Edinburgh/DivisionPopper/Modelling
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This pages contains the mathematical and computational models we constructed in order to analyze the behaviour of the Division PoPper system. You can find the model of two systems (the proof of concept construct or the whole construct), different views on the system (the single cell behaviour or the behaviour of the population), different approaches to modeling (ODEs, CTMC, hybrid). Look at the table of contests belove for the section you are interested in.
Contents |
The proof of concept system
As explained in the design section, the first part of our project consists in the realization of a proof of concept system. This is a smaller and less complex construct that we use to test our main assumption: the DNA region in between the two Dif sites is "flipped" (reversed) at each cell division. The model should help us in answering the following questions:
- Is the system working well with standard E.Coli division time?
- Is the system working well with normal GFP,RPF Expression and degradation rate?
- How can we tune these parameters in order to have meaningful tests from the construct in the lab?
Since the mechanisms and the values that characterize the system are sometimes not known or time consuming/difficult to discovery in the lab, we use the models as "in silico" test. Thus our models should be dependent (functions of) on the following quantities:
- Cell division frequency (units: minutes): is the time elapsed from one division to the next one.
- Flipping duration (units: minutes): is the time elapsed from starting the flipping to the complete execution.
- GFP/RFP Expression rate (units: protein per second): the rate at which fluorescent proteins are expressed.
- GFP/RFP Degradation rate (units: protein per second): the rate at which fluorescent proteins degrade.
In order to construct the proper model, we need to identify which are the dynamics of the system. Since the real biological mechanisms are too complex, several approximations and abstractions are introduced at this step. In this sense, we can simplify the dynamics of the system by observing that three are the states in which our construct can be during the time evolution: Forward, Flipping and Backward phase. This three phases happens in a order controlled by cell division. In detail:
- Forward phase: The system starts in this phase. It is the phase in which the promoter is oriented in the 5' to 3' direction, thus controlling the expression of GFP coding region. In this phase in the cell there is expression of GFP and no expression of RFP.
- Flipping phase: The system is in this phase. It is the phase in which the promoter is oriented in the 5' to 3' direction, thus controlling the expression of GFP coding region. In this phase in the cell there is expression of GFP and no expression of RFP.
- Backward phase: this is the phase that
