Team:Newcastle/Modeling/Stochastic

Stochastic Switch model
Our heads or tails stochastic switch is used in our system to a give a decision to be a metal container and sequester cadmium, or continue to normal vegetative life. This cell fate decision is given based on a number of parameters stochastically. Hin invertase which inverts a promoter is also included in the same region. Its expression is controlled by LacI controlled pspac promoter (inducable by IPTG) on the left site and XlyR controlled xylA promoter (Inducable by Xylose) on the right side. The promoter inside the invertible region is used to express downstream genes either on the left side or rigth side depending on its position.

LacI binds to Pspac promoter and represses its expression whereas XylR binds to xylA promoter and represses the expression from xylA promoter. When induced with IPTG, LacI falls off from the Pspac promoter and when induced with Xylose, XylR falls off from xylA promoter and does not repress it any more. The differences between LacI's and XylR's binding affinities to promoters and to their inducers affect the expression of Hin, hence the direction of the invertible region. When this region is oriented from left to right and Pspac promoter is not repressed by LacI, sigA promoter in the invertible region expresses Rfp. When the region is oriented from right to the left, 'sigA promoter in the invertible region is also turned to right and expresses Gfp, when its way is not blocked by XlyR bound to xylA promoter.

Hence Gfp and Rfp concentrations can be used as an indication of cell fate decisions and other downstream genes can be added to the left or right sides of the switch to trigger those decisions.

This circuit is controlled by IPTG and Xylose. As a third control, Arabinose can also be used. The orientation of the invertable region highly effects the outcome of this circuit and the direction is changed by Hin protein. By doing so, its expression is also affected and this situation also adds to the stochasticity. In our design, Hin proteins are tagged with the modified version of ssrA degradation tag which requires SspB adaptor protein to target Hin proteins for the degradation by ClpXP system. Hence by controllling the expression of SspB by arabinose (via araE promoter controlled by AraR), concentration of Hin can be controlled. Where necessary just a pulse of Hin can be created.

For more information about the design of the switch: Team:Newcastle/Stochasticity



Simulations
In the diagrams below X-Axis shows IPTG and Y-Axis shows Xylose concentration. IPTG and Xylose concentrations are changed between 0 and 9000nM. Three sets of model outputs were created for 0nM, 1000nM and 10000nM of arabinose. The first column shows Gfp concentrations and the second column shows Rfp concentrations.

Single Runs
Models can also be run with specific values of IPTG, Xylose and Arabinose.

We assumed that 60nM of Hin would be enough to invert the invertible segment with HixC sites. At every 60nM increase of Hin concentration, we flipped the region by 40% chance. Flips can be noticed from the diagram below for the expression of Hin mRNA.





When arabinose is not added, SspB adaptor protein level does not increase much and Hin is not degraded quickly.



Effect of the addition of 1000nM arabinose can be seen below. Hin starts to degrade more quickly.



Equations
Fluxes:

ODEs:







Matlab Files

 * [[Media:Team_Newcastle_iGEM_2009_StochasticSwitchRuntime.m‎]]
 * [[Media:Team_Newcastle_iGEM_2009_StochasticSwitch_initial_values.m]]
 * [[Media:Team_Newcastle_iGEM_2009_StochasticSwitch.m]]
 * [[Media:Team_Newcastle_iGEM_2009_StochasticSwitch_SingleRun.m]]

Previous versions
Here are the matlab files for our stochastic switch model, and below are some graphs which the model produced earlier.
 * [[Image:Newcastle Metalcontainerruntime.m]]
 * [[Image:Newcastle Metalcontainer initial values.m]]
 * [[Image:Newcastle Metalcontainer.m]]