*Review* **Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces**

**Jeel Raval <sup>1</sup> , Ekaterina Gongadze 2 , Metka Benˇcina 3 , Ita Junkar 3 , Niharika Rawat 2 , Luka Mesarec 2 , Veronika Kralj-Igliˇc 4 , Wojciech Gó´zd ´z <sup>1</sup> and Aleš Igliˇc 2,5, \***


**Abstract:** In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces' nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO<sup>2</sup> nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO<sup>2</sup> nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

**Keywords:** lipid bilayer electrostatics; zwitterionic lipid bilayers; electric double layer; osmotic pressure; orientational degree of freedom of lipid headgroups; orientational ordering of water dipoles; adhesion of lipid vesicles; lipid bilayer elasticity; lipid vesicle shapes

Biological membranes are an essential constituent of living cells. Their main role is to separate the interior of the cell from its surroundings, allowing for selective transport of specific materials across the membrane [1]. This article focuses on the interaction of biological membranes with nanostructured surfaces and nanoparticles [1–3]. The main building block of the biological membranes is the lipid bilayer with embedded inclusions such as proteins and glycolipids. Isotropic and anisotropic membrane proteins may induce local changes in

**Citation:** Raval, J.; Gongadze, E.; Benˇcina, M.; Junkar, I.; Rawat, N.; Mesarec, L.; Kralj-Igliˇc, V.; Gó ´zd ´z, W.; Igliˇc, A. Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces. *Membranes* **2021**, *11*, 533. https://doi.org/ 10.3390/membranes11070533

Academic Editor: Monika Naumowicz

Received: 17 June 2021 Accepted: 5 July 2021 Published: 14 July 2021

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the membrane curvature [1,4,5], often resulting in global changes in the cell shape [6–12]. The nonhomogeneous lateral distribution and the phase separation of membrane inclusions (nanodomains) can induce local changes in the membrane curvature and are, therefore, the driving force for transformations of the cell shape [6–9,12–14]. The biological and lipid membranes possess some degree of in-plane orientational ordering [1,7,8,10,15–18], including the nematic type of ordering [19–21], which are also important for the stability of different membrane shapes.

The configuration and shape changes of membranes are, in general, correlated with many important biological processes [1,6,13,22]. The shapes of cells are also influenced by the membrane skeleton and cytoskeleton forces [1,11,13,22–28]. Among them, the ATP consuming forces of the membrane skeleton and cytoskeleton are of major importance for sustaining different cell functions [11,12,22,28,29]. Consequently, new theoretical approaches for modeling these cell shape changes under the influence of energy-consuming active forces have been developed recently [11,12,28,29].

The focus of this paper (partially a mini review) is the interaction of nanoparticles (NPs) and nanostructured solid surfaces with cell membranes and lipid bilayers. Certain aspects of membrane–solid surface electrostatics and adhesive interactions are elucidated too.
