Figure 4: Electrical circuit diagram of the electrophoresis system.

Legend: 1 – battery, 2 – switch, 3 – potentiometer, 4 – voltmeter, 5 – voltmeter activation switch, 6 – milliammeter, 7 – six-pole switch, 8 – chamber, 9 – non-polarizable electrodes.

The power source consisted of a rechargeable battery with a voltage of 80 V to 100 V. A Rustrat-type rheostat with a resistance of 4 kOhm to 5 kOhm was used as a potentiometer and connected in series. A voltmeter was connected in parallel to the potentiometer. The current was supplied to the measurement chamber via a commutator that allowed for easy reversal of the current direction. The current was applied to non-polarizable electrodes. As shown in the figure, copper conductors were immersed in containers filled with a saturated solution of CuSO₄. These containers were connected to others containing a 10% KCl solution. The latter were connected to the chamber via agar bridges (siphons). A milliammeter with a measuring range of 50 mA to 100 mA was included in the circuit to monitor current intensity. The chamber was placed on the microscope stage, while the non-polarizable electrodes were positioned on a stand on either side of the microscope.

Procedure and calculations

The object of the study was erythrocytes, which were placed into a chamber equipped with non-polarizable electrodes. Cell movement was monitored using a microscope, the eyepiece of which was fitted with a calibrated reticle. The scale calibration of the grid was: 30 divisions=10 µm.

For each blood sample, two in vitro experiments were performed. The first used an untreated blood sample from a patient; the second used the same patient’s blood sample treated with magnetite nanoparticles (MCS-B).

A small volume of blood was diluted in an 8% sucrose solution buffered with McIlvaine’s citrate buffer to prevent the solution from conducting electric current. The pH of the solution was adjusted to 7.4, matching physiological blood pH to avoid hemolysis.

For each sample, seven measurements of erythrocyte velocity were taken in opposite directions relative to the electric current in order to eliminate the effect of surface tilt. The mean value was then calculated.

Calculations were performed according to the following formulas:

where:

ω - electrophoretic mobility (cm/ V·s);

S - distance (in cm) travelled by the particle during time t;

t - time (in seconds);

E - potential gradient, i.e., voltage drop per unit length of the conductor;

U - voltage (in V);

r - distance between the ends of the agar siphons (in cm).

The study was conducted in vitro in three stages:

Stage I - electrophoretic mobility of erythrocytes from healthy donors;

Stage II - baseline electrophoretic mobility of erythrocytes from patients with toxemia syndrome;

Stage III - electrophoretic mobility of erythrocytes from patients after treatment with magnetite nanoparticles (MCS-B).

The optimal effective dose of MCS-B was determined based on erythrocyte electrophoretic mobility under different volume ratios of blood to MCS-B (3:1, 2:1, 1:1).

For an in-depth characterization of erythrocyte surface charge, a modern method for determining ζ-potential was additionally employed using Laser Doppler Electrophoresis (LDE) based on phase-shift light scattering (Malvern Zetasizer Nano ZS). The use of this method allowed for the direct quantitative assessment of erythrocyte membrane ζ-potential, validation of EPM data, and elimination of the influence of medium viscosity and ionic strength. Thus, the combined analysis (EPM + ζ-potential) enables a more accurate interpretation of the electrophoretic properties of erythrocytes.

Method for determining the minimum magnetic field strength required for effective extraction of MCS-B from blood.

MCS-B was introduced in vitro into the blood of practically healthy individuals. Using an external constant magnetic field at different field strengths -100 kA/m to 150 kA/m and 200 kA/m to 250 kA/m (measured with a Tesla ammeter F 4354/1; GOST 5.1977-73) - MCS-B was extracted from the blood plasma mixture within 2-3 minutes.

The effectiveness of MCS-B removal from plasma was assessed by determining the concentration of iron (Fe) in plasma in vitro [23] at three time points: before MCS-B administration, after MCS-B administration, and after its extraction using permanent magnets with field strengths of 100 kA/m to 150 kA/m and 200 kA/m to 250 kA/m.

Statistical analysis

Statistical analysis was performed according to the structure of the dataset, including paired evaluation of erythrocyte electrophoretic mobility (EPM) and ζ-potential.

Assessment of data normality:

• Each variable was tested using the Shapiro-Wilk test.

Comparison between groups:

• For normally distributed data, the student’s t-test was used.
• For non-normally distributed data, the Mann-Whitney U test was applied.

