Team:HIT-Harbin/Modeling

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!align="center"|[[Team:HIT-Harbin/Attributions|Attributions]]
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<p>Before experiment, a mathematical model is developed to describe our system and make a prediction about our following experiment. Our model is based on the following assumption.</p>
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<p>(1) Transcription follows Hill equation, other reactions follows mass action principle and saturation kinetics.<p/>
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<p>(2) Parameter values are partly found on current publications[1,2] and partly guess in a reasonable way.<p/>
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<p>(3) The amount of protein binding to promoter is negligible because the amount of protein binding to promoter is trace compared to the total amount of the protein</p>
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<h1>Model of AND gate</h1>
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<img src="https://static.igem.org/mediawiki/2013/7/75/HIT-Harbin_Project_Andgate.png" />
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<p>Figure 1 : A Schematic of the Biological Andgate</p>
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<p>As described before, HrpS binds to HrpR forming a complex HrpRS. HrpRS then binds to promoter hrpL triggering transcription of the downstream gene. We use two inducible promoters--the isopropylthiogalactoside (IPTG)-inducible Plac and the arabinose-inducible PBAD as the AND gate inputs. A quantitative dynamic model based on protein and protein-promoter interactions for the hrp gene regulatory is described below:</p>
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<h2>1 Transcription of hrpR and hrpS mRNA</h2>
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<p>A transcription function named Hill function[3] was used to explain how IPTG, Arabinose and HrpRS influence the promoters. The Hill function and its curve are</p>
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<img src="https://static.igem.org/mediawiki/2013/4/42/HIT-Harbin_Project_HillFunction.png" />
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<img src="https://static.igem.org/mediawiki/2013/8/86/HIT-Harbin_Project_HillCurve.png"/>
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<p>Figure 2 : Example of regulation functions (a)Hill function;(b)Step function;(c)logoid function</p>
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<p>θj is the threshold for the regulatory influence of the xj on a target gene, m is the steepness parameter. h+ explain the positive regulation on the target gene, while h- is the negative regulation function. </p>
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<p>IPTG binds to promoter Plac and trigger the transcription of hrpR_mRNA at a maximum rate constant vmr, </p>
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<img src="https://static.igem.org/mediawiki/2013/4/4c/HIT-Harbin_Project_TranscriptionFun1.png"/>
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<p>while hrpR_mRNA degrade at a rate constant Drnar, so the dynamic change for hrpR_mRNA is </p>
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<img src="https://static.igem.org/mediawiki/2013/f/f8/HIT-Harbin_Project_ODE_Fun1.png"/>
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<p>Similarly, we get the reaction for PBAD, they are</p>
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<img src="https://static.igem.org/mediawiki/2013/a/ae/HIT-Harbin_Project_TranscriptionFun2.png"/><p></p>
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<img src="https://static.igem.org/mediawiki/2013/5/53/HIT-Harbin_Project_ODE_Fun2.png"/>
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<h2>2 Translation of HrpR and HrpS protein</h2>
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<p>To simplify our model, we made some assumption</p>
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<p>(1) the level of translation product is assumed to be proportional to mRNA levels</p>
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<p>(2) There is no delay in synthesis of either component or delay because of protein transportation</p>
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<p>HrpR and HrpS are synthesized at the rate constants Kr and Ks respectively, and degrade at the rate constant Dr and Ds. </p>
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If you choose to include a '''Modeling''' page, please write about your modeling adventures here.  This is not necessary but it may be a nice list to include.
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Revision as of 05:21, 14 August 2013

Home Team Official Team Profile Project Parts Submitted to the Registry Modeling Notebook Safety Attributions

Before experiment, a mathematical model is developed to describe our system and make a prediction about our following experiment. Our model is based on the following assumption.

(1) Transcription follows Hill equation, other reactions follows mass action principle and saturation kinetics.

(2) Parameter values are partly found on current publications[1,2] and partly guess in a reasonable way.

(3) The amount of protein binding to promoter is negligible because the amount of protein binding to promoter is trace compared to the total amount of the protein

Model of AND gate

Figure 1 : A Schematic of the Biological Andgate

As described before, HrpS binds to HrpR forming a complex HrpRS. HrpRS then binds to promoter hrpL triggering transcription of the downstream gene. We use two inducible promoters--the isopropylthiogalactoside (IPTG)-inducible Plac and the arabinose-inducible PBAD as the AND gate inputs. A quantitative dynamic model based on protein and protein-promoter interactions for the hrp gene regulatory is described below:

1 Transcription of hrpR and hrpS mRNA

A transcription function named Hill function[3] was used to explain how IPTG, Arabinose and HrpRS influence the promoters. The Hill function and its curve are

Figure 2 : Example of regulation functions (a)Hill function;(b)Step function;(c)logoid function

θj is the threshold for the regulatory influence of the xj on a target gene, m is the steepness parameter. h+ explain the positive regulation on the target gene, while h- is the negative regulation function.

IPTG binds to promoter Plac and trigger the transcription of hrpR_mRNA at a maximum rate constant vmr,

while hrpR_mRNA degrade at a rate constant Drnar, so the dynamic change for hrpR_mRNA is

Similarly, we get the reaction for PBAD, they are

2 Translation of HrpR and HrpS protein

To simplify our model, we made some assumption

(1) the level of translation product is assumed to be proportional to mRNA levels

(2) There is no delay in synthesis of either component or delay because of protein transportation

HrpR and HrpS are synthesized at the rate constants Kr and Ks respectively, and degrade at the rate constant Dr and Ds.

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