"
Team:Tsinghua-A/Modeling/P3A
From 2011.igem.org
| Line 220: | Line 220: | ||
<p>Parameters in equations are listed below.</p> | <p>Parameters in equations are listed below.</p> | ||
<p align="CENTER" style="text-indent:0em"><img src="https://static.igem.org/mediawiki/2011/2/22/Part3-2.png" width="753px" height="355px"></p> | <p align="CENTER" style="text-indent:0em"><img src="https://static.igem.org/mediawiki/2011/2/22/Part3-2.png" width="753px" height="355px"></p> | ||
| - | <p align="CENTER" style="text-indent:0em"><B>Table | + | <p align="CENTER" style="text-indent:0em"><B>Table 4</B> Parameters in Dimensionless Model</p> |
<h1 id="Results">Results</h1><hr width="100%" size=2 color=gray> | <h1 id="Results">Results</h1><hr width="100%" size=2 color=gray> | ||
| - | |||
<h2 id="Sensitivity analysis">Sensitivity analysis</h2> | <h2 id="Sensitivity analysis">Sensitivity analysis</h2> | ||
| - | + | <p>In order to find out the key parameters which will affect stability of the system at most, we need to make a sensitivity analysis on each. At first, we did brief and instinctive analyses on each parameter as follows. τ<sub>1</sub><sup>*</sup> and τ<sub>2</sub><sup>*</sup> represent time delay in cell 1 and cell 2 respectively, which have been discussed in part 2, have little influence on stability of system but intend to affect the oscillation period merely. Parameters a and b refer to feedback factors indirectly, which have not been discussed before, we will see how a and b affect our system later. We have clarified that parameter u is equivalent to μ/γ, thus, u is directly decided by the dilution rate of signal molecules 3OC12HSL and 3OC6HSL in environment and will inevitably influence stability of oscillation. As for m and n, they are inseparably connected to the Hill parameters whose sensitivity have been analyzed in part 2, so we can deduce that m and n are both sensitive parameters to our system.</p> | |
| + | <p>Here we mainly did sensitivity analyses on parameters m, n and u. Parameters were set fundamentally as Table 4 shows.</p> | ||
| + | <p>Simulation results reveal that the system can oscillate stably only when u<5.3(fixed the other two sensitive parameters), 11.9<m<71.3 and n>34.4. In other words, to ensure the stability of oscillation, the dilution rate cannot be too high, while the promoter 2 and 4 which affect m and n should be chosen appropriately.</p> | ||
<h2 id="Stability analysis">Stability analysis</h2> | <h2 id="Stability analysis">Stability analysis</h2> | ||
Revision as of 17:58, 25 October 2011
Modeling::Dimensionless Model
Contents |
Dimensionless process
In order to make a further analysis on stability of the system, sensitivity of parameters, feedback factors-we manipulate all the arguments and parameters to make them dimensionless. Analysis of this part is crucial since parameters in vivo experiment may be different and even at odds with modeling ones but a proper dimensionless can reveal the mathematical essence of our model.
Considering the Hill equation in the simplification DDEs, A1c1 and KM1/ρ1 should be the same order of magnitude, thus KM1/ρ1 is a well measurement of quantities of A1c1. We have:
Parameters
Parameters in equations are listed below.
Table 4 Parameters in Dimensionless Model
Results
Sensitivity analysis
In order to find out the key parameters which will affect stability of the system at most, we need to make a sensitivity analysis on each. At first, we did brief and instinctive analyses on each parameter as follows. τ1* and τ2* represent time delay in cell 1 and cell 2 respectively, which have been discussed in part 2, have little influence on stability of system but intend to affect the oscillation period merely. Parameters a and b refer to feedback factors indirectly, which have not been discussed before, we will see how a and b affect our system later. We have clarified that parameter u is equivalent to μ/γ, thus, u is directly decided by the dilution rate of signal molecules 3OC12HSL and 3OC6HSL in environment and will inevitably influence stability of oscillation. As for m and n, they are inseparably connected to the Hill parameters whose sensitivity have been analyzed in part 2, so we can deduce that m and n are both sensitive parameters to our system.
Here we mainly did sensitivity analyses on parameters m, n and u. Parameters were set fundamentally as Table 4 shows.
Simulation results reveal that the system can oscillate stably only when u<5.3(fixed the other two sensitive parameters), 11.9
Stability analysis
Feedback analysis