Comparison among multiple groups:

• One-way Analysis of Variance (ANOVA) with Tukey’s post-hoc test was performed.

Effect size:

• Differences were quantified using Cohen’s d.

Correlation analysis:

• The relationship between EPM and ζ-potential was assessed using Pearson’s correlation coefficient (r). For each paired dataset (EPM vs. ζ-potential), both the correlation coefficient (r) and the statistical significance (p-value) were reported.

Statistical significance criterion:

• Two-sided p<0.05 was considered statistically significant.

Research Results and Discussion

Erythrocyte electrophoretic mobility and its dose dependent response to Magnetite Nanoparticles (MCS-B).

The electrophoretic mobility of erythrocytes serves as an indirect indicator of two fundamental physiological parameters:

1. the bioelectrical charge of the erythrocyte membrane, which reflects the functional state and surface potential of red blood cells;
2. the rheological properties of blood, particularly the ease with which erythrocytes move through the vascular system under various flow conditions.

Alterations in electrophoretic mobility may therefore signal changes in membrane integrity, surface charge distribution, or systemic hemorheological status - especially under pathological conditions such as toxemia.

In this study, we investigated the dose-dependent effect of magnetite nanoparticles on erythrocyte electrophoretic mobility in patients with toxemia. The data, presented in Table 8, illustrate the dynamic response of this parameter following exposure to varying blood-to-MCS ratios.

Table 8: Electrophoretic mobility of blood erythrocytes before and after treatment with magnetite nanoparticles (М ± m).

Indicator	Practically Healthy Individuals (n=10)	Patients with Toxemia Syndrome (n=20)
		Primary Data	Variants of Blood-to-MCS Ratio
			03:01	02:01	01:01
Electrophoretic mobility of erythrocytes, 10−4cm2/V·s	3.5×10−4 ± 0.2	1.26×10−4 ± 0.2	2.70×10−4 ± 0.2	3.76×10−4 ± 0.2	3.8×10−4 ± 0.2
		P<0.01	P<0.05	P>0.05	P>0.05
			P1<0.01	P1<0.001	P1<0.001
				P2<0.05	P2<0.05
					P3>0.05

The data presented in Table 8 indicate that, in donors (practically healthy individuals), the erythrocyte Electrophoretic Mobility (EPM) was 3.5 × 10-4 ± 0.2 cm2/V·sec, whereas in patients with toxemia syndrome (main group), the baseline value was 1.26 × 10-4 ± 0.2 cm2/V·sec.

As a result of blood treatment with magnetite nanoparticles (MCS-B) at a ratio of 3 parts blood to 1-part MCS-B, EPM significantly increased compared to baseline (p<0.01), yet remained significantly different from the normal reference values (p<0.05).

All values are presented as mean ± standard deviation. Statistical significance was determined using Student’s t-test; P<0.05 was considered significant.

At the ratios of 2:1 and 1:1, the EPM decreased even more significantly compared to baseline values (p<0.001) and no longer differed from the normal range (p>0.05). It should also be noted that no statistically significant difference was found between the 1:1 and 2:1 ratio (p>0.05).

Thus, the optimally effective dose of magnetite nanoparticles for improving erythrocyte electrophoretic mobility is the 2:1 ratio (two parts blood to one-part MCS-B). The observed changes provide insight into the potential of magnetite nanoparticles to modulate cell surface charge and improve microcirculatory flow.

The electrophoretic mobility indices of erythrocytes (mean ± standard deviation) in healthy individuals and patients with toxemia before and after treatment with magnetite nanoparticles at different ratios of blood and MCS-B are presented in Figure 5.

Figure 5: Electrophoretic mobility of erythrocytes at different experimental stages (mean ± SEM).

To visually illustrate the treatment effect, Figure 6 depicts the morphofunctional state of erythrocytes in heparinized blood from a patient with toxemia syndrome, before and after in vitro exposure to MCS-B at a blood-to-sorbent ratio of 2:1.

Figure 6 illustrates pronounced morphological changes in erythrocytes from heparinized blood of a patient with toxemia syndrome before and after in vitro treatment with the nanodrug MCS-B. Following exposure, a resolution of erythrocyte sludging, restoration of the normal discocyte shape, and an increase in the electronegativity of the cell surface were observed. These findings indicate a reestablishment of erythrocyte dispersion and normalization of blood rheological properties.

