Team:Paris/Modeling

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==An Oscillatory biological Model==
 
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===Introduction===
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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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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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= BOB (Based On Bibliography) Approach =
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[[Image:BOB.jpg|250px|thumb]]
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===Bibliography===
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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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We whall refer to those three articles :
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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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<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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The key points of this approach:
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*  FlhDC ---> FliL        (1)
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*  FlhDC ---> FlgA        (2)
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*  FlhDC ---> FlhB        (3)
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<br>
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*  FliA ---> FliL        (4)
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*  FliA ---> FlgA        (5)
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*  FliA ---> FlhB        (6)
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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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<br>    <b>promoter activity = β<sub>i</sub> x [FlhDC] + β<sub>i</sub>' x [FliA]</b>
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<br>
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<br> where [X] denotes the effective protein-level activity at time.
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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:equationfliL.jpg|center]]
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[[Image:equationflgA.jpg|center]]
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[[Image:equationflhB.jpg|center]]
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<br>
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----
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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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*
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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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<center>[[Team:Paris/Modeling/BOB|Read more]]</center>
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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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* 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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===Parameters summary===
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*[[Team:Paris/Modeling/Bibliography|Bibliographic References]]
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===Graph screenshots===
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*[[Team:Paris/Modeling/linear_approach|Preliminary approach]]
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*[[Team:Paris/Modeling/Roadmap|Roadmap]]
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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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As a first modeling, we have considered a set of five ordinary differential equations that are likely to represent the generic behaviour of the biological processes. The corresponding results and the associated code can be found there :
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*[[Team:Paris/Modeling/first_parameters|First Parameters obtained]].
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We will precise this description in the following part, entering into the details of the chemical reactions involved.
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Moreover, once the oscillations have been obtained, it is interesting to focus on their robustness. To do such an analysis, we have used a rather intuitive algorithm which divides the parameter space into regular areas and compute a kind of 'score function' to test whether oscillations are observed. Then, for 2 parameters, a simple visualization is possible.
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Therefore, the two aspects to describe a bit more are the following ones :
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* [[Team:Paris/Modeling/Score_function|Design of a score function]]
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* [[Team:Paris/Modeling/Robustness_analysis|Evaluation of the robustness of the sytem]]
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* There is a [[Team:Paris/Modeling/Second_Score_function|second score function]], much simplier but quite efficient.
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* We tried this one in association with a self made [[Team:Paris/Modeling/Genetic_Algorithm|genetic algorithm]], that allows us to find many convenient sets of parameters,  in order to compare them.
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==More precise Bio-Mathematical Description==
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===What kind of Mathematical Simulation ?===
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We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells.
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Eventually our modellisation would just help us to find which ones of the sets of "biologicaly available parameters"/"logical circuit" are the bests, but it may help further simulations on similar protocols, too.
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===Bio-Chemical General Assumptions===
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We know that the following equations do not describe properly what ''really'' happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an ''hexamere'' flhD<sub>4</sub>C<sub>2</sub>. But, as we will surely not get access to the ''dissociation constant'' of the ''hexamerisation'', we just treat it as an ''abstract'' inducer protein ''flhDC'', with an order in its ''Hill function'' probably between 3 and 6 (but perhaps completly different; the estimation of the error by the [[Team:Paris/Modeling/Programs|'findparam']] program will tell us if we are right to do so).
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For the moment, at each part of our modelisation, we reduce the expression of a gene at its '''transcription'''. The '''translation''' process is not taken into acount.
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To see more details about the modelisation and the values of the involved constants, see [[Team:Paris/Modeling/Bibliography|the bibliography]].
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===Separated and detailed Parts of our Project===
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* [[Team:Paris/Modeling/Oscillations|Oscillations]]
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* [[Team:Paris/Modeling/FIFO|FIFO]]
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* [[Team:Paris/Modeling/Synchronisation|Synchronisation]]
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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

Retrieved from "http://2008.igem.org/Team:Paris/Modeling"