Team:PKU Beijing/Modeling/ODE

From 2009.igem.org

(Difference between revisions)
Line 6: Line 6:
==='''Catagories of Equations'''===
==='''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.
+
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.
*'''Transcription'''
*'''Transcription'''
Line 32: Line 32:
The process translation can be regarded as elementary reaction.
The process translation can be regarded as elementary reaction.
-
<math>\frac{\mathrm{d}\mathrm{[A]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>
+
<math>\frac{\mathrm{d}\mathrm{[B]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>
{|cellpadding=3
{|cellpadding=3
-
|[A]||Concentration of the product
+
|[B]||Concentration of the product
|-
|-
|k||Rate of translation
|k||Rate of translation
Line 41: Line 41:
|[mRNA]||Concentration of the mRNA
|[mRNA]||Concentration of the mRNA
|}
|}
 +
 +
*'''Degradation'''
 +
 +
This process can also be regarded as elementary reaction.
 +
 +
<math>\frac{\mathrm{d}\mathrm{[C]}}{\mathrm{d}t}=-\gamma\mathrm{[C]}</math>
 +
 +
{|cellpadding=3
 +
|[C]||Concentration of mRNA, protein, et.al.
 +
|-
 +
|γ||Degradation rate
 +
|}
 +
 +
*'''AND Gate Module'''
 +
 +
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.
 +

Revision as of 16:25, 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 module. 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{[B]}}{\mathrm{d}t}=k\mathrm{[mRNA]}</math>

[B]Concentration of the product
kRate of translation
[mRNA]Concentration of the mRNA
  • Degradation

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.
γDegradation rate
  • AND Gate Module

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



^Top


 

Retrieved from "http://2009.igem.org/Team:PKU_Beijing/Modeling/ODE"