Figure 6: Morphology of erythrocytes in heparinized blood from a patient with toxemia syndrome, before and after in vitro treatment with MCS-B (blood-to-MCS ratio 2:1).

Based on the Electrophoretic Mobility (EPM) data of erythrocytes, a study of membrane ζ-potential was conducted to quantitatively assess the cells’ surface charge. The ζ-potential values enabled the comparison of changes in the electrical properties of the membranes with the functional EPM parameters. Effect size was determined using Cohen’s d, calculated from the difference between baseline and post-MCS-B treatment means with the pooled standard deviation. While d values above 0.8 are considered large, the observed values (d>2.0) reflect an exceptionally strong effect. The magnitude of erythrocyte ζ-potential changes and Cohen’s d effect sizes across study groups following MCS-B treatment is presented in Table 9.

Table 9: Magnitude of erythrocyte ζ-potential changes and Cohen’s d effect sizes across study groups following MCS-B treatment (in vitro, n=30).

Group	ζ-potential (mB), mean ± SD	95% CI	Cohen's d (vs baseline)
Healthy donors (n=10)	-18.5 ± 1.8	[-19.8; -17.2]	-
Patients with toxemia (baseline, n=20)	-11.2 ± 2.0	[-12.1; -10.3]	-
Post-MCS-B (3:1)	-15.4 ± 1.9	[-16.3; -14.5]	2.16
Post-MCS-B (2:1)	-18.0 ± 1.7	[-18.8; -17.2]	3.44
Post-MCS-B (1:1)	-18.2 ± 1.6	[-18.9; -17.5]	3.61

The data in Table 9 demonstrate a comparable dose dependent trend. Patients with toxemia exhibited a pronounced decrease in ζ-potential (-11.2 mV ± 2.0 mV), whereas treatment with MCS-B restored it to values not statistically different from controls at ratios of 2:1 and 1:1. The effect size was extremely large (Cohen’s d=2.16-3.61), indicating a marked modulation of erythrocyte membrane surface charge.

For each data pair (EPM ↔ ζ-potential), the Pearson correlation coefficient (r) and the corresponding p-value were calculated, providing an assessment of the strength and statistical significance of the relationship between the parameters. Summary results are presented in Table 10, including means, standard deviations, and correlation coefficients for all studied groups.

The Table 10 data demonstrate a strong linear correlation between erythrocyte Electrophoretic Mobility (EPM) and ζ-potential (r=0.98, p<0.001) with a determination coefficient of R2=0.96. Linear regression analysis yielded the equation ζ=-2.84 × EPM - 8.63, indicating that EPM reliably reflects membrane surface charge. Percentage changes (Δ%) were calculated relative to the baseline intoxication level. Notably, MCS-B treatment resulted in a dose-dependent recovery of both parameters, with EPM values slightly exceeding control values at 2:1 and 1:1 ratios, indicating enhanced membrane electrokinetic activity.

Table 10: EPM, ζ-potential and normalized changes after MCS-B treatment*.

Group	EPM (×10-4 cm2/V·s)	ζ-potential (mV)	ΔEPM (%)	Δζ (%)
Control (donors)	3.5	-18.5	-	-
Toxemia (baseline)	1.26	-11.2	-64.00%	-39.50%
MCS-B (3:1)	2.7	-15.4	114.30%	37.50%
MCS-B (2:1)	3.76	-18	198.40%	60.70%
MCS-B (1:1)	3.8	-18.2	201.60%	62.50%

For clarity, the correlation between erythrocyte electrophoretic mobility and ζ-potential is shown in Figure 7.

Figure 7: Correlation between electrophoretic mobility and ζ-potential.

Abbreviations: Donors, healthy controls; Baseline, toxemia (initial).

Figure 7 clearly demonstrates an almost perfect inverse correlation between erythrocyte Electrophoretic Mobility (EPM) and ζ-potential (Pearson correlation coefficient r=-0.987, R2=0.975, p<0.001), indicating a very strong relationship between membrane surface charge and the electrokinetic behavior of erythrocytes. Data points represent healthy donors, baseline toxicosis, and post-treatment conditions at different MCS-B ratios (3:1, 2:1, 1:1).

Linear regression analysis showed that the restoration of electrophoretic mobility is directly associated with normalization of the ζ-potential to physiological values.

No statistically significant deviations from linearity were observed, ruling out substantial effects of nonlinear factors such as changes in medium viscosity or ionic strength.

