Team:Freiburg/Project/modeling

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Revision as of 17:39, 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:

References

(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

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