Team:Paris/Analysis/Construction2

Introduction
In this section, we investigate possible improvements of the core system. Our objective is twofold : the system has to provide sustained oscillations and these oscillations should be synchronized amongst a population of cells. To this aim we explore designs inspired by quorum sensing and model in a chemostat cell growth and species diffusion outside cells. We consider two models relying on different designs principles.

Modeling Alternatives
The proposed systems are:


 * In the first system, we use a modular design. Since the core system is a 'poor' oscillator we hope that by coupling it with a 'good' oscillator we could obtain sustained oscillations in the whole system. Thus, we consider that the core system is one of the modules of the system and that the other module is a two gene oscillator system presented in [2] that accounts for quorum sensing. We call this alternative the 'HSL mediated coupled oscillators'.


 * In the second system, namely the 'HSL mediated simple oscillator', we rewire the architecture of the core system to introduce delay via HSL export in the environment in a single circuit.

Both the coupled and simple oscillators describe events that happen not only at the cellular level (as in the core system) but also at the population level due to interactions needed between a cell and its environment.

In the following sections, we first describe the common part among the two proposed models and then focus our attention to the  alternatives description where the characteristics that are specific to each of the modeling alternatives are presented.

Kinetic parameter values
Remarkably, almost all parameter values are available from experimental measurements in [1] and from the work of Garcia-Ojalvo in [2]. Additionally minimizing the number of parameters is possible by rescaling as done for the core system. Relevant values for the sole two missing parameters are found by exploiting a modularity assumption as described in the next section. The following table summarize our findings: