**1. Introduction**

The Langmuir monolayers formed by insoluble amphiphiles at the free water surface have mainly been analyzed using the classical method based on recording surface pressure (π)–area (A) isotherms, which enables researchers to monitor changes of the physical state of film molecules upon compression [1]. Their visualization is possible with microscopic methods like Brewster angle microscopy [2] and fluorescence microscopy [3]. Changes in the electric potential (∆V), which provide important information on the orientation of molecules at the surface, are performed less frequently. Such measurements complement the characterization of the film's electrical properties (including dipole moments and dielectric permittivity), which play an important role in many intermolecular interactions.

**Citation:** Chachaj-Brekiesz, A.; Kobierski, J.; Wn ˛etrzak, A.; Dynarowicz-Latka, P. Electrical Properties of Membrane Phospholipids in Langmuir Monolayers. *Membranes* **2021**, *11*, 53. https://doi.org/10.3390/membranes 11010053

Received: 13 December 2020 Accepted: 11 January 2021 Published: 13 January 2021

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Their analysis provides the basis for an insight into the understanding of biomolecular processes in membranes.

A Langmuir monolayer can be considered as an array of electric dipoles of filmforming molecules situated at the air/water interface. Of particular interest are phospholipid monolayers, which provide a simplified, two-dimensional membrane model that is suitable for studying interactions [4]. Particularly important are those between the polar groups of film molecules and substances dissolved in the subphase (ions and soluble biomolecules). During interactions, the electrical surface potential of the monolayer can be decreased or increased. The measurements of such modifications are of great value as they can be used to screen drugs and check their effectiveness [5–8].

The experimental surface potential changes of a monolayer have usually been interpreted in the terms of so-called effective dipole moments (µ⊥). In the simplest approach, derived from the parallel plate condenser model [9], ∆V is expressed by the Helmholtz equation:

$$
\Delta \mathbf{V} = \frac{\mu\_{\perp}}{\mathbf{A} \varepsilon \varepsilon\_{0}} \tag{1}
$$

where ε is the dielectric permittivity of the film, ε<sup>0</sup> is the dielectric permittivity of the vacuum, <sup>µ</sup>⊥. is the normal (to the interface) component of the dipole moment of the film molecule at the interface (note that this is different from the molecular dipole moment of the free molecule) and A is the average area occupied by the molecule at the surface (A = 1/N, where N is the total number of molecules at 1 cm<sup>2</sup> of the surface). The above equation applies to un-ionized molecules. For ionized ones, the double layer potential (ψ<sup>0</sup> ) must be taken into account [9,10]. The main problem in Equation (1) is the unknown value of the permittivity of the film, ε. One of the approaches assumes that ε = 1, either because molecules are considered as isolated entities or because of the lack of a known value [10], however, this can be assumed only for gaseous films. Some authors have claimed that a value 5 < ε < 10 should be used [11]. Others suggest that for condensed monolayers, ε can be taken as 2, which is the dielectric permittivity of hydrocarbons [12]. In another approach, the unknown value of ε has been included in the so-called "apparent dipole moment" of a film molecule, µ<sup>A</sup> = µ⊥ ε [13]. µ<sup>A</sup> can be easily determined from the experimental values of ∆V as a function of A. Apart from the Helmholtz model, other approaches have been suggested in order to interpret surface potential changes (reviewed in [14,15]). A frequently used model was provided by Demchak and Fort [16], which treats the monolayer as a three-layer capacitor. In this model, the effective dipole moment of a film molecule can be divided into the contributions from the reorientation of water molecules in the monolayer, the polar and apolar part of the film molecule (µ w ⊥ , µ p ⊥ and µ a ⊥ , respectively), divided by their local dielectric permittivities:

$$
\Delta \mathbf{V} = \frac{1}{\mathbf{A}\varepsilon\_0} \left( \frac{\mu\_\perp^\mathbf{w}}{\varepsilon\_\mathbf{w}} + \frac{\mu\_\perp^\mathbf{P}}{\varepsilon\_\mathbf{P}} + \frac{\mu\_\perp^\mathbf{a}}{\varepsilon\_\mathbf{a}} \right) \tag{2}
$$

