Team:TU-Delft/Project/Modelling
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=== The Regulatory Model === | === The Regulatory Model === | ||
- | + | '''Description''': | |
To perform simulations, a numerical ordinary differential equation solver of MatLab was used (ode45). | To perform simulations, a numerical ordinary differential equation solver of MatLab was used (ode45). | ||
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Since mRNA is rather unstable, it will degrade with a factor α_(mRNA_AraC ). α_(mRNA_AraC ) = log(2) / THalf life time mRNA, with Thalf life time mRNA= 4 min (Taniguchi Y. et al, 2010). | Since mRNA is rather unstable, it will degrade with a factor α_(mRNA_AraC ). α_(mRNA_AraC ) = log(2) / THalf life time mRNA, with Thalf life time mRNA= 4 min (Taniguchi Y. et al, 2010). | ||
Therefore, the rate of change (per iteration) in mRNA of AraC is described as: <br/><br/> | Therefore, the rate of change (per iteration) in mRNA of AraC is described as: <br/><br/> | ||
- | dC_(mRNA_AraC )= β_(mRNA_AraC )- α_(mRNA_AraC )*C_(mRNA_AraC )<br/><br/> | + | (dC_(mRNA_AraC ))= β_(mRNA_AraC )- α_(mRNA_AraC )*C_(mRNA_AraC )<br/><br/> |
''Translation: the production of the protein, mRNA to protein''<br/><br/> | ''Translation: the production of the protein, mRNA to protein''<br/><br/> | ||
Given the calculated amount mRNA, the related amount of produced protein can be calculated, based on the same principle. Per strand mRNA several translation will be performed, pAraC = 10 (Alon, 2007). At steady state, a constant amount of mRNA will be produced and degraded, meaning C_(mRNA_AraC ) is constant if this is equal to β_(mRNA_AraC )/(α_(mRNA_AraC ) ). Multiplying these two factors, will lead to the concentration of ArAC protein. However, the AraC protein will also partly degrade, leading to the following equation to describe the production rate of Arac protein (Alon, 2007): <br/><br/> | Given the calculated amount mRNA, the related amount of produced protein can be calculated, based on the same principle. Per strand mRNA several translation will be performed, pAraC = 10 (Alon, 2007). At steady state, a constant amount of mRNA will be produced and degraded, meaning C_(mRNA_AraC ) is constant if this is equal to β_(mRNA_AraC )/(α_(mRNA_AraC ) ). Multiplying these two factors, will lead to the concentration of ArAC protein. However, the AraC protein will also partly degrade, leading to the following equation to describe the production rate of Arac protein (Alon, 2007): <br/><br/> | ||
- | dc_AraC=p_AraC* β_(mRNA_AraC )/(α_(mRNA_AraC ) )–α_(p_AraC )*C_AraC<br/><br/> | + | (dc_AraC) =p_AraC* β_(mRNA_AraC )/(α_(mRNA_AraC ) )–α_(p_AraC )*C_AraC<br/><br/> |
The α_(p_AraC ) is calculated by log(2)/ THalf time AraC, with THalf time ArAC = 2 min (Kolodubretz et al., 1981). | The α_(p_AraC ) is calculated by log(2)/ THalf time AraC, with THalf time ArAC = 2 min (Kolodubretz et al., 1981). |
Revision as of 20:38, 30 January 2012
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