**4. Discussion**

The natural cell lipid bilayer is a complex and dynamic protein-lipid structure. The complexity of biological membranes determines many equilibria, both between the membrane components and between cell membranes and the surrounding ions. Particularly important to the cell's functioning are the equilibria between the membrane and the surrounding aqueous solution. The ions present in the solution, adsorbing on the membrane, modulate many of its physicochemical and electrical properties, such as electric charge. Due to the lack of literature data on the effect of fatal poisoning with ethyl alcohol on the equilibria between blood cell membranes and their surroundings, we adopted the theoretical model proposed by Dobrzy ´nska et al. [32] (presented in full detail in [24]) to describe these equilibria. The given model allowed us to verify the theoretical data with experimental data.

Equations (1)–(7) describe the assumptions of the presented model. H<sup>+</sup> , OH−, Na<sup>+</sup> , and Cl− ions from the electrolyte solution adsorb at the erythrocytes' and thrombocytes' surface. Two of the four equilibria described are associated with positive groups (phospholipids or proteins and sodium or hydrogen ions). The other two are associated with negative groups on the phospholipids' or proteins' surface and hydroxide or chloride ions. The equations of adsorption of H<sup>+</sup> , OH−, Na<sup>+</sup> , and Cl− ions on functional groups located on the membrane surface are presented in Equations (1)–(4):

$$\text{A}^- + \text{H}^+ \Leftrightarrow \text{AH} \tag{3}$$

$$\rm{A}^- + \rm{Na}^+ \Leftrightarrow \rm{ANa} \tag{4}$$

$$\rm B^{+} + OH^{-} \Leftrightarrow BOH \tag{5}$$

B <sup>+</sup> + Cl<sup>−</sup> <sup>⇔</sup> BCl (6)

$$c\_A = a\_{A^-} + a\_{AH} + a\_{ANa} \tag{7}$$

$$c\_B = a\_{B^+} + a\_{B\!\!\!
\/ ,H} + a\_{B\!\!\!
\/ ,\!\/} \tag{8}$$

$$\delta = (a\_{B^+} - a\_{A^-}) \cdot F \tag{9}$$

where *aAH*, *aANa*, *aA*<sup>−</sup> , *aBOH*, *aBCl*, and *aB*<sup>+</sup> are the surface concentrations of the corresponding groups on the membrane surface; *aH*<sup>+</sup> , *aNa*<sup>+</sup> , *aOH*<sup>−</sup> , and *aCl*<sup>−</sup> are the volume concentrations of solution ions; *c<sup>A</sup>* is the total surface concentration of the membrane acidic groups; *<sup>c</sup><sup>B</sup>* is the total surface concentration of the membrane basic groups, *<sup>F</sup>* <sup>=</sup> 96, 487 <sup>h</sup> *C mol* <sup>i</sup> is the Faraday constant; and *δ* is the surface charge density.

Final equations [24,32]:


$$\frac{\delta}{F} = \frac{\mathcal{C}\_B}{1 + K\_{BOH}a\_{OH^-} + K\_{BCl}a\_{Cl^-}} - \frac{\mathcal{C}\_A}{1 + K\_{AH}a\_{H^+} + K\_{ANd}a\_{Na^+}} \tag{10}$$


$$\frac{\delta a\_{H^{+}}}{F} = \frac{\mathbb{C}\_{B}}{1 + K\_{B \gets I} a\_{Cl^{-}}} a\_{H^{+}} - \left( \frac{\mathbb{C}\_{B} \mathbb{K}\_{B \gets H} \mathbb{K}\_{W}}{\left(1 + K\_{B \gets I} a\_{Cl^{-}}\right)^{2}} + \frac{\mathbb{C}\_{A}}{\mathbb{K}\_{AH}} \right) \tag{11}$$

$$\frac{\delta}{\delta a\_{H^{+}}} = -\left(\frac{\mathcal{C}\_{A}}{1 + K\_{ANd}a\_{Na^{+}}}\right)\frac{1}{a\_{H^{+}}} + \left(\frac{\mathcal{C}\_{B}}{K\_{BOH}K\_{W}} + \frac{\mathcal{C}\_{A}K\_{AH}}{\left(1 + K\_{ANd}a\_{Na^{+}}\right)^{2}}\right) \tag{12}$$

where *KAH*, *KANa*, *KBOH*, and *KBCl* are association constants.

The above linear function coefficients can be easily determined using the linear regression method and then used to calculate the membrane parameters (Equations (9) and (10)). The necessary parameters are the total concentrations of functional acidic (*cA*) and basic (*cB*) groups on the blood cell surfaces and their average association constants with hydrogen (*KAH*) and hydroxyl (*KBOH*) ions. Determination of all the necessary parameters was possible only based on the assumption that the association constant values *KANa* and *KBCl* are the same as the values obtained for phosphatidylcholine liposomes. The *KANa* and *KBCl* values of the surface groups of phosphatidylcholine with sodium and chloride ions were reported previously and amount to 0.230 and 0.076 [m3/mol], respectively [18]. To calculate the theoretical values of the erythrocyte and thrombocyte membranes' surface charge density, the values of *cA*, *cB*, *KAH*, and *KBOH* were determined and substituted into Equation (8).

