Team:Paris/Modeling

Roadmap

If you want to have a look at our roadmap : Roadmap

Bibliography

In order to choose a proper modeling approach for our system, we have decided to list all the chemical reactions we will take into account. Afterwards, we will find the needed parameters reading articles or devising the required experiments.

An overview of the work that has to be done can be found here : Bibliography

Estimation of parameters

If we want to use the promoters used for the formation of the flagella ( Description of the project), we will have to clearly defined their dynamics. To do so, a rather huge experimental work will be undertaken, consisting in providing the so-called 'Hill functions' for each promoters.

Therefore, we have written a little module which can estimate the parameters of the 'Hill functions', even with some noise and few data available. Some details and the corresponding code can be found here : Programs.

The method we have employed is just based on a least-square optimization. Then, it could be generic enough for many applications and we would be glad to share the code if you feel it could be usefull.

Thus, we need experimental datas. To quantify the strength of an inducer on a promoter, we will use measurements of GFP fluorescence, and compare to the strength of the constitutive promoter [J23101], as it was proposed by the iGEM competition. The datas we are looking for must appear as a table of values, giving several 'transduction rate' with their corresponding 'inducer concentration'.

For this aim, we made several hypothesis, which we will verify as good as it is possible for us :

(1) We do not take into acount the 'traduction' phase, so we directly correlate the expression of a gene with the concentration of its protein.

(2) We assume that, whatever is the gene behind the promoter, its expression depends only of the inducer of the promoter, and not, for instance, of the weight of this gene. That's why comparing promoter strength is relevent only if the genes behind have similar length.

(3) We consider that the activity of a promoter is well described as a Hill function of its inducer. Thus, we suppose that the protein concentration follows this equation :

where gamma is a constant, due to degradation and of dillution of the protein, along time and cell divisions. Therefore, if we consider a steady-state, for given concentration of the inducer, we will have :

(4) Endly, knowing gamma will give us the kind of datas we are looking for. In a first approach, we assume that, as long as the barcteria are in their exponential phase of growth, the degradation is far smaller than the dilution, and can be omitted. But we will probably discuss that later.

(5) Unless we find further documents dealijng with the relation between the intensity of fluorescence and the concentration of GFP, we will directly use the measure in fluorescence, that we will treat as a protein concentration, more or less arbitrary normalised.

Now, we must use as a variable of reference an element that could be introduced in the bacteria, well-controlled, and from which will depends all the concentrations of our inducer.

The different fonction we would like to determine are the followings. They are linked to the bases of the 'experimental protocal' that will allow us to get the expected datas.

[expr.(p-lac)] = f1(IPTG)

According to the hypothesis (1) and (2), we assume this will directly give us [Protein] = f1(IPTG), for a given Protein coded by a gene put behind the p-lac promoter.

[expr.(p-Tet)] = f2([TetR],aTc) (in particular, we could compare f2(x,y) and f2(x-y,0), because aTc fixes at TetR in order to repress the inhibition of p-tet).

[expr.(p-flhDC)] = f3([OmpR*])

[expr.(p-fliA)] = fiA([flhDC],0) and [expr.(p-fliA)] = fiA(0,[fliA])

[expr.(p-fliL)] = fiL([flhDC],0) and [expr.(p-fliL)] = fiL(0,[fliA])

[expr.(p-flgA)] = fgA([flhDC],0) and [expr.(p-flgA)] = fgA(0,[fliA])

[expr.(p-flgB)] = fgB([flhDC],0) and [expr.(p-flgB)] = fgB(0,[fliA])

[expr.(p-flhB)] = f4([flhDC],0) and [expr.(p-flhB)] = f4(0,[flhB])