Influence of Temperature and Ionic Strength of Medium on Surface Potential of Human Erythrocytes

During freezing of cell suspensions the ionic strength of extracellular and, subsequently, intracellular media is responsible for the changes in membrane potential of cells. In this research we revealed the temperature and concentration dependencies of the surface potential of human erythrocytes during freezing of the cell suspension at the points corresponding to the values of temperature and 1:1 concentration of the electrolyte according to the phase diagram of a water-NaCl binary system. The concentrations of sodium ions on the surface of erythrocytes depending on concentration and temperature of the bulk solution were determined. It has been shown that the concentration of sodium ions on the surface of cells was 1.5 times higher than that in the bulk solution. The kink of surface potential temperature dependence for human erythrocytes for 0.15 and 0.3 M concentrations of 1:1 electrolyte within 8...12°C temperature range was of special interest. This temperature dependence feature of the surface potential calculated for the charged surface with a particular surface charge density from the purely physical considerations without taking into account the structure and composition of the surface could be one of the causes of rearrangements in membrane at these temperatures. Misbalance of electrostatic interactions on the surface of membrane outer monolayer appeared as a result of an increased concentration of counterions on the surface of cells and correspondingly the reduced surface potential might trigger the rearrangements and changes in relationships between membrane protein and lipid components.


Фізико-математична модель
Розглянемо вплив концентрації позаклітинного розчину на поверхневий потенціал клітин на прикладі еритроцитів людини.Рівняння Пуассона-Больцмана визначає електростатичний потенціал Nowadays there is a generally accepted conception that cell cryodamage is a direct or indirect result of the formation and growth of ice crystals in freezing cell suspension.The existence of optimal cooling rate is explained by the two-factor theory of cryodamage by P. Mazur [10], whereby the cell survival following crystallization of cell suspension is affected by two types of cryoinjuries.First one acts during crystallization of extracellular medium and is caused by dehydration of cells, an increase in concentration and ionic strength of extra-and intracellular solutions through the transformation of water into ice.The second type of cryoinjury of cells is stipulated by the formation of intracellular ice crystals, which causes the same effects and moreover leads to mechanical destruction of membrane structures.Damaging effect of hypertonic medium is of a multifactor nature.This may be either a direct effect of hypertonic solutions on cell membranes (lyotropic action) or a damage caused by osmotic factors, including the critical reduction of cell volume.
One of the consequences of ionic strength extracellular medium effect and, consequently, intracellular one, is a change in membrane potential of cells being in this environment.Static electric fields in cell membranes are characterized by surface (ϕ s ), dipole (ϕ d ) and transmembrane (ϕ t ) potentials [1], which differ in origin and localization.The surface potential is generated by charged groups of phospholipid heads and adsorbed ions at the membrane-water interface.It is measured between the membrane surface and bulk water and is closely related with the pH at the interface.The dipole potential is originated from ordered dipoles of lipids (ether groups and bipolar groups of heads) and ordered water molecules.It is localized between the membrane surface and central hydrophobic part of bilayer.Transmembrane potential is generated by the difference in concentrations of ions on both sides of bilayer and is measured across its entire length [4].
The research purpose was to calculate the surface potential of erythrocytes and concentration of Na + ions near their surface in the Stern-Helmholtz layer depending on the medium temperature and concentration of 1:1 electrolyte in bulk solution.
Counterions density on the surface is determined by the next formula [8]: , (2) kT The formula (2) shows that the concentration of counterions on the surface depends only on the surface charge density σ and concentration of counterions in the bulk solution.Thus, for the isolated surface the ρ 0 value never may be less than kT and on the surface (at x = 0) the density value ρ and potential ϕ will be associated via the ratio where ρ ∞ i is the concentration of i-th ions in the bulk solution (at x = ∞), where ϕ ∞ = 0. are expressed in some proper concentration units, such as M (1 M = 1 mol/L), and correspond to the concentration of ρ = 6.022×10 26 m -3 , where 6.022× ×10 23 denotes Avogadro's number, and 10 3 multiplier is used for the transition from cubic meters to liters.
Full concentration of ions near isolated surface with charge density σ according to the formula (2) equals to ; , ( 5) where from one can get the ratio between surface charge density σ and surface potential ϕ 0 : .
where the units to measure concentration [NaCl] are moles and kelvins are for temperature.

