The Toxic Influence of Excess Free Iron on Red Blood Cells in the Biophysical Experiment: An In Vitro Study

Iron is needed for life-essential processes, but free iron overload causes dangerous clinical consequences. The study of the role of red blood cells (RBCs) in the influence of excess free iron in the blood on the pathological consequences in an organism is relevant. Here, in a direct biophysical experiment in vitro, we studied the action of free iron overload on the packed red blood cell (pRBC) characteristics. In experiments, we incubated pRBCs with the ferrous sulfate solution (Fe2+). Wе used free iron in a wide range of concentrations. High Fe2+ concentrations made us possible to establish the pattern of the toxic effect of excess iron on pRBCs during a reduced incubation time in a biophysical experiment in vitro. It was found that excess free iron causes changes in pRBC morphology, the appearance of bridges between cells, and the formation of clots, increasing the membrane stiffness and methemoglobin concentration. We created a kinetic model of changes in the hemoglobin derivatives. The complex of simultaneous distortions of pRBCs established in our experiments can be taken into account when studying the mechanism of the toxic influence of excess free iron in the blood on pathological changes in an organism.


Introduction
Iron is a significant metal for various processes in biological systems, but there is no active mechanism for the excretion of excess iron from the body under conditions of iron overload (hemochromatosis) [1][2][3].
In these cases, RBCs are the key elements. erefore, we raised a question what is happening or can potentially happen in RBCs under toxic influence of free blood iron. e changes in RBC morphology after influence of iron on them are shown in a number of scientific articles. ere are studies that have established a change in the morphology of RBCs in vitro as a result of the action of free iron ions in high concentrations. e shape change was observed in the blood of people with hemochromatosis [36,42].
As a rule, RBC shape distortion and an increase in their membrane stiffness are associated with the acceleration of oxidative processes under the action of physical and chemical factors [43][44][45][46].
Free iron is potentially extremely toxic due to its ability to generate reactive oxygen species (ROS), which are involved in various redox processes [9,31,[47][48][49]. One of the consequences and at the same time a biomarker of the development of oxidative processes in the blood is the formation of methemoglobin (MetHb) [50,51].
In this work, we conducted direct biophysical experiments to solve the problem of revealing and quantitative estimation of toxic effects of free iron on pRBCs in an in vitro model. Wf used free iron in a wide range of concentrations. High Fe 2+ concentrations made us possible to establish the pattern of the toxic effect of excess iron on pRBCs during a reduced incubation time in a biophysical experiment in vitro. For quantitative registration of pRBC modifications, we used atomic force microscopy (AFM). Atomic force spectroscopy (AFS) allowed us to measure the local Young's modulus of native membranes. High-resolution digital spectroscopy and the nonlinear curve fitting method for the analysis of optical spectra allowed us to experimentally establish the kinetics of MetHb formation under the influence of excess Fe 2+ . We created a mathematical kinetic model of changes in the concentrations of Fe 2+ and hemoglobin derivative concentrations, which adequately describes the experimental data and allows to estimate the rate constants of redox processes.

Blood Products.
Packed red blood cells were obtained from the clinical centers of blood transfusion in Moscow, Russian Federation. All of the experiments were conducted in accordance with guidelines and regulations of the Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology, V.A. Negovsky Scientific Research Institute of General Reanimatology, Moscow, Russian Federation. All of the experimental protocols were approved by this institute.
A total of 5 bags with pRBCs were used in the study. pRBC units were prepared from the whole blood (450 ml ± 10%) by removing the plasma fraction after centrifugation. Leukocytedepleted pRBCs in airtight bags were stored with standard CPD anticoagulant (63 ml) (citrate, phosphate, and dextrose) and SAGM additive solution (100 ml) (saline, adenine, glucose, and mannitol) at a temperature of +4°S. e hematocrit of the pRBCs was 60-65%. Samples of pRBCs for in vitro experiments were withdrawn on days 3-5.
Stages of the study are shown in detail in Figure 1.  B). e initial concentration of Fe 2+ in lysate/suspension was 1700 μM, and this is designated as Fe 2+ 1700. To study the influence of Fe 2+ in initial various concentrations, we changed solution A to receive C Fe 2+ from 212.5 to 13600 μM. Wf used free iron in a wide range of concentrations C Fe 2+ .

