2.2.5. Electrodeformation of GUVs

The specific electrical capacitance, *Cm*, of POPC and SOPC membranes in the presence of small carbohydrates (sucrose, glucose and fructose) is measured from the frequencydependent deformation of GUVs in alternating electric field [37]. The vesicle shape transformation has been established to depend on the ratio Λ between the conductivity *λin* of the aqueous solution, enclosed by the vesicle membrane, and the conductivity *λout* of the external (suspending) medium [38,39]. In the case of more conductive external medium, upon increasing the AC field frequency, a vesicle with radius *r* placed in a more conductive aqueous solution changes its shape from prolate to oblate with respect to the field direction. During this morphological transition, the intermediate frequency, *fcr*, at which the quasispherical shape is assumed, is given by the expression [38]:

$$f\_{cr} = \frac{\lambda\_{\text{in}}}{2\pi r \overline{C}\_{\text{m}}} [(1 - \Lambda)(\Lambda + 3)]^{-1/2} \tag{4}$$

*C<sup>m</sup>* denotes the resultant capacitance of a series of three capacitors. These are the bare lipid bilayer, *Cm*, and the capacitances of the diffuse charge regions resembling electric double layers in the aqueous solution at the two sides of the bilayer, denoted by *CD*,*in* and *CD*,*ex*, respectively:

$$\overline{\mathbb{C}}\_{m} = \left(1/\mathbb{C}\_{m} + 1/\mathbb{C}\_{\mathrm{D},\mathrm{in}} + 1/\mathbb{C}\_{\mathrm{D},\mathrm{ex}}\right)^{-1} \tag{5}$$

On the length scale of GUVs with radii ~10 µm and bilayer thickness *d* ~ 5 nm (*d* ≪ *r*) [37] the membrane is described as a two-dimensional surface with dielectric permittivity *ε<sup>m</sup>* = *εrmε*0, where *εrm* stands for the relative dielectric constant of the bilayer and *<sup>ε</sup>*<sup>0</sup> <sup>≈</sup> 8.85 <sup>×</sup> <sup>10</sup>−<sup>12</sup> F/m is the vacuum permittivity. Therefore, the specific capacitance *C<sup>m</sup>* of the bilayer is given by:

$$\mathbb{C}\_m = \varepsilon\_m / d \tag{6}$$

The capacitance of the electric double layers is represented by the capacitance of a planar capacitor with thickness equal to the Debye length, *λD*, and dielectric constant equal to the dielectric constant of the aqueous solution *ε<sup>r</sup>* ≈ 80 [40]. The Debye length is related to the molar concentration *c* of a 1:1 electrolyte by the expression *λ<sup>D</sup>* = 0.303/ √ *c* nm [41]. Considering the concentrations of NaCl applied here, we estimate the capacitance for the double layers of free charges in the aqueous solution on both sides of the bilayer *CD*,*in* and *CD*,*ex*. As discussed in [38], their contribution increases at lower salt concentrations as well as for high enough values of the bilayer capacitance.

It has been established that the dielectric properties of the ionic double layers near the membrane are related to the orientational ordering of water dipoles in the aqueous surroundings as well as in the headgroup region of lipid bilayers. We analyze the former in the light of the theoretical evaluations published so far [40,42,43], while the latter corroborates the necessity to investigate the effect of sugar molecules on the bilayer dielectric properties. In the case of lipid membranes composed of zwitterionic phosphatidylcholines, studied here, it has been shown that at much higher monovalent salt concentrations the relative permittivity in the dipolar headgroup region is decreased as a result from the saturation effect in orientational ordering of water dipoles [44]. In the present study, we consider PC membranes in sugar-containing electrolyte solutions with ionic strength, which is two orders of magnitude lower than in [44]. At zero surface charge density corresponding to the model lipid system studied here, the value taken for *ε<sup>r</sup>* ≈ 80 represents a good evaluation for the relative permittivity of the aqueous solution surrounding the bilayer as shown in [43]. The electric field strengths applied are far below the electroporation threshold [37,45].

The electrodeformation measurements are conducted in a chamber consisting of two parallel glass slides, which are separated by a 0.5 mm-thick inert spacer (Sigma-Aldrich Inc., St Louis, MO, USA). AC electric field from an arbitrary waveform generator (33120A, HP/Agilent, Santa Clara, CA, USA) is applied to a pair of two rectangular parallel ITOelectrodes deposited on the lower inner surface of the chamber at 1 mm apart. The measurement is performed by varying the frequency of the imposed uniform field in the range of 10–200 kHz. The field strengths ≤ 7 kV/m, applied here, are two orders of magnitude lower than the electroporation threshold [37,45]. The vesicle electrodeformation is observed and recorded using a phase-contrast microscope (B-510PH, Optika, Ponteranica, BG, Italy) equipped with a dry objective (×40, 0.65 numerical aperture) and Axiocam ERc 5s camera 5 MP (Zeiss, Jena, Germany) connected to a computer for image recording and processing with resolution of 0.1 <sup>µ</sup>m/pixel. The ratios 0.87 ≤ <sup>Λ</sup> ≤ 0.95 correspond to a more conductive suspending solution. We perform data analysis following the original approach of Salipante et al. [16,38].
