Team:Paris/Modeling

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== Introduction ==
 
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* Aims of the modeling part
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= Our train of thoughts... =
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* First approach proposed
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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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** Hill functions
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Furthermore, we wished to describe our thought process, the way these models interact, their respective roles. 
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** first model + score function
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An overall description of the way we model our biological system can be found below :
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** bibliography
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<center>[[Team:Paris/Modeling/History|Read more !]]</center>
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** findparam
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**experiments
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*Second approach
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**bibliography
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**equations
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**results
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**experiments
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* Continue the previous model
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**Synchronyzation
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**Estimation of the FIFO processes
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**Stochastic modeling (Gilespie)
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*Test of robustness
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**repressilator
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**comparison
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*Enhancing the system
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**Better FIFO behaviour
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**Other interactions to increase the robustness
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===Roadmap===
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= BOB (Based On Bibliography) Approach =
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[[Image:BOB.jpg|250px|thumb]]
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If you want to have a look at our modeling notebook: [[Team:Paris/Modeling/Roadmap|Notebook]]
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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 Oscillatory Biological Model==
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The key points of this approach:
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[[Image:Globalmodel.jpg|frame|<center><b>Overall Model</b></center>|center]]
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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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===Introduction===
 
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<br>The goal here is to present the differential equations we used in the system modelization. At each step, we shall describe why we chose this precise model, its drawbacks and possible improvments, the parameters involved and enventually a biologically coherent value.
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<center>[[Team:Paris/Modeling/BOB|Read more]]</center>
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<br>The key problem with a dynamic system consists in the fact that adding a new equation gives a more detailed idea of the overall process, but one looses precision by doing so since new parameters appear.
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<br>In that respect (in all cases but one) we chose not to model the mRNA steps, that is translation and transcription. We then assumed that we could act as if a protein would directly beget another one, without loosing too much precision.
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<br>This first approach only refers to a single cell. We shall examine later on what happens if we put more cells together.
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===Bibliography===
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= APE (APE Parameters Estimation) Approach=
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Musch of our inspiration comes from four articles to which we shall refer in the next subsections :
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[[Image:APE.jpg|250px|thumb]]
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<br>
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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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* [1] Shiraz Kalir, Uri Alon. Using quantitative blueprint to reprogram the dynamics of the flagella network. Cell, June 11, 2004, Vol.117, 713-720.
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*[2]Jordi Garcia-Ojalvo, Michael B. Elowitz, Steven H. Strogratz. Modeling a synthetic multicellular clock : repressilators coupled by quorum sensing. PNAS, July 27, 204, Vol. 101, no. 30.
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* [3]Nitzan Rosenfeld, Uri Alon. Response delays and the structure of transcription networks. JMB, 2003, 329, 645-654.
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* [4]Nitzan Rosenfeld, Michael B. Elowitz, Uri Alon. Negative autoregulation speeds the response times of transcription networks. JMB, 2003, 323, 785-793.
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===Equations===
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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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* <b>Steps</b>
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**  flhDC &rarr; fliA &nbsp;&nbsp;&nbsp; (1)
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**  flhDC &rarr; fliL &rarr; Fluorescent Protein 1 (FP1)  &nbsp;&nbsp;&nbsp;    (2)
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**  flhDC &rarr; flgA &rarr; Fluorescent Protein 2 (FP2)  &nbsp;&nbsp;&nbsp;    (3)
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**  flhDC &rarr; flhB &rarr; Fluorescent Protein 3 (FP3)  &nbsp;&nbsp;&nbsp;    (4)
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**  flhDC &rarr; flhB &rarr; lasI                        &nbsp;&nbsp;&nbsp;    (5)
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**  fliA &rarr; fliL &rarr; Fluorescent Protein 1 (FP1)  &nbsp;&nbsp;&nbsp;    (6)
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<center> >> [[Team:Paris/Modeling/hill_approach|Explanations and description]] </center>
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**  fliA &rarr; flgA &rarr; Fluorescent Protein 2 (FP2)  &nbsp;&nbsp;&nbsp;    (7)
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**  fliA &rarr; flhB &rarr; Fluorescent Protein 3 (FP3)  &nbsp;&nbsp;&nbsp;    (8)
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**  fliA &rarr; flhB &rarr; lasI                          &nbsp;&nbsp;&nbsp;    (9)
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<br>
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* Specific experiments focused on finding relevant parameters have been designed and planned.
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* <b>Model</b>
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<center> >> [[Team:Paris/Modeling/estimation|Estimation]] </center>
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The transcription hierarchy of the flagella genes have been studied in [1]. It resuted that the promoter activity of the seven class 2 operons, among which fLiL, flgA, flhB, may be mathematically described in that way :
