forget to tell us!
==='''Result'''===
==='''Result'''===

Revision as of 07:30, 20 October 2009

Modeling

Modeling Home
ODE
Parameters
Result
Stochastic Model
Improvement

 
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!

Construction

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!

Result



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