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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.
Construction
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 ODE page, on which there're detailed explainations for each equation we used.
| Equations | Remark
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| d[tRNA]/dt= | Synthesis of tRNA
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| | Degradation of tRNA
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| | Transformation from tRNA to Aa-tRNA
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| | Degradation of Aa-tRNA (Aa-tRNA->tRNA)
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| | Dilution of Aa-tRNA
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| | Transcription of T7RNAP
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| | Degradation of T7RNAP
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| | AND Gate 1
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| | Degradation of T7RNAP protein
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| | Transcription of trigger CI
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| | Transcription of Bistable CI
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| | Degradation of trigger CI mRNA
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| | Degradation of bistable CI mRNA
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| | Translation of trigger CI mRNA
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| | Translation of bistable CI mRNA
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| | Degradation of CI protein
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| | Transcription of CI434
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| | Degradation of CI434 mRNA
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| | Translation of CI434 mRNA
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| | Degradation of CI434 mRNA
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| | Transcription of T3
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| | Degradation of T3 mRNA
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| | AND Gate 2
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| | Degradation of T3
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| | Transcription of GFP - OR Gate
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| | Transcription of GFP - AND Gate - OR Gate
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| | Degradation of GFP mRNA
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| | Translation of GFP mRNA
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| | Degradation of GFP
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Parameters
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 parameters page for more detailed information.
Result
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