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<br>
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[[Image:eqpromact.jpg|center]]
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<br>
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<br> where [X] denotes the effective protein-level activity.
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<br>
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<br>
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For each operon, Shiraz Kalir and Uri Alon came up with numerical values of β and β', available in [1]. 
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<br>
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<br> Furthermore, the protein-level activity can be presented (for a more detailed presentation, see[4]) as
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<br> [[Image:equation1.jpg|center]]
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<br>Thus :
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[[Image:fliA.jpg|center]]
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[[Image:FP1.jpg|center]]
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[[Image:FP2.jpg|center]]
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[[Image:FP3.jpg|center]]
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[[Image:lasI.jpg|center]]
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* <b>Discution and Asumptions</b>
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= Old but still usefull pages =
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** As presented in the first equation below, there is a retroaction from fliA over fliA. In a first approach, we decided not to take into account this interaction, that is setting β'<sub>FliA</sub> to zero. In a second approach, we will consider this retroaction, and find a way to describe it mathematically.
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** Another step consists in choosing the proper units, so as to have a homogenous set of parameters. In fact we need temporal parameters, but those given in the article are measured with the derivative of GFP over OD. Since we will work with a constant population density, we should only need to add a multiplicative factor, that we shall determine thanks to biological processes.
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<br>
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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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----
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*[[Team:Paris/Modeling/Roadmap|Roadmap]]
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* <b>Steps</b>
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** lasI &rarr; HSL<sub>ext</sub> &nbsp;&nbsp;&nbsp; (10)
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** lasI &rarr; HSL<sub>int</sub> &nbsp;&nbsp;&nbsp; (11)
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* <b>Model</b>
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[[Image:HSLint.jpg|center]]
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[[Image:HSLext.jpg|center]]
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* <b>Discution and Asumptions</b>
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** Even though we considered a single cell, we decided to model both HSL inside and outside the cell. In a first approach, we assumed that HSL could be modelized in the same fashion as AHL. The process was well detailed in [2] and we adapted their model to our present situation. Furthermore, a biologically coherent set of parameters is also given in this article. We decided then to use them as well for our simulation.
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** As explained before, in this model, we only considered a single cell. The method to model the interactions with other cells is also described.
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<br>
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----
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* <b>Steps</b>
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** HSL<sub>int</sub> &rarr; tetR mRNA &nbsp;&nbsp;&nbsp; (12)
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** tetR mRNA &rarr; tet R &nbsp;&nbsp;&nbsp; (13)
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* <b>Model</b>
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[[Image:tetR mRNA.jpg|center]]
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[[Image:tetR.jpg|center]]
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* <b>Discution and Asumptions</b>
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** Here is the only case where we have not yet found out how we could manage to skip the mRNA step. However, this is acceptable since every parameter should be available. Then, (12) represents the binding and transcription steps ; (13) represents the translation step.
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** The effect of HSL over
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<br>
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----
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Finally, the close the loop, we saw the necessity to use a little refinment. tetR influence over pTet, being the promoter of flhDC, is a repression. To express the non-instantaneous character of this interaction, we used a step function. To fully define this function, two parameters are needed, so as to describe the time when the step has to occur, and the initial value of this step. We are facing two solutions. The more accurate procedure would consist in getting those values from the wet-lab. However, we may also look for it in the literature. Anyhow, as presented in the conclusive part, there is a really wide range of parameters that enable the system to oscillate.
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<br>
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[[Image:flhDC.jpg|center]]
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===Parameters summary===
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===Graph screenshots===
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==First Mathematical Approach==
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===Introduction===
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As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below).
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Nonetheless, after reading some more articles, we have decided to change several asumptions of the modeling choice. Therefore, we have devised a perhaps more biologically relevant framework (see above).
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This part describes in detail the first approach and the codes that have been produced.
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===Bibliography===
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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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An overview of the work that has to be done can be found here : [[Team:Paris/Modeling/Bibliography|Bibliography]]
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===Estimation of parameters===
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[[Team:Paris/Modeling/estimation|Estimation of the parameters]]
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===First Approach===
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[[Team:Paris/Modeling/first approach| First Approach]]
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===More precise Bio-Mathematical Description===
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[[Team:Paris/Modeling/description|Bio-Mathematical Description]]
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|}<br style="clear:both" />
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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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