"
Team:NTU-Taida/Modeling/Plasmid-Stability
From 2012.igem.org
(→There can be three kinds of plasmid instability condition:) |
(→Three kinds of plasmid instability condition:) |
||
| Line 33: | Line 33: | ||
3.Negative growth rate difference >> segregation instability<br /> | 3.Negative growth rate difference >> segregation instability<br /> | ||
| - | Knowing the condition of your expression system is important, if growth rate difference is much greater than segregation instability, partition system cannot help stabilize such system. We will show how to discriminate between three conditions and how to use our parts to solve the condition.<br /> | + | <p style="text-indent: 2em;">Knowing the condition of your expression system is important, if growth rate difference is much greater than segregation instability, partition system cannot help stabilize such system. We will show how to discriminate between three conditions and how to use our parts to solve the condition.</p><br /> |
1.Growth rate difference >> segregation instability[[File:NTU-Taida-Stability-eq9.png|100px]]<br /> | 1.Growth rate difference >> segregation instability[[File:NTU-Taida-Stability-eq9.png|100px]]<br /> | ||
| Line 46: | Line 46: | ||
R=10^-5 init=0.01 x-axis:generation y-axis:p- ratio<br /> | R=10^-5 init=0.01 x-axis:generation y-axis:p- ratio<br /> | ||
| - | The simulation shows that initial condition greatly affect the result, and the curve is sigmoid. | + | <p style="text-indent: 2em;">The simulation shows that initial condition greatly affect the result, and the curve is sigmoid. |
The segregation instability shows minor effect on the plasmid loss rate (not shown). | The segregation instability shows minor effect on the plasmid loss rate (not shown). | ||
So that plasmid loss derive mainly from growth rate difference, reduce burden effect is primary mission. | So that plasmid loss derive mainly from growth rate difference, reduce burden effect is primary mission. | ||
Avoid protein/RNA overexpression, and reduce gene dosage; most important of all, well-designed circuit. | Avoid protein/RNA overexpression, and reduce gene dosage; most important of all, well-designed circuit. | ||
| - | Our multimer resolution system might reduce dimer caused metabolic burden. | + | Our multimer resolution system might reduce dimer caused metabolic burden.</p> |
2.Growth rate difference =< segregation instability[[File:NTU-Taida-Stability-eq11.png|100px]]<br /> | 2.Growth rate difference =< segregation instability[[File:NTU-Taida-Stability-eq11.png|100px]]<br /> | ||
| Line 57: | Line 57: | ||
[[File:NTU-Taida-du smaller or equal to R.jpg|550px|center]] | [[File:NTU-Taida-du smaller or equal to R.jpg|550px|center]] | ||
| - | Under this condition, plasmid-bearing cell shows exponential decay. | + | <p style="text-indent: 2em;">Under this condition, plasmid-bearing cell shows exponential decay. |
Segregation instability greatly affect the stability. | Segregation instability greatly affect the stability. | ||
| - | Our partition system and our toxin-antitoxin can solve the problem, multimer resolution system can also relieve the multimer caused segregation instability. | + | Our partition system and our toxin-antitoxin can solve the problem, multimer resolution system can also relieve the multimer caused segregation instability.</p> |
3.Negative growth rate difference >> segregation instability[[File:NTU-Taida-Stability-eq13.png|200px]]<br /> | 3.Negative growth rate difference >> segregation instability[[File:NTU-Taida-Stability-eq13.png|200px]]<br /> | ||
[[File:NTU-Taida-Stability-eq14.png|350px|center]] | [[File:NTU-Taida-Stability-eq14.png|350px|center]] | ||
[[FIle:NTU-Taida-Negative du.jpg|550px|center]] | [[FIle:NTU-Taida-Negative du.jpg|550px|center]] | ||
| - | If plasmid provide host selective advantage(ex:antibiotic resistant gene under antibiotic selection pressure), plasmid loss/plasmid retained ratio will approach a constant: P*. | + | <p style="text-indent: 2em;">If plasmid provide host selective advantage(ex:antibiotic resistant gene under antibiotic selection pressure), plasmid loss/plasmid retained ratio will approach a constant: P*. |
| - | Segregation instability will decide the constant. <br /> | + | Segregation instability will decide the constant. </p><br /> |
| - | Our partition system and our toxin-antitoxin can reduce the constant. | + | <p style="text-indent: 2em;">Our partition system and our toxin-antitoxin can reduce the constant.</p> |
===Reference=== | ===Reference=== | ||
Revision as of 03:47, 27 September 2012
Modeling-Plasmid
Plasmid-Instability-Modeling
Contents |
plasmid instability modeling:
We use Cooper's model (Cooper, N.S., M.E. Brown, and C.A. Caulcott, A ) to model plasmid instability, and set a protocol to suggest users which modules can be used to prove their system stability.
Cooper’s model:
Under steady state, population distribution of bacteria follows underlying equation:
Growth rate and dilution rate have such relation:
Substitute in
produce
This equation belongs to the Bernoulli form of Differential equation and can be solved as:
Initially, plasmid loss usually is 0. 
So the equation can be simplified as:
Three kinds of plasmid instability condition:
1.Growth rate difference >> segregation instability
2.Growth rate difference =< segregation instability
3.Negative growth rate difference >> segregation instability
Knowing the condition of your expression system is important, if growth rate difference is much greater than segregation instability, partition system cannot help stabilize such system. We will show how to discriminate between three conditions and how to use our parts to solve the condition.
1.Growth rate difference >> segregation instability
The equation can be further simplified.
R=10^-5 x-axis:generation y-axis:p- ratio
R=10^-5 init=0.01 x-axis:generation y-axis:p- ratio
The simulation shows that initial condition greatly affect the result, and the curve is sigmoid. The segregation instability shows minor effect on the plasmid loss rate (not shown). So that plasmid loss derive mainly from growth rate difference, reduce burden effect is primary mission. Avoid protein/RNA overexpression, and reduce gene dosage; most important of all, well-designed circuit. Our multimer resolution system might reduce dimer caused metabolic burden.
2.Growth rate difference =< segregation instability
Under this condition, plasmid-bearing cell shows exponential decay. Segregation instability greatly affect the stability. Our partition system and our toxin-antitoxin can solve the problem, multimer resolution system can also relieve the multimer caused segregation instability.
3.Negative growth rate difference >> segregation instability
If plasmid provide host selective advantage(ex:antibiotic resistant gene under antibiotic selection pressure), plasmid loss/plasmid retained ratio will approach a constant: P*. Segregation instability will decide the constant.
Our partition system and our toxin-antitoxin can reduce the constant.
Reference
1. Cooper, N.S., M.E. Brown, and C.A. Caulcott, A Mathematical Method for Analyzing Plasmid Stability in Microorganisms. Journal of General Microbiology, 1987. 133: p. 1871-1880.
