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Team:TUDelft/Modeling Cascade
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==ODEs== | ==ODEs== | ||
| - | The kinetic equations were written out in a Matlab script for | + | The kinetic equations were written out in a Matlab script. A total of ten equations were used: one for the diffusion of IPTG into the cell, one for the binding of IPTG to LacI, four transcription equations, and four translation equations for the various levels of the cascade. |
[[Image:TUD_eq_cas.png]] | [[Image:TUD_eq_cas.png]] | ||
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| - | The | + | The solution with the [[Team:TUDelft/Modeling_Parameters|default parameters]] of the system of ODEs can be seen below: |
[[Image:TUD ODE default solution.png|thumb|550px]] | [[Image:TUD ODE default solution.png|thumb|550px]] | ||
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| + | A function was written to determine the point at which the concentration of the final product reached a certain threshold. A threshold of 1E-8 M was used in our simulations. | ||
==Sensitivity== | ==Sensitivity== | ||
Revision as of 21:27, 17 October 2009
Modeling the Transcriptional Cascade
A full description of the Transcriptional Cascade can be found here.
ODEs
The kinetic equations were written out in a Matlab script. A total of ten equations were used: one for the diffusion of IPTG into the cell, one for the binding of IPTG to LacI, four transcription equations, and four translation equations for the various levels of the cascade.
The notation in this system of equations can be seen in the table below:
| Symbol | Definition |
| kIPTGin, kIPTGout | rate constants |
| k50IPTG, k50LacI, k50TetR, k50CI | dissociation constants |
| dmRNA | mRNA degradation rate |
| dTetR, dCI, dRFP, dGFP | protein degradation rates |
| apLac, apTet, aλp | transcription leakage (%) |
| cpLac, cpTet, cλp | maximum transcription rates |
| α1, α2, α3, α4 | translation rates |
| nIPTG, nLacI, nTetR, nCI | Hill coefficients |
| [X]mRNA | concentration of X mRNA |
The solution with the default parameters of the system of ODEs can be seen below:
A function was written to determine the point at which the concentration of the final product reached a certain threshold. A threshold of 1E-8 M was used in our simulations.
Sensitivity
| Parameter | Normalized Sensitivity |
| kIPTGin, kIPTGout | |
| k50IPTG, k50LacI, k50TetR, k50CI | |
| dmRNA | |
| dTetR, dCI, dRFP, dGFP | |
| apLac, apTet, aλp | |
| cpLac, cpTet, cλp | |
| α1, α2, α3, α4 | |
| nIPTG, nLacI, nTetR, nCI | |
| [X]mRNA |
Parameter Sweeps
In the following plots the delay time of the cascade is shown as a function of two different parameters. A delay time off 500 is used to represent an infinite delay (maroon colour). The delay is considered to be over once the concentration of the final product (in this case GFP) goes above 10nM.
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Stability
Jacobian
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Design Recommendations
Based on the results of the simulations, a series of recommendations were given to the delay team to aid them in choosing parts which would maximize the delay time.
- Significant transcription leakages greatly shorten the delay time. Attempt to minimize leakages. Leakage of λp is a far bigger problem than pTet leakage.
- Use a weak promoter and a weak RBS on the last stage (λp) of the cascade.
- A weak pLac promoters is favorable.
- A strong pTet promoter is favorable.
- A strong RBS on CI gene is favorable.
- A weak RBS on TetR gene is favorable.
- A weak RBS on the endonuclease is favorable although a strong RBS can be used for the GFP gene.
- When choosing RBS and promoter strengths avoid the red areas on the stability plots.
