Team:Paris/Modeling

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==Roadmap==
 
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If you want to have a look at our roadmap : [[Team:Paris/Modeling/Roadmap|Roadmap]]
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= Our train of thoughts... =
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We hereby propose different and complementary approaches to model the biological system. We found interesting to explain two of the paths that we chose to follow in order to understand and predict our system. It is important to note that both models aim at different goals in the process of understanding our system.
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Furthermore, we wished to describe our thought process, the way these models interact, their respective roles. 
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An overall description of the way we model our biological system can be found below :
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<center>[[Team:Paris/Modeling/History|Read more !]]</center>
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==Bibliography==
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= BOB (Based On Bibliography) Approach =
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[[Image:BOB.jpg|250px|thumb]]
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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.
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Our first approach is quite rough and simple but effective. The goal here was to guess the behavior of our Bacteri'OClock, considering the overall system. Since it is a preliminary approach, we could not yet fill the model with data from the wet lab. This is why our work is mainly based on a bibliographic work, which allows us to use parameters and data from scientific articles.
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An overview of the work that has to be done can be found here : [[Team:Paris/Modeling/Bibliography|Bibliography]]
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The key points of this approach:
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==Estimation of parameters==
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* Simplicity for itself is not that important. In fact, what we were looking for was understandability at first.
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* We used linear equations as much as possible: wherever it had been proved in a paper than an interaction could be efficiently modeled with a elementary expression, we kept it.
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* Too many parameters in a model mean less relevancy. In addition, the more parameters you have, the hardest it is to tune the system in order to have the behavior you are looking for.
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If we want to use the promoters used for the formation of the flagella ( [[Team:Paris/Project|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.
 