Equation (2) has been used to interpret electric surface potentials for both adsorbed [17] as well as insoluble monolayers [18]. Group dipole moments, µ p ⊥ and µ a <sup>⊥</sup> were calculated from bond dipole moments and angles between them, whereas local dielectric permittivities ε<sup>a</sup> and ε<sup>p</sup> were obtained by solving in pairs equations of type (2) for molecules having the same apolar parts and different polar parts, and vice versa, assuming that the contribution from the reorientation of water molecules (µ w ⊥ /εw) in each pair of equations is the same. Using this procedure for adsorbed films [17] and Langmuir monolayers [18,19] formed by carboxylic acids, alcohols and their derivatives, the following values were obtained: ε<sup>p</sup> = 4.2; ε<sup>a</sup> = 2.4; (µ w ⊥ /εw) = −100 ÷ −200 mD; ε<sup>p</sup> = 6.4; ε<sup>a</sup> = 2.8; (µ w ⊥ /εw) = −65 mD, and ε<sup>p</sup> = 7.6; ε<sup>a</sup> = 4.2; (µ w ⊥ /εw) = 25 mD, respectively. Upon analyzing surface potential changes for terphenyl derivatives [16], the following values were obtained: ε<sup>p</sup> = 7.6; ε<sup>a</sup> = 5.3; (µ w ⊥ /εw) = 40 mD. Although there are some differences as regards the values of local dielectric permittivities, ε<sup>p</sup> is always higher than εa. The greatest discrepancies

concern values of (µ w ⊥ /εw), which are generally small, but their sign was determined to be positive or negative.

The history of measuring surface potentials of Langmuir films from membrane lipids is relatively long but there are many discrepancies in the reported values [20–22]. This can result from the applied approaches, laboratory procedures as well as equipment (including types of measuring electrodes used). Although nowadays this technique is routinely applied in order to analyse the electrical properties of surface films [7,8,23,24], in the literature there are results for selected, single molecules only and no systematic studies, especially for biologically important molecules, are available. The main constituent molecules of biomembranes, i.e., phospholipids, are of particular importance. Therefore, the aim of this paper was to provide the characteristics of the electrical properties of the most abundant membrane phospholipids, i.e., phosphatidylcholines (PCs), differing in acyl chain length (1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC); 1,2-distearoyl-sn-glycero-3 phosphocholine (DSPC); 1,2-diarachidoyl-sn-glycero-3-phosphocholin (DAPC) and unsaturation (1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). For comparison, other phospholipids, such as phosphatidylethanolamines (represented by 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) and sphingolipids (represented by N-(hexadecanoyl) sphing-4-enine-1-phosphocholine (SM) were also investigated. The chemical structures of the studied phospholipids are shown in Figure 1. All phospholipids selected for our study have net charge zero at pH 7.

**Figure 1.** Chemical structures of the studied phospholipids together with acyl chain lengths. Chain melting temperatures of the hydrocarbon chains are given in parentheses. DPPC- 1,2-dipalmitoyl-sn-glycero-3-phosphocholine; DSPC- 1,2 distearoyl-sn-glycero-3-phosphocholine; DAPC -1,2-diarachidoyl-sn-glycero-3-phosphocholine; DOPC- 1,2-dioleoyl-snglycero-3-phosphocholine; DPPE- 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine; SM- N-(hexadecanoyl)-sphing-4 enine-1-phosphocholine.

The theoretical models used so far for determining the apparent dipole moments and local dielectric permittivities were developed for very simple molecules such as carboxylic acids, alcohols and amines. The use of these models to determine the electrical properties of more complex molecules has not worked well. Therefore, an additional goal of our research was to develop a universal model to be used for molecules of any structure, based on density functional theory (DFT) modeling and multiple linear regression.
