Difference between revisions of "Team:KU Leuven/Modeling/Internal"
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− | <h2> 3. Quest for parameters </h2 | + | <h2> 3. Quest for parameters </h2> |
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We can divide the different processes that are being executed in the cells in 7 classes: transcription, translation, DNA binding, complexation and dimerization, protein production kinetics, degradation and diffusion. We went on to search the necessary parameters and descriptions for each of these categories. To start making our model we have to chose a unit. We choose to use molecules as unit because many constants are expressed in this unit and it allows us to drop the dillution terms connected to cell growth. We will also work with a deterministic model instead of a stochastic model. A stochastic model will show us the molecular noise, but we will check this with parameter scans. <br> <br> The next step is to make some assumptions: <br> | We can divide the different processes that are being executed in the cells in 7 classes: transcription, translation, DNA binding, complexation and dimerization, protein production kinetics, degradation and diffusion. We went on to search the necessary parameters and descriptions for each of these categories. To start making our model we have to chose a unit. We choose to use molecules as unit because many constants are expressed in this unit and it allows us to drop the dillution terms connected to cell growth. We will also work with a deterministic model instead of a stochastic model. A stochastic model will show us the molecular noise, but we will check this with parameter scans. <br> <br> The next step is to make some assumptions: <br> | ||
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− | <h3> 3.1 Transcription </h3 | + | <a href="" return false><h3> 3.1 Transcription </h3> </a> |
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First we will try to find the maximum transcription rate. The prediction of the transcription rate has been an important hold-back in the past, even though Polymerases per Second was introduced as a unit. This is the amount of Polymerases that passes through a given position in the DNA per time unit and is essentially the transcription rate at a particular location on the DNA (open wetware http://openwetware.org/wiki/PoPS). We can use this value as the transciption rate of the whole gene because it is the value of the slowest and rate-defining step, the binding of polymerase on the promoter. The other step being the movement of polymerase over the gene. It remained difficult to measure in vivo but Kelly et al have introduced a way to measure the activity of promoters using an in vivo standard, promoter J23101. This gave rise to a new unit: Relative activity of promoter (RPU)$=\frac{PoPS_{phi}}{PoPS_{J23101}}$. By using relative units, the variability due to equipment and conditions was drastically decreased. The PoPS of J23101 was found to be 0.03.<br> | First we will try to find the maximum transcription rate. The prediction of the transcription rate has been an important hold-back in the past, even though Polymerases per Second was introduced as a unit. This is the amount of Polymerases that passes through a given position in the DNA per time unit and is essentially the transcription rate at a particular location on the DNA (open wetware http://openwetware.org/wiki/PoPS). We can use this value as the transciption rate of the whole gene because it is the value of the slowest and rate-defining step, the binding of polymerase on the promoter. The other step being the movement of polymerase over the gene. It remained difficult to measure in vivo but Kelly et al have introduced a way to measure the activity of promoters using an in vivo standard, promoter J23101. This gave rise to a new unit: Relative activity of promoter (RPU)$=\frac{PoPS_{phi}}{PoPS_{J23101}}$. By using relative units, the variability due to equipment and conditions was drastically decreased. The PoPS of J23101 was found to be 0.03.<br> | ||
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− | As our constitutive promoter, we used J23114. On the iGEM website we found that the J constitutive promoter family had been characterized | + | As our constitutive promoter, we used J23114. On the iGEM website we found that the whole J constitutive promoter family had been characterized and we found that J23101 had a strength of 1791 au and J23114 had a strength of 256 au with J23112 as standard in this measurement. We conclude that J23114 has a PoPS of 0.00429. The iGEM team of UNIPV-Pavia 2010 also measured the activity of J23114 in E. coli in LB with a high copy number. The RPU is equal to around 0.05. This means that J23114 has a PoPS of 0.0015. The two values are of the same magnitude but we take the smaller one to play on safe. <br> |
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The strength of the pLuxPR promoter has been measured relatively to pLacIQ by iGEM Tokyo_Tech 2010. They found a value for pLuxPR of 550 and for pLacIQ of 390. pLacIQ has also been measured by iGEM Upssala university 2012 and was found to have a RPU of 0.04 giving it a PoPS of 0.0012. From these values we calculate the PoPS of pLuxPR to be 550/390 * 0.0012 =0.00169 PoPS. <br> | The strength of the pLuxPR promoter has been measured relatively to pLacIQ by iGEM Tokyo_Tech 2010. They found a value for pLuxPR of 550 and for pLacIQ of 390. pLacIQ has also been measured by iGEM Upssala university 2012 and was found to have a RPU of 0.04 giving it a PoPS of 0.0012. From these values we calculate the PoPS of pLuxPR to be 550/390 * 0.0012 =0.00169 PoPS. <br> | ||
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− | Next we sought values for pCI. iGEM NYMU-Taipei 2009 measured the pLux promoter relative to pCI, which allows us to calculate the PoPS for pCI: $\frac{1}{0.43} {\cdot} 0.00169=0.0394$ PoPS. Their | + | Next we sought values for pCI. iGEM NYMU-Taipei 2009 measured the pLux promoter relative to pCI, which allows us to calculate the PoPS for pCI: $\frac{1}{0.43} {\cdot} 0.00169=0.0394$ PoPS. Their results of pPen were not consistent and the team mentioned they lacked experience in the beginning. Results of the earlier used pCI and pLux were consistent though. This is why we only used their last results and took the mean of pPen compared to pTet: $(0.801 {\cdot} 0.537 + 0,191) {\cdot} {\frac{1}{2}}=0.3106$. Using this mean value we were able to calculate the PoPS: $0.3106 {\cdot} 0.0394=0.01224$. <br> |
