## 4 Conclusions  
The conclusions from the study are as follows: The vanadium complexes have a stronger effect on the fluidity of the membranes of EYL liposomes compared to DPPC liposomes. This is because the membranes of EYL liposomes at 22 \({}^{\circ}\)C (temperature of the experiment) were in the liquid crystalline phase, while the membranes of DPPC liposomes were in the gel phase. As reported in [38], the surface part of the lipid bilayer of membranes located in the liquid crystalline phase has gaps of different sizes (Figure 12), through which molecules of the vanadium complexes can diffuse deep into the lipid bilayer. In addition, the hydrocarbon chains of the membrane-building lipids are more mobile in the liquid crystalline phase than in the gel phase, which favours the dissolution of the additives. The relationship is clearly illustrated by the graphs shown in Figures 7 and 9. In the liquid crystalline phase, the changes induced by the additives were evident, changing \(\tau/\tau_{0}\) in the 25-35% range. In the gel phase, **V2** and **V1** did not induce any changes in \(\tau/\tau_{0}\) at low concentrations. The negligible effect of the vanadium complexes on the fluidity of the DPPC membranes as compared to the EYL membranes is due to the compact structure of the polar head groups in the gel phase (Figure 12). Computer simulations of this layer [38] show that a number of defects can be formed when the membrane is in the liquid crystalline phase. Given the size and number of such gaps (defects) in the compact structure of the membrane surface, hydrophobic molecules were able to penetrate its interior. The greater influence on the membrane fluidity of the DPPC liposomes of **V3** (Figure 11) is due to its different molecular structure as compared to **V2** and **V1** (Figure 3). It was probably easier for it to pass through the polar head group's region and penetrate into the central part of the lipid bilayer. The exceptionally strong effect of **V1** on the surface layer of EYL liposomes (Figure 8) is due to the presence of a certain pool of relatively weakly bound electrons in the structure of the molecule that can easily interact with the surface region of the membrane. This is shown in Figure 7. For **V1**, the spectral line marked \"0\" corresponds approximately to the value of g = 2 (Table 1), which is typical for weakly bound electrons. The EPR spectra of **V3** and **V2** did not have the line. Figure 11: Effect of the vanadium complexes on the central part of the liposome DPPC membrane, as featured by EPR measurements involving the 16-DOXYL spin label; \(\tau/\tau_{0}\) represents the relative rotational correlation time parameter for spin label; values less than 1 and greater than 1 indicate the increase and decrease in fluidity, respectively. The effect of the vanadium complexes on the fluidity of the liposome membranes strongly depends on the phase. There are two different effects observed for the same complexes: a strong increase in the fluidity of the membranes that were in the liquid crystalline phase and a slight decrease in the fluidity of the membranes that were in the gel phase. Furthermore, the effects of the complexes in the liquid crystalline phase are several times stronger than in the gel phase, which is probably due to the gaps in the polar head group layer. This may have important implications for further research in some areas of medicine and pharmacy (controlled drug release, drug absorption by cells), as well as in the areas of technology involving the transport of active substances across semipermeable membranes. It seems that the critical point here is to precisely control the fluidity of the surface layer of the membranes by controlling the number and size of the gaps. Conceptualization, D.M. ; methodology, D.M. and M.B. ; software, D.M. ; validation, D.M., B.P. and M.B. ; formal analysis, D.M. ; investigation, D.M. and B.P. ; resources, D.M. ; data curation, D.M. and B.P. ; writing--original draft preparation, D.M. ; writing--review and editing, D.M. and B.P.