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Modeling Overview
In our project, we are dedicated to design a quorum-sensing oscillator which consists of two types of cells. Cells of the same type can fluctuate synchronously and certain designs were made to adjust the phase and the amplitude of oscillation. These are the things that our modeling part aims to simulate. We built and simplified our simulation system step by step and deepened into further characteristics of the system, which would provide firm evidence proving that our design does work.
PART 1 Accurate Model
prep | para | Res
In our first step, we wanted to describe the system thoroughly without leaving out any seemingly unimportant actions and factors. As a result, the description of the system contains every possible mass actions as well as some hill kinetics, Henri-Michaelis-Menten. We came up a set of ODEs with 19 equations.
PART 2 Simplified Model
Although ODEs provide a thorough, precise description of the whole system, they contain too many equations and parameters which would act as a barrier for simulation and further analysis. A simplification of complicated ODEs is necessary. We simplify every single ODE according to certain appropriate assumptions. Finally, we came up with a set of DDE equations.
PART 3 Dimensionless Model
In order to make a further analysis on stability of the system, sensitivity of parameters, feedback factors-we manipulate all the arguments and parameters to make them dimensionless. Analysis of this part is crucial since parameters in vivo experiment may be different and even at odds with modeling ones but a proper dimensionless can reveal the mathematical essence of our model.
PART 4 Quorum-sensing Effect
What we have done insofar is focused on two-cell oscillation. Quorum-sensing oscillator is not simply a matter of expansion in magnitude, but a matter of robustness in allowing difference of each individual cell. Moreover, we test the adjustment of phase and amplitude of oscillation in this part.
