Our thought process

• One can find many different approaches to model a biological system. We then found interesting to propose at least two distinct exemples of coherent models. It seems important to understand that both models aim at different goals in the process of understanding our system.
• Furthermore, if you wish to have a look at our roadmap. Please click here !

I - Linear Approach

• We wish to present at first a rough and simple, though effective, approach. The goal here was to determine a possible behavior of our Bacteri'OClock, considering the overall system. We then wished to ground our model on studies, so as to find quickly parameters on which we could work, awaiting for the data we shall get from the wet lab.
• We introduced this approach as being rough, since about every interaction is modelized by linear equations. Two elements motivated this approach :
  • Firstly, we argue that what with putting too many parameters, the model tends to loose relevance. We wanted to be able to control most of our parameters in the wet lab.
  • Secondly, we found in the literature that many author had already considered this kind of approach, and were able to obtain relevant results.
• Let's see a detailed version of our Oscillatory Biological Model !

II - "Hill" Approach

• This second approach was motivated by our will to understand our system in the most precise way. We decided to examine each part of our project (Oscillation, FIFO, Synchronization) incrementally, and tried to take into account the fundamental kinetics processes.
• We hereby use mostly Hill function, hence the name of this approach. We analyzed in the most precise fashion every interaction that took place. The Hill functions are introduced to describe relationships between transcription factors and promoters, since we thought secondary to take into acount the translation phases.
• Let's go see our Hill approach, which we would like to study as deeply as possible !

III - Estimation of Parameters

• What is at stake here is to determine the real parameters that govern the dynamics of our system.
  • First of all, you can find here the description of how we intend to find relevent parameters for our models.
  • We will need many parameters to fully describe the system according to the asumptions of the previous models. A natural way to have access to their value, after looking them up in the litterature, is to design specific experiments. As a consequence of the characterization of the promoters activity, some Hill functions could be obtained.
  • In a second step we shall try to find a way to translate the natural noise to our model, given the numerical values obtained in the wet lab.
    • Firstly, we could compute the standard deviation for each set of points at a given inducer concentration, and to normalize it according to the mean value of the set itself.
    • The next stage is to get the mean of those normalized sd values at every inducer concentration.
    • Since the beta/Vmax parameter of the Hill function has a linear influence, it is possible to translate this error directly on the parameter; for example: Vmax_err = random('norm',Vmax,err) where Vmax is the estimated value of the parameter and err is the mean of the normalized standard deviations of the experimental values.
    • For each cell in the model, we could use such noised values for Vmax parameter, in order to reproduce randomness estimated in the wet lab.

IV - Parameters & Bibliography

• We were naturally inspired by the literature available. You can find here the references

• Since we have diferent models, and since a large stock of parameters is attached to each approach, we propose here a direct access to the Linear Approach parameters and to the Hill Approach parameters.

V - Attached documents