Preparation of
High Fe 2+ concentrations make it possible to establish the pattern of the toxic effect of excess iron on pRBCs during a reduced incubation time in a biophysical experiment in vitro.

pRBC Lysate and Suspension Preparation In Vitro.
To prepare the lysate and suspension of pRBCs in vitro, the components of the solution in which the pRBCs were stored were removed. To do this, 200 μl of pRBCs was washed in 1 ml of phosphate buffer saline (PBS) at pH 7.4 (MP Biomedicals, France).
is suspension was centrifuged at 2,000 rpm for 5 minutes in a Universal 320 centrifuge (Andreas Hettich GmbH & Co. KG, Germany). is procedure was carried out twice. en, the lysate (L) was prepared by mixing 15 μl of pRBCs and 100 μl of distilled water, and the pRBC suspension (S) was prepared by mixing 15 μl of pRBCs and 100 μl of PBS. en, 100 μl of lysate/ suspension were diluted in 4.1 ml of solution B. e time of iron interaction with pRBCs was named as the incubation time and designated as t inc . Stages of the experiment are shown in Figures 1(b) and 1(c).

Spectrophotometry.
For the spectrophotometry study, 100 μl of lysate was diluted in 4 ml of distilled water, or 100 μl of suspension was diluted in 4 ml of PBS with 100 μl solution A as shown in Figures 1(b) and 1(c). e working solution with ferrous sulfate and lysate was designated as LFe 2+ 1700, and the similar suspension solution was designated as SFe 2+ 1700; the solution without ferrous sulfate for lysate was designated as LFe 2+ 0, and the suspension was designated as SFe 2+ 0. e incubation times of the lysate of pRBCs were 0, 15, 30, 45, 60, 90, 120 min, and 24 hours, and for the suspension of pRBCs, the incubation times were 1, 5, and 24 hours.
To determine the concentration of hemoglobin derivatives, the optical absorption spectra were measured using a Unico 2800 digital spectrophotometer (United Products & Instruments, USA). e experimental spectrum D(λ) exp was measured in the wavelength range of 500-700 nm with steps of 0.5 nm. e concentrations of hemoglobin derivatives (HbO 2 , Hb, and MetHb) were measured according to their individual absorptivities at different wavelengths using the nonlinear curve fitting method of experimental spectra.

Nonlinear Curve Fitting Optical Spectra.
For the determination of hemoglobin derivatives, the nonlinear curve fitting method was used as described in [52,53]. Briefly, it is necessary to experimentally obtain the set of optical densities measured at corresponding wavelengths D l (λ l ) exper , where l is the number of wavelengths and λ l is the set of wavelengths. en, we define our own function D l (λ l ) theor by using Origin's flexible Fitting Function Builder by Origin Pro 2019 (OriginLab Corporation, USA): (1) In this equation, there are known values: molar absorptivity coefficients at given wavelengths λ l (ε HbO 2,l , ε Hb,l , and ε MetHb,l ) [50] and the thickness of the layer L. ere are also unknown values: concentrations of corresponding hemoglobin derivatives (C HbO 2 , C Hb , and C MetHb ) and coefficients of scattering (K and S). ese parameters must be determined by fitting the model. is function is created according to biophysical considerations. Because red blood cells are studied in PBS, it is necessary to consider not only the absorption but also the scattering processes. e intensity of these processes will be different for various wavelengths. e coefficient K describes the scattering of light on pRBCs when the wavelength is smaller than the diameter of pRBCs, λ ≪ d.
e coefficient S corresponds to Rayleigh scattering when the scattering particles are very small, λ ≫ d ′ . In the nonlinear curve fitting model, the experimental optical density data (D l (λ l ) exper ) are used instead of D l (λ l ) theor . Computing the fitted values in nonlinear regression is an iterative procedure performed using the Levenberg-Marquardt algorithm. Iteration to adjust parameter values continues to make data points closer to the theoretical curve. e adjusted R-squared is the measure of the goodness of fit.     e concentration of total hemoglobin C total is the sum of hemoglobin derivative concentrations, in mmol/l. e percentage of each derivative in pRBCs is the ratio, particularly,

