Deformation of an Invaginated Phospholipid Vesicle by Electric Field

Primoz Peterlin, France Sevsek, Sasa Svetina and Bostjan Zeks

Introduction

Amphipatic molecules like phospholipids tend to form a lipid bilayer in an aqueous medium. The two layers can slide one along the other, yet they are inseparable due to the hidrophobic interaction. Furthermore, it is energetically favourable if a sheet of bilayer closes upon itself into a vesicle. Invaginated phospholipid vesicles are commonly observed shapes: the membrane is invaginated by forming a smaller sphere within a larger one (Figure 1a). The two spheres are connected with a narrow neck.

Figure 1.

Experiment

Vesicles of average diameter around 20 micrometers were prepared from commercially available POPC using a standard procedure. When AC electric field (10 kHz, up to 200 V/cm) is applied to the aqueous solution of vesicles (distilled water or 0.1 M sucrose), the electric forces which arise on the membrane/solution boundary tend to deform the outer vesicle into a prolate rotational ellipsoid, while the inner one stays nearly spherical (Figure 1b). As the field is increased, the deformation of the outer vesicle increases as well (Figure 1c). The inner vesicle stays nearly spherical, but gets diminished, thus providing the area neccessary for the expansion of the outer one. Then, at some non-zero radius of the inner vesicle, the neck opens abruptly, yielding an elongated prolate rotational ellipsoid (Figure 1d). Decreasing the field strength reverses the process, with some hysteresis. The observation was performed by means of a phase contrast microscope and a CCD video camera attached to it.

Theoretical Model

The vesicle shape is modelled as a sphere within a prolate rotational ellipsoid, thus parametrized with three variables (Figure 2). The two constraints are the total area of the membrane and the volume of the vesicle, which are kept constant. Minimization of the total vesicle energy over the remaining variable yields the equilibrium shape. The total energy of a vesicle consists of the local and nonlocal membrane bending elastic energy and the energy due to electric field. The membrane bending elastic energy is increasing as the spherical vesicle is elongated into a prolate rotational ellipsoid. It thus opposes the ellipsoidal deformation. The energy of electric field, on the contrary, favours ellipsoidal deformation. Clearly, the two effects balance each other at certain level of deformation, and this equilibrium deformation is dependent on the field strength.

We determine the field strength needed to open the neck by comparing the energy of the invaginated shape with the energy of the fully extended one. As field strength increases, the invaginated shape becomes more and more deformed, and the energy difference between it and the fully extended shape diminishes. At some point, this energy difference becomes equal to the bending elastic energy of the invaginated vesicle. Further increase in field strength makes the fully extended shape energetically favourable to the invaginated one, so at this point the transition occurs.

Results

The results of the theoretical calculation have shown that apart from the material constants, the field strength needed for the transition is dependent of the vesicle size and its relative volume. Dependence on the vesicle size is a simple one. The graph below shows critical field strength in volts per centimeter as a function of membrane area (in square micrometers), calculated for a few different values of vesicle relative volume.

One can avoid the dependence on the vesicle size altogether if one doesn't look at the critical field strength, but rather at the corresponding critical eccentricity. On the graph below, critical eccentricity has been calculated for three different values of nonlocal bending constant (q is the ratio between non-local and local bending constant), and is plotted as a function of relative volume of vesicle.

Comparision with the experimentally obtained data (Figs 1a-e) shows the same qualitative behaviour, although the experimental values show somewhat higher stability of the invaginated shape of a vesicle. This may indicate that some other effect helps stabilizing the vesicle. One possibility may be van der Waals forces acting on the neck between the inner and the outer vesicle.

Conclusion

The model described provides good qualitative description for the experiment with invaginated vesicles in applied electric field. With more experimental data collected, it can yield an estimation for the nonlocal bending constant of the phospholipid membrane.

The text is based on the poster presented at the 1994 Conference on Life Sciences, October 1-3, Gozd-Martuljek, Slovenia.