Overall, more than 97% of the variability in ζ-potential is explained by changes in EPM, confirming that the primary mechanism of MCS-B action is the restoration of erythrocyte membrane surface charge rather than modification of plasma rheological properties. In vitro treatment with magnetite nanoparticles (MCS-B) resulted in near-complete recovery of both EPM (94.4%) and ζ-potential (95.1%), indicating restoration of erythrocyte electrostatic stability.

Restoration of the electrokinetic properties of erythrocyte membranes, as evidenced by the near-perfect correlation between ζ-potential and EPM, reduces intercellular aggregation and eliminates the sludging phenomenon. This improves erythrocyte deformability and passage through the microcirculation, thereby directly enhancing capillary perfusion and oxygen delivery to tissues.

Numerous clinical observations of MCS-B use as an extracorporeal hemoadsorbent confirm that its therapeutic effects in endogenous intoxication are primarily mediated through restoration of erythrocyte membrane surface charge. This is particularly evident in the treatment of sepsis, multiple organ dysfunction syndrome, and severe inflammatory conditions.

Thus, MCS-B can be considered a pathophysiologically justified and effective agent for pathogenetic therapy of severe toxemias, which are accompanied by pronounced hemorheological disturbances and impaired oxygen delivery to tissues.

Physiological model of the protective mechanisms of MCS-B of MCS-B on erythrocyte membranes in toxemia is based on previously reliably obtained data:

I. Membrane restoration and detoxification.

Magnetite nanoparticles (MCS-B) effectively adsorb circulating toxins, lipid peroxidation products, and reactive oxygen species [30]. This contributes to the stabilization of the erythrocyte membrane lipid bilayer and the restoration of activity of membrane-associated enzymes such as Na+/K+-ATPase [31]. Restoration of the structural and functional integrity of the membrane is essential for the normal function of glycolytic enzymes that support erythrocyte energy metabolism [32].

II. Reactivation of glycolytic enzymes.

• By correcting ionic balance, pH, and redox potential, glycolytic enzymes regain activity.
• Glycolytic flux increases → more ATP and 1,3-BPG are produced.
• 1,3-BPG is then diverted both to ATP production and to the Rapoport shunt → simultaneous increase in ATP and 2,3-DPG.

III. Restoration of Metabolic Balance.

• After membrane and redox normalization, erythrocytes can resume adaptive responses to hypoxia or acidosis, increasing 2,3-DPG.
• At the same time, global glycolytic output ensures that ATP levels are restored to physiological range.
• This paradox - concurrent increase of both ATP and 2,3-DPG - is possible only after reversal of toxic suppression.

The combined protective mechanisms of MCS-B action on erythrocyte membranes under conditions of toxemia are summarized in Table 11.

Table 11: Summarizes the integrated protective mechanisms exerted by MCS-B on erythrocyte membranes in the setting of toxemia.

Parameter	Before Treatment (Toxemia)	After Magnetite Exposure
Membrane potential	Disrupted	Restored
Glycolytic activity	Suppressed	Re-activated
ATP	Decreased	Increased
2,3-DPG	Decreased or unstable	Increased
Electrophoretic mobility	Impaired	Restored

The aforementioned mechanisms are supported by previous studies in patients with toxemia, which reliably demonstrated a significant decrease in ATP and 2,3-DPG levels due to a generalized suppression of anaerobic glycolysis in erythrocytes [33,34]. Treatment of blood with magnetite nanoparticles (MCS-B) promotes the effective removal of circulating toxic substances, protects and restores the structural integrity of erythrocyte membranes, and stimulates the activation of key enzymes in the glycolytic pathway [32,35]. This leads to simultaneous restoration of ATP and 2,3-DPG concentrations, which, despite their inverse correlation under physiological conditions, reflects the recovery of metabolic potential and energy homeostasis in the pathological state of toxemia [36,37]. Improvement in cellular energetic status induces modulation of the bioelectrical charge on the erythrocyte outer membrane, contributing to normalization of their electrophoretic mobility, reduction of aggregation, and enhancement of microcirculation.

In the present in vitro study, MCS-B was shown to restore erythrocyte electrophoretic mobility and ζ-potential, as well as normalize discoid morphology. Based on these results and literature data [38-42], it can be concluded that the primary interaction of MCS-B with erythrocytes occurs via surface adsorption onto the membrane, which stabilizes the lipid bilayer and the bioelectric charge of the membrane.