Kinetic Model of Change of Hemoglobin Derivative
Concentrations under the Influence of Fe 2+ . e mathematical modeling was used to study the dynamics of the increase in the concentration of MetHb under the actions of ferrous sulfate solution in different concentrations. e kinetics of the Fe 2+ and H 2 O 2 interaction as well as the kinetics of an increase in the concentration of MetHb are analyzed. Based on the law of mass action, ordinary differential equations describing the kinetics of chemical reactions were recorded. e kinetic equations were solved using the method of separation of variables, taking into account the initial conditions. Details of the model are given in the text. e obtained theoretical dependence C MetHb theor (t) was used as the basis for the approximation of the experimental data C MetHb exper (t). As a result, the unknown parameters of the approximation were estimated-the rate constants of the reactions and the concentration of H 2 O 2 .

Atomic Force Microscopy.
To obtain images of cells, a smear of pRBC was formed. First, 4.2 ml of pRBC suspension (SFe 2+ 0 and SFe 2+ 1700) was sedimented by centrifugation at 2,000 rpm for 5 minutes. Next, 50 μl of 1% glutaraldehyde solution (Panreac Quimica S.L.U., Spain) was added to 50 μl of sediment for 4 minutes. To wash the cells, 500 μl of distilled water was added to the pRBC suspension. After centrifugation at 2,000 rpm for 5 minutes, the supernatant was removed and 300 μl of distilled water was added. en, the sample was centrifuged again, and the supernatant was removed. e smear of sediment was prepared using V-sampler (Vision, Austria).
For the analysis of cell morphology, an NTEGRA Prima atomic force microscope (NT-MDT Spectrum Instruments, Russian Federation) was used. Scanning was carried out in semicontact mode with the NSG01 probe (probe radius 10 nm, resonance frequency 87-230 kHz, and force constant 1-15 N/m) (TipsNano, Estonia). During scanning, fields with sizes of 50 × 50 μm 2 , 30 × 30 μm 2 , and 10 × 10 μm 2 were selected. e number of dots per line was 1024. e characteristic incubation times for pRBC samples were 1, 5, and 24 hours. Various concentrations of ferrous sulfate were studied. For each incubation time and concentration of ferrous sulfate, images and their profiles were obtained, which made it possible to estimate the spatial characteristics: L is the spatial period between the minima of the structure, and h is the average height from the concaves to the maxima. e SPM Nova software (NT-MDT Spectrum Instruments, Russian Federation) was used to record AFM images.

Atomic Force Spectroscopy.
e stiffness of pRBC membranes is characterized by Young's modulus (E). e method of sedimentation was used to prepare the sample. To do this, 300 μl of pRBC suspension (SFe 2+ 1700 and SFe 2+ 0) was applied to glass coverslips coated in poly-L-lysine hydrobromide (MP Biomedicals, France) and was left for 30 minutes for adhesion. en, the coverslips were washed in PBS. For this, the type of cantilever SD-R150-T3L450B-10 (Nanosensors, Switzerland) was used (probe radius 150 nm, resonance frequency 21 kHz, force constant 1 N/m). Force curves were measured only on native cells, without adding chemical fixatives. Measurements were carried out after 1 and 24 hours.

