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Collaboration

We spent a happy summer working with our wet team, USTC-China, through intimate collaboration on how our software tool can help and guide their experimental designs before they are actually constructed in the tube. It cannot be denied that most of our members are lack of biological background but do not worry, they are there available to discuss with us to help us understand their proposals. Specially, we are going to thank Junhui Peng, the modeler of USTC-China, who contributed very much to our cooperation.

The main idea of their project is to use quorum sensing mechanism to guide bacteria towards the concentration gradient. The toggle switch plays a central role to run the device by switching the expression of chemotaxis protein cheZ on and off iteratively. When the density of the cell population has reached a certain criteria, the accumulation of AHL molecules exceeds the threshold and thus trigger the toggle switch to change its state from the other one(auotomatic toggle). More information are available here.

To test our software tool, we planned to use our rule-based modeling approach to get some insights about their work. It can be divided further to two parts: (1) automatically generate the biochemical network of the quorum sensing subsystem combined with toggle switch as a central part; (2) analyze the phase space of the toggle switch.

The design-b is our target system to be modeled. 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:

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.

The parameters we tried are as follows:

   1  NA             6.020e+23  
   2  f              1.000e+00  
   3  Ve             4.000e-01   # f*0.4
   4  V              7.000e-16   # f*7e-16
   5  N              1.000e+00  
   6  theo_init      0.000e+00  
   7  ahl_init       0.000e+00  
   8  dna1_init      2.373e-08   # 10/NA/V
   9  dna2_init      2.373e-07   # 100/NA/V
  10  pulse1_start   2.000e+04  
  11  pulse2_start   4.000e+04  
  12  pulse1_conc    1.000e-04  
  13  pulse2_conc    1.000e-04  
  14  transp3_pout   1.000e-01  
  15  transp3_pin    1.000e-01  
  16  transp4_pout   1.000e-01  
  17  transp4_pin    1.000e-01  
  18  rule20_k       5.000e-04  
  19  rule15_k       5.000e-01  
  20  rule17_k       5.000e-01  
  21  rule34_k       1.000e-04  
  22  rule35_k       1.000e-04  
  23  rule24_k       1.155e-02  
  24  rule26_k       5.783e-03  
  25  rule21_k       1.000e+08  
  26  rule1_k        1.000e+07  
  27  rule33_k       2.310e-03  
  28  rule27_k       2.310e-03  
  29  rule22_k       2.000e+01  
  30  rule25_k       1.155e-02  
  31  rule5_k        1.000e+07  
  32  rule32_k       2.310e-03  
  33  rule28_k       2.310e-03  
  34  rule23_k       1.000e-08  
  35  rule29_k       2.310e-03  
  36  rule9_k        1.540e+05  
  37  rule11_k       1.250e+07  
  38  rule30_k       2.310e-03  
  39  rule2_k        1.000e+01  
  40  rule3_k        1.000e+08  
  41  rule31_k       2.310e-03  
  42  rule6_k        1.000e+01  
  43  rule7_k        2.000e+08  
  44  rule10_k       2.000e-01  
  45  rule12_k       1.000e+01  
  46  rule4_k        1.000e-02  
  47  rule18_k       5.000e-04  
  48  rule8_k        1.000e-02  
  49  rule16_k       5.000e-04  
  50  rule13_k       2.000e+10  
  51  rule14_k       4.000e-02  
  52  rule19_k       5.000e-01 

Files: File:Amitosis.zip

Mysql input file: amitosis_2.sql function.sql inducer.sql medium.sql
MoDeL input file: amitosis_2.model
MoDel output file: amitosis_2.net
SBML output file: amitosis_2.xml

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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.

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.

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.

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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