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Team:Freiburg/Project/modeling
From 2013.igem.org
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| - | <p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/1"> | + | <p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/1"> Introduction </a></p> |
<p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/effector"> Effectors </a></p> | <p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/effector"> Effectors </a></p> | ||
<p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/induction"> Effector Control </a> </p> | <p class="first_order"><a href="https://2013.igem.org/Team:Freiburg/Project/induction"> Effector Control </a> </p> | ||
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parameters is smaller than all other values. (f(p0)<=f(p)). In three dimensions the function can be thought as a landscape and minimization is finding the deepest | parameters is smaller than all other values. (f(p0)<=f(p)). In three dimensions the function can be thought as a landscape and minimization is finding the deepest | ||
| - | valley. Depending on the method you use different problems arise. The most common problem is finding only a local minimum and not the global one. </p> | + | valley. Depending on the method you use different problems arise. The most common problem is finding only a local minimum and not the global one <span id="refer"> <a href="#Fig3">(Fig. 3)</a></span>. </p> |
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to be sure to have found a global minimum we started our minimization procedure using different start values for our parameters. To sample these parameters we used | to be sure to have found a global minimum we started our minimization procedure using different start values for our parameters. To sample these parameters we used | ||
| - | the latin hypercube sampling on a logarithmic scale. </p> | + | the latin hypercube sampling on a logarithmic scale <span id="refer"> <a href="#Fig4">(Fig. 4)</a></span>. </p> |
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| - | <p> | + | <p>The number of different initial parameter settings is set to N and thus the parameter space is divided in N*N subspaces. For the initial parameter the values are chosen so that there is only one parameter in each row and column. </p> |
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<p id="h3"> Data generation </p> | <p id="h3"> Data generation </p> | ||
| - | <p> | + | <p> Cas9 is quantified by using Western blot and we used SEAP as target protein that can be quantified by a SEAP assay. |
For more detailed information refer our <a id="link" href="https://2013.igem.org/Team:Freiburg/Notebook/modeling">modeling notebook</a>. </p> | For more detailed information refer our <a id="link" href="https://2013.igem.org/Team:Freiburg/Notebook/modeling">modeling notebook</a>. </p> | ||
<p id="h3"> Fitting Procedure and Results </p> | <p id="h3"> Fitting Procedure and Results </p> | ||
| - | <p id="h4"> dCas-VP16 </p> | + | <p id="h4"> 1. dCas-VP16 </p> |
| - | <p>Assuming the given ODE and using the fminsearch-function implemented in matlab with various initial parameter vectors the fitting process results in one optimal parameter composition | + | <p>Assuming the given ODE and using the fminsearch-function implemented in matlab with various initial parameter vectors the fitting process results in one optimal parameter composition . Our measurement time starts with the transfection, therefore we assumed the initial concentrations for Cas, tracr/crRNA and the gene recognition complex as zero and fixed during the fitting process. However there might be some production of these components bevor time point zero, because the transfection end point is not clearly to define and therefore a second process followed the first one. This time all 14 parameters were set variable, not only the kinetic parameters, but also the initial concentrations. The change between fixed and variable parameters was easily to perform, because of an additional vector (qfit). This vector contains boolean values depending on wether the parameter is fixed or flexible during the fitting process. Moreover another parameter is required for adjusting the absolute values of the duplicates. This second fitting process results in small not zero initial concentration and a lower error value and thus the parameter are assuemd as more likely <span id="refer"> <a href="#Tab1">(Table 1)</a></span>. </p> |
<p> | <p> | ||
| - | The model reflects the general construction of the network <span id="refer"> <a href="# | + | The model reflects the general construction of the network <span id="refer"> <a href="#Fig5">(Fig. 5)</a></span>. As assumed Cas9 seems to converge asymptotically to a stable state and there is an exponential increase in the SEAP concentration. |
| - | The model also shows a potential behaviour of the not measured components, the free tracr/crRNA-complex and the gene recognition complex. The tracr/crRNA-complex seems to rise linearly, however the small curvature underlines the assumption of a steady state. There is however no possibility to distinguish between the two different RNAs. There might be some differences in their expressions, especially because of the different promoters (crRNA expressed under U6-promoter; tracrRNA expressed under h1-promoter), however the model won't show them. <br> There is no free gene recognition complex during the measured time | + | The model also shows a potential behaviour of the not measured components, the free tracr/crRNA-complex and the gene recognition complex. The tracr/crRNA-complex seems to rise linearly, however the small curvature underlines the assumption of a steady state. There is however no possibility to distinguish between the two different RNAs. There might be some differences in their expressions, especially because of the different promoters (crRNA expressed under U6-promoter; tracrRNA expressed under h1-promoter), however the model won't show them. <br> There is no free gene recognition complex during the measured time period, which means that after tracr/crRNA binding the complex immediately binds to DNA. <br> |
