The aqueous environment inside and outside the bilayer prevents the lipids from escaping, but nothing stops these molecules from moving about and changing places with one another within the plane of the bilayer. Therefore, it behaves as a twodimensional fluid, which is crucial for the cell membrane function. Besides this high degree of lateral motility, lipid molecules rotate very rapidly about their long axis, due to the temperature. In fact, as we could observe in our experiment, as the temperature increases, so does the fluidity of the bilayer. Another type of movement is the transverse movement (flipflop), but it is very rare.
Lipid bilayer membranes play an important role in cell function. Cell membranes have the appropriate permeability barrier, establishing a distinction between the inside and the outside of the cell. The lipid bilayer from the cell membrane helps to sustain osmotic gradients across the membrane, blocking the passage of almost all watersoluble molecules, due to the hydrophobic interior of the bilayer.
There are also other biological processes in which bilayers are crucial, such as endocytosis (phagocytosis, pinocytosis) and ion channel regulation.
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I. Surface Tension
Consider the following liposome:
where:
 P _{A} is the atmospheric pressure
 P _{V} is the pressure inside the vesicle
 R _{V} is the radius of the vesicle (considering the vesicle an sphere, with flat surface)
 σ is the surface tension with units: J/m ² or N/m
So the energy of this system is
E = σAΔPV,
where A is the surface area of the sphere and ΔP = P_{V} – P_{V}. Then
E = σ4πR^{2}ΔP4/3πR^{3}
We have ΔP fixed (nothing leaves the interior of the vesicle, and P A does not change) and σ depends on the composition of the vesicle. So what is the radius R?
To find that, we have to minimize the energy with respect to R:
This is called Laplace relation.
In this case, we assumed that σ and P_{V} are constant. We can get the same result if we look at an infinitesimal region of the vesicle
without the assumption that σ and P_{V} are constant :
Since the vesicle is in equilibrium (it is not shrinking or expanding), the total force over any region must be zero. The forces acting on the vesicle are 1) the one due to the difference between the inner and outer pressure, and 2) the one due to the surface tension.
 If we approximate the spherical region to a circular region of radius r, the force is just F _{T} = Δ P( π r ² )
 We can sum all the infinitesimal forces dF acting on each small piece of length dx. But
σ = dF/dx and dF = σ dx
Since the components dF h cancel, we can integrate over dF v and use the relation above to get
F_{T} = σ 2πr sinθ
Therefore,
ΔP (π r^{2}) =σ 2π r sinθ ,
where
sinθ = r/R
Finally,
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II. Model
O ur experiment consists of a micropipette applying some pressure over the surface of such a sphere that contains a certain domain:
Using the relation we derived for the radius, we can find three equations:
where we assumed that the surface tension is constant over the vesicle, and different on the domain.
We know R _{v} , R _{p}, R _{e}, P _{a} (we can measure) and P _{p} (we control). So we can solve the equations above for our unknowns and obtain:
Another parameter that we are more interested in is the line tension between the domain and the liposome. We use again the argument of equilibrium of forces to get the equation for the line tension γ :
(σ_{v}σ_{e})A_{e} = γl
Using the solutions above, we get
It is easy to see if these equations are wrong, just by checking the sign (everything should be positive).
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Procedure
The lipid mixture we used in our experiments is 35% dioleoylphosphatidylcholine (DOPC), 35% dipalmitoyl phosphatidylcholine (DPPC) and 30% chloroform. Also included is 0.8% DPPELiss Rhodamine for domain labeling.
1. The unilamellar liposomes we used were made by electroformation.

Everything should be cleaned with DI water and ethanol

With a 10ul glass syringe, we applied on the slide a 23ul droplet of the solution of lipid and chloroform in the center of the ITO slide

Under the right angle, it is possible to see a green reflexion of the light

We used two types of lipids so that we could see two different phases on the surface of the vesicle

Immediately after that, the device was placed in a vacuum desiccator for about 1 hour, to let the solution dry

After that, we placed a buffer solution in the Oring

Then we put the top half of the chamber on using the alignment pins

Carefully we took it to the microscope and placed the chamber there

After attaching the BNC connector to the chamber, we set a voltage no more than 5V (more than that could damage the ITO coating) and a frequency of about 10Hz

We waited for about 3 hours to have the liposomes formed (the exact mechanism of such formation is yet not very clear)

These liposomes are good for some hours (about 12 hours, in our experiments
2. After the formation, we made a solution of 1:200 of the liposomes in glucose. We had to cut the tip of the pipette we used, because the size of its opening was about the size of the vesicles, and they could get stuck there or be damaged.
3. We had to make also the micropipettes that we used

First, we got a long capillary and cut it into pieces (about 10 cm long)

Each smaller capillary was placed in the Sutter P97 Micropipette Puller, an equipment that heated the center of the capillary and pulled the edges, breaking it in half. We only used the right half, because the tip from the left half was deformed
Sutter P97 Micropipette Puller

Now the tip of the capillary was thin enough, but it was closed, so we had to open it. To do this, we chose the capillary that had the straightest tips

Using another equipment, we inserted the tip of the capillary into a heated glass sphere (about 1mm in diameter) and let the sphere cool down – a foot pedal controlled the heating device

Then we pulled the capillary, breaking it in the tip. Although we had a hole in the capillary, the edges were deformed. So we inserted it again into the heated sphere

Glass from the sphere entered the capillary and then we let everything cool down again. A light knock on the table was enough to break the tip once more

This process made the tip now too sharp for the liposomes, so we just approached the tip to the heated sphere, without touching it, to make the edges smoother

We cleaned the micropipette with ethanol, and used a syringe to check if water could go through the micropipette and get rid of any bubble in it, by filling it entirely with water
4. With the micropipette ready, we placed it in the microscope, avoiding bubbles.
5. We inserted it into the opening at the center of the chamber and placed it in the field of view of the microscope, focusing on the pipette.
6. Then we placed a solution of BSA (Bovine serum albumin) within the opening, avoiding bubbles
7. After 15 minutes, we removed the BSA with a Kim Wipe and replaced it with water, letting it there for 5 minutes
8. We removed the water and placed the solution with the liposomes in the opening, after gently mixing the solution .
9. We set a temperature for our experiment between 10 oC and 20 oC and waited for about 5 minutes, to let everything reach equilibrium and have everything ready. For most of the time, we keep the temperature at 18 o C .
10. Using the micropipette, we tried to capture vesicles, by placing the pipette and the vesicle we want in the same plane. Normally the vesicles were at the bottom of the solution and were aligned almost vertically.
11. Using a device that can vary pressure based on the height of a column of water, we captured vesicles that had large domains, so that we could calculate the line tension between the lipids and the surface tension for each of the lipids, according to our model.
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We write a simple matlab program to process the images and calculate the unknowns including the line tension. Each time the program is executed, one image is processed. The program first prompts for the image. Then it converts the image from 16 bits to 8 bits and performs appropriate scaling on it. Next a image is displayed and a getline function is evoked to let user select the curve for Rv calculation. The results are saved as coordinates in two vectors. We use the zoom in from Tools menu before the selection. This process repeats for Re, Rp and l calculation. For l, only two points are selected. The curvatures are calculated with formula as below with difference operation:
And the radius is just the inverse of curvature. Finally all the unknowns are calculated as in boxed equations in model section.
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