Statistical Analysis.
For each bag, 3 smears of pRBCs were prepared. On each smear, 3 fields of 50 × 50 μm 2 were scanned. For one bag, morphology analysis was carried out for an average of 500 cells. In total, approximately 2500 cells were studied. For each bag, 100 force curves were measured for one sample. A total of 2000 pRBCs were analyzed in the study. For each blood sample for spectrophotometry, the experiments were performed three times.
Statistical processing was performed using the Origin Pro 2019 software. All data are presented as the mean ± SD, and replicate information is indicated in the figure legends. e normality Shapiro-Wilk test for all data was used. e one-way ANOVA test followed by the Tukey's post hoc test for experimental data comparison was used. Pearson correlation analyses were performed to determine the close relationships between MetHb level, hemolysis level, and the average number of discocytes on a smear.

RBCs as a Possible Key Link in the Adverse Effect of Excess
Free Iron. Various primary factors F i (frequent blood transfusion F 1 , hereditary hemochromatosis F 2 , severe blood loss F 3 , bacteria and viruses F 4 , sepsis F 5 , and chemical pharmaceuticals F 6 ) results in free iron overload (Fe 2+ ) in the blood leading to pathological consequences in the organism P i (organ dysfunction P 1 , atherosclerosis P 2 , microvascular pulmonary thrombovasculitis obliterans (in particular, with SOVID-19) P 3 , carcinogenesis P 4 , intravascular hemolysis P 5 , and diabetes P 6 ). In the chain of these events, RBCs play a key role as the transfer function between the primary factors and the pathological consequences P i , F i ⟶ RBCs ⟶ P i (Figure 1(a)).
In this study, we consider the potential distortions of excess Fe 2+ action on RBCs, shown in red in Figure 1(a). In particular, changes in the content of hemoglobin derivatives (RBC Hb ), and changes in cell morphology (RBC M ), hemolysis (RBC hemol ), and membrane stiffness (RBC mst ), arising simultaneously under the influence of excess Fe 2+ are considered.
We investigated the impact of free Fe 2+ on the pRBC suspension and lysate (Figure 1(b) and 1(c)) in vitro and identified disruption in cell elements. In the experiments, dissolved FeSO 4 was added to the test sample (Figure 1(b) and 1(c)). Analysis was performed using digital spectrophotometry (Δλ � 0.5 nm), AFM (resolution limit of 0.1 nm in height and 10 nm in length), AFS, and mathematical modeling ( Figure 1(d)). More details about the in vitro systems are indicated in Materials and Methods.

Nonlinear Kinetics of MetHb Formation Was Registered with Excessive Content of Free Fe 2+ .
e absorption spectrum of pRBC lysates after the addition of FeSO 4 salt solution changes significantly over time (Figure 2(a)). When the pRBC lysate is incubated with free iron, the absorption peak at λ 3 � 630 nm appears and grows, so the process of conversion of oxyhemoglobin HbO 2 to MetHb develops. For Fe 2+ of 1700 μM during a 60 min incubation, the MetHb content developed almost linearly (Figure 2(b)). After 60 minutes, nonlinear kinetics of the MetHb increase in the pRBC lysate was observed (Figure 2(b)). e instantaneous rate of MetHb formation can be calculated as ree hemoglobin derivatives play important roles in the absorption process: HbO 2 , Hb, and MetHb. e nonlinear curve fitting method was used to estimate unknown concentrations of the hemoglobin derivatives C HbO 2 , C Hb , and C MetHb , which best described the experimental data ( Figure 2(a)). For this, the optical spectrum D l (λ l ) exper was approximated by the theoretical curve D l (λ l ) theor , according to which for each wavelength λ l optical density is a sum of products of the molar absorption coefficient (ε HbO 2,l , ε Hb,l , and ε MetHb,l ) and concentrations C i for the corresponding hemoglobin derivatives (Equation (1)). Equation (1) was used earlier in our studies [52][53][54].
Figure 2(c) shows the measured spectra D l (λ l ) exper and fitting curves D l (λ l ) theor , plotted for the parameter C i , calculated by equation (1), to determine the effect of Fe 2+ 1700 μM on the pRBC lysate with incubation times of 0, 30, 60, and 120 min. For the pRBC lysate, the calculated scattering coefficients K and S (equation (1)) equaled zero. Free Fe 2+ exposure at different concentrations C Fe 2+ led to increasing of C MetHb (t). Moreover, the rate of C MetHb (t) growth increased with the increment of the initial concentration of Fe 2 (Figure 2(d)). Experimental data for incubation times up to 120 min are shown a larger scale in Figure 2(e). In the first 15 min, the initial rates of MetHb formation were V MetHb (t) � tgα � 0.04%, 0.13%, 0.27%, and 2.2% for Fe 2+ 212.5, 850, 1700, and 6800 μM, correspondingly.

