Team:PKU Beijing/Modeling/ODE

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*'''Transcription'''
*'''Transcription'''
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The equation used to describe the transcription process is Hill's equations, which is well-known in biomodeling. Here's the general formula.
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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>
<math>\frac{\mathrm{d}[mRNA]}{\mathrm{d}t}=k(\frac{(\frac{[A]}{K})^n}{1+(\frac{[A]}{K})^n})</math>
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[mRNA] is the product of transcription, i.e. mRNA of the protein. d[mRNA]/dt
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{|cellpadding=3
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|[mRNA]||Concentration of the product
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|-
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|k||Maximum rate of transcription
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|-
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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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|-
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|K||Microscopic dissociation constant. K^n is the equilibrium constant for dissociation
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|-
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|n||Hill constant
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|-
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|μ||Activate: μ=0, Repress: μ=1
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|}
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*'''Translation'''
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The process translation can be regarded as elementary reaction.
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<math>\frac{\mathrm{d}\mathrm{[A]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>
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 +
{|cellpadding=3
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|[A]||Concentration of the product
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|-
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|k||Rate of translation
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|-
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|[mRNA]||Concentration of the mRNA
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|}
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==='''AND Gate 1'''===
==='''AND Gate 1'''===

Revision as of 16:17, 10 October 2009
 
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 Model. In this section, we will demonstrate equations for each type, which will let you be more familiar with our model.

  • Transcription

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
kMaximum rate of transcription
[A]Concentration of Protein A. A interacts with the promoter to activate or repress the transcription process.
KMicroscopic dissociation constant. K^n is the equilibrium constant for dissociation
nHill constant
μActivate: μ=0, Repress: μ=1
  • Translation

The process translation can be regarded as elementary reaction.

<math>\frac{\mathrm{d}\mathrm{[A]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>

[A]Concentration of the product
kRate of translation
[mRNA]Concentration of the mRNA


AND Gate 1

Bistable

AND Gate 2

Output

Full Model



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