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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==An Oscillatory biological Model==
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= BOB (Based On Bibliography) Approach =
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[[Image:BOB.jpg|250px|thumb]]
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===Introduction===
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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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<br>The goal here is to present the differential equations we used for our 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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The key points of this approach:
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<br>The key problem with a differential 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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* Simplicity for itself is not that important. In fact, what we were looking for was understandability at first.
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We whall refer to those three articles :  
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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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<br>[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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* 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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<br>[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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<br>[3]Nitzan Rosenfeld, Uri Alon. Response delays and the structure of transcription networks. JMB, 2003, 329, 645-654.
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<br>[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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*  flhDC ---> fliL ---> Fluorescent Protein 1 (FP1)      (1)
 
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*  flhDC ---> flgA ---> Fluorescent Protein 2 (FP2)      (2)
 
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*  flhDC ---> flhB ---> Fluorescent Protein 3 (FP3)      (3)
 
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*  flhDC ---> flhB ---> lasI                            (4)
 
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<br>
 
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*  fliA ---> fliL ---> Fluorescent Protein 1 (FP1)      (5)
 
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*  fliA ---> flgA ---> Fluorescent Protein 2 (FP2)      (6)
 
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*  fliA ---> flhB ---> Fluorescent Protein 3 (FP3)      (7)
 
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*  fliA ---> flhB ---> lasI                              (8)
 
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<br>
 
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<br>
 
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For all these equations, we found in [1] that in that precise case, the promoter activity 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 at time.
 
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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: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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<br>
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<center>[[Team:Paris/Modeling/BOB|Read more]]</center>
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----
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= APE (APE Parameters Estimation) Approach=
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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].
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[[Image:APE.jpg|250px|thumb]]
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* lasI ---> HSL<sub>ext</sub>
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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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* lasI ---> HSL<sub>int</sub>
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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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<center> >> [[Team:Paris/Modeling/hill_approach|Explanations and description]] </center>
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* Specific experiments focused on finding relevant parameters have been designed and planned.
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<center> >> [[Team:Paris/Modeling/estimation|Estimation]] </center>
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= Old but still usefull pages =
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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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*[[Team:Paris/Modeling/Roadmap|Roadmap]]
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===Parameters summary===
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===Graph screenshots===
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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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==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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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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