Excess Free Iron Results in pRBC Polymorphism.
e result of the interaction of Fe 2+ and H 2 O 2 is the formation of a highly reactive radical OH · , which attacks lipids and proteins in RBC membranes. It is known that, as a result of the violation of ionic equilibrium during the development of oxidative processes under the action of various physical and chemical factors, cell cytoskeleton and membrane nanosurface changes [46,[55][56][57][58], resulting in RBC morphology alterations [45,56,58,59].
us, the most part of the cells hemolyzed and became ghosts. We experimentally established that pRBC damage in result of Fe 2+ exposure occurs through two mechanisms: (1) swelling of cells, the formation of spherocytes, and ultimately their hemolysis and formation of ghosts and (2) the formation of microspherocytes. ese forms are irreversible and their formation, even in small amounts, can significantly reduce the quality of pRBCs and their functional ability. e effects of altering the pRBC morphology were enhanced with increasing concentrations of free Fe 2+ in suspension (Figure 4(d)). An inverse correlation was established between the mean MetHb level and the mean number of discocytes on a smear r MetHb−Discocyte � −0.72.
We identified pRBC ghosts in AFM images, and accordingly, decreases in the level of optical density in the optical spectra were fixed (Figure 4).
ere was a good Journal of Toxicology 5 correlation of the percentage of ghosts on AFM images with the number of hemolyzed cells measured by the residual level in the absorption spectrum of the pRBC suspension: ghosts 18 ± 4% and hemolysis level 21 ± 3% after 5 hours of incubation, and ghosts 60 ± 4% and hemolysis level 58 ± 5% after 24 hours of incubation; thus, r Hemolysis−Ghost � 0.99.

Bridges, Chains, and Clots of pRBCs Were Formed.
In experiments, there were the self-organization of pRBCs.
Connections between cells arose in the form of bridges, and chains were formed; as a result, they were combined into conglomerates and clots ( Figure 5(a)). e height of the bridges between the cells ranged from 300 to 600 nm, the 3.3±0.1% width ranged from 400 to 700 nm, and the length ranged from 20 to 200 nm. Some examples of bridges and chains are shown in Figure 5(b). Figure 5(c) shows the moment of chain formation from two microspherocytes, between which there is a spherocyte in the process of hemolysis, and bridges are formed between these three cells. Up to 10-12 cells were observed in chains. 30-40 cells formed clots. We observed these phenomena precisely after Fe 2+ exposure for t inc � 24 hours. e bridges were absent in the control and were practically not observed for t inc � 60 min . e formation of such structures by free iron may increase the probability of blood clot forming in blood vessels. e structure of aggregates in such clots was different from that of aggregates in the form of coin columns from control cells. We have already observed similar aggregate clots in the case of exposure of blood to carbon monoxide [53,60] as well as zinc ions [61]. Perhaps, this effect is associated with a change in the ratio of hemoglobin derivatives or with partial local hemolysis. In the scientific literature, two alternative mechanisms of RBC aggregation have been conceived, namely a bridging model [62] and a local osmotic gradient model [63]. Based on the bridge model, large macromolecules are adsorbed on the cell surface and thereby connect two adjacent cells. When these bridges exceed disaggregation forces such as electrostatic repulsion, membrane deformation and mechanical shear, aggregation occurs [64]. ese mechanisms may manifest themselves in the case of the action of excess iron on RBCs. Like agglutination, the phenomenon we observed is dangerous due to an increase in the formation of blood clots in vessels of various diameters.

