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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===Presentation of our work===
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The key points of this approach:
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The different phases of our modeling work...
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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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The following presentation is not necessarly chronological, but presents the advantage of introducing our work from the simplest model to the most complicated.
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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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==== I - Linear Approach ====
 
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An [[Team:Paris/Modeling/linear_approach|Oscillatory Biological Model]], with almost only linear relationships.
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<center>[[Team:Paris/Modeling/BOB|Read more]]</center>
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==== II - "Hill" Approach ====
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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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That was our [[Team:Paris/Modeling/hill_approach|first approach]], which we would like to study as far as possible. The estimation of parameters is mostly for this one.
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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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We use mostly ''Hill functions'' to describe relationships between ''transcription factors'' and promoters, and do no take into acount the ''translations'' phase.
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<center> >> [[Team:Paris/Modeling/hill_approach|Explanations and description]] </center>
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==== III - Estimation of Paramaters ====
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* Specific experiments focused on finding relevant parameters have been designed and planned.
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==== IV - Parameters & Bibliography ====
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<center> >> [[Team:Paris/Modeling/estimation|Estimation]] </center>
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==== V - Annexes ====
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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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==First Mathematical Approach==
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*[[Team:Paris/Modeling/Roadmap|Roadmap]]
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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 assumptions 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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<br> <font color=blue> So, if I understand well,the model above does not include Hill functions -is a simplification-  and is your second approach, right?</font>
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===First Approach===
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As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on).
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In this framework, we have found parameters that have provided oscillations as well as a function that automatically detects whether the output of the ode system is oscillating. This has allowed to screen a little the parameters used, in order to evaluate the robustness of the system.
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The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]].
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===More precise Bio-Mathematical Description===
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After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : [[Team:Paris/Modeling/description|Bio-Mathematical Description]].
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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|Parameters we have to use]].
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===Estimation of parameters===
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Then, we will need many parameters to fully desribe the system according to the asumptions of the previous section. A natural way to have access to their value, after searching in the litterature, is to devise specific experiments. As a consequence of the characterization of the promoters activity, some Hill functions could be obtained.
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Thus, we have described the experimental approach required : [[Team:Paris/Modeling/estimation|Estimation of the parameters]].
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Nonetheless, as mentioned above, we have changed the way to model the biological reactions. As a result have stopped investigating in this way to focus on the [[Team:Paris/Modeling#An_Oscillatory_Biological_Model|An Oscillatory Biological Model]].
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[[Too be continued]]
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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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