A method for measuring the elastic properties of phospholipid membranes is presented, based on the shape changes of invaginated vesicles in an electric field.
At experiment, vesicles of various shapes are observed. At some, membrane is invaginated, and they appear as a vesicle containing another smaller vesicle. The two vesicles are connected with a narrow neck. When AC voltage is applied, giving rise to the electric field between the electrodes (1-100 kHz, up to 200 V/cm), the outer vesicle deforms into a prolate rotational ellipsoid, while the inner one stays roughly spherical, only getting diminished. When increasing the field strength, the eccentricity of the outer vesicle at first gradually increases as the field strength increases, and at certain level of field strength increases abruptly, when the neck opens and the two parts form one prolate rotational ellipsoid. When diminishing the field strength, membrane develops the invagination again at sufficienly low field strength.
The shape of phospholipid vesicle is modelled as a prolate rotational ellipsoid with a smaller sphere inside and is parametrized by three parametres. Minimizing the total energy of the vesicle yields the equilibrium shape. Two constraints are taken into account, stating the constant membrane area and the constant vesicle volume. Both local and non-local bending energies are contributing to the energy, along with the energy of the electric field. The latter one is calculated as the work exerted by the electric forces on the water-membrane boundary. The first two terms in the energy are independent of the electric field and are opposing the deformation, while the latter one is increasing with the field strength and is favouring deformed shapes. The two opposing effects balance at a certain value of ellipsoid eccentricity. The higher the field, the higher this value is.
The energy of the deformed invaginated shape is then compared with the elongated shape where the invagination is completely flattened out. Above certain high enough field strength, this latter one is energetically favourable, and a discontinous shape transformation occurs. The threshold field value is calculated.
The described model shows that the threshold field strength is depending on the size and relative volume of the phospholipid vesicle, apart from the material constants. Since we can measure the size and the relative volume of a vesicle, and the other material constants are known from other experiments, this method could be employed for the measurement of the non-local bending modulus of a phospholipid bilayer, after the proposed improvements of the theoretical model are made.
Last change: November 12, 1995 (P.Peterlin)