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Lipid Membrane Mechanics

All biological membranes are composed of amphiphilic lipid molecules which self-organize to form fluid bilayers. Considering these membranes serve a variety of mechanical and organizational roles within a cell, it is of some interest to understand their mechanical properties. Arguably the two most important mechanical properties of a membrane are its area stretch modulus and bending modulus (presuming it is a linear elastic material). These membranes exhibit some very unique properties in that they are fluid in-plane, hence any localization of surface tension quickly equilibrates with the rest of the membrane. Our goal in this experiment was to measure the area strech modulus of a DOPC bilayer (dual 18 carbon chain).

Structure of DOPC (Avanti Polar Lipids)


Testing the stretch properties of a bilayer require that we make giant unilamellar vesicles (GUV's). These vesicles are formed by depositing a thin layer of pure lipid dissolved in cholorform onto a conductive glass substrate. The lipid layer is dried and then hydrated in the desired aqueous buffer. This hydrated lipid layer is then subjected to an oscillating electric field, and over the course of a few hours, GUV's form.

A rough sketch of the electroformation chamber. The purple coating on the bottom represents the lipid, electrical contacts are attached to the conductive substrate on both sides of a chamber filled with aqueous buffer and the oscillating field is applied across the chamber. The results are shown in the picture to the right.

Once formed, the GUV's are diluted significantly and put into a temperature controlled microscope stage. In this stage they will be manipulated with a micropipette, which when suction is applied, deforms the GUV's in a well characterized way.

Diagram showing the basic setup for an area stretch experiment.
Vesicles are imaged on an inverted, epi-fluorescence microscope.

Finding the percent area change (areal strain) and surface tension as a function of suction pressure reduces to measuring simple geometric features of the GUV.

Knowing the geometric features shown on this diagram
and the suction pressure allows one to calculate the areal
strain and surface tension.

As the suction pressure rises the membrane stretches and the surface tension increases, until finally the membrane ruptures. It can be shown that the GUV maintains constant volume over the course of the experiment (to within ~1%).


Membrane shape as a function of suction
pressure- last frame is after membrane rupture.

We then use custom written software to analyze the shape changes in the GUV's. We select certain regions of the vesicle:

To get a measure if Lp we take
a line scan across the vesicle.


To measure Rv we select a region
around the spherical part of the vesicle.


To measure the pipette radius (Rp) we select
a region encompassing the vesicle within the pipette.

After a top secret algorithm is applied, the shape of the vesicle in each image is known within a few 10's of nanometers.

Results of the pipette and line scan measurements.

Snapshots showing vesicle shape as a function increasing surface tension.

Finally, we verify that (in stretch) lipid bilayers are a linear elastic material with a well defined stretch modulus.


Multi-component Lipid Vesicles

In reality biological membranes are composed of multiple lipid components with varying head-group chemistry and lipid carbon chain length. These differences lead to liquid-liquid phase segregation at certain temperatures - known as immiscibility transitions. When this transition occurs a series of interesting kinetic steps take place that allow individual lipid molecules to form domains (groups of a single kind of lipid). One biological hypothesisis that these domains are crucial for spatially organizing transmembrane and membrane associated proteins. These domains are fairly stable and continue to difffuse in the membrane over the course of minutes. The nature of their movements is of some interest to us, and is being pursued further. Using a similar electroformation technique as mentioned above and with some help from Sarah Keller (U. of Wash.) we made these multi-component GUV's.

Kinetic Monte Carlo simulation of a quenched
lipid mixture phase segregating.

(periodic boundary conditions)

Domains diffuse in the bilayer - note in the
lower right two fusion events during the movie.

A surprise to us; when we lowered the temperature even further these darker liquid domains became solid and took on some very 'non-equilibirium' shapes. We have some theories as to why this might happen.

This movie is a scan in the z direction
from the top of the GUV to the bottom.

Finally, we noticed these solid, oddly shaped domains were actually quite rigid. The movie below shows the liquid membrane thermally fluctuating around the solid domain which is actually holding the GUV in a non-spherical shape.



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