No direct evidence of nanoparticle endocytosis by erythrocytes was observed. The physicochemical properties of MCS-B (negative ζ-potential of -19 mV, size 6 nm to 12 nm, high magnetic responsiveness) and the in vitro experimental results support that the nanoparticles predominantly remain on the membrane surface and can be effectively removed by an external magnetic field.

Thus, membrane adsorption represents the primary and clinically relevant mode of MCS-B interaction with erythrocytes, whereas endocytosis was not detected and, according to the literature, is unlikely for mature erythrocytes.

Determination of magnetic field intensity capable of removing Magnetite Nanoparticles (MCS-B) from blood.

The plasma iron concentrations in practically healthy individuals in vitro at different stages of the study are presented in Table 12.

Table 12: Plasma Fe levels in practically healthy individuals in vitro at different stages of the study (n=10; M ± m).

Study Stage	Plasma Fe Level (nmol/L, mean ± SD)	p-value
Before MCS-B administration	124.3 ± 25.6	-
After MCS-B administration	656.3 ± 31.3	<0.001
After exposure to constant magnetic field (2-3 min):
• 100 kA/m -150 kA/m	214.3 ± 25.6	<0.05
• 200 kA/m -250 kA/m	127.4 ± 24.1	>0.05

As shown in Table 6, exposure of blood plasma from practically healthy individuals to a constant magnetic field with an intensity of 100 kA/m 150 kA/m for 2-3 minutes resulted in a statistically significant reduction in plasma iron concentration (p<0.05) compared to post-MCS-B administration values. Nevertheless, the iron level remained significantly elevated relative to baseline, suggesting only partial removal of MCS-B from the plasma under these conditions.

Conversely, application of a stronger magnetic field (200 kA/m to 250 kA/m) for the same duration led to a near complete normalization of plasma iron levels. No statistically significant differences were observed between these post-exposure values and the baseline data (p>0.05), indicating effective elimination of MCS-B from the plasma.

These findings support the hypothesis that magnetically controlled removal of MCS-B is both intensity-dependent and reversible. Specifically, magnetic fields of 200-250 kA/m are capable of achieving highly significant clearance of MCS-B nanoparticles from plasma within 2-3 minutes (p<0.001), confirming the feasibility of external magnetic modulation in regulating the biodistribution of magnetite based nanomaterials.

Safety and regulatory considerations of MCS-B.

This study did not address the toxicity of MCS-B, as it utilized a clinically approved and safe dosage form and a well-established method of administration, both officially approved by the Ministry of Health of Ukraine in 2004. MCS-B, the world’s first magnetite nanoparticle-based sorbent, has over 30 years of extensive experimental and clinical studies confirming its safety and efficacy.

However, it should be emphasized that the overall toxicity of nanoparticles depends on numerous physicochemical characteristics (composition, size, coating, dose, route of administration, sorption capacity, polarizing properties, etc.). Accordingly, the regulatory assessment of nanomedicines is based on function, application, and mechanism of action and includes a comprehensive assessment of safety, quality, and efficacy. In each case, MCS-B complies with national and international regulatory standards, ensuring strict control and confirmed biocompatibility.

Conclusions

1. Biocompatible magnetite nanoparticles (MCS-B) effectively restore erythrocyte Electrophoretic Mobility (EPM) in toxemia, representing a novel targeted approach.
2. In vitro treatment with MCS-B increased erythrocyte Electrophoretic Mobility (EPM) from 1.26 × 10-4cm2/V·s to 3.76 × 10-4cm2/V·s at a 2:1 blood-to-nanoparticle ratio, corresponding to a 198.4% increase (p<0.001), nearly threefold relative to the toxemia baseline.
3. Membrane ζ-potential was restored toward normal (Δζ=+60.7%), with a strong correlation between EPM and ζ-potential (r=0.91-0.95; Cohen’s d>1.2).
4. Maximal efficacy was achieved at a 2:1 ratio; intermediate effects were observed at 3:1 and 1:1 ratios.
5. Application of a constant magnetic field (200 kA/m to 250 kA/m, 2-3 min) allows efficient removal of MCS-B from blood (p<0.001).
6. The innovation lies in controllable nanostructures with defined magnetic and surface properties to modulate bioelectrical membrane properties.

This approach has no direct analogues in current clinical practice and provides a foundation for novel therapeutic strategies in transfusion medicine, intensive care, and regenerative medicine.

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