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Team:UCSF/Modeling
From 2008.igem.org
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Revision as of 19:44, 24 October 2008
As we mentioned before, our team is interested in cellular memory, when the cell state established after a transient stimuli can be "remembered" for longer times. One way to establish memory is using two repressor proteins that control the synthesis of each other, i.e. a "toggle" switch. So for the modeling portion of our iGEM project, we decided to focus on coming up with an intuitive model for a heterochromatin-based toggle switch that will allow us to show some of the advantages of using heterochromatin in building such synthetic circuits.
Starting Simple: Using the Gardner-Collins Toggle Switch Model
Previous work by the Collins group (Gardner, et al. Nature 2000) has shown that in a transcription-based circuit, at least one of the repressors needs to cooperatively repress transcription to achieve the bistability necessary for the formation of a toggle switch. In addition, the cooperativity needs to be much greater than 1 for a robust system, i.e. one that will generate a wide bistable region in the parameter space that is composed of different values for the two promoter strengths. Since heterochromatin formation, by nature, is a highly cooperative phenomenon, we plan to exploit this property as a tool for building our toggle switch.
Because only one "leg" of our toggle switch would be regulated by heterochromatin and be highly cooperative, we first wanted to check how the system would behave with only one high cooperativity constant (and with the other constant set to 1). For this, we simply implemented the Gardner model in Matlab and plotted the resulting bistable regions:
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| Figure 1: Bistable region (shaded) as gamma changes |
As you can see in Figure 1, the region of bistability expands as one of the cooperativity constants (gamma, in this case) is increased. This shows that even if only one leg of our toggle switch has high cooperativity, then there is a large region of parameter space where we can get bistable or toggling behavior.
Toggle Switch 2.0: Extending the Gardner Model
The model by Gardner, et al was a really useful starting point for modeling a toggle switch, but since our switch will be built using heterochromatin, we decided to extend the model slightly to incorporate the additional step of heterochromatin formation. To do this, we first derived equations very similar to those in the Gardner model:
Equation (1) describes the transcriptional repression side of the toggle switch, e.g. Gal80 represses the expression of LexA-Sir2. Equation (2) describes the effective repression due to the presence of heterochromatin, e.g. the silencing of Gal80 expression. Equation (3) describes the formation of heterochromatin when the nucleator (LexA-Sir2) is present.
We then implemented this model in Matlab and analyzed it by solving for the null clines (steady state solutions) of the system:
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| Figure 2: Null clines of the toggle-switch system as gamma increases |
As you can see from the above figure, ...
Although we liked this set of equations as a model of a heterochromatin-based toggle due to its simplicity and because it's a logical extension of the Gardner model, we realized that it has various problems. The fact that we're modeling heterochromatin as a concentration and we're using a transcriptional activation equation to describe the formation of heterochromatin seemed inappropriate to us. So for our next task, we wanted to come up with a somewhat more realistic model for describing heterochromatin formation.
Heterochromatin Formation Like Polymerization?
So how does heterochromatin achieve such a high cooperativity? Traditionally, it's thought that the high cooperativity is due to the spreading of heterochromatin from an initiation site. To us, this sounds awfully similar to the process of nucleation and polymerization.
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