e pRBC Membrane Stiffness Was Increased.
In our experiments, morphological changes and the formation of MetHb were accompanied by an increase in pRBC membrane stiffness as a result of free Fe 2+ exposure of the blood. AFS was used to investigate the deep bending of pRBC membranes up to h � 1000-1300 nm under the action of a probe (Figure 6(a)). Typical force curves for the control and experimental samples for t inc � 24 hours are shown in Figure 6(a). e force curve for the cell membrane after exposure to F Fe 2+ 1700 (h) is sharper than that for the control cell F Fe 2+ 0 (h) (Figure 6(a)). e 100 measured force curves were calculated using the Hertz formula, and histograms of Young's modulus for membranes of these groups were plotted (Figure 6(b)).  Journal of Toxicology e corresponding mean and variances were calculated: E Fe 2+ 0 � 11 ± 4 kPa and E Fe 2+ 1700 � 17 ± 5 kPa for t inc � 1 h and E Fe 2+ 0 � 15 ± 5 kPa and E Fe 2+ 1700 � 23 ± 8 kPa for t inc � 24 h. Figure 6(c) shows the distribution functions of Young's modulus for t inc � 1 h and for t inc � 24 h, corresponding to the study and control groups. Based on these curves, it was found that after t inc � 1 h after exposure to Fe 2+ 1700 μM, 35% of pRBC membranes had Young's modulus values that were beyond the control values (at a level of 0.95). e results were almost the same after t inc � 24 h, 37%. ese results indicate that almost one-third of the cells had increased stiffness, which reduced their deformability and potentially caused microcirculation disorders. Earlier studies showed that the reason for the change in the stiffness of RBC membranes with an increase in oxidative processes is a change in the structure of the cytoskeleton of cells [46,52,58,[65][66][67].

Kinetic Model of Changes in Hemoglobin Derivative
Concentrations.
e biomarker for the development of oxidative processes in RBC suspensions under the influence of various physicochemical factors is the MetHb level [52,54]. To describe the change in the MetHb level under the action of free iron, we proposed a mathematical model based on kinetic equations. e kinetic model is derived from fundamental principles as mass balance considering a constant volume and describes interactions between network components and the processes they undergo. A firstorder ordinary differential equation (ODE) based on the law of mass action stating that the rate of the chemical reaction is directly proportional to the product of the reactants allowed us to describe the kinetics of the processes.

Model Assumptions.
e following assumptions were made that define the model's validity range: (1) e initial main triggering reaction for subsequent processes is the reaction of the interaction of iron ions Fe 2+ with ROS, namely, with peroxide H 2 O 2 :

Derivation of a Differential Equation and its Solution.
We suggest the kinetic model describing the interaction of free Fe 2+ with H 2 O 2 in (equation (3)).
Let us denote y(t) � S Fe 2+ (t); (dy/dt) is the rate of change in the concentration of iron ions Fe 2+ ; β is the rate constant; and a � S H 2 O 2 � const. We rely on the fact that the rate of the chemical reaction (equation (3)) is directly proportional to the product of the reactant concentrations, and then the ODE is as follows: Initial condition is Solving the differential equation (equation (4)) by the method of separation of variables and taking into account the initial conditions (equation (5)), we get the dependence of the Fe 2+ change on time: For illustration, an Euler diagram for the two-component reaction (green, Fe 2+ ions and blue, H 2 O 2 molecules) is presented in Figure 6(d), 2. e intersection area is highlighted in yellow and corresponds to the reaction product hydroxyl radical OH · . is a long-lived representative of ROS that can diffuse over long distances. However, at the same time, it has a lower reactivity in comparison with the rest of the ROS which are short-lived and diffuse over short distances but exhibit high reactivity. As a result of the reaction (equation (3)), a hydroxyl radical OH · is formed, which is highly reactive and short-lived. It is the hydroxyl radical that triggers and participates in subsequent redox reactions. e radical OH · will be able to enter into further reactions with other closely located ROS and HbO 2 .
Let us denote Z 0 is the initial concentration of HbO 2 ; under the experimental conditions Z 0 � 5 ± 0.5 μM and (Z 0 − x(t)) is the concentration of HbO 2 at any time.
According to the mass action law, the rate of the chemical reaction is directly proportional to the product of the reactant concentrations: where c is the rate constant. Initial condition: we assume that the initial level of MetHb at t � 0 is Taking into account the dependence equation (6), we write down the ODE (8a) in the form is is the first-order ODE. It is solved by the method of separation of variables: where B is the arbitrary constant.
Taking into account the initial condition equation (8b), we can find that Substituting equation (9d) into equation (9c), we get the dependence of MetHb concentration change: e steady state level of MetHb can be found depending on the initial concentration of Fe 2+ ions (y 0 ).
In this case, in equation (10), t ⟶ ∞. en, For illustration, an Euler diagram for the 3-component reaction (red: HbO 2 molecules) is presented in Figure 6, 2. e intersection area is highlighted in brown and corresponds to the final reaction product MetHb.

