Experimental observations demonstrated a slow rotation of erythrocytes around their own axes with varying frequency in the frequency range of and the electric field intensity. Figure 1 shows the dynamics of rotation of a selected individual cell. Measurements showed that its rotation frequency was ~.

The external electric field with the frequency and the phase applied to the cell induces the redistribution (polarization) of the set of its free and bound, positive and negative charges within the whole cell volume. As a result of polarization, in the cell there emerge uncompensated charges, which create within it its own field with the intensity directed against the external one,. The field in the cell vo-

lume forms the induced dipole, which is the sum of a set of n elementary [5] [9] . In

NUAEF, the cell dipole is influenced by the time-averaged force vector, which makes the cell move [10] .

where:—dielectric permittivity of the medium;

—dielectric permittivity of the cell;

—the gradient of the square of intensity of the medium electric field;

—polarizability coefficient of a spherical cell along a single selected direction, for example, axis.

The vector of the cell electric field intensity with the frequency and the phase follows the vector

The superposition of two harmonic oscillations results in the emergence of the frequency combinations.

The condition and is fulfilled for the linear polarization of a cell. If the frequencies are equal to each other up to the phase, any rotation around own axis is impossible (2).

The nonlinear polarization of a cell requires the condition to be fulfilled. If, the cell starts rotating around its own axis, which can be recorded and analyzed by instrumental video monitoring.

The typical value of the erythrocyte transmembrane potential is about [11] . This potential creates on the membrane a potential barrier with the electric field intensity ~ whose vector is normal to the cell surface. According to the statistical mechanics, the charge¹ (ion) should possess the energy required for overcoming the total potential barrier of the cell membrane

where:

—the unit positive charge of the ion [K];

—the membrane own instantaneous voltage [B];

—the external medium voltage affecting the membrane [В].

The density of positive charges capable of overcoming the above barrier is described by Expression [5] .

where:

—the initial density of positive charges on the membrane surface depending the concentration and thermal equilibrium of ions in cell suspension [5] ;

—the initial potential energy of the membrane;

—the potential energy of the external medium affecting the membrane [J];

—Boltzman constant [J/deg];

is the absolute temperature [K].

The exponential function (4) can be determined using the Maclaurin series, which converges at any [7] .

If the summand is much smaller than 1,the contributions of sum-mands of higher

orders (starting from the third, quadratic, one) in (5) can be neglected. As a result, the density of the charges ca-

pable of overcoming the potential barrier has a linear character. If the exponent is equal

to or more than 1, the contributions of individual summands of higher orders to nonlinearity become dominant. However, with increasing n value in (5) a general trend is observed: the values of individual summands of the series rapidly decrease.

The interrelations between Expressions (1, 3, 4, 5) allow us to consider the cell polarization process to be nonlinear, too. From the mathematical point of view, nonlinearity in Equation (5) emerges when

and. Retaining the summand and proceeding from the classical definition that

current is determined by the rate of change of the charge, Equation (5) can be rewritten in a form of a sum of currents flowing through the membrane at.

From Equation (6), the calculated values of the members of the Maclaurin series depending

on their serial numbers are presented in Figure 2, Figure 3. By further simplifying Equation (6), let us reduce it to.

where:

—the change in the constant component of the membrane current, equals zero;

is the instantaneous voltage of the membrane;

are the coefficients of proportionality, in particular, is resistance with the dimension [ohm].

From the consideration of the first three summands of Equation (7) it follows that the alternating current of the membrane contains only the linear and the quadratic components

Taking into account that, let us write

The analysis of Expression (8) shows that the total current through the cell membrane is determined by the combination of individual harmonic components with frequencies and and the constant compo-

nent. This allows us to consider the cell as a nonlinear element, which explains the emergence of the

cell currents with the frequency and that of beat frequencies determining the cell rotation around its own axis.

The linear model of polarization of the medium and the cell in the external alternating electric field is relatively simple. In each point, the electric field induces in their volume the dipoles with the harmonic frequency, which coincides with the external one. In the case of the nonlinear polarization, the formation of the induced dipole moment of the cell by electric charges is associated with the fact that their movement is not harmonic any more. In this case, the energy of the cyclic frequency of the external field is transferred to the second and higher harmonics, and there also emerge multiple combinations between them [11] .

The analysis of the presented known trigonometric expressions also shows that the member of the series with the serial number in (6) also takes into account the harmonics of the current flowing through the cell membrane. Thus, in Figure 2, Figure 3, the serial number along the abscissa agrees with the current harmonics.

Experimental data and the conducted theoretical analysis of the interaction between the cell and alternating electric field suggest that under the study conditions the erythrocyte can be presented as a nonlinear element whose membrane permeability for positive ions is higher in one direction than in the reverse direction. This is consistent with the selective permeability of the membrane, for example, for potassium ions [12] known from literature. Interestingly, the transition in electronic devices, for example, a diode is characterized by similar different conductivities in different directions [13] . The special case of the nonlinear equivalent electric circuit of the cell for positive charges is shown in Figure 4 where the membrane is presented by a diode with nonlinear resistance and capacity.

The conducted work allowed us to draw the following conclusions.