## 3 Results and Discussion
### Changes in Lipid Order Parameter in P. aeruginosa Cell Membrane
The k\({}_{\rm q}\) values for all studied temperatures (see Table 1) were larger than the maximum collision quenching constants (2 \(\times\) 10\({}^{10}\) M\({}^{-1}\) s\({}^{-1}\)), which suggests that the fluorescence quenching occurs through a static mechanism. It allowed us to conclude that used C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) tannin formed complexes with the membrane proteins of _P. aeruginosa_. Our results are in good agreement with the other works. For example, [PERSON] et al. demonstrated that hydrolysable tannins (PGG, dGVG, and b-dGVG) form complexes with the membrane proteins of _S. mutans_[16]. [PERSON] described that PGG as well as dGVG formed complexes with _S. aureus_ membrane proteins [19] as well as with staphylococcal toxin (alpha-hemolysin) [20]. To find out whether the complex formation between C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) and _P. aeruginosa_ membrane proteins is reversible, the binding constants (log K\({}_{\rm b}\)) were determined (Table 1). The obtained logarithmic values ranged between 5.2 and 5.6, which for non-logarithmic values falls within the range of 10\({}^{4}\)-10\({}^{6}\). The interaction is reversible when non-logarithmic values are between 1 and 15 \(\times\) 10\({}^{4}\) M\({}^{-1}\)[39]. The binding constants obtained, after being converted from logarithmic values, exceed the range of 1-15 \(\times\) 10\({}^{4}\) M\({}^{-1}\), suggesting more \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**C\({}_{55}\)H\({}_{40}\)O\({}_{34}\)**} \\
**Binding Parameters** & & **Temperature [K]** & \\  & **296** & **303** & **310** \\ \hline K\({}_{\rm SV}\) [M\({}^{-1}\)\(\times\) 10\({}^{5}\)] & 1.66 \(\pm\) 0.10 & 1.65 \(\pm\) 0.10 & 1.76 \(\pm\) 0.17 \\ k\({}_{\rm q}\) [M\({}^{-1}\) s\({}^{-1}\)\(\times\) 10\({}^{13}\)] & 3.32 \(\pm\) 0.20 & 3.30 \(\pm\) 0.20 & 3.53 \(\pm\) 0.34 \\ Log K\({}_{\rm b}\) & 5.28 \(\pm\) 0.21 & 5.46 \(\pm\) 0.23 & 5.56 \(\pm\) 0.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Binding parameters of the C\({}_{55}\)H\({}_{40}\)O\({}_{34}\)–protein interaction of _P. aeruginosa_ membranes for C\({}_{55}\)C\({}_{40}\)O\({}_{34}\). Figure 5: (**A**,**C**,**E**) Stern–[PERSON] plots of Trp fluorescence quenching in _P. aeruginosa_ membrane proteins and (**B**,**D**,**F**) double logarithmic plots under C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) at 296 K (23 \({}^{\circ}\)C); 303 K (30 \({}^{\circ}\)C) and 310 K (37 \({}^{\circ}\)C). robust and more durable binding, which could indicate irreversible binding of C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) to the membrane proteins of _P. aeruginosa_. Thermodynamic Parameters of C\({}_{55}\)H\({}_{40}\)O\({}_{34}\)-Membrane Protein Interactions in P. aeruginosa  
Different ligands and biomacromolecules can interact through hydrogen bonds, hydrophobic interactions, van der Waals forces, and electrostatic interactions [40; 41; 42]. To define which type of interaction is responsible for C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) affinity to _P. aeruginosa_ membrane proteins, the thermodynamic parameters (\(\Delta\)H, \(\Delta\)S, \(\Delta\)G) were determined (Table 2) using the Van 't Hoff equation (Equation (6)) and Van 't Hoff plot was shown in Figure 6. Hydrophobic interactions occur when the value of enthalpy (\(\Delta\)H) and entropy (\(\Delta\)S) is positive. On the other hand, if both \(\Delta\)H and \(\Delta\)S have a negative value, it suggests the presence of van der Waals interactions and hydrogen bonds. When \(\Delta\)H < 0, and \(\Delta\)S > 0, then the electrostatic forces are engaged in the interaction [26]. Calculated thermodynamic parameters allowed us to conclude that the interactions between C\({}_{55}\)H\({}_{40}\)O\({}_{34}\) and the _P. aeruginosa_ membrane proteins are the results of hydrophobic interactions (\(\Delta\)H > 0 and \(\Delta\)S > 0), which are observed when a non-polar aromatic ring in phenolic compounds engages in hydrophobic interactions with hydrophobic amino acid residues in proteins [43]. An example is the study by [PERSON] et al.