The comparison of the experimental (calculated from Equation (11)) and theoretical (calculated from Equation (8)) surface charge density values of the erythrocyte and thrombocyte membranes versus pH are presented in Figures 3 and 4 (the points indicate the experimental data and the curves indicate theoretical data).

The following conclusion can be drawn from the curves presented in Figures 3 and 4: There is an agreement between the theoretical and experimental values in the pH range of 2–7. Above pH 7, the theoretical curves differ from the experimental points. Variations at pH above 7 may be caused by interactions between the functional groups of the cell membranes of blood morphotic elements. The mathematical model we proposed takes into account only the equilibrium of the membrane surface with electrolyte ions.

In Tables 3 and 4, we summarize the obtained values of the parameters characterizing the equilibria between the erythrocyte and thrombocyte surfaces. The presented results were analyzed using standard statistical analysis and are expressed as means with standard deviations. The effect of fatal alcohol poisoning on erythrocyte and thrombocyte membranes caused changes in the values of the calculated parameters (*cA*, *cB*, *KAH*, and *KBOH*) (Tables 3 and 4).

**Figure 3.** A comparison of experimental and theoretical surface charge density values of erythrocytes vs. pH of the electrolyte solution: • control, fatal ethyl alcohol poisoning. Points represent the experimental values and curves represent theoretical values.

**Figure 4.** A comparison of experimental and theoretical surface charge density values of thrombocytes vs. pH of the electrolyte solution: • control, fatal ethyl alcohol poisoning. Points represent the experimental values and curves represent theoretical values.


**Table 3.** The acidic and basic total concentrations of functional groups of erythrocytes and their association constants with H<sup>+</sup> and OH− ions.

**Table 4.** The total acid and base concentrations of the functional groups of thrombocytes and their association constants with H<sup>+</sup> and OH− ions.


In this study, the *cA*, *KAH*, and *KBOH* values for an erythrocyte cell membrane were affected by ethyl alcohol and were smaller than the same parameters assayed in unmodified cells; only *c<sup>B</sup>* values were higher (approximately double, Table 3).

In the case of a thrombocyte cell membrane, the *cA*, *KAH*, and *KBOH* parameters were affected by ethyl alcohol and were higher than the same parameters assayed in unmodified cells. Only *c<sup>B</sup>* values were smaller, by about seven times (Table 4).

Alcohol intoxication causes changes in the amounts of both phospholipids and integral proteins of erythrocyte membranes [17], resulting in the appearance of new negatively and positively charged functional groups. Therefore, variations in the kind and number of these groups result in changes in the parameters describing equilibria in cell membranes: *cA*, *cB*, *KAH*, and *KBOH*. It is believed that other mechanisms can also influence the above parameters, such as the movement of molecules forming membranes between monolayers (the flip-flop phenomenon) or the appearance of receptor proteins or their components on the surface of cell membranes, which, as a result of stopped life processes, no longer perceive signals from the external environment and remain in an inactive form. Scheidt and Huster [33] demonstrated that ethyl alcohol partitions the lipid–water interface of the phospholipid bilayer by forming hydrogen bonds with lipid molecules and, also, by the hydrophobic effect. Rowe showed that at a higher ethanol concentration, a significant reduction (up to 30%) in phosphatidylcholine lipid membrane thickness is observed as it transitions into the interdigitated phase [34]. In natural lipid membranes, ethanol-induced membrane perturbations may have many possible effects. A considerable reduction in membrane thickness caused by lipid interdigitation would likely profoundly affect membrane protein function and conformation [35]. Membrane thickness changes can result in the exposure of hydrophobic amino acid residuum in integral proteins of the membrane and an occurrence like a hydrophobic mismatch, leading to membrane protein aggregation [36] and possibly producing a conformational change in the membrane protein [37]. Zeng et al. [38] demonstrated that ethanol-induced fluidization and interdigitation of the lipid bilayer lead to an increase in the membrane's ion permeability. Lee [39] examined the effects of ethanol exposure on human erythrocytes using quantitative phase imaging techniques at the level of individual cells. The author demonstrated that erythrocytes exposed to ethanol (at concentrations of 0.1 and 0.3% *v*/*v*) exhibited cell sphericities higher than those of normal cells. Bulle and co-workers [40] studied the association between erythrocyte membrane alterations and hemolysis in chronic alcoholics. They showed that frequent alcohol consumption increases oxidative/nitrosative stress. The result is a change

in the lipid composition of the erythrocyte membrane and the protein content, resulting from increased hemolysis.

There are no data on ethyl alcohol's effect on blood platelets' electrical properties in the literature. Slowed blood flow in ethyl alcohol poisoning promotes platelet activation, leading to changes in the exposure of phospholipids (phosphatidylserine and phosphatidylethanolamine) in the clotting process to the surface of the cell membrane. Since phospholipids are endowed with an electric charge, we believe that their presence in the membrane will result in changes in the surface charge density and, consequently, the determined parameters (*cA*, *cB*, *KAH*, and *KBOH*).
