* the process of gene expression: activation by *promotor*, *trancription* in RNA, and *translation* in proteins (discovered by François Jacob and Jacques Monod, Nobel prize 1965)
* the stochastic effects caused by low numbers of molecules (a gene is in one single copy)
* the expressive power of autocatalysis
The importance of stochastic effects in gene expression will lead us in the sequel of the MODAL to favor programming with high numbers of molecules, i.e. using proteins, enzymes and post-translational regulation, instead of gene networks.
A *gene* is sequence of DNA which codes for an *RNA*, itself coding for a *protein*.
The *RNA polymerase* is a protein complex which transcripts the *DNA sequence* of the gene in the corresponding *RNA sequence*.
The binding of the RNA polymerase on the binding site of the DNA can be
* either spontaneous (*basal expression*)
* or facilitated by the binding of a *promotor* protein already bound on that site (*gene activation*)
* or inhibited by the binding of a repressor protein (*gene repression*)
* may make us prefer to reason in the differential semantics
* but with the risk of missing qualitative behaviors only visible in the stochastic semantics
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```
option(method:bsimp). % implicit method of integration for the differential semantics
numerical_simulation. plot.
```
%%%% Output: display_data
%%%% Output: display_data
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# Part II: Gene expression control
* A *gene promotion factor* is a protein which binds to the gene (gene+promoter => genepromoter)
and which promotes the binding of RNApolymerase with a faster binding rate (genepromoter+RNApolymerase => geneRNApolymerase)
* A *gene inhibitor* is a protein which binds to the gene (gene+inhibitor => geneinhibitor) but prevents (instead of promoting) the binding of the RNA polymerase simply by the absence of binding rule of the RNA polymerase to the inhibited gene
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# Question 2) Add reactions for promotion factor and inhibitor
* show how to control the expression of the gene by changing the concentraiton of promotion factor and inhibitor
* compare inhibition and absence of promotor
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```
```
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# Question 3) Find parameters to maintain a protein concentration equal to 5
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```
```
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# Question 4) Give a control law to obtain oscillations of the protein with a period of 24 time units
* the control can be implemented with time events
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```
```
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# Part III: Autocatalysis
* when the synthesized protein is (transformed to) the promoter of its own gene (protein => promoter)
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# Question 5) Implement autocatalysis
* show the effect of autocatalysis in presence of an inhibitor
* both in the differential and stochastic semantics
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```
```
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# Part IV: Example of virus phage T7
Some viruses like phage T7 can be produced from RNA (template tem)
* by back tanslation to DNA
* and synthesis from the DNA
* of its RNA and the structure proteins to form a new virus
The bacteriophage T7 is a virus that infects a cell with its DNA and uses the gene expression machinery of the cell to reproduce itself:
* after translocation of the DNA of the virus through the membrane of the cell
* the infected DNA of the cell can
* replicate the DNA of the virus
* and synthesize the structure proteins of the virus
* to form a new virus that may leave the cell and infect other cells
### This is one example where you will show that the differential and stochastic behaviors may be qualitatively very different (explaining why some of you would survive and some would not)
