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Team:Wageningen UR/Project/ModelingProj1
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'''Fig.1:''' ''Basic oscillating genetic circuit as published by Danino & Hasty.'' [http://www.nature.com/nature/journal/v463/n7279/abs/nature08753.html] | '''Fig.1:''' ''Basic oscillating genetic circuit as published by Danino & Hasty.'' [http://www.nature.com/nature/journal/v463/n7279/abs/nature08753.html] | ||
| - | The genes luxI and | + | The genes luxI and AiiA can be expressed when a AHL-LuxR complex binds to the promoter region. The circuit uses both a positive and negative feedback loop to control the AHL concentration and therefore the expression of the resulting proteins LuxI and AiiA. In the positive loop, LuxI generates more AHL, which – together with LuxR – can form more of the activating AHL-LuxR complex and therefore stimulates even more production of LuxI and consequently AHL. This complex also activates the expression of AiiA. In the negative feedback loop, AiiA degrades the AHL produced. For more detailed information about the circuit read more about the [[Team:Wageningen_UR/Project/CompleteProject1Description#2._Mechanism| mechanism]] in the [[Team:Wageningen_UR/Project/CompleteProject1Description| complete project description.]] |
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=== Mathematical model of the Hasty construct === | === Mathematical model of the Hasty construct === | ||
| - | Since our | + | Since our BioBricked oscillatory system is based on the circuit published by Danino et al. in the paper [http://www.nature.com/nature/journal/v463/n7279/abs/nature08753.html “A synchronized quorum of genetic clocks”], our first model of the system is a reproduction of the mathematical model in the [http://www.nature.com/nature/journal/v463/n7279/suppinfo/nature08753.html supplementary information] accompanying the publication mentioned. In their simulations, Danino et al. used a set of four delay differential equations, which we also used as starting point for our modeling work. |
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[[File:Equations_hasty_WUR.png|350px|left]] | [[File:Equations_hasty_WUR.png|350px|left]] | ||
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{{:Team:Wageningen_UR/Templates/Style | text= __NOTOC__ --> | {{:Team:Wageningen_UR/Templates/Style | text= __NOTOC__ --> | ||
| - | The steps (transcription, translation, maturation etc.) from the luxI and | + | The steps (transcription, translation, maturation etc.) from the luxI and AiiA genes to the corresponding proteins are not modeled separately, but the delay of the correlation between the internal AHL concentration, which triggers the expression of the genes, and the corresponding AiiA and LuxI concentrations is simulated by a Hill function which takes the history of the system into account, i.e. the concentration of AHL at the time it binds to LuxR to form the activation complex. |
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| - | + | Tau represents the time step. It can be seen that the function takes the history of the system into account, since the production of the proteins depend on the past concentration of internal AHL as in: | |
| + | [[File:Equations3_hasty_WUR.png]]. | ||
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| - | === Writing a modeling tool in | + | === Writing a modeling tool in Matlab === |
[[File:Oscillation_GUI_WUR.png|center]] | [[File:Oscillation_GUI_WUR.png|center]] | ||
| - | '''Fig.1:''' ''GUI of the | + | '''Fig.1:''' ''GUI of the Matlab modeling tool created by team Wageningen UR'' |
| - | For the first simulations, the same parameters were used as in the cited paper | + | For the first simulations, the same parameters were used as in the cited paper. The only variables thus being the cell density and flow rate. To get an idea about the different conditions in which oscillations could occur, our team created a script for a Matlab modeling tool which uses nested for-loops to vary the flow rate and cell density over a range of values. The resulting tool allows the user to enter the range in which the variables should be varied. The tool then iterates over the values and plots graphs of all combinations possible for that range of values. Figure 2 shows an example output of the tool. |
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=== Preliminary conclusions for our system === | === Preliminary conclusions for our system === | ||
| - | The first observation from the model was that, for oscillations to occur, the flow rates may not be too fast, especially at lower cell densities. Since the device used for our system has larger dimensions than the microfluidic device used by Danino et al. the flow rates | + | The first observation from the model was that, for oscillations to occur, the flow rates may not be too fast, especially at lower cell densities. Since the device used for our system has larger dimensions than the microfluidic device used by Danino et al. the flow rates required could not be achieved by varying height differences alone. <!-- Further information can be found in the information about the [[Team:Wageningen_UR/Project/Devices#Setup| platform used to measure oscillations.]] --> |
| - | Furthermore, an interesting observation was that applying a flow rate over the cells was not essential to obtain | + | Furthermore, an interesting observation was that applying a flow rate over the cells was not essential to obtain oscillations. Figure 3 shows how, according to the model, oscillations can potentially occur at 0 flow rate. Interesting is that this happens only at high cell densities. |
[[File:Model0flow_WUR.png|770px|center]] | [[File:Model0flow_WUR.png|770px|center]] | ||
| - | '''Fig.3:''' ''Graphs showing oscillatory | + | '''Fig.3:''' ''Graphs showing oscillatory behavior increasing with cell density even when the flow rate is set to 0'' |
| - | Disregarding the strictly mathematical model, some more conclusions were drawn from modeling work as to whether to use a | + | Disregarding the strictly mathematical model, some more conclusions were drawn from modeling work as to whether to use a microdish or microsieve as platform for measuring oscillations. This is described in more detail in the [[Team:Wageningen_UR/Project/DevicesSetup| section about the setup of the device.]] |
=== Expansion of the model for the double tunable oscillatory construct === | === Expansion of the model for the double tunable oscillatory construct === | ||
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| - | To | + | To accommodate the idea of the [[Team:Wageningen_UR/Project/CompleteProject1Description| double tunable oscillator]], the original set of delay differential equations in the paper was expanded by two additional differential equations for the LacI and TetR repressors and the equations for the LuxI and AiiA production were adjusted to take the influence of the corresponding repressors lacI for LuxI and TetR for AiiA respectively into account. Below the adjusted set of differential equations is shown. |
'''Top: ''Adjusted set of differential equations for the double tunable oscillator'' | '''Top: ''Adjusted set of differential equations for the double tunable oscillator'' | ||
| - | Since the lacI repressed hybrid promoter used for this system was designed by the [http://parts.mit.edu/igem07/index.php/Tokyo/Works Tokyo iGEM 2007] team, the equations were derived according to their model. The | + | Since the lacI repressed hybrid promoter used for this system was designed by the [http://parts.mit.edu/igem07/index.php/Tokyo/Works Tokyo iGEM 2007] team, the equations were derived according to their model. The TetR repressor was then modeled using the same template. |
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Revision as of 10:58, 21 September 2011
