We had different approaches to model the biological system. We found interesting to explain at least two ways that we went throught. It is important to understand that both models aim at different goals in the process of understanding our system.

Preliminary 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 and preliminary, since about every interaction is modelized by linear equations. Three 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.
  • Finally, we found really important to build a model on which we could work, awaiting for experimental results.
• Let's see a detailed version of our Oscillatory Biological Model !

"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 !

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 β parameter of the Hill function has a linear influence, it is possible to translate this error directly on the parameter; for example: β_err = random('norm',β,err) where β 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.

Bibliographic References - Depreciated Roadmad