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Therefore, we have written a little module which can estimate the parameters of the 'Hill functions', even with some noise and few data available.
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<center>[[Team:Paris/Modeling/BOB|Read more]]</center>
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Some details and the corresponding code can be found here : [[Team:Paris/Modeling/Programs|Programs]].
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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.
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= APE (APE Parameters Estimation) Approach=
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[[Image:APE.jpg|250px|thumb]]
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The second approach was motivated by our will to characterize our system in the most precise way. What is at stake here is to determine the "real parameters" that govern the dynamics of our system.
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Thus, we need experimental datas. To quantify the strength of an transcription factor on a promoter, we will use measurements of GFP fluorescence, and compare to the strength of the constitutive promoter [[http://partsregistry.org/Measurement/SPU/Learn J23101]], as it was proposed by the iGEM competition.
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* Each step is taken into account at a fundamental kinetic processes level or at a more global level by a function describing the complexation, which is a simple way to take into account multiple interactions and more especially cooperative binding.
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The datas we are looking for must appear as a table of values, giving several 'transduction rate' with their corresponding 'transcription factor concentration'.
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For this aim, we made several hypothesis, which we will verify as good as it is possible for us :
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<center> >> [[Team:Paris/Modeling/hill_approach|Explanations and description]] </center>
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'''(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.
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* Specific experiments focused on finding relevant parameters have been designed and planned.
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'''(2)''' We assume that, whatever is the gene behind the promoter, its expression depends only of the transcription factor 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.
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<center> >> [[Team:Paris/Modeling/estimation|Estimation]] </center>
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'''(3)''' We consider that the activity of a promoter is well described as a '''Hill function''' of its transcription factor (TR).
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= Old but still usefull pages =
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Thus, we suppose that the protein concentration (Prot) follows this equation :
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<center> dProt/dt = beta*hill(TR) - gamma*Prot </center>
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*[[Team:Paris/Modeling/Bibliography|Bibliographic References]]
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*[[Team:Paris/Modeling/linear_approach|Preliminary approach]]
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where gamma is a constant, due to degradation and of dillution of the protein, along time and cell divisions.
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*[[Team:Paris/Modeling/Roadmap|Roadmap]]
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Therefore, if we consider a '''steady-state''', for given concentration of the transcription factor, we will have :
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<center> beta*hill(TR) = gamma*Prot </center>
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'''(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.
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'''(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''.
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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 transcription factor. We propose a construction in which our transcription factor is put after the promoter p-lac, which is under the repression of LacR. Since IPTG is a small diffusive molecule that binds to LacR and inhibits this way the repression of p-lac, we can use it as an 'inducer'. To do so, we must place in the bacterium LacR after a constitutive promoter (like J23101). According to previous hypothesis, this will provide at steady-state a 'constant concentration' of LacR (we note [LacR*], and it is supposed to be the TOTAL concentration of LacR,  under every form) in the bacterium. If we consider the binding reaction this way (where LacR_IPTG denotes the complex)
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<center> LacR + IPTG = LacR_IPTG </center> with a dissociation constant K,
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we find at the steady-state
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<center> LacR = [LacR*] - [lacR_IPTG] = [LacR*] - ([LacR*].[IPTG]/(K + [LacR*]))</center>
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where [IPTG] denotes the concentration of IPTG we introduced in the medium, that will stay constant in all the bacteria along time, assuming that its degradation is near 0, and that the diffusion is quick.
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According to the hypothesis '''(3)''', the activity of p-lac would verify (keeping the same notations) :
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<center> beta*hill(TR) = gamma*Prot</center>
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The different functions 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.
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[[Team:Paris/Modeling/f1|[expr.(p-lac)] = f1(IPTG)]]
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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.
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[[Team:Paris/Modeling/f2|[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).
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[[Team:Paris/Modeling/f3|[expr.(p-flhDC)] = f3([OmpR*])]]
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[[Team:Paris/Modeling/fiA|[expr.(p-fliA)] = fiA([flhDC],0)]] and [[Team:Paris/Modeling/f1|[expr.(p-fliA)] = fiA(0,[fliA])]]
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[[Team:Paris/Modeling/fiL|[expr.(p-fliL)] = fiL([flhDC],0)]] and [[Team:Paris/Modeling/f1|[expr.(p-fliL)] = fiL(0,[fliA])]]
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[[Team:Paris/Modeling/fgA|[expr.(p-flgA)] = fgA([flhDC],0)]] and [[Team:Paris/Modeling/f1|[expr.(p-flgA)] = fgA(0,[fliA])]]
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[[Team:Paris/Modeling/fgB|[expr.(p-flgB)] = fgB([flhDC],0)]] and [[Team:Paris/Modeling/f1|[expr.(p-flgB)] = fgB(0,[fliA])]]
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[[Team:Paris/Modeling/fhB|[expr.(p-flhB)] = f4([flhDC],0)]] and [[Team:Paris/Modeling/f1|[expr.(p-flhB)] = f4(0,[flhB])]]
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Latest revision as of 04:46, 30 October 2008

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Contents

Our train of thoughts...

We hereby propose different and complementary approaches to model the biological system. We found interesting to explain two of the paths that we chose to follow in order to understand and predict our system. It is important to note that both models aim at different goals in the process of understanding our system. Furthermore, we wished to describe our thought process, the way these models interact, their respective roles. An overall description of the way we model our biological system can be found below :

Read more !

BOB (Based On Bibliography) Approach

BOB.jpg

Our first approach is quite rough and simple but effective. The goal here was to guess the behavior of our Bacteri'OClock, considering the overall system. Since it is a preliminary approach, we could not yet fill the model with data from the wet lab. This is why our work is mainly based on a bibliographic work, which allows us to use parameters and data from scientific articles.

The key points of this approach:

  • Simplicity for itself is not that important. In fact, what we were looking for was understandability at first.
  • We used linear equations as much as possible: wherever it had been proved in a paper than an interaction could be efficiently modeled with a elementary expression, we kept it.
  • Too many parameters in a model mean less relevancy. In addition, the more parameters you have, the hardest it is to tune the system in order to have the behavior you are looking for.


Read more

APE (APE Parameters Estimation) Approach

APE.jpg

The second approach was motivated by our will to characterize our system in the most precise way. What is at stake here is to determine the "real parameters" that govern the dynamics of our system.

  • Each step is taken into account at a fundamental kinetic processes level or at a more global level by a function describing the complexation, which is a simple way to take into account multiple interactions and more especially cooperative binding.
>> Explanations and description
  • Specific experiments focused on finding relevant parameters have been designed and planned.
>> Estimation

Old but still usefull pages

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