All in all the model shows that Cas might be the limiting factor of the Cas induced SEAP an not one of the RNAs. | All in all the model shows that Cas might be the limiting factor of the Cas induced SEAP an not one of the RNAs. | ||
</p> | </p> | ||
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</div> | </div> | ||
| - | <p> Because of the fact that the fminsearch algorithm is not proved to converge to a minimum <span id="refer"> <a href="#(1)"> [1]</a></span>, we started at different points in the parameter space and therefore the probability of having found the global minimum is high | + | <p> Because of the fact that the fminsearch algorithm is not proved to converge to a minimum <span id="refer"> <a href="#(1)"> [1]</a></span>, we started at different points in the parameter space and therefore the probability of having found the global minimum is high <span id="refer"> <a href="#Fig6"> Fig. 6 </a></span>.</p> |
<div> | <div> | ||
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| - | <p id="h4"> dCas-KRAB </p> | + | <p id="h4"> 2 dCas-KRAB </p> |
<p></p> | <p></p> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
| - | <td> <b >Fig. 7: Modeling Result:</b><br> Shown are the experimental results (purple square) in comparison to the model prediction values (cyan cross) for SEAP and | + | <td> <b >Fig. 7: Modeling Result:</b><br> Shown are the experimental results (purple square) in comparison to the model prediction values (cyan cross) for SEAP and Cas9, as well as the model prediction for the not measured component tetR. </td> |
</tr> | </tr> | ||
</tbody></table> | </tbody></table> | ||
</div> | </div> | ||
| - | <p> This time we also fitted the different error values. <span id="refer"> <a href="# | + | <p> This time we also fitted the different error values. <span id="refer"> <a href="#Fig8"> Fig.8 </a></span>.</p> |
<div> | <div> | ||
Revision as of 17:01, 3 October 2013
Modeling our dCAS
Introduction
We used a thermodynamic approach to model and characterize our system. It is based on various ordinary differential equations (ODE) that describe the behaviour of our network. Due to the limited measurment possibilities and the unwritten law, that you should at least measure half of the number of components of your network we started by using a small network with a limited amount of different components.
The Networks
1. dCAS-VP16
Our network includes four different components dCas-VP16, a RNA complex (tracr/cr RNA), a RNA-dCas-VP16 complex and the Secreted alkaline phosphatase (SEAP). DCas-VP16 binds the RNA-complex and the whole complex binds the DNA, which leads to the production of SEAP.
 |
| Fig. 1: Transcriptional Activation via dCAS-VP16: The dCAS-VP16 fusion protein is guided to the desired DNA sequence by a co-expressed crRNA and tracrRNA. The binding of the gene recognition complex leads to an expression of SEAP. |
Setting up the ODE
According to the graphical reaction network the ODE can be set up.
Cas9 is constitutively expressed by the CBh promoter and degraded proportional to the current concentration. It is used to build the DNA recognition complex and produced during complex decay.
The RNA-complex is build linearly. The production constant can be seen as production constant of the lower expressed RNA, because this expression limits the complex building. It is assumed that the RNA is degraded after DNA recognition complex decay and therefore the complex decay does not lead to more RNA.
The DNA recognition complex is built, when Cas9 and RNA meets and degraded proportional to the current DNA recognition complex concentration.
There is a leaky SEAP production and one that depends on the current concentration of the Cas9/RNA Complex. This dependency is assumed to follow the Monod-kinetic. Because of the long half time (T2 > 500 h) of SEAP we can neglect the SEAP decay [2, 3].
| The parameters are: | |
|---|---|
| k1: linear production rate of Cas9 k2: Cas9 degradation rate k3: tracr/crRNA production rate k4: tracr/crRNA degradation rate k5: gene recognition complex building rate |
k6: cr/trRNA /Cas9 degradation rate k7: SEAPs leaky production rate k8: Complex dependent SEAP production rate k9: |
Sources
(1) Lagarias, J. C., J. A. Reeds, M. H. Wright, and P. E. Wright.
(1998). Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions." SIAM Journal of Optimization, Vol. 9, Number 1,
112–147
.
(2) Müller K, Engesser R, Metzger S, Schulz S, Kämpf MM, Busacker M, Steinberg T, Tomakidi P, Ehrbar M, Nagy F, Timmer J, Zubriggen MD, Weber W.
(2013). A red/far-red light-responsive bi-stable toggle switch to control gene expression in mammalian cells. Nucleic acids research 41:e77.
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3627562&tool=pmcentrez&rendertype=abstract.
.
(3) Müller K, Engesser R, Metzger S, Schulz S, Kämpf MM, Busacker M, Steinberg T, Tomakidi P, Ehrbar M, Nagy F, Zubriggen MD, Weber W.
(2013). A red / far-red light-responsive bi-stable toggle switch to control gene expression in mammalian cells Supplementary Information . Design and parameterization of the mathematical model.
The Code Files