Fitting of Experimental Data.
Nonlinear curve fitting of the experimental data of the MetHb concentration change (Figures 2(b) and 2(e)) was performed according to equation (10) by using Origin Pro 2019.
e unknown values of concentration a and rate constants β and c were considered as model parameters which describe the experimental data in the best way. e known values were x(t) and y 0 . e criterion for the optimal fitting was that the theoretical values of x theor (t) fit best the experimental data x exper (t), at a level R 2 > 0.96. As a result of the fitting, the values of a, β, and c were obtained for each curve corresponding to a different initial iron level y 0 . Taking into account the data averaging, we obtained that a � 0.00090 ± 0.00008 (μM), β � 0.973 ± 0.171 (μM − 1 min − 1 ), c � 0.0030 ± 0.0006 (μM − 2 min − 1 ), and R 2 � 0.977 ± 0.026.
It is noteworthy that the theoretically found concentration of a(C H 2 O 2 ), which was in the equations as quasi-steady state condition, coincided with the experimental value with an accuracy of 5-10%. is also indicates the adequacy of the model and, accordingly, the mechanism of the kinetics of the interaction of H 2 O 2 , Fe 2+ , and HbO 2 . Figure 6(d), 4 shows lines according to dependence (equation (10)) for different initial concentrations of Fe 2+ ions which fit the experimental data (indicated by symbols) from Figure 2(d) in the first t inc � 120 min. e steady state level of the MetHb content (saturation) and the time to reach it (or the rate) depend on the initial concentration of Fe 2+ according to equation (11) (Figure 6(d), 5). With an increment in the initial C Fe 2+ , the steady state level of MetHb increases in good agreement with the experimental data ( Figure 2(d)). is is the confirmation of the adequacy of the model. e increase in MetHb was accompanied by a decrease in HbO 2 (Figure 6(d), 6). At a high initial concentration of C Fe 2+ � 6800-13600 μM, the rate of the Fenton reaction and, accordingly, the rate of decrease in HbO 2 will be large, and accordingly, for a short incubation time of 100-200 min, almost all HbO 2 will be converted to MetHb (Figure 6(d), 6). e reason for the steady state of the MetHb level in this case is the use of all HbO 2 molecules during this time of observation. In another situation, with a low initial concentration of iron, the rate of MetHb formation will be insignificant. In this case, a steady state of MetHb concentration will be observed but already at a lower level. e reason for the steady state will be already an insufficient amount of iron ions decreasing with the time.

