Team:Paris Bettencourt/Modeling/Assisted diffusion/From membrane tension to liquid flux
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Revision as of 01:42, 29 October 2011
From membrane tension to liquid flux
Now when we have the analytical expression for membrane tension we can calculate the pressure difference between two bacteria. For doing this we need to know the kinetics the membrane.
To deduce the force exercising on the tube from membranian pressure, please refer to an explanation figure below:
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 :
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.
Click here to come back to Assisted diffusion section.
References