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Collaboration

We had a great time during the summer with our wet team and the Ecoli they raised.

They helped us a lot with biology background, and we offer necessray modeling and technical support for them. The project they designed is interesting and creative.

We discuss a lot with them, expecially with their modeler, Junhui Peng.

The main ideal of their project is to use quorum sensing to guide bacteria towards the concentration gradient.The toggle swtich is an important device in their design, which can turn on and off the chemotaxis protein cheZ expression. When the density of the cell population reached certain criteria, there are enough AHL molecules to toggle the swtich to another state(auotomatic toggle).

For more information about their project, see here.

We did a lot of collaboration, including using our rulebased modelling approach to automatically generate the network for their design and analyze the phase space of the toggle switch.

figure1

We choose their design-b to test our software. In terms of simplicity, we try to ignore their quorum sensing part by setting of parameter of the lasi catalyzing ability low, and add IPTG and AHL deliberately at certain timepoints.

From such a mere assembly, our software can generate the network associated with the assembly.

The network generated and visualized by our software's rule based modeling part and visualization part is shown below:

figure2

There are so many species generated by our approch(however, this is an advantage of our approach, in the future version of our software, we plan to offer visualizing tool to show the structure of the species, ie, the binding state dna chain)

In order to test the validity of our softare, we tried the time course.

We select different interesting species eachtime to see the time course. We worked hard on adjusting the parameters of the system to acquire a good behaviour. And the result is quite satisfactory.

At time point 20000s, the theophline is added and at timepoint 40000s AHL both with e-4 moles or 100micro moles.

All the figures below are in one simulation.

figure3-9

OTHER collaborations(not all): bifurcation analysis of the toggle switch

In the simulation of the design-a (see figure above), their modeler Junhui Peng told us that he was confused by a phenomenon: if the promoter P-lasbox strength excess a critical value, no matter how much AHL molecules are produced by lasI (in silicon), the toggle switch just stay in one state and can’t leap to the other.

We conducted a survey to this phenomenon , trying to figure out the mechanism of it.

But the network of the their origial design is a little bit complex to analyze , so we first tried a much simplied model of the toggle switch. We believe that a good work start from the simple thing.

With the help of Professor Haiyan Liu, our team’s mathematical student Hui Li developed an algorithm to analyse the effects of parameters to the phasespace of the toggle swtich. Later, Hui Li speeded up her algorithm.

We first worked out the nullclines of the toggle switch system, with a symmetric toggle switch equation, we get a figure as below.

figure 10

There are three cross sections ,or three steady state, two of them are stable steady state and one of them unstable, as indicated by the vector fields.

From the vector field we can interpret an important mechanism, after the inducer is added to the system for long enough time, even the induder is removed from the system, the system still stay in the induced state and wouldn’t come back to the orginal one . See the figure above, The state space of this system is divided into two regions, each with an “attracting center”, once the system enters an arbitray state in one region, it will defininitely be “attracted” to the stable steady state of that region.

The task of the inducer is to change the state point of the system, moving it from the orginal region to the oppisite region.

Then we devise a way to move the two nullclines by variating the parameters, trying to separate the two nullclines with less cross sections.

Below is a figure of critical parameter values, the bifurcation point.At this critical point, there are only two cross-sections , ie two equlibrium state.

figure11

If we variate the parameter more, as illustrated as below, there is exactly one equlibrium state, indicating that no matter what the initial condition is, the system will be draged to it’s mono-steady state of one side on and the other side of the toggle switch down.

figure12

So the problem may be the parameter of the promoter strength.

When Junhui Peng modified the promoter strength to a lower value and simulate, he found that this time with enough amount of the AHL inducer, the system is able to switch between the two steady states.

During the spare time, we hang out with our wet friends and talked a lot.

We are going to collaborate more in the future.

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