Introduction
- Aims of the modeling part
- First approach proposed
- Hill functions
- first model + score function
- bibliography
- findparam
- experiments
- Second approach
- bibliography
- equations
- results
- experiments
- Continue the previous model
- Synchronyzation
- Estimation of the FIFO processes
- Stochastic modeling (Gilespie)
- Test of robustness
- Enhancing the system
- Better FIFO behaviour
- Other interactions to increase the robustness
Roadmap
If you want to have a look at our modeling notebook: Notebook
Presentation of our work
The different phases of our modeling work...
The following presentation is not necessarly chronological, but presents the advantage of introducing our work from the simplest model to the most complicated.
I - Linear Approach
An Oscillatory Biological Model, with almost only linear relationships.
II - "Hill" Approach
That was our first approach, which we would like to study as far as possible. The estimation of parameters is mostly for this one.
We use mostly Hill functions to describe relationships between transcription factors and promoters, and do no take into acount the translations phase.
III - Estimation of Paramaters
IV - Parameters & Bibliography
V - Annexes
First Mathematical Approach
Introduction
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).
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).
This part describes in detail the first approach and the codes that have been produced.
So, if I understand well,the model above does not include Hill functions -is a simplification- and is your second approach, right?
First Approach
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).
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.
The methods employed are described there : First Approach.
More precise Bio-Mathematical Description
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 : Bio-Mathematical Description.
Bibliography
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.
An overview of the work that has to be done can be found here : Parameters we have to use.
Estimation of parameters
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.
Thus, we have described the experimental approach required : Estimation of the parameters.
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 An Oscillatory Biological Model.
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