**6. Conclusions**

The growing number of nanomaterial-based commercial products (medical implants, biosensors, antibacterial surfaces, cancer therapy, etc.) has generated an increasing need for thorough scientific studies to evaluate the interactions of nanomaterials with biological cells and the influence of these interactions on the stability and growing of cells. The cell membrane is a nanoscale barrier that protects the cell and constitutes the initial contact area with the nanostructured surface. The nanomaterial–membrane interactions are strongly dependent on the membrane curvature and is influenced by geometrical/topological constraints and mechanical and electrical properties of the membranes and nanostructured surfaces [1,2,22,47,49,53,54,62,66,67]. Hence, in the future, one of the major goals of the research will be to gain a deeper understanding into the mechanisms of nanomaterial–cell membrane interactions.

In this article, we describe briefly some selected experimental methods for studying the interactions between nanostructured surfaces and biological cells. As an example, we chose TiO<sup>2</sup> nanotubular and octahedral surfaces and characterized them via AFM and XPS. The adhesion of human blood platelets to these surfaces was studied via SEM to elucidate the influence of the surface topography on the behavior of human cells adhered to TiO<sup>2</sup> nanostructured surfaces.

In the theoretical part of the article, it is shown, among others, that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet of the lipid bilayer and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. This may induce, among others, a more tightly packed gel phase of lipids in the adhered part of the vesicle membrane and stronger orientational ordering of water dipoles between the proximal lipid layer and the supporting solid surface. In the final part of the paper, we theoretically examined the influence of the vesicle size, bending modulus, and adhesion strength on the shapes of adhered lipid vesicles. The next step would be a thorough study of the changes in the thermodynamic properties such as the phase behavior of lipid bilayers associated with the lipid bilayer response to the supported nanostructured surface [62].

**Author Contributions:** Conceptualization, A.I.; methodology, W.G., E.G., A.I. and V.K.-I.; software, W.G., E.G. and L.M.; numerical calculations, E.G., J.R. and L.M.; experiments, M.B., I.J. and N.R.; experiments and writing—original draft preparation, A.I., L.M., I.J. and M.B.; writing—review and editing, A.I., L.M., N.R., E.G. and V.K.-I.; visualization, L.M., E.G., I.J., M.B. and J.R.; supervision, A.I., W.G., I.J. and V.K.-I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 801338 (VES4US project) and from grant nos. P2-0232, P3-0388, J3-9262, J1-9162, and J2-8166 from the Slovenian Research Agency (ARRS). This publication is also a part of a project that has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 711859. The scientific work was funded from the financial resources for science in the years 2017–2021 awarded by the Polish Ministry of Science and Higher Education for the implementation of an international co-financed project. WG would like to acknowledge the support from NCN grant No. 2018/30/Q/ST3/00434.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki and approved by Slovenia's Ethics Committee (number of approval; 56/03/10, date of approval; March 2010).

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Marko Jeran for technical assistance.

**Conflicts of Interest:** The authors declare no conflict of interest.