RBCs as a Key Link in the Influence of Free Iron Overload:
e Scheme Representation. Despite the publication of numerous studies concerning the problems of iron overload, the comprehensive study of excess iron influence on RBCs remains limited. To better identify the processes in RBCs under iron overload, we used biophysical methods to perform a modeling study in vitro.
In a healthy organism, there is a dynamic balance of concentrations of Fe 2+ /Fe 3+ , H 2 O 2 /ROS, and HbO 2 /MetHb. Normally, the iron balance is maintained by iron transport proteins [1]. Free iron overload occurs in a number of diseases (Figure 7 (a)). In critically ill patients, particularly in cases of sepsis, the capacity to detoxify cell-free hemoglobin is reduced [16,18]. As a result, the equilibrium is disturbed, and the system goes into another state, while collective disproportions arise in all elements of the system in one way or another (Figure 7 (b)).
In this chain of pathological process development, RBCs play a key role (Figure 7 (b) 1-6). Excess iron accumulation causes distortions through the production of ROS [2] via the Fenton reaction (Figure 7 (b1) and (b2)), with the generation of toxic hydroxyl OH · radicals, which are highly reactive and toxic [70]. e generation of ROS (Figure 7 (b3)) leads to the peroxidation of membrane lipids and cellular proteins, resulting in membrane and cytoskeleton distortions and hemoglobin derivative transformations (Figure 7 (b4)). As has already been noted repeatedly, RBC hemolysis is a dangerous consequence of the action of free iron on the blood. When OH • interacts with membrane lipids, chain reactions of lipid peroxidation occur (Figure 7 (b4)). As a result, the hydrophilicity of bonds in lipid tails increases locally, and local hydraulic pores are formed. is leads to disruption of the ionic balance in RBCs, and osmosis occurs. is leads to a change in cell morphology as well as partial and complete hemolysis of spherocytes.
Also, high iron condition might induce RBC surface protein denaturation, leading to their adhesion to each other. Probably with excess iron, changes in the band 3 proteins and spectrin occur (Figure 7 (b4)). is leads to change of cytoskeleton and membrane surface nanostructure. We observed similar phenomena using AFM studies of the influence of Zn ions, UV radiation, and hemin, during long-term storage of pRBCs [52,57,71,72]. Clusterization of protein may be the reason of bridge and clot formation.
Serious disorders in the pRBCs due to ROS in result of iron overload are shown in Figure 7 b4 and b5, and we established those in our experiments in vitro (Figures 3 and  4).
e effect of Fe 2+ on RBCs occurs under conditions positive feedback in the system free iron-blood (Figure 7). An excess of free iron leads to the appearance of free HbO 2 , MetHb, and to a high concentration of free hemes, which in turn leads to free iron and ROS [9,73].
RBCs may be potential sources of clinical changes in vivo in the cardiovascular system (Figure 7 (c)). In particular, the clinical consequence of excess iron is atherosclerosis, which increases the possibility of hemolysis of pRBCs, therefore leading to an increase in the production of free iron and oxidized products. In addition to hypoperfusion, up to a complete blockage of blood flow, massive hemolysis occurs with the appearance of free hemoglobin and the increase in the level of free iron. A vicious cycle is created when iron initiates an inflammatory process, including thrombovasculitis, and the blockade of micro-and macrocirculation creates conditions for hemolysis and an increase in the level of free heme iron in the blood serum [8,26,84]. As a result, a rapid increase in respiratory insufficiency occurs due to blockage of the pulmonary blood flow. Microvascular pulmonary thrombovasculitis obliterans, which is characterized by thrombosis of not only microcirculatory vessels but also larger vessels, is typical for COVID-19.
In our in vitro studies, we tried to answer the question what disorders can occur in RBCs which can modify their functions. We established the pattern of the simultaneous development of heterogeneous processes under the action of excess iron: changes in the morphology of pRBCs, the formation of bridges between cells, the formation of clots (such as pRBC agglutination), the formation of MetHb, and increasing of membrane Young's modulus (Figures 2-7 (b5), (b6)).

Conclusion
In conclusion, iron is useful and nontoxic, when bound in our bodies in optimal quantities. However, overload of free iron is dangerous and can cause powerful oxidative stress. In biophysical experiments in vitro, we have experimentally established a complex of changes that can occur in pRBCs and lead to the development of pathological processes. us, we have shown that pRBCs may be the key link in the pathology influence of free iron overload. Patterns established in our experiments in vitro can allow to expand the understanding of the mechanisms of the toxic adverse effect of excess free iron on the blood and the circulatory system, and, consequently, to develop adequate methods for patient treatment.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.