Modeling > ODE
Catagories of Equations
Writing the ODEs is the first step of constructing the deterministic model. For practice, we first catagorized all the reactions appeared in our design into four types - Transcription, Translation, Degradation and AND gate module. In this section, we will demonstrate equations for each type, which will let you be more familiar with our model.
The equation used to describe the transcription process is Hill equations, which is well-known in biomodeling.
<math>\frac{\mathrm{d}[mRNA]}{\mathrm{d}t}=k(\frac{(\frac{[A]}{K})^n}{1+(\frac{[A]}{K})^n})</math>
| [mRNA] | Concentration of the product
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| k | Maximum rate of transcription
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| [A] | Concentration of Protein A. A interacts with the promoter to activate or repress the transcription process.
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| K | Microscopic dissociation constant. K^n is the equilibrium constant for dissociation
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| n | Hill constant
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| μ | Activate: μ=0, Repress: μ=1
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The process translation can be regarded as elementary reaction.
<math>\frac{\mathrm{d}\mathrm{[B]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>
| [B] | Concentration of the product
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| k | Rate of translation
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| [mRNA] | Concentration of the mRNA
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This process can also be regarded as elementary reaction.
<math>\frac{\mathrm{d}\mathrm{[C]}}{\mathrm{d}t}=-\gamma\mathrm{[C]}</math>
| [C] | Concentration of mRNA, protein, et.al.
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| γ | Degradation rate
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This year, we construct AND gates similar to J Christopher Anderson's work(Molecular Systems Biology 3:133). Thus, we use the corresponding equation in the supplementary information of the paper.
AND Gate 1
Bistable
AND Gate 2
Output
Full Model
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