Team:Paris Bettencourt/Modeling/Assisted diffusion/From membrane tension to liquid flux
From 2011.igem.org
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The nanotube dimentions we have taken from the article published by Dubey and Ben-Yehuda <a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion#references"> [1]</a></html> (r = 100 nm, L = 1 µm). The ideas about what values to take for R1, R2 and N1, N2 we got from the bionumber's site <html><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion#references"> [2]</a></html>. We have checked several sets of parameters : | The nanotube dimentions we have taken from the article published by Dubey and Ben-Yehuda <a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion#references"> [1]</a></html> (r = 100 nm, L = 1 µm). The ideas about what values to take for R1, R2 and N1, N2 we got from the bionumber's site <html><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion#references"> [2]</a></html>. We have checked several sets of parameters : | ||
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* N<sub>1</sub> = 2*10<sup>6</sup>, N<sub>2</sub> = 1*10<sup>6</sup>, R<sub>1</sub> = R<sub>2</sub> = 0.5 µm; | * N<sub>1</sub> = 2*10<sup>6</sup>, N<sub>2</sub> = 1*10<sup>6</sup>, R<sub>1</sub> = R<sub>2</sub> = 0.5 µm; | ||
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We still have to work on this model in order to tinker with some of the problem parameters. This might permit us to see a faster and more significant molecule transport through the nanotubes. | We still have to work on this model in order to tinker with some of the problem parameters. This might permit us to see a faster and more significant molecule transport through the nanotubes. | ||
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Revision as of 00:51, 29 October 2011
![](https://static.igem.org/mediawiki/2011/1/19/Tubeornottube.png)
From membrane tension to liquid flux
To deduce the force exercising on the tube from membranian pressure, please refer to an explanation figure below :
![]() |
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Fig1: Tension-force_explanation / The force applied to the nanotube as a function of the surface tension force. | Fig2: Geometry / The system geometry. state during the steady state phase. |
Here T is a surface tension, N is a resulting force of the area of the tube attachment to the bacterium, Δα or α is the half of the angle with a vertex in the center of the bacterium and between the tube extremities. Only this zone is giving a non-compensated contribution to the resulting force.
So the force exercising on the tube is given by the formula :
![](https://static.igem.org/mediawiki/2011/7/7b/Tension-force.png)
![](https://static.igem.org/mediawiki/2011/9/96/Speed_of_the_membrane1.png)
![](https://static.igem.org/mediawiki/2011/3/39/ODEnumber_of_phl_1.png)
![](https://static.igem.org/mediawiki/2011/4/45/ODEnumber_of_phl_2.png)
![](https://static.igem.org/mediawiki/2011/d/d2/Pressure_difference.png)
![](https://static.igem.org/mediawiki/2011/b/bd/Speed_inside_the_tube.png)
![](https://static.igem.org/mediawiki/2011/c/c5/The_flow_of_the_liquid.png)
![](https://static.igem.org/mediawiki/2011/3/35/Mass_passed.png)
Getting good parameters
We have done several simulations where the system consisted of two spherical bacteria of radius R1 and R2, the nanotube of the length L and the radius r between them, and the number of phospholipids N1 and N2 on them. The nanotube dimentions we have taken from the article published by Dubey and Ben-Yehuda [1] (r = 100 nm, L = 1 µm). The ideas about what values to take for R1, R2 and N1, N2 we got from the bionumber's site [2]. We have checked several sets of parameters :* N1 = 2*106, N2 = 1*106, R1 = R2 = 0.5 µm; * N1 = 1*107, N2 = 5*106, R1 = 2 µm, R2 = 1 µm; The value of dynamic viscosity of phospholipid bilayer taken is 10 Pa.s, a bit more than what can be found for castor oil.
Analysing the results and conclusion
Here is the representation of the cinetic between the emitter and receiver - the number of phospholipids passed from the emitter to the receiver through the nanotube.
![](https://static.igem.org/mediawiki/2011/e/e5/Phospholipids_ParisBettencourt.png)
Assisted diffusion section.
References