Results and discussion
Based on the formula (12) we performed computer calculations and obtained the erythrocyte surface potentials at different temperatures and concentrations of NaCl in extracellular solution (Fig. 1).To determine the change in surface potential of erythrocytes during freezing of cell suspension in physiological saline we constructed a graph of the surface potential dependence vs. temperature (Fig. 2) or concentration (Fig. 3) using the points corresponding to these values according to the phase diagram of a water-NaCl binary system (Fig. 4).
The concentrations ρ 0i of individual ions on a surface can be calculated using the formula (5), substituting the calculated values of surface potential for the studied solutions.Obviously, the concentration of sodium [Na + ] ions on the surface of erythrocytes will be higher than in the bulk solution, and the concentration of chloride ions [Cl -] will be lower.Dependence of surface concentration of Na + ions vs. the concentration in the bulk solution calculated using the formula (5) for two temperatures (275 and 255 K) is presented in Fig. 5, showing that the temperature did not virtually affect the surface concentration of counterions.The value of sodium concentration on the surface of erythrocytes per se greatly exceeded the value in the bulk solution.
In particular, at 1 M concentration of solution the
surface concentration made 1.5 M, and at 2 M concentration it increased up to 3 M.
Для пояснення процесів, які відбуваються в зоні структурно-фазового переходу при температурі 12…8°С, було зроблено припущення, що у мембрані еритроцита змінюється відношення між площею зовнішнього та внутрішнього моношарів мембрани, наприклад, за рахунок «занурення» білків конічної форми вглиб бішару [13].При цьому molecules exchange with erythrocytes [7] have shown that within the range of 8...12°C the Arrhenius dependencies for erythrocytes undergo a rupture with a significant increase in the activation energies below the temperature of 8°C.Human erythrocytes permeability for 1,2-propanediol (1,2-PD) and dimethyl sulfoxide (DMSO) cryoprotectants also has the kinks in Arrhenius dependencies at the temperature of 8...12°C with increasing activation energy of penetration of these substances at the subzero temperature [2,6].It was suggested that a sharp change in the activation energy of permeability at the temperature of 8...12°C was associated with a decrease in permeability of protein channels because of structural transition in erythrocyte membranes.T. Forte et al. [5] showed that cytoskeleton-membrane complex, including the protein band 3 and 4.1, was responsible for thermotropic transition in erythrocyte membranes at the temperatures close to 8°C.Our previous study of the temperature dependence in the permeability of erythrocytes demonstrated that treatment of cells with the blocker of protein channels did not eliminate the bend of Arrhenius dependence at the temperatures below 12°C either for hydrophilic cryoprotectant 1,2-PD or hydrophobic DMSO [2].Therefore, the increase in activation energy appearing during cooling below 12°C was associated by us with the state of lipid matrix (viscosity, presence of effective hydrophilic pores) but not with closing of protein channels.
The results of microscopic examination were entirely consistent with those obtained by determining the distribution of erythrocyte sphericity index.Destruction of 'rouleaux' and loss of discoid shape by some cells correlated with the number of cells with low sphericity index at a temperature below 15...12°C.Exactly in the temperature zone below 12°C there were observed an increased activation energy and large variations in the permeability for both cryoprotectants [2,6] and water molecules [7].
To clear up the processes occurring in the zone of structure-phase transition at 12...8°C it was assumed that erythrocyte membrane aquired a changed ratio between the area of outer and inner membrane monolayers, for example, by an 'immersion' of proteins with conical shape deeply into bilayer [13].Suchwise, the ratio between external and inner monolayars of membrane increased.According to the bilayer-couple model [14] this leads to a rapid formation of stomatocytes by specular protrusion of one of the erythrocyte depression relative to the tangent plane to lateral surface of erythrocyte [12].'Roleaux' are formed by means of the 'bridges' between external surfaces of adjacent erythrocytes, binding membranes and opposing the forces of electrical repulsion.The gap between membranes of erythrocytes in the contact zone makes about 25 nm.The power of aggregation, stipulated by the formation of 'bridges' per unit area of contacting surfaces is 10.2 N/m 2 , herewith the bond between the cells is easily broken even after appearance of small shear flows [9].Therefore, we can assume that the repulsive forces arising at the instant discocyte-to-stomatocyte transition are sufficient to collapse 'roleaux'.
The found feature of surface potential dependence vs. temperature within the range of 12...8°C (see Fig. 1) calculated for the charged surface with a certain density of surface charges for purely physical reasons, with no regard to the structure and components of surface is probably one of the causes of alterations in membrane at these temperatures.Appearance of a misbalance in electrostatic interactions on the surface of membrane outer monolayer due to increased concentrations of counterions on the cell surface and therefore the reduced surface potential can trigger rearrangements and changes in interactions between the protein and lipid components of membranes.This assumption is consistent with the results of our research and conclusions [2] about the reasons for increasing the activation energy of penetration of water and cryoprotectants molecules through the membranes of human erythrocytes when cooled below 12°C.

Conclusions 1 .
There is a change in surface potential of erythrocytes during freezing of cell suspension in points corresponding to the values of temperature and conпроблемы криобиологии и криомедицины problems of cryobiology and cryomedicine том/volume 27, №/issue 1, 2017