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− | These values all depend on measuring activities and since the strains, media and antibiotic markers won’t be completely the same, the real values will diverge from the values found with these simple calculations. | + | These values all depend on measuring activities and since the strains, media and antibiotic markers won’t be completely the same, the real values will diverge from the values found with these simple calculations. Nevertheless, these values can give us an idea about the relative strength of the different promoters. We could gather the real values of mRNA concentration in our cells by executing a qPCR, but for now we will use the found values for our model. The last important parameter for transcription is the copy number in which the genes are present in the cell. The plasmid that incorporates the used genes, has an ORI with a copy number between 100 and 300. In our model we will use a mean copy number of 200. |
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− | For inducable promoters the maximum transcription rate has to be multiplied with a factor to integrate the effect of the transcription factors. Our system includes two types of DNA binding proteins: repressors and activators. These proteins bind certain regions in the promoter DNA. This binding can either repress or activate the promoter activity, affecting transcription. The repressors used in our system are the cI protein of the lambda phage and the PenI protein. The activator protein is LuxR, which should be activated by AHL. All proteins first need to form homodimers before being able to bind their target DNA.</p> <br> <p> | + | For inducable promoters the maximum transcription rate has to be multiplied with a factor to integrate the effect of the transcription factors. Our system includes two types of DNA binding proteins: repressors and activators. These proteins bind certain regions in the promoter region of the DNA. This binding can either repress or activate the promoter activity, affecting transcription rate. The repressors used in our system are the cI protein of the lambda phage and the PenI protein. The activator protein is LuxR, which should be activated by AHL. All proteins first need to form homodimers before being able to bind their target DNA.</p> <br> <p> |
DNA binding will be simulated using the Hill function : ${\theta} = \frac{{[L]}^n}{{K_d}^n + [L]^n} = \frac{1}{1+(\frac{K_{d}}{[L]})^{n}}$. $\theta$ is the amount of DNA bound by the protein, $L$ is the amount of protein, $K_d$ is the dissociation constant and $n$ is the Hill coefficient. This Hill function has values between 0 and 1 and acts like an ON/OFF switch.<br> | DNA binding will be simulated using the Hill function : ${\theta} = \frac{{[L]}^n}{{K_d}^n + [L]^n} = \frac{1}{1+(\frac{K_{d}}{[L]})^{n}}$. $\theta$ is the amount of DNA bound by the protein, $L$ is the amount of protein, $K_d$ is the dissociation constant and $n$ is the Hill coefficient. This Hill function has values between 0 and 1 and acts like an ON/OFF switch.<br> | ||
For repressors we are interested in how much of the DNA is still unbound and active: | For repressors we are interested in how much of the DNA is still unbound and active: | ||
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− | < | + | <h4> Leakiness </h4> <br> <br> |
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A last important value in transcription is the leakiness of the promoter. A shutdown promoter still has a very small transcription which is called the leakiness of the promoter. This value should be as low as possible, because there should be a big difference between ON and OFF promoters. The effect of leakiness of promoters is something that should be checked. <br> | A last important value in transcription is the leakiness of the promoter. A shutdown promoter still has a very small transcription which is called the leakiness of the promoter. This value should be as low as possible, because there should be a big difference between ON and OFF promoters. The effect of leakiness of promoters is something that should be checked. <br> |
Revision as of 08:49, 17 September 2015
Internal Model
1. Introduction
We can think of many relevant questions in implementing a new circuit: how sensitive is the system, how much will it produce and will it affect the growth? As such, it is important to model the effect of the new circuits on the bacteria. This will be done in the Internal Model. We will use two approaches. First we will use a bottom-up approach. This involves building a detailed kinetic model with rate laws. We will use Simbiology and ODE's to study the sensitivity and dynamic processes inside the cell. This is the bottom-up approach. Afterwards, a top-down model, Flux Balance Analysis (FBA), will be used to study the steady-state values for production flux and growth rate. This part is executed by the iGEM Team of Toulouse as part of a collaboration and can be found here
2. Simbiology and ODE
In the next section we will describe our Simbiology model. Simbiology allows us to calculate systems of ODE's and to visualize the system in a diagram. It also has options to make scans for different parameters, which allows us to study the effect of the specified parameter. We will focus on the production of leucine, Ag43 and AHL in cell A and the changing behavior of cell B due to changing AHL concentration. In this perspective, we will make two models in Simbiology: one for cell A and cell B. First we will describe how we made the model and searched for the parameters. Afterwards we check the robustness of the model with a parameter analysis and we do scans to check for the effects of molecular noise.
3. Quest for parameters
We can divide the different processes that are being executed in the cells in 7 classes: transcription, translation, DNA binding, complexation and dimerization, protein production kinetics, degradation and diffusion. We went on to search the necessary parameters and descriptions for each of these categories. To start making our model we have to chose a unit. We choose to use molecules as unit because many constants are expressed in this unit and it allows us to drop the dillution terms connected to cell growth. We will also work with a deterministic model instead of a stochastic model. A stochastic model will show us the molecular noise, but we will check this with parameter scans.
The next step is to make some assumptions:
- The effects of cell division can be neglected
- The substrate pool can not be depleted and the concentration (or amount of molecules) of substrate in the cell is constant
- The exterior of the cell contains no leucine at t=0 and is perfectly mixed
- Diffusion happens independent of cell movement and has a constant rate
4. System
5. Results
Cell A graph of all, graph of Leucine, graph of AHL
Cell B graph of all, graph with induction and without induction
Sensitivity analysis
Conclusion and discussion